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Properties of lightning derived from time series analysis of VHF radiation data

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Title:
Properties of lightning derived from time series analysis of VHF radiation data
Creator:
Rustan, Pedro Luis, 1947-
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English
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viii, 376 leaves : ill. ; 28 cm.

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Subjects / Keywords:
Channel noise ( jstor )
Electric fields ( jstor )
Electric pulses ( jstor )
Electrical phases ( jstor )
Electromagnetic noise ( jstor )
Lightning ( jstor )
Pulsed radiation ( jstor )
Signals ( jstor )
Velocity ( jstor )
Very high frequency radiation ( jstor )
Dissertations, Academic -- Electrical Engineering -- UF
Electrical Engineering thesis Ph. D
Lightning ( lcsh )
Genre:
bibliography ( marcgt )
non-fiction ( marcgt )

Notes

Thesis:
Thesis--University of Florida.
Bibliography:
Bibliography: leaves 369-375.
General Note:
Typescript.
General Note:
Vita.
Statement of Responsibility:
by Pedro L. Rustan, Jr.

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University of Florida
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University of Florida
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Copyright [name of dissertation author]. Permission granted to the University of Florida to digitize, archive and distribute this item for non-profit research and educational purposes. Any reuse of this item in excess of fair use or other copyright exemptions requires permission of the copyright holder.
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PROPERTIES OF LIGHTNING DERIVED FROM
TIME SERIES ANALYSIS OF VHF RADIATION DATA












By

PEDRO L. RUSTAN, JR.

















A DISSERTATION PRESENTED TO THE GRADUATE COUNCIL OF
THE UNIVERSITY OF FLORIDA
IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE
DEGREE OF DOCTOR OF PHILOSOPHY













UNIVERSITY OF FLORIDA 1979










































UNIVERSITY OF FLORIDA

11 l 1111 I ll 1 1 1111 1 1 11 111 11 il 1 I
3 1262 08676 742 2
















ACKNOWLEDGEMENTS


I gratefully express my appreciation to the members of my supervisory committee for their support and cooperation. In particular, I thank Dr. M. A. Uman for his guidance, enthusiasm, and professional expertise, and Dr. D. G. Childers for his probing questions and constant support of this research. Special thanks are due to Dr. J. McClave (Statistics) for providing programs for data modeling. I am also thankful to Mr. Paul Krehbiel at the New Mexico Institute of Mines and Technology, and Mr. Carl L. Lennon and Mr. William E. Jafferis at the Kennedy Space Center for their generous help in providing data, the main ingredients of this work. I acknowledge the work of Mr. Ronald Jacobs from Eglin AFB in digitizing the analog tapes. A special note of appreciation for the continuing help of Dr. W. H. Beasley and Mr. W. G. Baker and many other colleagues working in the University of Florida Lightning Research Laboratory. The author especially thanks his wife, Alexandra, without whose love, patience, and understanding this work could not have been completed.

This investigation was made possible by the Air Force Institute of Technology. The research reported here was jointly supported by NASA KSC Contract NAS1O-9378; NSF Grant ATM-76-01454; and ONR Contract N0001475C0153.
















TABLE OF CONTENTS

Page

ACKNOWLEDGEMENTS...........................ii

ABSTRACT . . . . . . . . . . . . . . v

CHAPTER

I INTRODUCTION .........................1

II GENERAL REVIEW OF LIGHTNING AND PREVIOUS LIGHTNING
VHF TOA RESEARCH .......................6

2.1 Description of Cloud-to-Ground and Intracloud
Lightning..... .....................6

2.2 Description of Electromagnetic Radiation Emitted
by Intracloud and Cloud-to-Ground Flashes. .......10

2.3 Lightning Direction Finders ...............14

2.4 Review of Proctor's Work................16

2.5 Review of Lennon's Work .................25

III DATA ACQUISITION AND PROCESSING...............29

3.1 Data Recording....................29

3.2 Telemetry System...................33

3.3 Data Pre-Processing and A/D Conversion .........40

3.4 Electric Field Meters ..................43

3.5 Charge Locations Derived from Electric Field
Stations........................44

3.6 Charge Locations Derived from VHF Noise Sources . 47

IV COMPUTER ALGORITHM FOR LOCATION OF LIGHTNING
CHANNELS..........................49

4.1 General.........................49









Page

4.2 Data Characteristics . . . . . . . . 50

4.3 Technique for Determining Delays Based on the
Data Characteristics . . . . . . . . 55

4.4 Algorithm Flow Chart . . . . . . . . 62

4.5 Display of Three-Dimensional Locations and
Their Time of Occurrence . . . . . . . 68

V ANALYSIS OF RESULTS . . . . . . . . . 72

5.1 The 165959 Flash . . . . . . . . . 73

5.2 The 180710 Flash . . . . . . . . . 123

5.3 The 181806 Flash . . . . . . . . . 166

5.4 The 182356 Flash . . . . . . . . . 220

5.5 The 180644 Flash . . . . . . . . . 264

5.6 The 181416 Flash . . . . . . . . . 273

VI DATA MODEL . . . . . . . . . . . 281

6.1 Noise Level . . . . . . . . . . 284

6.2 Stepped Leader . . . . . . . . . 284

6.3 i-Change . . . . . . . . . . . 285

6.4 Characteristics of VHF Radiation . . . . . 286

VII CHARACTERISTICS OF THE VHF RADIATION DURING THE
DIFFERENT PHASES OF LIGHTNING . . . . . . . 287

7.1 Cloud-to-Ground Lightning . . . . . . 290

7.2 Intracloud Lightning . . . . . . . . 305

VIII CONCLUDING COMMENTS AND SUGGESTIONS FOR FUTURE
RESEARCH . . . . . . . . . . . . 309

APPENDIX

A DERIVATION OF SOURCE LOCATION FROM DIFFERENCE
OF TIME OF ARRIVAL MEASUREMENTS . . . . . . 311

B ACCURACY OF THE LOCATION OF LIGHTNING SOURCES
USING THE HYPERBOLIC EQUATIONS . . . . . . 315


iv









Page

B.1 Error Analysis for the Locations of the 165959
Flash on 19th July 1976 . . . . . . . 324

B.2 Error Analysis for the Locations of the 181806
Flash on 8th August 1977 . . . . . . . 324

B.3 Error Analysis for the 180710 and 182357 Flashes
on 8th August 1977 . . . . . . . . 324

C COMPUTER ALGORITHM TO DETERMINE VHF SOURCE LOCATIONS
FROM THE DIFFERENCE IN THE TIME OF ARRIVAL OF VHF
RADIATION DATA . . . . . . . . . . . 330

D COMPUTER ALGORITHM TO DISPLAY A THREE-DIMENSIONAL
DRAWING OF VHF NOISE SOURCES . . . . . . . 356

E FREQUENCY DOMAIN APPROACH TO DETERMINE DIFFERENCE
IN THE TIME OF ARRIVAL . . . . . . . . . 364

E.I. Measurement of Time Delay by Determining the
Peak of the Impulse Function . . . . . . 366

E.2 Measurement of Time Delay by Measuring the
Phase of the Frequency Response Function . . . 367 REFERENCES . . . . . . . . . . . . . . 369

BIOGRAPHICAL SKETCH . . . . . . . . . . . . 376




























v
















Abstract of Dissertation Presented to the Graduate Council
of the University of Florida in Partial Fulfillment of the Requirements
for the Degree of Doctor of Philosophy



PROPERTIES OF LIGHTNING DERIVED FROM
TIME SERIES ANALYSIS OF VHF RADIATION DATA By

Pedro L. Rustan, Jr.

December 1979

Chairman: Martin A. Uman
Co-Chairman: Donald G. Childers
Major Department: Electrical Engineering

The purpose of this research is to derive lightning properties by correlating three-dimensional VHF source locations, characteristics of the VHF (30 to 50 MHz) radiation, and electric field intensity (0.1 Hz to 1.5 MHz). We study the discharge initiation, propagation, overall geometry, and charge magnitude and location for the various phases of both cloud-to-ground and intracloud lightning. We analyze in detail four cloud-to-ground and three intracloud flashes, all selected randomly. The experimental data were recorded during the summers of 1976 and 1977 at the Kennedy Space Center (KSC). The VHF radiation was recorded using the multiple VHF stations of the KSC Lightning Detection and Ranging (LDAR) system. We located the VIlF noIso sources from the difference in the time of arrival (DTOA) between the pulses received at the multiple VILF stations using a hyperbolic geometry. The electric field data were recorded by the New Mexico Institute of Mines and Technology (NMIMT) and the University of Florida. Leader-return strokes vi









charge magnitude and locations, calculated for us by NMIMT, were correlated with our VHF source locations.

Previous work on three-dimensional "channel structure" during lightning flashes was performed by Proctor in South Africa, who pioneered the technique of VHF source locations. Proctor's determination of DTOA was done manually by pulse shape identification on 253 MHz signals. The three-dimensional source locations presented in this thesis for the different phases of lightning discharges were obtained using a computerized technique which allows a large amount of data to be analyzed quickly.

The data were recorded with a wideband VHF receiver having a bandpass filter of 30-50 MHz and a logarithm envelope detector. The detected signals from three of the stations were transmitted to the fourth station where all were recorded on four tape channels having a bandwidth of 400 Hz to 1.5 MHz. The analog tapes were digitized at

4.35 MHz, a sample every 229 nanoseconds. Between 20 x 10 3and 25 x 10 4 pulses per flash were recorded during active VHF radiation. A newly developed computer algorithm employing cross-correlation and pattern recognition was written to determine the DTOA between the individual pulses. Once the DTOA's were calculated, we used a three-dimensional hyperbolic position measuring system to determine the source locations.

The significance of this research is the following: (1) We develop an important niew tool for lightning research: a computer program which, using d igitalI tape data from four VIII' st [ois, cani determine. source locations every 7 to 10 microseconds. An average of about 20,000 locations was found for each one of the studied flashes. (2) We derive properties of the lightning flashes studied. Some of these results vii









are: a) From observing the initial lightning VHF noise we can determine whether a flash will become a cloud-to-ground or an intracloud discharge. b) Cloud-to-ground flashes were initiated by a process we name preliminary breakdown. The VHF sources during the preliminary breakdown formed an inclined cylinder 5 to 12 km long and about 500 meter radius between a height of 4 and 10 km. c) The VHF radiation of stepped leaders and return strokes during cloud-to-ground flashes have unique characteristics which can be used to identify these events by studying the VHF noise alone. The stepped leader has the lowest level of radiation of any process in the flash, but it radiates along the whole path from the charge center to ground. d) Dart leaders do not emit VHF radiation along their paths to ground, but rather in the neighborhood of the previous J-changes. e) The paths of the VHF sources during J-changes were inclined 250, 350, 450, and 550 off vertical. The path of the VHF sources during J-changes was well defined after the first few strokes of a cloud-to-ground flash, but the path became less organized as the stroke order increased. The first J-change of all the ground flashes propagated downward toward the previous charge center lowering negative charge.




















viii
















CHAPTER I

INTRODUCTION


The main purpose of this research is to determine V11F lightning source locations in three dimensions and to relate these results to other simultaneously recorded data, notably the dc to 1.5 KHz wideband electric field, in order to obtain a better understanding of the physics of the lightning discharge. The VHF radiation data were recorded during the summers of 1976 and 1977 at the Kennedy Space Center (KSC) using the KSC Lightning Detection and Ranging (LDAR) system. The VHF locations were determined from the difference in the time of arrival of the VHF radiation pulses at four LDAR ground stations. This study was part of the Thunderstorm Research International Project (TRIP). TRIP brought together a group of outstanding scientists in atmospheric electricity from the USA and foreign countries with the purpose of performing coordinated measurements during thunderstorms. The work reported in this thesis represents an important new dimension in lightning research. For the first time the use of a fully computerized algorithm has made it possible to understand in more detail the different phases of a lightning flash. We now have a much fuller understanding of the electrical activity inside a thundercloud and we are better able to describe the generation and propagation of the different phases of both cloud and ground lightning flashes. It is to be hoped that the new techniques developed as a part of this study will facilitate future research in the field of atmospheric electricity.

I





2


In this introductory chapter we shall briefly survey the organizational aspects of this thesis as well as some of the information presented. Chapter II presents a general review of lightning and previous lightning VHF time of arrival (TOA) research. Systematic lightning research started in the middle of the eighteenth century with tile work of Benjamin Franklin. Modern lightning, however, did not start until the early part of the twentieth century with the electric field measurements of C. T. R. Wilson published in 1916. Within ten years, cathoderay-oscillography and high speed photography were introduced to the study of thunderstorm electricity. The first published suggestion that VHF radiation might be used to determine source locations in three dimensions appears to be due to Oetzel and Pierce (1969). The pioneering work in the determination of source locations by calculating tile difference in the time of arrival was published by Proctor (1971). Proctor's original work was performed manually and provided new information about the different phases of a lightning discharge.

Chapter III presents a description of the system used to perform the VHF measurements. In addition, this chapter presents a brief discussion of the measuring system used for the electric field measurements and of the point charge models which are used to interpret the results. The original VHF data are analog (400 Hz to 1.5 MHz) tape recordings of the output of envelope detectors of four ground-based VHF (30 to 50 M11z) receivers located at tile Kennedy Space Center. The

aniplitude scale of the Vill" radiation was nmde logarithiiiie to provide 80 dB dynamic range for tile input signal. The VHF analog data for the four stations were subsequently digitized at a sampling rate of 4.35 MHz.






.3


Chapter IV describes the computer algorithm used for the location of lightning VHF sources. Digital tapes containing VHF time-series data from four stations were processed with the purpose of determining the differences in the time of arrival (DT0A) between pulses in one reference station and the remaining three stations. The computer algorithm to determine DTOA was based on cross-correlation and pattern recognition techniques. The cross-correlation function was optimized to determine DTOA between the central and each one of the remote stations every 94 isec. For long processes when there was little variation from one IJTOA to the next by using 94 pisec intervals, a longer sampling interval of 376 psec was used. Even though the crosscorrelation provides the DTOA for the 94 visec intervals, it does not determine the DT0A for individual pulses with a width much less than 94 p.sec. Therefore, we used pattern recognition to determine DT0A between individual pulses which were within 3.7 isec of the crosscorrelated DTOA result. Using this technique we obtained a source location every 7 to 10 microseconds.

Chapter V gives the lightning source locations and other derived physical properties for the selected flashes. We randomly selected four cloud-to-ground and two intracloud flashes from a group of about 1,000 which had correlated electric fields. The six flashes are referred

to in this thesis by the Universal Time of occurrence of the flash. Except for the first flash at 165959 on 19th July 1976, all of the remaining flashes were recorded on 8th August 1977. The cloud-to-ground flashes are presented in sections 5.1 through 5.4, followed by the two intracloud flashes in sections 5.5 and 5.6. We correlated the different phases of each lightning flash with the electric field record at a






4


University of Florida station and at a network of eight electric field stations designed and operated by the New Mexico Institute of Mines and Technology (NMIMT). In addition, for two of the ground flashes, we correlated our results with photographs of the lightning channels to ground obtained from the KSC TV network.

Chapter VI presents a statistical model for the V11F radiation data. This model was derived with the purpose of classifying the properties of the time-series data. The Box and Jenkins (1976) technique was used to identify a time-series model and to estimate the parameters of the model.

Chapter VII summarizes the properties of the different phases of cloud-to-ground and intracloud lightning derived from the flashes studied in Chapters V and VI. The main properties of the different phases studied were the characteristics of the VHF radiation, the length, direction and velocity of propagation of the various lightning paths associated with different discharge phases, the charge transfer associated with each of the lightning phases, and the total volume occupied by the flashes.

Finally, Chapter VIII provides some concluding remarks and suggests some of the areas for future research.

Appendices A through E are provided to present mathematical derivations or computer listings which were not appropriate for the text. Appendix A gives the derivation of three-dimensional locations obtained from the difference in the time of arrival. Appendix B provides the error analysis in the determination of the three-dimensional locations. Appendix 13 also shows four tables with tabulated RMS errors associated with channel locations as a function of position. Appendix C gives a Fortran computer listing used to determine DTOA In accordance with the






5


techniques described in Chapter IV. Appendix D provides a listing of the computer algorithm to display the channel locations in three dimensions. Lastly, ,Appendix E presents two frequency domain techniqules which could be uised to obtain DTOA. These techniques were not used because they do not adapt to the experimental data as well as the selected time domain technique described in Chapter lV.

















CHAPTER TI

GENERAL REVIEW OF LIGHTNING AND PREVIOUS LIGHTNING VHF TOA RESEARCH


2.1 Description of Cloud-to-Ground and Intracloud Lightning

This section contains an introduction to the basic terminology of the physics of lightning. Lightning is a transient, high current electric discharge whose path length is measured in kilometers. A lightning discharge starts when the electric field in some region of the cloud exceeds the breakdown strength of air, that is, equal to or less than 3 x 10 6V/m, depending on pressure, temperature, and the presence of precipitation. The most common source of lightning and the only one considered in this thesis is the thundercloud. A typical Florida thundercloud has a top between 9 and 15 km above sea level (Jacobson and Krider, 1976).

The lightning produced by the thundercloud can take place within a cloud (intracloud), between cloud and earth, between clouds, or between the cloud and the surrounding air. Our study includes the intracloud and the cloud-to-earth lightning usually called cloud-toground or ground discharge. A complete discharge is called a flash. Either discharge, the intracloud or the cloud-to-ground flash, typically lasts 0.5 seconds.

Regardless of the type of flash being studied, one of the most important factors in thunderclouds is the location and size of the charge regions. The simplest and most accepted model of a thundercloud was given by Wilson (1916). lie assumed that the center of electric charges

6







7



within a thundercloud might be considered as point charges if the dimension of the charge region was small compared to the ground distance to the ground observation point. Under these assumptions the thundercloud charge was treated as an electric dipole with an upper part that carried a positive charge and a lower part that carried a negative charge. Electric field measurements performed by Malan (1963), and balloon tests made by Simpson and Robinson (1941), and Gish and Wait (1950) yielded an average value of 40 coulombs for each of the charge regions. However, measurements of charge neutralization of the order of 40 coulombs or larger in single ground flashes made by Brook et al. (1962), Uman et al. (1978), and Krehbiel et al. (1979) make us suspect that 40 coulombs is too low an estimate for cloud charge. In addition, Malan (1952) estimated that about half of the cloud negative charge was neutralized during the lightning flash. Since the external electric field often used to compute the cloud's static charge is due to the net of the thundercloud charge and the surrounding space charge, the actual .value of the thundercloud charge is larger than reported values. In our study we used the difference in the electric field during the different phases of a lightning flash to determine the charge being transferred or destroyed in a thundercloud, so the actual value of static charge is not important to our work.

A ground flash is composed of one or more separate strokes in the same or separate channels. Each stroke lasts For milliseconds and the time interval between strokes is roughly 50 msec. A stroke is composed of a downward propagating leader, which lowers cloud charge and cloud potential toward ground level, followed by a return stroke, an earthpotential wave, which propagates back up the leader channel, discharging










the leader to ground. Stepped leaders precede first strokes and some subsequent strokes and move downward in about 50 meter steps with about 50 microseconds interval between steps. The velocity of the individual steps is too fast to be determined from available streak photographs. The stepped leader moves toward earth with a typical average velocity of 2.0 x 105 m/s. Dart leaders precede most subsequent strokes. Dart leaders occur if additional charge is moved from another region of the cloud to the top of the leader channel in a time less than about 100 msec. A dart leader serves the same purpose as the stepped leader in that it deposits charge along the channel and lowers cloud potential to ground. The dart leader is less branched and has higher velocity than the stepped leader. The elucidation of these processes is mostly credited to Schonland and his co-workers in South Africa (1934 to 1938) who used photographic techniques and electric field measurements. Discharges also take place in the cloud in the time between strokes. Interstroke electric field changes observed on the ground are termed J-changes; interstroke impulsive electric field changes are termed K-changes (Kitagawa and Kobayashi, 1953; Uman, 1969; Pierce, 1977).

Ground flashes can be classified as hybrid or discrete flashes

(Malan, 1954; Kitagawa et al., 1962). A lightning flash which involves one or more continuing currents between strokes is called a hybrid flash. A flash which involves only discrete strokes and no continuing current is called a discrete flash. Between 29 and 46 percent of all ground flashes have strokes followed by a continuing current (Livingston and Krider, 1978; Kitagawa et al., 1962), that is, hybrid characteristics. The J-change is differentiated from the continuing current stroke because the J-change has no channel luminosity and at close range the J-change electric field






9



has different polarity. The work on cloud-to-ground discharges presented in this thesis will provide the VHF noise source locations for each phase of hybrid and discrete flashes. Whenever wideband electric field measurements were available, we attempted to calculate the charge involved along the radiating paths. These findings provide additional insights into the mechanisms of ground flashes.

The intracloud discharge is not as thoroughly investigated as the ground discharge. On the basis of electric field waveforms, Kitagawa and Brook (1960) studied the nature of electrical discharges inside thunderclouds. They included the cloud to cloud, cloud to the surrounding air, and the intracloud discharge, treated them as identical, and referred to them as cloud flashes. Three phases of the cloud flash were classified: initial, very active, and junction phase. The initial phase was characterized by a large number of small impulses. The active phase had larger and more regular impulses. The final phase had a number of rapid regular impulses. Ogawa and Brook (1964) studied the variations of the electric field with time and distance during the initial. and junction phases of intracloud discharges. They claimed that positive charge was lowered during the initial phase by downward positive streamers, and that negative recoil streamers occurred during the junction phase. This viewpoint is partially shared by Takagi (1961) who proposed a mid-gap streamer where positive

streamers propagate downwards into the negative charges and negative streamers propagate upwards into the positive charges. However, earlier work by Pierce (1955) and Smith (1957) suggested that the intracloud discharge raised negative charges. Khastgir ahd Saha (1972), using questionable models attempted to prove analytically that the experimental electric field curves of Ogawa and Brook (1964) could be interpreted as






10



either positive descending streamers, negative ascending streamers, or a combination of both of these processes. The work in intracloud discharges presented in this thesis will provide the VHF noise source locations in three-dimensional space and in time. These findings should provide additional information to help understand the mechanisms of the intracloud discharge.


2.2 Description of Electromagnetic Radiation Emitted by Intracloud
and Cloud-to-Ground Flashes

The most recent comprehensive study of the electromagnetic radiation produced by lightning discharges is given by Pierce (1977). Briefly, this section presents a review of the radiation fields due to the intracloud and cloud-to-ground flashes over the frequency range from 1 KHz to 1 GHz.

One means of learning about discharge processes associated with cloud-to-ground and intracloud lightning discharges is by measuring the resultant electromagnetic radiation. Numerous investigators (e.g., Malan, 1958; Brook and Kitagawa, 1964; Takagi and Takeuti, 1963; Pierce, 1960; Kimpara, 1965; Uman, 1969; Proctor, 1971; Takagi, 1975; Krider et al., 1977, 1979; Taylor, 1978; LeVine and Krider, 1977; Serhan et al., 1979) have studied the electromagnetic radiation of lightning in various frequency ranges with the purpose of deriving some conclusions about the lightning discharge.

The electric field due to a small straight vertical conducting

element above a conducting plane can be calculated exactly at any distance. These results are found in Uman and McLain (197O), and McLain and Uman (1971).






11



Z(~t = E V2 2-3sin 2 0 t R~
2
2-3sin20i f i z,T dTdz
2T0IfzI R i3 0c




+ fz2 2-3sin2 8 R dz
zI cR2
J


z sin 6 r R
f / t zIt dz (2 )
2t a z (2.1)



where the subindex j represents the contribution due to one of the current elements. The pertinent geometry, distance, and angles are defined in Figure 2.1.

A spark channel carrying a transient current, usually referred to as current element, acts as a radio antenna and emits electromagnetic radiation. The radiation field from a current element is the term that contains the time derivative of the current in equation (2.1). That is



1 fz2 sin 2j Dir R,]
E (Dt) 2- Z t --I dz a (2.2)
Rad 2 c' zI R jc z


Malan (1958, 1963) first obtained correlation between the low

frequency electric fields and the radiation fields produced by intracloud and cloud-to-ground lightning flashes in the 1 KHz to 10 MHz range. Brook and Kitagawa (1964) measured radiation fields at frequencies of 420 and 850 MHz from lightning flashes 10 to 30 km away. Horner (1964), Kimpara (1965), Pierce (1967), Oetzel and Pierce (1969), and Pierce (1974) provided good reviews of correlated eleotric and radiation fields extending from 1 Khz to 100 MHz. These reports showed that at frequencies less than 300 KHz few current elements are active during the flash. Isolated radiation pulses were obtained primarily during return strokes






12

























Z OL

4





Ld z 44
< 0
0

44 rA r
0









CIO






13



and K-changes. The maximum energy of the radiation spectrum is at VLF. The average source spectrum has a maximum at about 5 K11z and decreases inversely proportional to frequency above 10 Kllz. In the frequency range from 300 Kllz to 30 Hiz the number of current elements increases but the magnitude of the return stroke radiation pulse decreases. As the frequency increases above 30 M4Hz the number of current elements increases with a peak at 50 MHz, and then decreases (Oetzel and Pierce, 1969). Above 30 Mh1z the magnitude of the pulses decreases with increasing frequency. At LF and VLF the length of the return stroke channel and the K-change channel are of the order of magnitude of these wavelengths, since the radiation half cycle time is the channel length divided by the propagating velocity and this is the only radiation that exists. As frequency increases into the HF and HF range, there are more current elements with length comparable to the wavelength. We expect that most current elements active during lightning discharges have lengths of the order of tens of meters which will be detected with a center frequency of tens of Miz.

Another important variable to consider in the study of atmospherics is the effect of the propagation medium between the current elements and the group receiving stations. Excellent reviews of the propagation conditions of atmospherics can be found in Horner and Bradley (1964), Oetzel and Pierce (1969), Harth (1974), and Pierce (1977). The characteristics are a function of the frequency of the emi tting source, the propagating distance, and the reflective properties of thle earth and the ionosphere. The ionosphere has complex reflection properties as a function of frequency. According to Pierce (1977), the propagating

conditions of atmospherics can be separated into three groups. Below






14



300 KHz the earth and the lower ionosphere create a quasi-waveguide; between 300 KHz and 30 Mlz reflections occur from the ionosphere; above 30 M4Hz atmospherics penetrate the ionosphere. In the research reported in this thesis, the atmospherics were recorded in the VHF range (30 to 50 MHz) where at the close ranges considered there is no appreciable ionospheric reflection.


2.3 Lightning Direction Finders

The distant electromagnetic radiation associated with lightning is usually called spherics. Spherics have been used as lightning direction finders in the VLF and VHF range. The standard method of location of distant ground flashes in the VLF range uses cathode-ray direction finders (CRDF). This method was originally developed by Watson-Watt and Herd (1926). It consists of two or more direction finding stations, each with two vertical loop antennas usually tuned to a VLF frequency. The azimuth angle of the flash is usually determined by displaying the two perpendicular antenna magnetic field outputs on the perpendicular scope axes. Two or more stations can be used to determine the location of the discharge from the intersection of the azimuth vectors. For discharge distances less than 100 or 200 km from the stations, the accuracy of this standard technique has been found to be poor. This is caused by the fact that if return strokes are not vertical, the antennas will be sensing not only the vertical magnetic field but also the horizontal component. As much as 20 degrees error hiis been found by Nishino et al. (1973) at a distance of 200 km from the discharge. Uman et al. (1975) observed that even at 10 km thle initial peak magnetic fields occurs in the first 5 pisec and hence is due to the vertical channel. position near ground. VLF direction finders have been improved






L5


considerably by Krider et al. (1976) using the properties of the magnetic field previously observed by Uman et al. (1975). The improved VLF direction finder has been successfully tested to detect the location of ground flashes within 200 km of the stations (Krider et al. (1976)).

Oetzel and Pierce (1969) suggested that time-of-arrival techniques could be used for line-of-sight direction finding in the VHF (30-100 MHz) range. VHF direction finders were developed along these lines by Cianos et al. (1972); Murty and MacClement (1973); MacClement and Murty (1978); and Taylor (1976, 1978). These VHF direction finders made it possible to locate lightning discharges within a range of 100 or 200 km from the stations. Cianos et al. (1972) used two VHF stations (25 to 35 MHz) separated by 122 meters. Using this system the difference in the time of arrival (DTOA) was measured with an accuracy of 10 nsec, and the azimuth angle of about 2000 impulses per flash was located. The Cianos VHF direction finder operated in real-time for distances up to about 150 km. The VHF direction finder described by Murty and MacClement (1973) operated in the 82-88 MHz range and used difference in the time of arrival (DTOA) to determine the azimuth angle of atmospherics up to 160 km apart. DTOA within 25 nsec were measured from the scope traces. The latter system was improved by MacClement and Murty (1978) to include a third station. The third station permitted measurement of elevation in addition to the azimuth angle. The system operated in the 66-72 MHz range and DTOA were measured with an accuracy of 10 nsec. This system operated in real-time and located the azimuth and elevation angles of about 300 impulses per flash. A two station VHF (20-80 14Hz) direction finder was also reported by Taylor (1975). This system was later improved by Taylor (1978) to include a third station






1.6



to determine elevation angles. His 1978 system used a vertical and a horizontal antenna, 13.7 meters apart, at each of two stations separated by 17.8 km. The horizontally and vertically spaced antennas were used to measure azimuth and elevation, respectively. Time measurements were performed to 0.4 nsec with angle accuracy of 0.5 degree.

In addition to the VLF magnetic field ratio techniques and the VHF time of arrival direction finders previously described, Lewis (1960) used a VLF direction finder with DTOA techniques. Lewis used four stations in a Y configuration with the central station at the intersection of the Y. The distance between the central and the remote stations (at the three ends of the Y) ranged between 100 and 120 km. This system was used in relation to a system implemented in England to detect spherics over the Atlantic Ocean and Western Europe. The waveforms from the four stations were photographed on continuously moving 35-mm film. Only three stations were needed for direction finders. The remaining two stations were used for redundancy. The reported accuracy for this system was about 0.5 degree of latitude and of longitude.


2.4 Review of Proctor's Work

In addition to the previously described direction finders, channel locations have been reported by other means, such as, thunder measurements (e.g., Holmes et al., 1971; Nakano, 1973; and Teer and Few, 1974), and radar studies based on the appearance and decay of ionized channels (Ifewitt, .1.953, 1-957). However the most relevant work to date is a DTOA hyperbolic system that uses a minimum of four stations to determine the three-dimensional channel locations (Proctor, 1976; Lennon, 1975).

By the time Oetzel and Pierce (1969) had suggested in print that

spherics locations could be determined by measurements of DTOA in the VHF






17



range, Proctor, working in South Africa, had built and tested a five station system to measure noise impulses in the VHF range_. Proctor has written only a Ph.D. thesis and a limited number of papers and reports about his work in South Africa. Next we will present a summary of Proctor's work (Proctor, 1971, 1974a, 1974b, 1974c, 1974d, and 1976) and its relationship to the work presented in this thesis.

Proctor (1971) describes his telemetry system and gives some preliminary results. The system consists of four 253 MHz crystalcontrolled receivers located at the ends of a cross (the remote stations), and a fifth station (the central station) at the center of thle cross. The distance from the central to the remote stations ranged between 10.7 and 26.7 km. All stations consisted of a 10 M{Hz bandwidth VHF receiver centered at 253 MHz and progression detection i.f. amplifiers to give the receiver a logarithm response near 80 dB. This detection technique is very similar to the band-pass filter and logarithm envelope detector used in the telemetry of the work reported in this thesis. The remote station spherics were retransmitted to the central station by frequency modulated 10 GHz links with 5 MHz bandwidth. Therefore the overall bandwidth was 5 M4Hz for the remote stations and 10 Mlz for the central station. All five signals together with 5-lisec timing markers were displayed on cathode ray tubes (CRT's) and they were photographed by

35-mm rotating drum cameras. The film movod with a velocity of 8 in/sec. CRT's were also used to display electric field change and time markers. When the operator had decided that the storm was sufficiently close for channel reconstruction (usually less than 20 kin'), a trigger signal selected a threshold level to start the film. The maximum continuous film time is 250 msec. Since most flashes last more than 250 msec






18



and the triggering signal might not detect the beginning of the flash, only limited information is recorded. The records are read by operators who first identify the same pulse in all the stations and then measure the DTOA between the four remotes and the central station. The records are enlarged to .36 cm/lisec for reading purposes. Using a transparent graticule, DTOA can be measured to .1 lisec. Redundant sets of readings are obtained by using the additional station. The by-hand DTOA for every pulse are fed into a computer which is programmed to solve the hyperbolic equations and print the three dimensional locations. This tedious technique required 8 man-months to determine the locations of one 250 msec sample. The reported accuracy of the locations for a 20 km range is 25 meters for X an~d Y, and 140 meters for Z. Proctor (1971) states that a limited number of 250 msec intervals had been processed. Actually, from studying the article, we reasonably infer that only one 250 msec interval was completely processed.

The results reported by Proctor (1971) for the different phases of the discharge are as follows. One stepped leader was processed with 225 locations. The radiation started at a height of 5 to 6.5 km above sea level (ground level 1.5 kin). The noise sources extended upward and downward but the median height moved downward at 3 x 10 rnm/sec for 7 msec. The active region became greater by the end of the leader and extended

from near ground to a height of 6.5 km above mean sea level (MSL) Poor height resolution at low heights does not permit the determination of accurate channels. The noise emitted by dart leaders was reported to be similar to stepped leaders. This information is in conflict with the work presented in this thesis. We claim that stepped leaders have unique, identifiable pulses not seen anywhere else in a cloud-to-ground






19



or intracloud discharge. It was reported by Proctor that the noise from dart leaders emanated from the upper part (heights of 5 or 6.5 kmn above sea level) of the channel. During the return strokes the noise was continuous for 100 or 200 psec. Many sources were active and few fixes were determined along the channel. Proctor (1971) reported activity within 250 psec following the return stroke. This activity was located in the previous return stroke branches. The interstroke process reported was confined to one flash. The interstroke emitted a large fraction of the VH1F noise during the ground discharge. It was reported to start 10 or 12 msec after the first return stroke and involved regions between 3 and 4 km of altitude. Interstroke noise after subsequent strokes was reported to extend the previous channel in an upward direction. Proctor (1971) reported no information about fixes in an intracloud discharge.

Proctor presented his next report in the 5th International Conference in Atmospheric Electricity (Proctor, 1974a) By this time 13 flashes (250 msec intervals) had been analyzed. This paper is the first publication to discuss the location of noise sources during a cloud flash. It is claimed that cloud flashes emit pulsed radiation during their initial and very active (VA) phases, but only pulsed trains, less than one millisecond width, in the final stage. These trains were also

reported In the VA phase. According to Proctor, these trains are emitted by two kinds of events. One produces a long propagation from the previous noise sources while the other one produces a shorter path which moves toward the starting volume of the flash going throughout non-previously located channels. Proctor associates these trains with K-changes. The speed of the train of pulses ranged between 3 x 10 6and






0



3 x 10 7 m sec. The manner in which the sources form appeared erratic. During the initial stage they seem to be confined to a volume less than

1 km 3 ; then the channel emerged. The emerging channel is accompanied with a sharp change of electric field during the beginning of the discharge. The propagating streamer during a cloud flash, according to Proctor, emits radiation from near the tip of the advancing leader, in contrast to the stepped leader which radiates from both extremities as well as in the intervening channels. Four isolated regions were presented in the horizontal projections of the source locations. It is reasonable to assume that these sources would in some way be connected if all the VHF noises were identified.

Proctor classifies two types of cloud flashes in accordance with the pulse rate of the emitting cloud. The low pulse repetition frequency (prf) flash emits about 2000 pulses/sec while the high prf flash emits about 30,000 pulses/sec.

Proctor (1974a) correlates VHF noise source locations with the

weather radar precipitation echoes. Some flashes were contained almost entirely in the regions of heavy precipitation. Some of the streamers terminated at the end of the precipitation echoes. Some other flashes followed the path of highest reflectivity gradients. The radar correlation reported was performed using a constant altitude plan position indicator (CAM'T).

Proctor (1974b, 1974c, and 1974d) consist of three special reports published by the Council for Scientific and Industrial Research (CSIR) in Johannesburg, South Africa. These reports d'eal with the sources of cloud-flash spherics, instantaneous spectra of spherics, and VHF radio pictures of lightning. Next we give our views of the significant findings in these reports which have not been discussed previously.






'21


Simultaneous recordings of the radiation field of lightning flashes were performed at one site. The selected frequencies were 30, 250, 600, and 1430 MHz. This experiment shows that pulses were emitted at all these frequencies for the low prf cloud flashes but were not the same, in general, for the high prf cloud flashes. This is an important result which has also been studied in recent years by Krider et al. (1979). Krider et al. compared the wideband electric field (1 KHz to 2 MHz) and the 300 KHz bandwidth RE receivers at 3, 69, 139, and 295 MHz for a distant storm (50 km away). These results illustrate that pulses were simultaneous in all these frequencies and a wideband (dc to 1.5 M4Hz) electric field pulse (radiation term) also occurred at the same time. Proctor determined the DTOA between the leading and trailing edges within single pulses and consecutive pulses. He could find no definite relationship between the direction of the vectors and the direction of the channel. But most vectors, either between the leading and trailing edge of the same pulse or between the trailing edge of one pulse and the leading edge of the next pulse, had a component in the direction of the channel tip.

From the study of the pulse width during cloud flashes, Proctor concluded that the average extent of the active source was about 240 meters. He claimed that channels are formed in a stepped information. This viewpoint was first proposed by Schonland et al. (1938) and later reported by Pierce (1955), Ishikawa (1960), Takagi (1961.), and Krider et al. (1979).

Proctor noted that the return stroke had differences in the pulse width (in the tens of microseconds) between the different stations. lie related the difference in the pulse width to the velocity of the propagating potential wave via a Doppler-type effect. Pulse width differences in the order of a few psec were found in all wide pulses (over 50 psec).






22


Proctor has estimated the amount of charge, the charge density, and the current flow during the initial phase of a cloud flash. VHF source locations during this phase propagated upwards in a path about 25 degrees off vertical. The technique used consists of determining the centroid of VHF locations every millisecond, and finding the amount of charge for the given field change. The charge density and the current are determined at each millisecond interval taking into consideration the field generated by the two point charges and the leader. Using this technique, the following parameters were determined: a) 10 Coulombs for the initial phase of the IC (fast field change), b) I Coul/km charge density, and c) a current of .2 kA every 3 msec. Since only one field meter was used to determine the electric field and a number of assumptions had to be used about the charge structure, these results are questionable.

The most recent work published by Proctor is his Ph.D. thesis

(Proctor, 1976). Next we will present a summary of our view of the new ideas presented in his thesis.

Proctor classifies the VHF noise (253 MHz, 5 MHz bandwidth) pulses in three groups: P pulses, Q noise trains, and S pulses. The P pulses are nearly rectangular in shape with an average pulse width of 1 psec. By comparing the same pulses with wider bandwidth (10 MHz), Proctor claimed that P pulses were a rapid succession of very short spikes which had been smeared into one pulse by the limited receiver bandwidth. During a cloud flash these pulses appear at a rate of about 4.7 for groups of 310 psec intervals. The time between groups was about 1.8 msec. The Q noise trains consist of rapid successions of spikes. They are common to all flashes and are more frequent in the junction phase of a cloud flash. They appear to be related to very rapid movement of charges and






23


often accompany a K-change. S pulses are those that do not fit the two categories previously described. In addition, Proctor often refers to R noise as the abrupt (starting noise) pulse which is characteristic of most return strokes.

The P-type of pulse has been the subject of additional analysis. In general, it was reported that the rate of electric field change was directly related to the frequency of P pulses. That is, a sequence of P pulses indicated fast E field change while their absence indicated a reduction in the slope of the field change. P pulses seem to be emitted from regions near the advancing tip. By determining a fix at the leading and trailing edge of the pulse, propagation vectors have been found. The sources appeared to form at very high velocities near the speed of light. The directions of the vectors grouped in cones whose axes appeared to lie in similar directions for any one storm. Proctor speculated that the geomagnetic field might have some influence in the direction of the sources.

The Q noise trains and K-changes were also studied further by

Proctor (1976). Of 26 Q noise trains reported in one flash, only eight had detectable K-changes and six of these were associated with positive streamers. Proctor attributed this difference to the low gain of the field meters. Contrary to Proctor, the work reported in the present finds that more. than 50 percent of the Q noise trains did not show any field meter change. Our equipment was sufficiently sensitive to detect a 2 volt/meter change. The Q noise that Proctor reported was weak and only 5 out of 26 channel locations were studied. These Q noises were emitted from regions below the lower extremity of the flash. K-changes










do not always involve the main channel. Some K-changes propagated in channels which were not connected with the previous channels.

The velocity of the main channel in a cloud flash reported by Proctor was 1.7 x 10 inm/sec. This value was obtained by finding the velocity between centroids 1 msec apart and located along the channel. The velocity determined in this manner during the propagation of the main channel in a cloud flash seems to be associated with the-P pulses. A high velocity between 2.7 x 106and 3.0 x 10 inm/sec is associated with Q noise trains.

From the five cloud flashes reported by Proctor (1976), four extended near-horizontal while one was near-vertical. The vertical flash extended between -110C and -520C (6.3 to 13.0 kmn MSL) while the horizontal flashes developed at temperatures of 0, -7, -10 and -210C. It is worth noting that the mainly horizontal flashes extended over a height of 5 kin while the vertical flash extended over a height of 7 km. The vertical flash was associated with upward propagation of negative charge. The diameters of the concentrated VH1F sources were between 100 and 600 meters. Even though some noise sources were located in a much wider diameter, Proctor attributed the wide channel to multiple branching.

Additional information in ground flashes provided by Proctor (1976) follows: (1) Dart leaders were characterized by one or more successions of wide pulses (tens of microseconds) separated by low amplitude Q noise

trains. The V111' noise sources during the dart leader connected separate regions that had been previously ionized, and were not located near the dart leader path to ground. (2) There was no apparent time difference (greater than 10 iisec) between the occurrence of the electric field and VHF for the first return stroke. However, in most cases the VH1F waveform






25



during consecutive return strokes either preceded or followed the electric field waveforms by as much as a few hundred microseconds. In two reported cases the VHF was absent during consecutive return strokes. The locations of the beginning of the return stroke were usually found near the top of the previous leader channel. The locations at the end of the return stroke were usually found I or 2 km above the previous return stroke sources. Very few locations were found near the previous leader channel to ground. (3) Proctor reported that the largest amount of VHF noise sources occurred during J-changes, but very little effort was spent analyzing the process. He reported near-horizontal and nearvertical J-changes and that some VHF noise sources active during J-changes occurred in sequence.


2.5 Review of Lennon's Work

Lennon (1976) described a VHF (30-50 MHz) DTOA Lightning Detection and Ranging (LDAR) "real-time" system operated at the Kennedy Space Center during the 1974-1975 period. Originally the system consisted of four remote and one central stations. During 1977 the system was extended to include six remote and one central station. Even though only three remote and one central station are needed for DTOA measurements, the additional stations provided redundancy. The remote stations were located an average of 10 km from the central station forming two Y configurations which share the central station. The system was designed

to sense Lhe Iog of the envelope detected V11F radiation from atmospherics in all the stations and retransmit the information from the remotes to the central station. The signals from three of the remote stations were retransmitted to the central station using 10 MHz bandwidth microwave










links (around 7.4 GHz). The signals from the other three remote stations used 5 Miz bandwidth cables. At the central station a Biomation 1010 was assigned to each of the VHF signals. Biomation 1010's were used to digitize 2048 consecutive samples with a sample every 50 nanoseconds. The output from the Biomation is transferred to the preprocessor. The preprocessor has several functions. First, it performs a reasonableness check by determining the largest signal in all the stations and by checking if the DTOA of the largest signal is within the limitations of the physical geometry. In addition, for this test to succeed, the central station largest peak has to occur first. If these conditions are met, the preprocessor is used to measure the DTOA between the largest signal in the central and each one of the remote stations. Using the hyperbolic system equations described by Holmes et al. (1951), Appendix A, two sets of three-dimensional locations are calculated. If the values of the two sets of stations do not agree within a few hundred meters, the data are rejected. Otherwise the data are stored in digital tape and displayed in a Plan Position Indicator (PPI) and a Range Height Indicator (RHI) CRT screen. Since this process takes less than 100 msec, the output locations are represented in near "real-time." Two milliseconds after the first sample, the Biomation 1010's are ready to receive a new set of data and repeat the same process.

This technique can provide very accurate fixes whenever only one

large VH1F pulse is detected in all the stations. Since the data bandwidth

is 5 M4Hz and the sampling frequency is 20 MHz, this is a highly accurate system. The system accuracy is within tens of meters for X and Y, and 150 meters for Z. For a study of lightning channels, however, this processing is not adequate because a maximum of one location is determined







27


every 2 msec. In practical applications reasonable locations are only obtained every 5 or 10 msec. In addition, using only amplitude thresholds the LDAR system can match the wrong pulses and pass the redundancy test. Let us illustrate this problem with an example. Assume that there are two active VHF regions emitting radiation of the same magnitude, and these regions are located at any height and are a few kilometers on the opposite side of the central station. Pulses, received from the A and B regions in an interval of a few tens of microseconds, will be tested simultaneously in the Biomation. The pulse from A will be larger in the station closer to A, whereas the pulse from B will be larger in the station closer to B. Regardless of redundancy, there will be a consistent matching of pulses from A and B and meaningless results will be obtained.

The work described in this dissertation used some of the components of the LDAR system. These components were the sensors and the telemetry for the four stations.- Instead of the Biomations, we recorded the 4-station (3 remotes and 1 central) VHF data on analog tape. The VHF noise from the analog tape was later digitized and processed to reconstruct the lightning VHF sources. By using a computer implemented algorithm. to process the data and display the output, our technique can provide source locations every 5 or 10 llsec. For any given flash we determine about 500 locations for every location of the original LDAR system. This

abundant information permits us to study the I ightnliig channels inside a thundercloud, not visible to any type of phiotographiy. Our computerized data processing provides tens of thousands of locations per flash after two hours of computer processing, thus far surpassing the by-hand technique used by Proctor (1976), which can determine about 1000 locations






) 8



per flash after 1.0 man-months of processing. However, since our data are recorded on analog tape with a frequency response between 400 Hz and

1.5 MHz, our source locations are not as accurate as those reported from the LDAR or Proctor (1976) systems. In the next two chapters we described the telemetry and data processing techniques used in this research.
















CHAPTER III

DATA ACQUISITION AND PROCESSING


Figure 3.1 shows a general block diagram of the data acquisition and processing used in this research. The VHF radiation generated by lightning flashes during thunderclouds was detected at four selected ground receivers (RX), and recorded simultaneously at one station (recorder). Four VHF radiation channels were simultaneously slowed down (data pre-processing) and then digitized (A/D converter) at a rate greater than twice the bandwidth of the recorded signal. A computer algorithm, to be described in Chapter IV, was developed to determine the VH1F source locations from the difference in the time of arrival (DTOA) of the four time series VHF data. The results were interpreted and related to other correlated data. In this chapter we describe the technique used for data recording, the properties of the telemetry system, the data pre-processing and A/D conversion, and other correlated measurements used to supplement this research.


3.1. Data Recording

The LDAR system used to obtain the original data consisted of a central and six remote stat, ons forming two Y con f'[ tiraLtions, w.tt the central station at the center of the Y. Figure 3.2 shows the station geometry. The detected VHF radiation at the remote stations was retransmitted to the central station and recorded. There were two methods of retransmission: microwave and wideband cables. Signals from


29













THUNDERC LOUD














DATA

PRE-PROCESSING



A/D
CONVERTER






AMDAHL SPATIAL DATA
470 V/6 II COORDINATE INTERPRETATION




I COMPUTER CORRELATION
ALGORITHM WITH OTHER
MEASUREMENTS


IMPROVE UNDERSTANDING OF THE PHYSICS OF LIGHTNING

Figure 3.1. General block diagram.















1


P "VA 8
CAL .

CENTRAL I5
STATION



w
7173 MHz




a










CNJ
) / <










Scole .5






32



the three remote stations in one of the Y configurations (Ml, M2, and M3, Figure 3.2) were retransmitted to the central station using 10 MHz bandwidth microwave links. Signals from the other three stations (Wi, W2, and W3, Figure 3.2) forming the second Y were retransmitted to the central station using 5 MHz bandwidth A-2A cables. All seven VHF radiation signals were recorded at 120 ips on a 14 channel analog recorder operating in a direct mode with a frequency response from 400 Hz to 1.5 M4Hz. Timing information in IRIG B format (accuracy to fractions of milliseconds) was recorded on one of the remaining tape recorder channels. minimum of four rece,'v~ag nations is needtoantViIrda t4'on used for the deter atiaja rof _e = rneQs _o-a _lo ctjp-41o lInes and Reedy, 1951). Appendix A contains a derivation of the threedimensional locations obtained from the measurement of the difference of the time of arrival between the remotes and the central station. The baseline between the remotes and the central station in Figure 3.2 is approximately 10 km. The 10 km choice was made by KSC personnel to obtain accuracy in the order of 100 meters using a real time system for source locations within the KSC geographical area. Figure 3.2 also shows the location of the Vertical Assembly Building calibration signal (VAB CAL) used to obtain the calibration error in the measurement of source locations. An error analysis for the three-dimensional locations is shown in Appendix B. During this research there were some variations in the selection of the three remote stations for different flashes. Appendix B also shows the selected remote stations for the different flashes analyzed in this thesis.






33


3.2 Telemetry System

Figure 3.3 shows the telemetry system used at each receiving station. The signal w.(t) is received by a 5 meter-high linear antenna array that detects the electric field. The signal is passed through a 30-50 MHz bandpass filter (30-50 MHz for 1976 data, 40-50 MHz for 1977 data), included in the VHF receiver. Then the logarithm of the magnitude of the envelope signal is obtained using an envelope detector.

Figure 3.3 is redrawn in Figure 3.4 to show the operation of the receiving system. Here, f = 40 MHz, and the bandwidth, 2B, is equal
0

to 20 MHz. Figure 3.5(a) shows an approximation to the squared bandpass filter. The gl(f) filter has gain N1. Figure 3.5(b) shows the corresponding time domain function, gl(t), of the wideband VHF receiver.



gl(t) = 2 N B sin(2uBt) cos(27tf) (3.1)



Equation (3.1) can be obtained from Figure 3.5(a) by doing the

inverse Fourier Transform of gl(t). The g1(t) term consists of a slow varying waveform of the form sint/t which constitutes the envelope of the waveform cos(2Trtf ) which has been modulated. The output ui(t) can be written as



ui(t) wi(t) 2N B sin(27rBt) cas(21f t (3.2)



where is the convolution operator.

The spectra of atmospherics from nearby'lightning discharges has been studied by various investigators (e.g., Takagi and Takeuti, 1963).













BANDPASS ENVELOPE
ANTENNA FILTER DETECTOR

BPF LOG_(_)LOG
W. (t) 30-50 MHz Ui () RECTIFIER Zoit



Figure 3.3. VHF receiver and envelope detector.






ENVELOPE
BPF DETECTOR
J, zfMH_ Zo W

Wf040 MHz




Figure 3.4. Description of VHF receiver and envelope detector.






g(f) g1(t)




1HI I1

I [F]


(a) (b)

Figure 3.5. Approximation for band-pass filter: (a) frequency domain,
and (b) time domain.






35



The general characteristics are shown in Figure 3.6(a). Figure 3.6(b) shows an approximation of the frequency domain of the signal after the VHF receiver.

The rectifier part of the envelope detector from u.(t) to
1
z (t) is a log IF device designed by RHG Lab with center frequency at 40 MHz for the 1976 data and 45 MHz for the 1977 data. The IF device has a 3 dB bandwidth which corresponds to the bandwidth of the VHF receiver. The device risetime is better than .05 microseconds and its dynamic range is about 80 dB. The input-output characteristic of the log IF is given in Figure 3.7. The actual values are tabulated in Table 3.1. It should be noted that the use of the log IF device is quite convenient in this application because it permits an input range

4
from 30 microvolts (-80 dBm) to 300 millivolts (0 dBm), a factor of 10 for an output range from .255 to 2.5 volts, a factor of 10.

Assuming that W. (f) is constant over the frequency range of interest
1

(30 to 50 MHz), the u.(t) can be represented as a time dependent
1

modulation P(t) multiplied by a phase displacement, i.e.,


u.(t) = P(t)cos(w t + e) (3.3)
1 0


Therefore


z(t) = logIP(t)cos(w t + 0)l = logiP(t)I


+ logjcos(w t + 8)1 (3.4)


The second term will be filtered out by t}he envelope detector because it is at a frequency higher than 50 Miz. The logIP(t)j will be recovered at the output.







W m()u (f)


-20
~ MHz
5KHz 40MHz


(a) (b)

Figure 3.6(a). Input spectra. Figure 3.6(b). Spectra after
the VHF receiver.



Output (volts)



2 1.5



.5

-80 -70 -60 -50 -40 -30 -20 dBm
.03 .1 .3 I 3 10 Millivolts
Figure 3.7 Log IF input-output characteristics.


Table 3.1. Log IF Test Values Input (dBm) Output (volts)

-80 .255
-70 __ .542
-60 .798
-50 1.090
-40 1.394
-30 1.675






37


z(t) = logIP(t)I (3.5)



The z(t) signal represents the time dependent logarithmic envelope of the VHF radiation.

From standard envelope detection treatment (e.g., Thomas, 1969;

Davenport and Root, 1958), we know that the frequency spectrum of z(f) is concentrated in several regions as shown in Figure 3.8. The z (t) output data is recorded on analog tape with a frequency response from 400 Hz to 1.5 MHz. Figure 3.9 shows the frequency content of the signal that is recorded in the tape recording channels. The z 0 (t) signal is composed of unipolar pulses. Since the recorder had a 400 Hz lower cutoff frequency, the VHF radiation out of the recorder has no frequency component below about 400 Hz and is roughly symmetrical about the centerline through the radiation.


3.2.1 Description of Center Frequency, Bandwidth, and Magnitude Level
in the Telemetry System

3.2.1.1. Center Frequency. The choice of the 30 to 50 MHz range for the band-pass filter was made for various reasons. First of all, the lower limit was selected above the HF range where multiple reflection of the ionosphere will occur disturbing the signal (Horner, 1964; Pierce, 1976). Furthermore, the upper frequency limit was chosen below the VHF band for television channels, FM radio, and other sources of interferences. Thus the use of the 30-50 MlIz range reduces the noise level. In addition, previous work (Oetzel and Pierce, 1969; Cianos et al. 1972) on measuring the radio emissions from lightning have proved that the largest number of detectable radiation pulses are present between 20 and 100 MHz. As the frequency increases above the HF range,












Z (f) SB(f)

A

A/2

2fo 2fo
-80MHz 2B- 80 MHz
20 MHz
Figure 3.8. Frequency spectrum at the output of the envelope detector.









Zo (f)


ZO>f




400 Hz I.5 MHz

Figure 3.9. Frequency spectrum at the recorder.






39



the number of pulses and their magnitude decreases. Oetzel and Pierce (1969) claimed that the maximum signal-to-noise ratio is obtained between 20 and 100 MHz. Probably the lower part of the VHF range, around 30 MHz, is the ideal center frequency to study lightning radiation channels.

3.2.1.2 Bandwidth. The receiver bandwidth is an important factor in determining the pulse characteristics. It is desirable to use wideband receivers, since if narrow bandwidths are used, the detected radiation pulses will appear almost identical making cross-correlation difficult. The minimum pulse width detected in a telemetry system is inversely proportional to the receiver bandwidth and the minimum risetime is the reciprocal of the bandwidth. Therefore, a VHF receiver with a narrow bandwidth of I KHz will only detect pulses equal or greater than 1 msec. Studies performed by Oetzel and Pierce (1969), Pierce (1977), and Proctor (1976) have shown that the maximum number of VHF lightning radiation pulses ranged between 10,000 and 500,000 pulses per second. That is a maximum pulse repetition rate of a pulse every 20 lisec. In order to measure time difference between the individual pulses, resolution of about one microsecond is needed, which requires a bandwidth of I MHz. However to determine lightning source locations to an accuracy of hundreds of meters, time differences must be measured to a fraction of a microsecond (Appendix B). With the exception of Lewis (1960), who used a bandwidth of 41 K[1z with center frequency in the VLF range., all the recent researchers who have measured the difference in the time of arrival on radiation from lightning have used a wideband system and a center frequency in the VHF range (e.g., Proctor (1971), bandwidth

5 MHz with center frequency at 253 MHz; Taylor (1973), bandwidth 60 MHz






/0



with center frequency at 50 M11z; Cianos et al. (1972), bandwidth of 10 MHz with center frequency at 30 MHz). In the work reported herein a 20 M4Hz bandwidth centered at 40 14Hz is used for 1976 and a 10 MHz bandwidth centered at 45 M4Hz is used for 1977 data.

3.2.1.3 Amplitude. Oetzel and Pierce (1969) summarized previous work on amplitude spectra of the radiation from lightning between 100 KHz and 10 GHz. The receiver bandwidths were normalized to 1 KHz and to 10 km range. The various data after normalization agreed within an order of magnitude. On the basis of those results, we have determined that the signal amplitude at 40 MHz with 20 M4Hz bandwidth is about 30 mV/in at a range of 10 km. The relative magnitude of the VHF radiation signals reported herein vary between a noise level of -70 dBm (.1 my) and a maximum detected amplitude about -20 dBm (30 my), a factor of 300.


3.3. Data Pre-Processing and AID Conversion

Analog tapes containing six randomly selected lightning flashes

recorded in the Kennedy Space Center, Florida, were sent to Eglin AFB for digitization. Figure 3.10 shows the digitization process used at Eglin AFB. The data pre-processing and A/D conversion consisted of four different steps, three of which were the slow-down process, the final step was the digitization process. The selected time intervals were first slowed

down by a factor of 4 in a direct-recording-reproduce mode. The purpose of this stop wns to reduce, the tipper frequency co~nten t o)f the dnta from 1.5 MHz to 375 KHz. Using the direct mode the recorded lowest frequency range will be multiplied by the slow-down factor, that is, from 400 Hz to 1.6 KHz. Since the wider pulses observed in the final processed data were in the neighborhood of 200 psec, limiting the





























0 Ln
co U
F- -i Ld
-i LLJ
LJ IL
3. 2
< L <
x
U
a) I







Ld m
0 LLJ :I
Z
0
U
Lij
V) 17,
0 OD U) 0
rn co n C)
cy
Z
-Li
Lo
LJ
LLJ 0
LL 2 fr
< < it LLI
>
CIJ T Lu
LL) CC5 2
0 LLI
:D 0 C\j x 41
LLI C) N

U <
Lo LL
0 x OD CQ
U-1
CIO co Lo ,
x <


Lij -j
CL
< -5
<

3; w
o
V) 0
c 14 Z
a:
uj m X <
0. LO z uj
:;: u -i
ui to


0, T zt U
< 0 uj w
Z 0 9
< 't co






4 2



pulse risetime to 1/1.6 Kllz =625 hisec did not reduce the information content. The significant aspect of this step was to reduce the bandwidth of the analog data to within 500 KHz, the maximum available bandwidth for FM modules. The remaining two slow down processes used FM modules, first a factor of 16, then by a factor of 8. The R1 modules were used because they maintain the low frequency content of the data. As part of the latter slow-down process, the four channels containing the desired information were digitized simultaneously at a rate of 8.5 KHz. Since the total slow-down rate was 4 x 16 x 8 = 512, the real time sample rate became 8.5 KHz x 512 =4.352 MHz. This sample frequency is well beyond the Nyquist rate of two times the maximum tape frequency. Using this high sampling rate, digitized points can be linearly interpolated with straight lines without significant loss of characteristics (Jerri, 1977).

Time correlation is an important factor of the slowing down and

digitization process. The original TRIG B recorded in the tape is still readable during the first factor of 4 slow-down. At this stage a different IRIG A (ten times faster than TRIG B) is recorded on a different channel and the initial desired processing time is converted to the new TRIG A code. In the next slow-down (a factor of 16), the previous IRIG A is still readable and a new IRIG A is introduced. The desired starting time is converted from the previous TRIG A to the new TRIG A. During the final slow-down process (a factor of 8), a time code generator automatically reads the initial converted starting time, which is typed in as part of the program, and starts'digitizing when this time is reached. Although the initial absolute time can only be read in millisecond or a fraction thereof, from the original TRIG B timing






11,3



signal, the time difference between different events in the same flash is only limited to a maximum of two or three microseconds due to tape stretching. This procedure of time conversion allows us to read accurately the original time-of-the-day with an absolute resolution of about 100 pisec.

The twelve seconds for the six selected lightning flashes were expanded to 12 x 512 = 6144 seconds prior to digitization. The 6144 second data were digitized at 4.352 M4Hz for a total of 52.244 x 10 6 sample points per channel or 208.9 x 10 total samples for the four

channels. The digitized data were recorded using 2400 feet, 7 track, 800 bpi, digital tapes. Approximately 1.638 x 10 samples per channel can be stored on a 7 track tape. Therefore about 52.244/1.638 = 32 tapes were needed for processing.

The tapes containing the calibration pulses were processed in a manner similar to the one previously described for the lightning data. Two differences were noted: 1) there was no need to convert timing information, and 2) the digitization rate was increased to 8 Miz, a sample every 115 nanoseconds. Appendix B shows the uncertainties in the three-dimensional locations due to the calibration error.


3.4 Electric Field Meters

The waveforms recorded by the electric field measuring systems of

the University of Florida. (U of F) and New Mexico ist-i ute of Mines and Technology (NMITi) were used for correlat ioi- witil Clio rad ft lin field. The electric field measuring systems used by U of F were similar to that described by Fisher and Uman (1972) and later by Krider and his co-workers (Krider et al., 1975, 1977). The correlated waveforms from the U of F electric field system for 1976 consisted of an FM channel with a frequency






44



response from DC to 20 KHz and a. direct recording channel with frequency response from 300 Hz to 300 KHz. The electric field input to the recorder had a response from 0.2 Hz to 1.5 MHz. In 1977 the recording system was improved such that the analog data was recorded with a FM frequency response from DC to 500 KHz, and a direct recording with a frequency response from 400 Hz to 1.5 MHz.

The correlated waveforms from the NMIMT electric field stations consisted of a network of nine stations spread out over the KSC area (Krehbiel et al., 1974). The electric field sensed at eight remote sites was retransmitted as amplitude modulation over a microwave telemetry link to the central station (station nine). At the central station the electric field from all the stations was recorded on analog tape. The NIMIT electric field meter had a system decay of 10 sec and a frequency response from 0.1 Hz to 5 KHz.

KSC IRIG B time code information was stored in all. the analog tapes containing electric field information. Time correlation between any of the electric field stations and the four LDAR VHF radiation data was accurate to one hundred microseconds.


3.5. Charge Locations Derived from Electric Field Stations

The electric field (E) detected at a horizontal distance d from a charge Q at a height z from a perfectly conducting ground plane is given by Uman, 1969, pp. 48-49.



E=-2 Qz 32(3.6)

4Trc (z 2+ d 2)I



where c0is the permittivity of free space. The term d 2can be expressed





45


as

d2 = (x-xi) 2 + (y-yi) 2 (3.7)



where (xiy.) is the ground coordinate at the electric field station. Therefore the electric field at any station can be expressed as


E. = 2 Qz (3.8)
47TEo((x-xi) + (y-yi) + z2 )



Assuming a one point charge model where the charge Q at (x,y,z) is removed producing a field change E., four electric field measurements are needed to determine the four unknowns Q, x, y, and z. Fitzgerald (1957) obtained an analytical solution for this equation when the ground-based electric field stations were located at the vertices of a parallelepiped. Krehbiel et al. (1974) derived an analytical solution to equation (3.8) without limiting conditions, assuming that a solution does exists. The solutions obtained from a set of four stations using this technique were

1 to 3 km away from each other because the electric fields at each station were slightly in error. However when several solutions of a group of four stations were used, about 75% of the solutions fell in a
3
volume of 1 or 2 km This is a reasonable technique for finding the charge center neutralized by return strokes whenever d >> z. When d is omparable to z, the point charge model is not a reasonable approxiniation to finding the value of Q and its location. and a solution using this model usually does not exist.

Jacobson and Krider (1976) improved the analytical solution derived by Krehbiel et al. (1974) using a nonlinear least square iteration technique where all the electric field stations are considered. Iterations are









performed to determine Q, x, y, and z which minimizes C2 in


2 N E.-E 2
2 mi ci (39)




where Em. and E are the measured and calculated field, N is the number of measurements, and G is the measurement error. The values of the
1

charge centers presented in this thesis, unless specified otherwise, have been obtained using the least square technique as described by Krehbiel et al. (1979).

A reasonable model for the charge neutralized during some

lightning phases, especially J-changes and the intracloud discharge, consists of a point charge which we move from height h2 and horizontal distance d2 to a height h and horizontal distance d The change of electric field is (Uman, 1969, p. 70),



E = 2Q h2 h1 (3.10)
47r0 h22 + d22] h12 + d12]3/



where Q is the charge moved and C is the permittivity of free air. The
0

values of d2 and d1 are expressed as
2 1)

d2 = ((x2 xi) + (Y2 Yi)

d (( -)2 2) (.11
dI = ((xI xd) + (yI y1) .)



Seven parameters are needed to solve equation (3 namely, the coordinates of each of the ends and the charge'involved. Jacobson and Krider (1976) extended their application of the nonlinear least square fit to solve equation (3.10).






."1 7



3.6 Ch~~Lcations D erived froIm VHF Noise Sources

The VHF radiation during initial and subsequent stepped leaders has unique properties. The stepped leader VHF radiation has lower amplitude arnd higher frequency than any other event during a lightning flash. Initial stepped leaders are preceded by lower frequency pulses with higher magnitude that we have called the preliminary breakdown (PB). Similarly, stepped leaders before subsequent strokes are preceded by higher magnitude pulses which characterize the J-process. In addition, the beginning of subsequent stepped leader VHF radiation is often accompanied by correlated change of slope in the electric field record. During the entire first stepped leader VHF radiation, significant correlated electric field change is detected. However, stepped leader electric field change has been detected as much as 1.2 msec prior to the first stepped leader VHF radiation which corresponds to about 2 km change in the VHF sources. These properties are discussed in detail in Chapters V and VI. In this section we discuss the use of VHF noise sources to determine the charge value and its location.

On the basis of the above statements, we have chosen the noise

source location where the VHF radiation changes characteristics from PB or J-change to stepped leader. The location of this point charge which will be lowered to ground by the stepped leader-return stroke process. This is a reasonable assumption since stepped leader VHF sources are detected from this point on and throughout most of its path to ground. We have proceeded to solve equation (3.8) for the value of the point charge (Q). The value of (x,y,z) in (3.8) corresponds to the VHF source for the beginning of the stepped leader in the VHF record; the value of (x.,y. ) and E.i are the ground coordinates and electric field change






48


during the correlated electric field change. Since the electric field records from at least eight ground stations in the KSC area were provided by Krehbiei (private comm.), we could verify our results by using different electric field stations. We found that as long as the horizontal distance from the electric field station to the point charge source was further than the height of the source, our charge calculation was within 20% for the E-field at each station. Throughout this work, we selected an electric field station which gave results in the middle of the 20% deviation. The fact that we obtained inconsistent results for a

horizontal distance less than the height is an indication that a point charge is not a good approximation within this range. For all the stepped leader-return stroke studied in this thesis, we have calculated the value of its charge source using this technique and whenever available we have compared this result with the values obtained by Krehbiel (private comm.) using the technique described by Krehbiel. et al., (1979). As we shall see, our results compare well with those of Krehbiel for charge magnitude and location.

















CHAPTER IV

COMPUTER ALGORITHM FOR LOCATION OF LIGHTNING CHANNELS


One important task of this research is the development of an algorithm to measure time delays between every "identifiable" pulse detected at the central and at the three remote stations. From the measured time delays, the three-dimensional locations of the VHF radiation sources are determined by using hyperbolic equations (Holmes and Reedy, 1951). In this chapter, we review the available techniques for determining time delays, and then we describe the technique chosen for the present study.


4.1 General

Two types of computer processing are performed as part of this thesis: First, we determine and display locations as calculated from the measured time delays. Second, we determine a data model for the VHF radiation time series data. The first task is described in this chapter whereas the second task is studied in Chapter VI.

Since the Second World War the measurement of time delays has been an important aspect of engineering work. Some important applications of time delay measurements over the last 30 years include:

a) Radar technology based on the measurement of time delay between

a transmitted and a received pulse (Siolnik, 1962). Some of

the applications required estimating the distance to other

planets.


49






50



b) Navigation (Aircraft, Missile, Vessel). Time delays are widely

used in the field of aircraft and missile navigation to determine a location update (Holmes and Reedy, 1951). The LORAN

worldwide system presently used for civilian and military aircraft navigation update is based on the measurement of time

delay between signals at known positions to determine the aircraft position (Pitman, 1.962).

c) Seismic signal, processing for oil and gas (Wood and Treitel,

1.975). Time differences between reflected seismic signals map

structural- deformation and provide tlie locations of oil -Ind

natural gas layers.

d) Ground response to earthquake conditions (Fnochson, 1973).

The time difference at two separate ground locations is used

to determine the transit time of particle velocity waves

through soil when activated with earthquake loading conditions.

e) Digital signal processing. Measurement of time delays between

a stimulus and a response to a system or between two time series has wide applications in the field of communication (Roth, 1971).

f) Determination of lightning channels. Oetzel and Pierce (1969)

proposed the determination of lightning channels by measuring

the time delays between four stations. A similar technique

was independently implemented in South Africa in 1968 and

described by Proctor (1971). In tlie USA a real-time system was

developed by Lennon (1975).


4.2 Data Characteristics

In order to find a systematic technique for measuring the difference in the time of arrival between four data channels, it is necessary to study





51



the properties of the multiple channel VHF radiation and the properties of the time-series data.


4.2.1 Properties of the Multiple Channel VHF Radiation

Some of the important properties of multiple channel VHF radiation are as follows:

1. The VHF radiation received at the three remote stations was

retransmitted to the fourth station (central). Since VHF radiation was also recorded at the central station, any radiation pulse, from anywhere in space, identified at the central station will arrive before the arrival of the same pulse retransmitted from the remote stations. Figure 4.1 shows an example of the four channel V11F radiation. The signal from the central station (A) arrives before the signal from the three remote stations (B, C, and D).

2. Since the radiation field is inversely proportional to the

distance from the space source location to the ground receiving stations, there are differences in the magnitude of the radiation at each of the stations. For ease of comparison the four channels are normalized with respect to the central station. The amplitude normalization has no effect in the shape of the pulses and provides a more effective comparison between the four stations' data.

3. From equation (2.1) we know that the radiation field is proportional to the sine square of the angle between the center line of the radiating element and the line to the ground station. I'lierefore, sonle high amplitude pulses in a ground station witli an angle near 90' might fall within the noise level. in another station 20 km away with an angle near 180'. This will be the case for a near-vertical radiating source located immediately above a ground based station. In this case 8 = 180'
































Figure 4.1. Four channel VHF radiation directly from the
recorder for the beginning of the intracloud
flash occurring at 181416 UT on 8th August 1977.
(A) is the VHF radiation at the central station 7.6 km from the discharge. (B), (C) and (D) are the VHF noise for the remote stations, 7.4, 4.1,
and 12.4 km from the discharge, respectively.





53




172 "sec































(B)





54



for that station and no VHF radiation is detected whereas significant radiation is located at the other stations.

4. Since the analog tape direct recording follows a Butterworth response with a 3 dB drop-off at 400 Hz and 1.5 MHz, only pulses with an original period between 2.5 msec and 0.66 lisec could be properly measured with this recorder bandwidth. The largest pulse width measured was about 500 vlsec; therefore,the lowest recorder frequency did not limit the characteristic of the data pulses. In addition, we studied the characteristics of the VHF pulses obtained with a 5 M4Hz bandwidth using the Biomation 1010 in the LDAR real-time system. We determined that about 5% of the VHF pulses had a width between 0.2 and 0.6 pIsec. These pulses and any shorter ones were lost in our analysis.


4.2.2 Properties of the Multiple Time-Series Data

We displayed some selected data with a 10 dB signal-to-noise ratio, from the four channels, with a resolution of 1 lisec per cm for the purpose of studying the characteristics of the pulses in the series. From this display we manually determined the DTOA between identifiable pulses. Some of the important characteristics that we identified are listed below:

1. With the exception of the stepped leader radiation discussed in Chapters V and VI, the time-series data contained an envelope with pulse widths between 5 and 500 lPsec. In addition, there were higher frequency pulses of a pulse width usually less thain 3 lisec superimposed on the envelope.

2. To identify uniquely the same pulse on any two of the timeseries, two selection criteria were used. First, we matched the lower frequency envelope on which the pulses were superimposed. Second, we









identified the corresponding pulses within the envelope. When we performed our manual matching of pulses, we attempted to determine a minimum time interval needed for a unique identification of the envelope. After studying different sections of the data, we determined that the minimum sample interval to uniquely characterize the envelope was about 100 jisec. In addition, we attempted to determine a time interval required to uniquely identify the duration of the individual pulses which are superimposed in a selected time interval of 100 lIsec. Our results indicated that a maximum interval of about 3 lisec was required.

3. An additional test that we performed was to pass the time-series data through a low pass filter that eliminated all pulses wider than 10 Ilsec. When we attempted to match the individual pulses manually, we were only 20% successful. On the other hand, when we smoothed the data, getting rid of the high frequency pulses, we were 100% successful on matching the envelope for a sample interval of about 100 Vsec. In the latter test, we have lost information on the individual high frequency pulses.

4. To determine some additional characteristics of the time-series, we measured the time delays of 185 consecutive individual pulses between the central and each one of the remote stations in one flash and 50 pulses in another flash. We learned that time delays for over 95% of the conscuit lye pulses are within a 2.5 jisec interval.

4.3 Techniqye for Determinin Deays Based on the Data Characteristics


Our next step was to develop a computer algorithm to determine time delays based on the data characteristics of our time-series. To meet the data properties in Section 4.2.2, we chose to use cross-correlation





5 6


and pattern recognition techniques. On the basis of Sections 4.2.2(1)

and (2), we decided to use cross-correlation functions with sample intervals of 94 or 376 ljsec, which correspond to either one or four blocks of digital data, to determine the time delay of the envelope signal. To comply with property 4.2.2(3), we smoothed the data before the calculation of the time delays. The smoothing was performed by using moving averages of 16 data samples across the cross-correlated interval. The peaks of the cross-correlation functions were used to determine the cross-correlated time delays and the corresponding locations. Thie cross-correlation functions are weighted toward tile locations of the envelope pulses in the sample interval. Once the crosscorrelation DTOA's are known, the computer uses a pattern recognition scheme to identify the DTOA between individual events in the envelopedetected signal. A search over a 3.7 psec interval around the crosscorrelated DTOA' s is used. This time interval was chosen to comply with the properties of the time-series described in Section 4.2.2(2). Next we present a description of the cross-correlation and pattern recognition techniques.


4.3.1 The Cross-Correlation Function

The cross-correlation technique we use has been applied in a variety of fields, e.g., statistical theory of communication (Lee, 1960), geophysics (Enochlsoni, 1973) biomed ical enig.ieerinig (French and ]Ioldenl, 1977), radar detectioti (Skolnik, 1962).

Let x nand y 11be two time-series. lri our application y n can be the central station data while the x n can represent any of the remote stations. The discrete cross-correlation function between x and ycnb

defined as









N-i
R xy(j) = x y (4.1)
n=O


where N is the number of data samples. Since the signal at the central station (yn) always arrives first (property 4.2.1(l)), we have to delay the yn signal by a certain amount T. In addition, a noise term r is used
n
to account for properties 4.2.1(2), (3), and (4), and different background noise. Therefore


n YnT +rn (4.2)



Substituting equation (4.2) into (4.1), we get


N-I N-1 N-1 (43)
Rxy(J) = (Yn+' + rn)y n+j= Yn+TYn+j + rnYn+j
n=0 n=O n=O


or


R xy(j) = R yy(j T)+ R ny(J) (4.4)



Depending on the cross-correlated value of the noise R (j), the ny
peak value of R xy(j) will occur in the neighborhood of j = T. Our task is to find the maximum value of R and see what the lag T is for a maxixy
mum. If data from ensemble averages of xn and yn are processed, the cross-correlated noise term can be averaged out and a more accurate value of R can be determined. However each selected intervaL of the
xy
multiple series has different time delays and additional data for averaging is not available. In addition, the VI1F radiation properties

4.2.1(2) to (4) indicated that there might be substantial differences between the data recorded in the different stations.






58


The cross-correlation function R x(j) was normalized as



r(0) = R(j)/ X J0 2 nj1 1 : r (j) 1 (4.5)




To prevent any error due to ambiguous selection of r (j ) when the function flattens out near maximum, four decimal digits are used for comparison. For S/N greater or equal to 10 dB the optimum value of r xy(j) ranged between 0.9300 and 0.9850. Once the four station timeseries data are cross-correlated for a selected time interval of either 94 or 376 psec, the procedure is continued for the next interval. For the cross-correlation function to be applied the signal level must be greater than the noise level. Before the beginning of the flash, the noise threshold level is calculated and the data is not processed if the S/N is equal to or less than 0 dB.

Once we have determined the cross-correlated time delays, we need to calculate the time delays of the higher frequency pulses superimposed on the envelope (see properties 4.2.2(l) and (2)). To achieve this task we used pattern recognition techniques.


4.3.2 The Pattern Recognition Technique

Widrow (1974) has divided the field of pattern recognition into two broad schools: the first group classifies the data by comparing individual features with a pattern recognition list, the other group attempts to fit the data to some type of template matching. Gottman and Gloor (1976) working in electroencephalogram and Weinberg and Cooper (1972) working in neurophysiology applied the first and second pattern recognition techniques, respectively, obtaining successful results. Additional pattern recognition applications include






59


chromotograms (Widrow, 1974), speech (Boudry and Dupeyrat, 1974), and picture rasters (Erich and Foith, 1976). We classified our data with a pattern recognition list similar to those described by Gottman and Gloor (1976). Before we could apply the pattern recognition list to match the individual pulses around the cross-correlation time delay, we had to define a pulse model. Next we provide our pulse model definition.


4.3.2.1 Pulse Model. We divided the four time-series in subsets of 3.7 psec (16 samples), roughly the maximum pulse rate for which the data could have the identifiable characteristics needed for pattern recognition. Then, the sample value which corresponds to the peak of the data subset is determined. This sample value is needed to perform peak recognition of the time-series. The peak recognition is performed as follows: 1) We determine the time delay for the cross-correlated interval of either 94 or 376 vlsec between the central and each of the remote stations. 2) We determine the time at which peak values occurred for each data subset within the 94 or 376 lisec interval for all the timeseries. 3) We add the time value of (1) and (2) above to obtain the corresponding cross-correlated value in the remote stations for the peak of the pulses. 4) Finally, we determine how many peaks in the remote station are within the 3.7 lisec search interval. This procedure limits the number of peaks to be considered to a maximum of 3. At this time in the algorithm the peak recogitioni Is comipleted; now we have to determine which pulse at the remote stations that produced the peaks which met (4) above, is similar to the pulse at the central station. one of these peaks within the search interval will be selected





60


only if the pulse that produced the peak has similar characteristics in the central and on each of the remote stations.

The pulse model used to determine whether any of the pulses from

the considered peaks in the remote stations correspond to the same pulse in the central station is a) values of ascending and descending slopes, b) number of reversals in the ascending and descending slopes, and c) the total area under the pulse. Figure 4.2 illustrates a typical pulse and how we selected the additional pulse properties to complete the pattern recognition technique.

Using the guidelines of identifiable characteristics, we selected 15 sample points for pulse recognition, centering the individual peak in the middle of the pulse. The description of the individual pattern recognition features mentioned in a, b, and c were as follows: a) the ascending and descending slopes (AS and DS) were calculated by making straight line approximations between the peak and the value of the extreme of the pulse. However if the pulse increases in magnitude in three consecutive samples before arriving to the pulse boundary (7th sample), the slope was arbitrarily determined between the peak and the 5th data sample. b) The number of reversals is determined by counting the number of times that there is a change of slope and dividing this number by 2. In Figure 4.2 there are two changes of slopes to the right of the peak (reversal to the right, RR), corresponding to one reversal and there are four changes of slopes to the left (reversal

to the Ieft, R1.), which correspond to two reversals. c) Since all the remote stations' data were normalized with respect to the central

station, we also calculated Lhe area under the curve as a measurement of the narrowness of the pulse (NAR). The tolerances allowed




(6 1








A S


RR=1











7 LEFT7 RIGHT
CENTER






Figure 4.2. Pulse model.





62



in matching pulses were: a 20' difference of slope was allowed for AS and DS, one difference in reversals was allowed for RR and LR, and a 25% variation was allowed for the area under the pulse (NAR). We refer to the five additional requirements needed for selecting the individual pulses as AS, DS, RR, LR, and NAR. We weighted these factors to match the individual peaks as a function of the time interval away from the cross-correlation time delay. If peaks were selected within 0.92 11sec (4 data samples) from the cross-correlation time delay, the pulse that generated the peak was required to meet at least two of the five requirements. Stricter requirements of 3 out of 5, 4 out of 5, and 5 out of 5 were needed to match peaks between 0.92 and 1.84 1sec (4 to 8 data samples), 1.84 to 2.76 vsec (8 to 12 data samples), and 2.76 to 3.7 1sec (12 to 16 data samples), respectively, from the cross-correlation time delay. It is worth noting that an identifiable pulse in the central station has to pass a separate test at each of the three remote stations before a location is calculated. A failure of the pattern recognition at any of the stations will prevent the determination of a source location.


4.4 Algorithm Flow Chart

A simplified algorithm flow chart is shown in this section. This algorithm has been developed using the techniques discussed in Section

4.3. Ony thOSC most general sLeps arc hine Idc, d In tie [Now chart. Tiis algorithm was written in FORTRAN language using a StrUc turned programming sequence (Rogers, 1975) for execution in the AMDAHL 470-VI. For a detailed description of the procedure used, reference is made to the LITMAT program in Appendix C. In the next flow chart (Figure 4.3) a set of data is defined as the time interval for which the





































Figure 4.3. Block diagram of the LITMAT algorithm to obtain
the cross-correlated and all the noise sources
based on the calculation of time delays.


















READ ONE
SET OF CENTRAL STATION DATA






INITIALIZATION







FORM DATA SUBSETS CALCULATE AVERAGES CALCULATE MOVING AVERAGES PRINT UNIVERSAL TIME








CALCULATE DETERMINE DETERMINE
ONE MAX EVERY ONE LOCAL TWO LOCAL
1/4 th OF SET MAX PER SUBSET MIN PER SUBSET




FORM NEW D SETS













PULSE PULSE
DEFINITION CHARACTERISTICS
(CENTRAL) FOR PATTERN RECOG.



FORM NEW
DATA SETS





(a)



















CCUA T E OEDEEMNON DEEIETW
- SET REMOTE
CHANNEL












MAX EVERY LOCAL MAXIMUM LOCAL MINIMUM
V4 OF SET PER SUBSET PER SUBSET
D ATA SETS _FORM NEW L PULSE ON PULSE
DATA SETS DEFINITION CHARACTERISTICS




PULSE NUMBER OF
WIDTH REVERSALS
DETERMINE EESL
MAXIMUM I
CROSS-CORRELATION t
I t FORM NEW
[DATA SETS]





PULSE MATCHING BETWEEN REMOTE AND CENTRAL
FORM NEW DATA SETS STORE SOE STORE
TIME TIME I




_____- _______ ________- ____NUMBER OF


FORM NEW
DATA SETS ALL STATIONS READ




(b)





16














CALCULATE
AVERAGE LOCATION





CALCULATE THREE- DIMENSIONAL LOCATIONS AND THE RELATIVE TIME OF THEIR OCCURRENCE FORM NEW DATA SETS








STORE RESULTS
IN DISK STORAGE


FORM NEW DATA SETS




I

REPEAT THE PROCEDURE FOR
THE NEXT TIME INTERVAL






(c)






67


cross-correlation is calculated, either 94 or 376 psec. The graph is expandedin Figures 4.3(a), 4.3(b), and 4.3(c). Figure 4.3(a) shows the algorithm initialization and the characterization of the central station. Figure 4.3(b) shows a similar technique for the remote station and its relationship with the central station to determine the time delays. Finally, Figure 4.3(c) concludes the algorithm with a determination of the three-dimensional locations. If additional data are desired, the algorithm is repeated.


4.4.1 The Algorithm Limitations

The principal limitations in the development of this algorithm are the time interval selected for the cross-correlation function and the selected features for pattern recognition. Next we provide some arguments about these limiting factors.

The longest time delay between the central and a remote station is determined for source locations near the ground and on the opposite side of the line joining the central and the remote stations. For a 10 km baseline between central and remote stations, the search for appropriate time delays should include 33 psec from the central station data. From the test described in Section 4.2.2(3), we could have several pulses which met any given tolerances for AS, DS, RR, RL, and NAR within the 33 psec interval. This argument implies that pattern recognition alone is not a sufficient factor for the determination of time

delays. Also from Section 4.2.2(3) we learned thnt we were 100% successful matching the envelope of the time-series data. Therefore, the use of the cross-correlation function is an essential part of the algorithm. The cross-correlation time interval of 94 or 376 Isec was chosen on the basis of the data properties and this is one of the






68



limiting factors of the algorithm development. If the individual pulses within the cross-correlated interval originate from the same source or from closely scattered sources, the cross-correlation locations represent a true representation of the source locations. For example, a spark channel which propagates at a velocity of 5 x 10 inm/sec will cover 47 meters during a 94 iasec cross-correlated interval. Therefore, consecutive cross-correlation locations represent a true representation of the locations of the spark channel. We successfully determined the location of the noise sources because 95% of the DTOA's measured in consecutive pulses were about 2.5 Vpsec from the cross-correlated value, which represents 2 or 3 km apart. However, if there were several channels located several kilometers apart or if there was at least one channel propagating at a velocity in the order of 1.0 8 m/sec, our locations may not represent the true location of the originating source.


4.5 Display of Three-Dimensional Locations and Their Time of Occurrence

All the VH1F source locations and their time of occurrence were

stored in digital tapes. The time was needed to differentiate between the different phases of a lightning flash. We developed three computer programs to display the source locations. 1) An algorithm was written to display the data in a three-dimensional isometric view. The computer code for this program is included in Appendix D. 2) The source loca-tions were displayed in two-dimensional projections. These p~rojectionls were: (a) EW-NS (1)) rq-hoi ght and (c.) NS-itoight 3) Fixed hi stograms are generated to show the relative radius, azimuth, and elevation of the noise sources with respect to a reference point. All these visual aids are used to display the results derived in Chapter V.






69


The value of computer graphics should not be underestimated. Any attempt to represent the locations by hand was tedious and resulted in large errors. All the graphics for the VHIF noise and its source locations were displayed on the Gould Electrostatic Plotter of the University of Florida Computer System.

Figure 4.4 shows a computer processing block diagram. This diagram shows the procedure that we followed to process and interpret the digital input data.


4.6 Velocity of Propagation of Noise Sources

We determined the velocity of propagation of the noise sources by using the three-dimensional locations and their time of occurrence. We chose only those lightning events on which the location of the noise sources formed a channel following a regular progressing sequence. To determine whether the events followed a progressing sequence we calculated the value of the velocity of propagation using all the crosscorrelated locations.

Let P 1(xvYvZ), P 2(x 2y2z, 2 P n(x ,'yz n) be the locations

of cross-correlated sources at time ti, t 2, ...,9 t n, respectively. Then velocities of propagation can be calculated by determining the distance P and dividing it by the time interval t where m and n are any two
mn ~nI

sources (m 2 ) oa fnn1 velocities can be calculated from n

locations. Only about 50 or 60% of all the velocities that we obtained during the speci fic [1guitn ing events Chat We Stud ie 1ts lg thl(:2 above techniques showed a velocity of propagation the same as would be found by taking the starting and ending point. Therefore, %we- decided to use the following procedure to determine channel velocities. 1) Determine whether the VHF sources followed a progressing sequence. A velocity of


































LL
0
CD

0 Z z m
LLJ
w U,
LLJ 0-- O
cr n w
V)
LLJ < 9 U)
LIJ
LJ
LLJ X >
O w 0
cr T cr
Ld 0


Ld Lj CC
Q cn cr,
0 H

LL
0
z 2 LLJ
0 < 0 LLJ CL
cr CD
< Z <
LLJ LLJ N)
U y) -J
0 0
w w LO
LLJ U) o 0
x t M: -j < < CID
IZ u Z
m U)
X U 0
ui 4
> cl.
0 4

T: Z) Qj
0 4j

w z m
z cl
0
iz: <
C 0
L X
(1) C) 0
LL Ln
Z L
< 0: LJJ
cr W
Fr P M
0 cr Ljj Z) 4
U) C) V)
w Lli
CL CD w z X C\J
LL LLJ LLJ
< -J w Z LLJ
m D LAJ aj
< Cl.
I'D
L
0 cy
n i w < U






71


propagation is calculated only for those events on which consecutive cross-correlated locations were in the neighborhood of the previous ones, and a path was formed by displaying the noise sources in the desired process (stepped leader and some PB, K- and J-changes). 2) Determine the n(n-1) velocities using all the cross-correlated source
2
locations. 3) Test if these velocities were grouped at any specific value. A velocity value is used only if a certain value or range of value repeats for at least 50% of the test data (n(n-l)/4). For an additional check we determined velocities using all the individual source locations for three stepped leaders, but the procedure was quite a bit longer and resulted in the same velocity value.

The results showed that we could determine the velocities of about 50 or 60% of the events that met conditions 1), 2), and 3) simply by their starting and ending points. In addition, about 15% of the events failed condition 3) and no velocity of propagation could be determined consistently. Throughout this thesis the only velocity values found are those that met the three conditions above.

















CHAPTER V

ANALYSIS OF RESULTS


This chapter presents a detailed description of six lightning flashes that occurred during the summers of 1976 and 1977 at the 'Iennedy Space Center. We have correlated the three-dimensional locations with other storm and lightning parameters measured (see Chapter III), primarily the electric field. We have studied four cloud-toground (CC)flashes and two intracloud (IC) flashes. The six lightning flashes are identified by their time of occurrence and type below:

(5.1) 165959, a three stroke CC flash to the 150 meter weather

tower on 19th July 1976 followed by an IC discharge.

(5.2) 18071.0, a three stroke CG flash on 8th August 1977.

(5.3) 181806, a six stroke CG flash on 8th August 1977 followed

by continuing current.

(5.4) 182356, an eight stroke CG flash on 8th August 1977.

(5.5) 180644, an IC discharge at the beginning of the storm on

8th August 1977.

(5.6) 181416, a small IC discharge on 8th August 1977.

All of the ablove flashes were at relatively close range, 3 to 17 km from the central stati on. The coordinates gi vei throughout thifs thesf s are referenced to the central station whose absolute coordinate in the Florida grid system is (187023,466021) meters. The three coordinate parameters given always correspond to the East-West location, North-South location, and altitude, respectively.

72






73


5.1 The 165959 Flash

This flash is the most comprehensively studied single lightning flash in the history of lightning research (Uman et al., 1978 and Rustan et al., 1979).

The flash consisted of a three strokes to ground followed by an IC discharge. The duration of the flash VHF radiation was 939 msec of which the last 600 msec were part of the IC discharge. The locations of the three charge regions for the three return strokes obtained from measuring the return stroke electric field change at multiple groundbased locations (Uman et al., 1978) correlate well with the VHF source locations. Figure 5.1 shows the relationship between the VHF radiation and the electric field for the entire discharge. Table 5.1 shows a complete summary of the identified phases of the flash For each phase we have provided the duration of the VHF radiation, the average velocity of propagation of the noise sources (if applicable), and the upper and lower location of the VHF noise sources. An error analysis for the VHF noise source locations is given in Appendix B. Table B.1 shows a summary of the uncertainty in the determination of the locations of the sources in this flash as a function of position. In the next subsections we consider in detail what we learned from the study of different phases of the flash, given in Table 5.1.


5.1.1 Preliminary Breakdown

Observation of the V11F records for oiic secotid prior to the first stroke shows that the VHF radiation above the system noise level began

4.9 msec before the return stroke and continued until the return stroke. The first 2.2 msec of the VHF pulses we identify with the "preliminary breakdown," the final 2.7 msec with the stepped leader. The wideband
































Figure 5.1. Simultaneous records of the logarithm amplitude VHF radiation observed at 10 km,
and the electric field 13 km away, during the 165959 flash. The following events in the flash are shown: Rl, R2, and R3 represent the three return strokes; SL is the stepped leader before Rl; DL is the dart leader before R2; SDL is the stepped
dart leader before R3; JI and J2 are the interstroke processes; FR is the activity
following the first return stroke, SP's are the solitary pulses; and IC is the
intracloud discharge, of which the final 99 msec is not shown.








1'5
















0
--o
co




8

. . . . . .

1-4
0


V)
0
z 00

t 0 Lo (-)



0 -J
02

z

Ld Ld 02
LU --o
V) > ro
5 LLI z -i
CL
_j K) 0
cn 0
-.0
(NJ

Cj

(L
0 C\j
cr

cr


8 0 0
NOUVICIV6 JHA Ln 8 Ul

(A@49W/SIIOA) (1-131J 3







76













0 01, CD
-4




CD CD



T-- co
4 0
cn

w 1.0 co 0 0
rX4 r 4
PL4

Ln
m
U')
m C14 in C) -i

0 C:) C C C


4J C)
H
u CD C) C)
0 110
41 CD

>
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41 to 0 0 Ln 0 c 0 0
Cd 4.J 41 4-1 4-J 4-)

co





41 Lr)
Lr) r- Ln .o r- Ln 00 r4 4-1 aj N r- C14 cli Lo N cq N Lr) r- Lr)
0 m Ln
44 4





r14
FX4

F-I
0 Q) -2 S4 4-4 LH 44
0 0 0 0 0
4
4 4-1
C) 4-1 V U 0 0 0
Lr) 4 4 V) 4-4 H
(1) pp a) 0 4
Id 0 r7j 4 71 A4 Q) P4
Cd 4 0 --3 0 4 ::I D. V) a4 U) 04 U)
a) :I r-4 4-1 .,-q C (1) 4-3
4-J 4 (2) $4 r ai j tj Lj
(1) Q) ce Q) 41 m Q) -4 Q) C14 (1) m
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4 H zi 0 :j cl U) P-4 P-4 4 P4
14 r-4 ol r-4 C > a: V) 1-1 U) cq rn cn M
I

Ln Ln C-A r, (7) -:1- 0 cq 0 Lr) m
L) C) C14 m Lr) 00 CY) Lr) (D' r- Lr) rl I c "t
4 (1) Q)
m fl w o
4,j cli r- r- r, 00 00 co 00 (ON
w













u') m
W
co Cl)



00 r1--1 0

4 0 0
Q)

rL4
-4
(a)
4..J
44
C m

C;
X




0 Ln %D Lr)
_q 0 CD 4
cu u co
> Q)
V) x x
Q) --- r-4
60 0 Lr) Lr) 0
cz
4

Q)



C1
0 Lo
-H U Lr) CY) cq CY)
4.j (U -7r CD C14 r-4 r-i co 00 C) 0'%
El Lo
4 C
C) 0 r
Lr)




cn
4-4 P4 m
c
cf)
4-4 4-1 to t4-4 0 4
N 0 H 0 co C)
10 4-1 4
41 0 p 4-1
H 4-4 0 0
4 0 rq P-4
a) 4-1 f Ili P4 "0
cz 4 4 p 0 U) 0
0 0 Cl) j H -r-A r GO
'r-j PL4 7:1 4-1 4 4 H a)
a) (V 41 00
P4 i' 4 4
0 a) -l j
PL4 CL "o 41
0 24 4-1 Q)
C-) f-4 Q) p H
4-3 :j P-4 ::j u 00
> Lf) co


0 V) Lr) Lr) 1r) no CD
u C) 'T .o 00 r- cq C14
(1) 4 Oj 0)
r--q ca m o 1 COO c3l* C
4.j all rn cn
cn C11 CN C )
H






78


electric field records indicate that there is a small electric field pulse of 2 1 sec width at about the time of the initial VHF radiation, but a clear correlation between VHF and electric field does not exist until the final .8 msec of the preliminary breakdown which corresponds to/a steady electric field change.

Figure 5.2 shows simultaneous records of VHF radiation during 117 psec of the preliminary breakdown that preceded the initial stepped leader. During the preliminary breakdown the log amplitude of the envelope-detected VHF noise is characterized by large pulses having a duration of 40 to 150 psec. Superimposed on these slow pulses are pulses of 1 to 5 psec width. Pulses 1, 2, 3, and 4 of Figure 5.2 illustrate the difference in the time of arrival of typical pulses at the four stations. The "r" value shown in the figure represents an approximate distance between the V11F source and the individual ground-based stations. The computer algorithm when applied to the data in Figure 5.2, generated source locations for pulses 1 through 4 and for 10 additional pulses.

Figure 5.3(a) shows all the 150 source locations identified during the preliminary breakdown which occurred between locations A and B. It is worth noting that most of the sources are concentrated within a cylinder of 500 meter radius and many are inside the Q 1 volume, source of the first return stroke charge (Figure 5.3(b)). Figure 5.3(b) shows the cross-correlated noise sources, 94 jisec intervals, associated with tl)e preliminary breakdown. The cross-correlaLed locations are weighted toward the location of the larger pulses in the 94 jjsec interval because it is these that play the dominant role in maximizing the crosscorrelation function. The cross-correlated noise sources started near






/9












2 4
1 ___ r = 12.5KM 3



A,,



3
r = 17.0 KM



V 2 r = '5KM4




2 r =7.5 KM1
3


4



r 1 2.5 K M '




II V V... IVY

00 13.00 26.00 39.00 52.00 65.00 78.00 91.00 104.00
TIME IN MICROSECONDS Figure 5.2. Simultaneous records of the logarithm VHF radiation at
four different ground-based stations. Pulses 1, 2, 3, and 4 are identified as examples of pulses arriving at different times at different stations. The parameter "r" represents the actual distance from the stations to the cloud
source.





















Figure 5.3(a). All of the 422 VHF noise sources detected for both the preliminary breakdown
(A to B) and the-stepped leader (below B) during the first 4.5 msec of the
4.9 msec before the first return stroke.
















Figure 5.3(b). Gross-correlated VHF noise sources, 94 lisec intervals during the preliminary
breakdown (A to B) and during the stepped leader (below B). The sphere Q1
represents an estimate of the volume enclosing the charge source for the first
return stroke as derived from electric field records (Uman et al., 1978).














0
0 0
C\j C "










co



E
x

N

LLJ



C\j











i6 'i

4
...... .....






LLJ



C\j
co Ln N 0 1

(w ainiiriv






82


the top and the back edge of the Ql volume and generally propagated in a downward direction. The preliminary breakdown started at a height of

7.1 km (point A at about -180C free air temperature) and propagated a distance of 2.3 km to a height of 5.1 kmn (point B at about -60C) before the first detectable slow change of the electric field associated with the stepped leader occurred. The cross-correlated source locations during the preliminary breakdown interval are very much in a straight line and exhibit an average velocity of propagation of about 1.0 x 106 rn/seC.

In addition to determining the cross-correlated and all the individual source locations (Figure 5.4(b)) using the computer algorithm described in Chapter IV, we determined the individual source locations manually during the first 537 psec of the preliminary breakdown. This task was performed to identify any propagation of the sources on a time scale of every 2 or 3 lisec instead of every 7 or 10 lisec, the limit using the computer algorithm. These results are shown in the threedimensional graph in Figure 5.4. The sources A through RR are time tagged and shown in alphabetical order A + Z, AA RR. This initial st age of the PB extends 1.5 km horizontally and 3.6 km vertically. The sequence of the VHF sources shows that the activity started at about 9 km and there was propagation initially upwards and downwards.


5.1.2 First Stepped Leader

T[he V11F raidiat ion duinLg the. stoppedl tvcadler cons Ist s of a low amplitude high frequency pulse train, a characteristic radiation observed during the first leader and again prior to the third stroke, but not in any other part of the flash. The stepped leader VHF is





































Figure 5.4. Three-dimensional view of the VHIF noise sources
during the first 537 visec of the preliminary breakdown, The sources A through RR are time
tagged (in microseconds) and shown in alphabetical order A Z AA -~ RR.





4





U- .-300C

10.

oiw=328 -200C




h 1v


8-~~~ c=10 c' ba3 e =125 fgF 494




7-~~ f 11 -~~ If
o=12Im=2
dp 53

1=- 5
7A

EASTe= (kin






85


markedly different from the preliminary breakdown VHF which precedes it. Figure 5.5 shows the VHF noise during the stepped leader.. By comparing the VHF noise during the preliminary breakdown shown in Figure 5.2 with Figure 5.5 we can see the remarkable difference between the two processes. The stepped leader pulses in Figure 5.5 have a pulse width less than one microsecond and an interpulse interval which decreases with increasing time, starting at about 11 jisec and decreasing to about I11lsec. The characteristic leader pulses start about 0.8 msec after initial electric field change of the flash. The leader pulses are probably related to the electrical breakdown associated with leader steps. As the leader progresses downward it generates more branches and hence more steps and pulses per unit time. If a normal interstep time is assumed to be 50 jisec (Uman, 1969), then at least four steps are simultaneously active during the beginning of the leader, increasing to about 50 simultaneous steps. Figure 5.3(a) shows all the 272 identified stepped leader radiation sources while Figure 5.3(b) shows the cross-correlated, 94 psec intervals, locations. Even though the VHF noise changed characteristics between the preliminary breakdown and the stepped leader, the source locations of the stepped leader appear continuous with that of the preliminary breakdown channel. In addition, the stepped leader, sources spread horizontally as the leader moves downward, most likely due to the stepped leader branches. The individual and the cross-correlated stepped leader source locations of Figure 5.3 did not occur in a regularly progressing sequence. The channel shape shown in Figure 5.3(b) is our best estimate from an overall view of tha individual locations, the cross-correlated locations, and the sequences of occurrence of the locations.






86








Cl)


F-t LL
----------- - co 0

co NNW.




-Zvi
Lr) Lr)





Q0 Z Lli

cr LLJI f

U
LO Lij g1jr.



C) 0-1
__7 -11 q __7101p. UJ Lu
CL
0

U)
MIND."-_7




04

Z C\j

C) -0

LIJ W
x co






t






87


A two-dimensional view with all the detected preliminary breakdown and stepped leader sources is shown in Figure 5.6. Figure 5.6(a) shows the plan view while Figures 5.6(b) and 5.6(c) show the elevation views of all the located stepped leader sources. In both graphs, Figures

5.3 and 5.6, the 150-meter weather tower struck by the flash is shown. The weather tower is located at (-1.1,9.5). Figure 5.6 also shows the cross-correlated locations represented with circles. It is worth noting that these cross-correlated locations form a narrow channel during the preliminary breakdown, but this channel is widened at a later stage during the stepped leader process.

The velocity during the first 700 microseconds of the stepped

leader ranged between 1.3 and 3.8 x 10 6 m/sec. and during the next 1.8 msec showed a nearly linear increase from about 1.5 x 10 6 m/sec at about

5 km altitude to about 7.0 x 10 6 m/sec. at 2.2 km. Although there was strong VHF radiation during the last 0.4 msec of the stepped leader, no sources were located during this time. It is probable that the pulses on the four channels could not be correlated because too many VHF sources, leader steps, were simultaneously active over a large volume.

Figure 5.7 shows three sequences of histograms of all the source locations from the beginning of the preliminary breakdown to the last detectable source in the stepped leader. The time sequences ti, t 29 and t 3 in Figure 5.7 correspond to 1.5 msec intervals from the beginning of the preliminary breakdown to the end of the detected VHF sources from the stepped leader. Figure 5.7(a) is a distance histogram referenced to the weather tower, as the time'progresses the radiation sources approach the 150 meter weather tower. Figure 5.7(b) and Figure 5.7(c) show polar histograms of all the radiation sources with reference














0 a)
rj
4.J
M
>


4-J (:X





ct
4

4-J
0 F-4



4-J 4

+
4 (U
(WM) iH913H 4
o


>

r 0 a) 0 4 4-J
-H U M 41 cl Q) > Ic
J 4






Q) pq U')

_0

41 LLJ



4
>

4 CY
0 "1 IJ 0 M 44 Cb l 11, N 0
ct
(W ) IH913H >
4 0




u 0
L 4 G) 4 > 0 co 0

4-1


0 o
CU H
w 71 Q)
1 4
4
E cl "ri


> ui



Ln




C j
(WM) HidON
































Figure 5.7. Three sequences of histograms, tl, t2, and t3 (1.5 msec intervals) of all the
detected sources in the PB and stepped leader. Sequences (a), (b), and (c)
correspond to tl, t2, and t3, respectively. There are three histograms in each
sequence. The top row shows distance histograms referenced to the weather
tower. The middle row shows histograms of the elevation angle of the sources
referenced to the weather tower. The bottom row shows histograms of the azimuth
angle of the sources referenced to the weather tower.









()o




























4-J !5 51





El


w N'll let I 11-h ddr
WJW Wl VA SLN I J




















C14










N m N ,,ors
3wuw m W3 101 2 .
































w M.1,
ONU W34 SINIM
5t






91.


to the spherical azimuth angle (~,and the elevation angle (e), respectively.


5.1.3 First Return Stroke

Figure 5.8 shows the VHF noise during the first return stroke.

The first return stroke was characterized by small high frequency pulses riding on the envelope of a high amplitude pulse of about 250 vlsec. Only five VHF pulses could be correlated during the stroke, probably because there were too many sources active and these sources were spread over too large a volume of space. Three of the correlated sources were located along the stepped leader channel, a fourth source was located at the top of the highest average location of the preliminary breakdown, and the fifth source was located 1 km above the fourth source. The estimated total length of the return stroke channel from the tower through the five sources was 8.8 km. Since the VHF return stroke noise lasted about 250 llsec, we estimated that the return stroke propagated at about 3.5 x 10 rnm/sec. Since the cross-correlated location might not be a true representation of the actual source location when a potential wave propagates in a channel at a velocity of 10 7or 10 8msec, return stroke velocities obtained from VHF source locations might be off by an order of magnitude.

Krehbiel (Uman et al., 1978) determined that a charge of -24 Coul was lowered by the first return stroke using the technique described in Sectin 3. 5. We used the technIque described -in Sect ion 3.6 anid determined that a charge of -19 Coul was lowered by the first leader-return stroke process. Our point charge source for the transition region between PB and stepped leader in the VHF record was within 1.5 km of the location determined using multiple electric field records.




Full Text
21 JUNE 1079
C ****************************************** ************>{:
C *
C THIS PROGRAM PLOTS THE THREE-DIMENSIONAL LOCATIONS OF THE *
C VHF NUISE SOURCES. THE INPUT IS A 9-TRACK 1600 3PI TAPE *
C WITH VHF SOURCE LOCATIONS. THE OUTPUT IS AN ISOMETRIC VIFW *
C OF THE COORDINATES OF THE NUISE SOURCES. *
C *
C *********************************************************** ***
C
C
REAL MUX, MUY, MUZ
DI MENS ION XM( loo).YM( 100) ,ZM( 100) ,T1ME{ l2d) ,A( 1S) ,B(15) ,
* C(15) iD( 15), E( 15) ,F( 15),XPM( 100) ,ZPM( 100),YP M( 100),
* XXM( 1 00) ,YXMI 1 00) ,XYM( 100) ,YY MI 1 00 ) ,XMP lOO).YMP(lOO),
* ZMP( l 00 ) YPPMI 100) XPEM 100) YPOI 100) X=>T( 1 00) YPT( 100) ,
* X XT ( 1 00 ) ,YXT( 100) YYT ( 100 ) ,XYT (100) XXB I 100) XYB I 100 ) ,
* YYBI 1 00) ,X YB( 100) YPPBI 1 00) YPPTI 100)
40 RE ADI 1 3, 1 0 ) { ( A( I ) I = 1,8 ) ( B( I ) 1= 1 1 5) ( C I I ) I = l l 5) )
10 FORMAT(33 X,0A4,//21X,L4 A4 ,A3,//20X, 15A4 )
PI=3.141593
KRS=1 0
N = 0
M= 1
NM=0
NN = 8
XSHIFT = l .0
Y S H I F T =2 .0
RX = 2.0
RY=2.0
RZ=2.0
DE GX= 0.0
D E GY = 3 3.0
C
C ** ANGX AND ANGY ARE THE PLANAR PRUJECTIUN ANGLES. **
C
ANGX =D EGX*PI/180.0
ANGY = DEGY*P 1/180.0
DO 29 II M = 1 NN
C
C ** READING TAPE HEADINGS **
C
READ!13, 12) I (A( l ) 1 = 1,5),LHOUR. (OI I) 1 = 1,2) ,LMIN, (CII),
* 1 = 1 2 ), L SEC.R I D ( I ) 1=1 ,2 ) ,LMIL ,( El I ) I = l ,2 ) )
12 FORMAT C11X,4A4,A2, I 4, IX *A4,A 1, 15, IX,A4.A3,
* 14, 1 X ,A4 A3 I 4,1 X ,2 A4 A3 )
READ! 13, 14)( (A{ I ), I= 1,4),LHOUR, (Oil) ,1 = 1,2) ,LMIN ICC I ) .
* 1=1,2) ,LSEC, I DI I), 1 = 1 ,2) .MILST,I El t), 1=l .3 ) ,MICRT, (FI I) ,
* 1=1,3))
14 FORMAT 14 A 4, I3.A4.At, 13,A4,A3.2X,£ 3, 1X.A4.A3,
* I 4,1X,2A4,A3, I 4 i X ,3A4)
DU 2 8 J= 1 5
RE AD (1 3 l 6) I I A ( I ), I = 1,3 ) ( t ( I ) I = l 3 ) I C I 1 ) I = 1,3 ) )
16 FORMAT( 10X.2A4,A3, l OX,2A4, A 3,10X.2A4 ,A3 )
C
C ** READING THE CROSS-CORRELATED LOCATION **
C
READ! 13, 18) X1,Y 1,Z1,ZERO
18 FORMAT(4F20.3>
IF(Xl.EQ.0.0> GO TO 28
IF I IZl .LE.O. ) .OR(Xl .GE.4 000. ) .UR.I V l,GE .400 0 0. ) )
* GO TO 28
N M = NM + 1
XM(NM) =X1/I0 00.0
YMINM)=Y1/I000.0
ZM I NM) = Z1 /I 0 00.0


59
ehromotograms (Widrow, 1974), speech (Boudry and Dupeyrat, 1974), and
picture rasters (Erich and Foith, 1976)* We classified our data with a
pattern recognition list similar to those described by Gottman and
Gloor (1976). Before we could apply the pattern recognition list to
match the individual pulses around the cross-correlation time delay,
we had to define a pulse model. Next we provide our pulse model defini
tion.
4.3.2.1 Pulse Model. We divided the four time-series in subsets
of 3.7 psec (16 samples), roughly the maximum pulse rate for which the
data could have the identifiable characteristics needed for pattern
recognition. Then, the sample value which corresponds to the peak of
the data subset is determined. This sample value is needed to perform
peak recognition of the time-series. The peak recognition is performed
as follows: 1) We determine the time delay for the cross-correlated
interval of either 94 or 376 psec between the central and each of the
remote stations. 2) We determine the time at which peak values occurred
for each data subset within the 94 or 376 psec interval for all the time-
series. 3) We add the time value of (1) and (2) above to obtain the.
corresponding cross-correlated value in the remote stations for the
peak of the pulses. 4) Finally, we determine how many peaks in the
remote station are within the 3.7 psec search interval. This proce
dure limits the number of peaks to be considered to a maximum of 3.
At this time in the algorithm the peak recognition is completed; now we
have to determine which pulse at the remote stations that produced the
peaks which met (4) above, is similar to the pulse at the central sta
tion. One of these peaks within the search interval will be selected


VHF RADIATION
Logarithmic-amplitude VHF radiation during the dart leader and the second return stroke.
Figure
5.12
ZO I


299
The point charges that we determined by using these techniques ranged
between -24.1 and -3.6 Coul for heights between 10.5 and 5.9 km.
7.1.5 Activity Following the First Return Stroke (FR)
During the FR interval we obtained the fastest pulse repetition
rate and largest amplitude in the CG and IC flashes. We chose to call
this process "FR" (following return) because the locations of the VHF
noise sources were directly related to the first stepped leader-return
stroke sequence. The pulse repetition rate during the FR was a pulse
every 3 or 4 p sec and the magnitude of these pulses were about 25 times
larger than that of the stepped leader. At the end of the FR we
measured return stroke-like pulses of a magnitude 40 to 50 times larger
than the stepped leader. For three of the four FR intervals, the VHF
noise started immediately after the return stroke, but for one of the
flashes (Section 5.1) there was a 2.4 msec quiet period between the
return stroke and the FR interval. The FR interval lasted between 4.3
and 8.8 msec and always ended with a wide pulse of the largest magnitude
in the CG, which because of its similarities to the return stroke pulse
we associated with the propagation of a potential wave.
The location of the VHF sources for three of the four FR's were in
the neighborhood of the previous PB-stepped leader-return stroke chan
nel. In the fourth case (Section 5.4), the VHF sources were located
right on the top of the previous PB-leader channel. The height of the
VHF sources ranges between 9.5 and .1.8 km. The HR phase of the CG flash
may be related to M-components (Malan and Schonland (1947), Kitagawa
et al. (1962), and Uman (1969)); that is, the increases in channel
luminosity following a return stroke. For two of the four FRs
intervals, the VHF sources propagated upwards in a regular progressing


:,ij 3
classified as stepped leaders, 1 as a stepped-dart leader, and 7 as
dart leaders. Even though we had a limited sample of 20, over 50% of
the return strokes were preceded by stepped leaders. The initial
stepped leader that followed the preliminary breakdown had slightly
different properties from the subsequent stepped leaders. Therefore
we chose to divide the stepped leader discussion in two subsections.
7.1.2.1 First Stepped Leader. At the end of the preliminary
breakdown the VHF radiation decreased to about twice the noise level,
corresponding to the lowest level of VHF radiation for any identified
process in either CG or IC flashes. This type of radiation was
characterized by high frequency pulses with less than 4 ysec width and
a pulse rate of one every 13 to 15 ysec (Figure 5.16). The stepped
leader VHF radiation has unique characteristics and has been used
throughout this thesis to identify the beginning of CG flashes. The
duration of the stepped leader VHF noise ranged between 2.9 and 7.9
msec. In contrast with the low amplitude, high frequency, stepped
leader pulses at 30 to 50 MHz shown in this thesis, Proctor (1976),
working at 253 MHz, and Brook and Kitagawa (1964), working at 420 and
850 MHz, observed strong radiation during the stepped leader. Work
reported by Malan (1958) showed an increase in the stepped leader
radiation between 3 KHz and 12 MHz. Therefore, it appears that the
stepped leader radiation increases are a function of frequency.
We studied the VHF noise sources during initial stepped leaders
and determined that about 70% of the sources followed a regular progres
sing downward sequence which extended the previous path formed by the PB
sources. The remaining 30% of the sources are detected in two other
regions as follows: (1) Sources detected in the horizontal direction
which widen the main PB-stepped leader path to about 1 or 1.5 km radius,


i+i
* M'ii* -
-i
DART JRETURNJ
LEADER I STROKE*!
IOO 200 300 400 500 600 700 800 900
TIME IN MICROSECONDS
Figure 5.52. Logarithmic-amplitude VHF radiation during the dart leader and
the third return stroke.


I I ... I I 11 I ,
00 1.00 2.00 3.00 y.00 5.00 5.00 7 00 5 00
TIME IN MILLISECONDS
Figure 5.46. Logarithmic-amplitude VHF radiation during the FR interval.
185


Figure 5.9.
Cross-correlated VHF noise sources, 94 ysec
intervals, during the FR period. The sources
are labeled A through S to indicate the pro
gressing sequence of their occurrence. Each
label is repeated three times. No time
sequence is given for each repeated letter.
The sphere Q1 is described in Figure 5.3.


201
and J3. The third J-change lasted 37.7 msec and extended in a path 35
off vertical between the heights of 5.7 and 13.0 km. The channel was
located 1.5 km east and .5 km north of the previous J-change channel.
As with J2, the locations of the VHF sources did not follow any regular
sequence along the channel. About 70% of all the sources were located
between the heights of 9 and 12 km in a path 35 off vertical. Some of
the VHF sources from J2 were still active during J3. These sources are
located west and north of the J3 channel as can be seen in Figure 5.53.
The VHF sources during the J3 process spread out over similar and
parallel paths, but at higher altitude than J2. The overall radiation
region during J3 becomes wider because active sources from the previous
J-change radiate again or continue to radiate.
5.3.11 Dart Leader and the Fourth Return Stroke
Figure 5.54 shows the VHF noise at the end of the J3 process and
during the dart leader preceding the fourth return stroke. Correlation
with the electric field records indicate that the dart leader started
at 20 30 psec from the beginning of Figure 5.54. We studied the VHF
records for 2 msec following the two 80 psec pulses that marked the
beginning of the dart leader but we did not detect any large pulses.
Since return strokes are characterized by wide pulses of large amplitude
and the multiple electric field stations showed an abrupt field change
characteristic of return stroke, we concluded that the fourth stroke
did not produce any VHF radiation. It appears that the VHF radiation
from consecutive return strokes is due to the extension of the previous
channel in a non-previously ionized region. Probably the fourth return
stroke propagated only throughout a previously ionized channel, con
sequently produced no VHF radiation.


n o Ci o
21 JUNE 1979
')()
SUBROUTINE NARRO(XI,NABCIS.NARROW)
** THIS SUBROUTINE FINDS THE STANDARD DEVIATION OR **
** NARROWNESS OF THE PULSF. AROUND THE LOCAL MAXIMUM **
D I MENS ION XI (2048)
N A RR = 0
NARL-0
DO 04 VL= 1 5
IF(X I ( NAOCI S + ML- 1 ) .GE.XI (NABCI S+ML) ) GO TO 38
N ARR=ML
GO TO 06
33 NARR=NARR + 1
34 CONTINUE
36 DO 40 KJ=1t 5
IF(XI(NABCI5-KJ+l)GE.XI(NABCIS-KJ))G0 TO 42
NA RL = K J
GO TO 44
4 2 NARL= N ARL + 1
40 CONTINUE
44 TSUM5=G.O
DO 46 JK-l.NARR
D I F=(X1 (NABCIS) XI (NABCIS+KJ) )**2
46 TSUMS=TSUMS+DIF
DO 48 JK=1NARL
D IF=(X1 (NABCIS)-Xl (NABCIS-KJ > )**2
48 TSLMS=TSUMS+DIF
NARROW=SQRT(TSUMS/FLGAT(NARR+NARL+1))
RETURN
END


Figure 5.11. Two dimensional views: (a) top view, EW-NS, (b) elevation view, EW-height, and
(c) elevation view, NS-height of all the 'hill noise sources detected during the
J1 process.


APPENDIX B
ACCURACY OF THE LOCATION OF
LIGHTNING SOURCES USING THE HYPERBOLIC EQUATIONS
The errors in source location can be determined from the solution
of the hyperbolic equations ((A.7) and (A.8)) previously discussed.
Solving equation (A.8) for the source locations, X, Y, and r^ we obtain
V1
Y1
U1
X1
V1
U1
X1
Y1
V1
V2
Y2
U2
X2
V2
U2
X2
Y2
V2
V3
Y3
U3
V
X3
V3
U3
X3
Y3
V3
X1
Y1
U1
X1
Y1
U1
0
X1
Y1
U1
X2
Y2
U2
X2
Y2
U2
X2
Y2
u2
X3
Y3
u3
X3
Y3
U3
X3
Y3
u3
or
X
Y
(B.2)
Since the coordinates of the three remote stations (X^,Y^), (X^jY^) and
(X^,Y^) are known to a tenth of a meter, the primary error in X, Y, and
Z will be caused by uncertainties in the measurements of Uj, u^, and u^.
The partial derivatives OX/du., DY/Ou., and dr /Ou. can be calculated
l i o i
from equation (B.2).
have that
Since Z
Y from equation (A.10) we
315


Figure 5.49. Two-dimensional views: (a) top view, EW-NS, (b) elevation view, EW-height, and
(c) elevation view, NS-height of all the sources (triangles) and the cross-
correlated source locations (squares), 376 psec intervals, during the Jl or PB2
and the second stepped leader. The labels A, B, C and E, F, G show different
- regions of propagation. The circles are the cross-correlated sources, 94 psec
intervals, of the second return stroke. The circle Q2 is the projection of Q2
in Figure 5.48.


Figure 5.29(a). Three-dimensional view of the cross-correlated noise sources during the second
stepped leader. Point A is the location of the first stepped leader cross-
correlated source.
Figure 5.29(b). Similar three-dimensional view for all the individual dectected sources.


ALTITUDE (km)
204
EAST (km)
Figure 5.55. Threedimensional view of the crosscorrelated noise
sources during J4, and the dart leader. Source locations
of the previous J3 channel which continues to radiate
during J4 are also shown. The location of the fifth
stroke spherical charge center is also shown.


CO CD
OJ1
NORTH
W OJ -t> U1 O) >J
HEIGHT
fCT


62
in matching pulses were: a 20 difference of slope was allowed for AS
and DS, one difference in reversals was allowed for RR and LR, and a 25%
variation was allowed for the area under the pulse (NAR). We refer to
the five additional requirements needed for selecting the individual
pulses as AS, DS, RR, LR, and NAR. We weighted these factors to match
the individual peaks as a function of the time interval away from the
cross-correlation time delay. If peaks were selected within 0.92 Usee (4
data samples) from the cross-correlation time delay, the pulse that
generated the peak was required to meet at least two of the five require
ments. Stricter requirements of 3 out of 5, 4 out of 5, and 5 out of 5 were
needed to match peaks between 0.92 and 1.84 Usee (4 to 8 data samples),
1.84 to 2.76 Usee (8 to 12 data samples), and 2.76 to 3.7 Usee
(12 to 16 data samples), respectively, from the cross-correlation time
delay. It is worth noting that an identifiable pulse in the central
station has to pass a separate test at each of the three remote stations
before a location is calculated. A failure of the pattern recognition
at any of the stations will, prevent the determination of a source
location.
4.4 Algorithm Flow Chart
A simplified algorithm flow chart is shown in this section. This
algorithm has been developed using the techniques discussed in Section
4.3. Only those most general steps are Included In the flow chart.
This algorithm was written in FORTRAN language using a structured pro
gramming sequence (Rogers, 1975) for execution in the AMDAHL 470-VI.
For a detailed description of the procedure used, reference is made to
the LITMAT program in Appendix C. In the next flow chart (Figure 4.3)
a set of data is defined as the time interval for which the


Figure 5.75.
Three-dimensional view of the cross-correlated noise sources (triangles) during
the J6 process. The location of four cross-correlated dart leader sources are
shown with squares near the center of the picture.


165
electric field change. Therefore we associated these pulses with
K-changes. At the beginning of the last K-change the VHF sources prop
agated downward about 4 km into the main negative charge region. At
the end of the K-change there was some upward propagation. Except by
the velocity of the downward propagation, this behavior is in agreement
with a model proposed by Kitagawa et al. (1958). That is, the lowering
of positive charges within the cloud is followed by mini-return strokes.
(7) A total of 34,478 noise sources, an average of one every 8 ysec, were
detected during the flash. The flash extended a volume of about 500 km^.


uuu^
146
2 1 JUNE 1979
FUNCTION STD SUB(XlLMiAVESFT MM)
** SUBPROGRAM TO CALCULATE THE STANDARD DEV. **
** OF THE SUBSET (STDSUB) **
I MENS ION X 1 LM ( l 6 )
T SUMS= 0.0
DO 14 1=1,MM
SUMS = ( XlL M( r 1 -AVESET ) **2
14 TSUMS=TSUMS+SUMS
S T DSUU = SQR T(T SUM S/FLOAT(MM1 ) )
RETURN
END


9
has different polarity. The work on cloud-to-ground discharges presented
in this thesis will provide the VHF noise source locations for each
phase of hybrid and discrete flashes. Whenever wideband electric field
measurements were available, we attempted to calculate the charge
involved along the radiating paths. These findings provide additional
insights into the mechanisms of ground flashes.
The intracloud discharge is not as thoroughly investigated as the
ground discharge. On the basis of electric field waveforms, Kitagawa
and Brook (1960) studied the nature of electrical discharges inside
thunderclouds. They included the cloud to cloud, cloud to the surrounding
air, and the intracloud discharge, treated them as identical, and referred
to them as cloud flashes. Three phases of the cloud flash were classified:
initial, very active, and junction phase. The initial phase was charac
terized by a large number of small impulses. The active phase had larger
and more regular impulses. The final phase had a number of rapid regular
impulses. Ogawa and Brook (.1964) studied the variations of the electric
field with time and distance during the initial and junction phases of
intracloud discharges. They claimed that positive charge was lowered during
the initial phase by downward positive streamers, and that negative recoil
streamers occurred during the junction phase. This viewpoint is partially
shared by Takagi (1961) who proposed a mid-gap streamer where positive
streamers propagate downwards into the negative charges and negative
streamers propagate upwards into the positive charges. However, earlier
work by Pierce (1955) and Smith (1957) suggested that the intracioud
discharge raised negative charges. Khastgir and Saha (1972), using
questionable models attempted to prove analytically that the experimental
electric field curves of Ogawa and Brook (1964) could be interpreted as


260
5.4.16 Volume of the Flash
Figure 5.77 shows all the 33,947 individual VHF noise sources
(triangles) detected during the 506 msec flash. All the cross-correlated
noise sources are also shown as squares. The average rate of pulse loca
tion throughout the flash was one every 14.9 psec. During the 337 msec
period preceding the DAFS the detected rate was a source every 9.5 msec.
This rate decreased considerably during the 169 msec DAFS interval. The
flash extended about 15 km in the EW direction, 14 km in the NS direc
tion, and up to 14 km in altitude. The volume occupied by the flash
3
was about 1500 km .
5.4.17 Concluding Remarks About the Flash
Now we provide a summary of what we learned about this flash.
(1) The flash lasted 506 msec and consisted of eight return strokes and,
six separate stepped leader channels to ground. (2) The flash started
with a PB that lasted 1.8 msec. During the first .6 msec of the PB the
VHF sources propagated upwards and there was no detectable electric
field change. For the next .6 msec the VIIF sources propagated down
wards within 500 meters of the previous ascending channel. In the
remaining .6 msec of the PB most of the propagation was horizontal at a
height of 6.5 km. (3) This flash had stepped leaders preceding return
strokes 1 to 5, and 7 and lasting 5.9, 14.2, 35.0, 5.2, 30.1, and 30.6
msec, respectively. The third and fourth stepped leader developed
simultaneously about 4 km apart and the 5.2 msec of the fourth stepped
leader is only the time of stepped leader propagation that occurred
after the third return stroke. Stepped leaders preceding Rl, R2, R3,
and R5 started within 2 km of each other while stepped leaders preceding
R4 and R7 were also 2 km apart but about 4 km from the region of the


100
200
300 400 500 600
700
800
TIME IN MICROSECONDS
Figure 5.16. Logarithmic-amplitude VHF radiation during the stepped portion of
the SDL preceding R3.


8 5
markedly different from the preliminary breakdown VHF which precedes it.
Figure 5.5 shows the VHF noise during the stepped leader.. By comparing
the VHF noise during the preliminary breakdown shown in Figure 5.2 with
Figure 5.5 we can see the remarkable difference between the two processes.
The stepped leader pulses in Figure 5.5 have a pulse width less than one
microsecond and an interpulse interval which decreases with increasing
time, starting at about 11 ysec and decreasing to about 1 ysec. The
characteristic leader pulses start about 0.8 msec after initial electric
field change of the flash. The leader pulses are probably related to
the electrical breakdown associated with leader steps. As the leader
progresses downward it generates more branches and hence more steps and
pulses per unit time. If a normal interstep time is assumed to be 50
ysec (Uman, 1969), then at least four steps are simultaneously active
during the beginning of the leader, increasing to about 50 simultaneous
steps. Figure 5.3(a) shows all the 272 identified stepped leader radia
tion sources while Figure 5.3(b) shows the cross-correlated, 94 ysec
intervals, locations. Even though the VHF noise changed characteristics
between the preliminary breakdown and the stepped leader, the source
locations of the stepped leader appear continuous with that of the pre
liminary breakdown channel. In addition, the stepped leader, sources
spread horizontally as the leader moves downward, most likely due to
the stepped leader branches. The individual and the cross-correlated
stepped leader source locations of Figure 5.3 did not occur in a regular
ly progressing sequence. The channel shape shown in Figure 5.3(b) is
our best estimate from an overall view of the individual locations, the
cross-correlated locations, and the sequences of occurrence of the
locations.


7.26
breakdown (PB). The VHP PB radiation consisted of a succession of six
pulses with widths between 80 and 150 ysec superimposed on a more slowly
varying envelope. Figure 5.64 shows the VHP radiation during the PB,
the stepped leader, first return stroke, and the activity following the
first return stroke. We can divide the 1.8 msec PB in three sections of
.6 msec each. Detectable electric field change started following the
first .6 msec period. During this first .6 msec interval the cross-
correlated source locations showed an ascending motion between the
heights of 5.5 and 9.8 km. During the second .6 msec interval, the VHF
noise sources propagated downward in a path that lies within 500 meters
of the previous ascending path. During the last .6 msec the noise
sources propagated for the most part horizontally in a northerly direc
tion.
Figures 5.65(a) and 5.65(b) show a three-dimensional graph of all
the sources and the cross-correlated sources, respectively, during the
PB and the stepped leader. The PB sources are located in the southern
part of the NS axis, and at an altitude between 5.5 and 9.8 km. We
have progressively lettered the first 23 cross-correlated noise sources
in Figure 5.65(b). Sources A through T correspond to the PB, and
sources U to W mark the initial portion of the stepped leader VHF noise.
The unlettered points occurred after W and are associated with the
stepped leader.
5.4.2 First Stopped Leader
The first stepped leader electric field change was detected at the
time the VHP sources were located in the D through J region in Figure
5.65, about 0.6 msec into the discharge. The stepped leader shown in
the VHF noise record propagated downward from a region in the neighborhood


V ANTENNA
W; (t)
BANDPASS
FILTER
ENVELOPE
DETECTOR
Figure 3.3. VHF receiver and envelope detector.
Figure 3.4. Description of VHF receiver and envelope detector.
9|(f)
(a)
9|(t)
Figure 3.5. Approximation for band-pass filter:
and (b) time domain.
(a) frequency domain,


?.l
Simultaneous recordings of the radiation field of lightning flashes
were performed at one site. The selected frequencies were 30, 250, 600,
and 1430 MHz. This experiment shows that pulses were emitted at all these
frequencies for the low prf cloud flashes but were not the same, in gen
eral, for the high prf cloud flashes. This is an important result which
has also been studied in recent years by Krider et al. (1979). Krider et
al. compared the wideband electric field (1 KHz to 2 MHz) and the 300 KHz
bandwidth RF receivers at 3, 69, 139, and 295 MHz for a distant storm
(50 km away). These results illustrate that pulses were simultaneous in
all these frequencies and a wideband (dc to 1.5 MHz) electric field pulse
(radiation term) also occurred at the same time. Proctor determined the
DTOA between the leading and trailing edges within single pulses and con
secutive pulses. He could find no definite relationship between the
direction of the vectors and the direction of the channel. But most
vectors, either between the leading and trailing edge of the same pulse
or between the trailing edge of one pulse and the leading edge of the
next pulse, had a component in the direction of the channel tip.
From the study of the pulse width during cloud flashes, Proctor con
cluded that the average extent of the active source was about 240 meters.
He claimed that channels are formed in a stepped information. This view
point was first proposed by Schonland et al. (1938) and later reported by
Pierce (1955), Ishikawa (1960), Takagi (1961), and Krider et al. (1979).
Proctor noted that the return stroke had differences in the pulse
width (in the tens of microseconds) between the different stations. He
related the difference in the pulse width to the velocity of the propa
gating potential wave via a Doppler-type effect. Pulse width differences
in the order of a few ysec were found in all wide pulses (over 50 ysec).


change that indicated the beginning of the leader preceding the third
return stroke. However, the VHF noise decreased in amplitude and
increased in rate about 35 msec prior to the third return stroke. As
discussed in this thesis, this characteristic is typical of stepped
leaders. Therefore, we suggest that a stepped leader started 35 msec
prior to the third return stroke.
Figures 5.68(a), 5.68(b), and 5.68(c) show two-dimensional graphs
of the cross-correlated source locations during the leaders that pre
ceded the third and fourth return strokes. Figure 5.69 shows a three-
dimensional view of the same noise sources. The locations A (-5.4, 8.9,
7.9), B (-4.1, 7.8, 6.1), C (-4.6, 12.1, 7.3), and D (-4.4, 12.8, 6.3)
shown in these figures are related to the propagation path of the third
and fourth stepped leaders.
The sequence of events leading to the third and fourth return
strokes is as follows: 1) The fourth stepped leader sources began
first and were located in the A region in Figures 5.68 and 5.69. During
the beginning of the fourth stepped leader the VHF noise sources were
located in the same region of the J2 change. For the first 10.1 msec
the noise sources propagated in the A-B region at an average velocity
of 2.9 x 10^ m/sec. 2) About 10.1 msec after the initiation of the
fourth stepped leader, the third stepped leader started in the C region in
Figures 5.68 and 5.69. The G location is 3.4 km from A. For the fol
lowing 5.6 msec the noise sources propagated in the C-D region at an
5
average velocity of 2.3 x 10 m/sec. 3) For the remaining 19.3 msec
prior to the third return stroke, the VHF sources propagated mainly
downwards from the A-B and C-D regions. 4) About 3.5 msec prior to the
third return stroke, the stepped leader that propagated from the C-D
region was detected at a height of 1.8 km. This stepped leader appears


nnoo nno
38
2 1 JUNE 1979
C ** NO SLR I NOSLLE, PENOR PENOLE AND NSTDEV ARE THE FIVE **
C ** PUL5E PROPERTIES BEING USED FOR PATTERN RECOGNITION. **
C ** THEY CORRESPOND TO THE NUMBER OF DESCENDING PATTFRN TO **
C ** THE RIGHT AND TO THE LEFT OF THE PULSE. THE SLOPES TO **
C ** THE RIGHT AND TO THE LEFT OF THE LOCAL MAXIMUM, AND **
C ** THE NOFROWNESS OF THE PULSE. **
C
NDSLRI (NCCUNT )-NUMDR2(MMM(J) )
NDSLLE NCOUNT)=NUMDL2{MMM(J) )
PENOR I (NCOUNT)=5LPR2(MMM(J > )
PENOLE(NCOUNT)=SLPL2 (M M M{J) )
N SIDE V(NCOUNT)=NRROW2(MMM { J) )
70 CONTINUE
IF{NCOUNT.EQ.OIGC TO 73
DO 75 J-l.NCOUNT
L P ASS-0
JPASS= 0
NPASS= 0
IPASS=0
KPAS S=0
** MATCHING CHARACTERISTICS FOR THE FIVE GIVEN PROPERTIES **
IF(IAOS(NUMDER(NNN(K) )-NDSLRI(J) ) .LE. 1 ) JPAS3=JPASStl
I F( I ABS( NUMDEL ( NNN( K ) ) -NDSLLF ( J) ).LE.l) L P A SS = L PASS + 1
IF (AL1S ( SLPR( NNNI K ) ) ) .GE. ( 1 0. ) A NO ABS( PENDRI< J) ).GE.( 10.> )
* GO TO 79
IE(AOS(3LPR( NNN(K) )-PENDR I (J) ) .LE.2.5) NPASS=NPASS+1
IF(ACS(SLPL(NNN(K))PENOLE(J)).LE.7.5) lPASS=IPASS+1
GO TO 81
79 IF(AOS(SLPRINNN(K) )-PENDRI{J) ) .LE .7.5) NPAS S= NP AS 5 + I
IF(AOS(SLPL(NNN(K))-PENDLE(J)).LE.7.5) IPAS5=IPA3S+l
81 IF ( I AOS( NRRO'wE ( NNN ( K ) ) NSTDEV (J)).LE.(10)> KPAS5-KPASS+ I
NGOOD( NCOUNT)=LPASS+IPASSFKPASSFNPASS+ JPASS
75 CONTINUE
IF(NCOUNT.EQ.1)GO TO 180
NO IFT E-15
DO 420 MK=1,NCOUNT
NDIFDQ (MK ) = I ABSL1 ( MK) MX2GE! N ( K ) )
IF(NO I FOB(MK ) .LE .NDIFTE)GO TO 435
GO TO 420
435 NDIF TE =NDIFOB(MK)
LKNM=MK
420 CONTINUE
** ALL THE PATTERN RECOGNITION PROPERTIES ARE USED TO **
** DETERMINE IF A PROPER MATCH HAS OCCURE. **
IF((ND 1FTE.LE.4.AND.NGOOD(LKNM) .GE.1>.OR.(NDIFTE.LE.8.
* AND. NGOOD(LKNM) .C.E.2) .OR. ( N D I FT E L E 1 2 A ND NGCUO < LK NM )
+ GE.3) .OR.(NU IFTE.LE 16.AND.NGOOD(LKNM) .GE.4) )GO TO 430
180 N DIF T E =I A US(Ll ( 1 )-MX2GEN(K ) )
I E{NDIFTE.LE.4.AND.NGOOD( l ) .GE .I ) GO TO 4 00
I F (N J I FTE .L E 8 AND N GOOD ( 1).GE.2)GU TO 400
IE(NDIETE.LE.12.AND.NGOOD(1).GE.3)GO TO 400
I F(M!) IETF .LE I 6. AND. NGOOD ( 1 ) .GE .4 ) GU TU 400
CO TU 73
400 IF( IAOStL 1 ( 1 )LAGLMAOLMA NNN (K+T) ) J.LE.NDI FT E ) GO TO 73
MOSCI(K)=L1(1)
IF{(K.CE.2) .ANO.(NO IFTE.GE.MDIETE) .ANb.(MBSCI (K).
* EQ.MBSCI (K-l ) ) ) GO TO 73
GO TU 84
43 0 IF((IA8S(LI ( l )-LAGL-MAOLMA{NNN( K l ) ) ).GT.NDIFTE). AND.
* { LK NM.EQ.l)) GO TO 491
I F ( ( IA ES(Ll (2)-L AGL-MAOLMA(NNN(K+I ) ) ).GT.NDIE TE). AND.


L55
preceded by stepped or by dart leaders. In addition, the amount of
charge lowered by the subsequent stepped leaders was larger than the
charge lowered by dart leaders. It is apparent in this flash that there
are other factors such as the wind which might destroy the old return
stroke channel and necessitate the formation of a new stepped leader.
5.2.10 Third Return Stroke
The VHF noise for the third stroke lasted 540 ysec. The five
return stroke VHF cross-correlated sources, 94 ysec intervals, were
located in the neighborhood of the previous stepped leader as shown in
Figure 5.34. Assuming A (4.9, 11.2, 6.8), the highest detectable noise
source at the beginning of the leader to be the point charge of the
stepped leader and using the technique described in Section 3.6, we
estimated that -9.3 Coul were lowered by the third stepped leader-return
stroke process.
5.2.11 VHF Activity After Third Return Stroke
We have divided the VHF radiation that followed the final return
stroke in two intervals. The first interval is described in this sec
tion as the continuous VHF radiation activity following the final
return stroke (CAFS). The second interval is designated as the discrete
VHF activity following the final return stroke (DAFS).
5.2.11.1 Continuous VHF Activity After Third Return Stroke. The
CAFS followed immediately after the third return stroke and lasted 87.1
msec. Figure 5.35 shows the cross-correlated noise sources, 94 ysec
intervals, during this interval. The noise sources were located in the
neighborhood of the previous J-changes but their path extended 2 km
further toward the north. In addition the source locations were spread


Figure 5.42. Three-dimensional view of all the VHF noise
sources during the first 120 usee interval
at the beginning of the 181806 cloud-to-ground
flash.


174
Schonland, B. F. J., D. B. Hodges and H. Collens, "Progressive Lightning -
V: A comparison of photographic and electrical studies of the discharge
process," Proc. Roy. Soc. London, A168, 455-469, 1938.
Serhan, G. I., M. A. Uman, D. G. Childers and Y. T. Lin, "The RF spectra
of first and subsequent lightning return strokes in the 1-200 km range,"
To be published in J. Geophys. Res., Spring 1979.
Simpson, G. C. and G. D. Robinson, "The distribution of electricity in
thunderclouds," Proc. Roy. Soc. London, A177, 281-329, 1941.
Skolnik, M. I., Introduction to Radar Systems, McGraw-Hill, New York,
1962.
Smith, L. G., "Intracloud lightning discharges," Quart. J. Roy. Meteorol.
Soc., 83, 103-111, 1957.
Takagi, M., "The mechanism of discharges in a thundercloud," Proc. Res.
Inst. Atmos. Nagoya Univ., 8B, 1-106, 1961.
Takagi, M., "Polarization of VHF radiation from lightning discharges,"
J. Geophys. Res., 80, 5011-5014, 1975.
Takagi, M. and T. Takeuti, "Atmospherics radiation from lightning dis
charge," Proc. Res. Inst, Atmos Nagoya Univ., 10, 1, 1963.
Taylor, W. L., "Radiation field characteristic of lightning discharges
in the band 1 kc/s to 100 kc/s," J. Res. NBS-D Radio Propagation, 67D,
539-550, 1963.
Taylor, W. L., "Lightning characteristics as derived from sferics," in
S. C. Coroniti (ed.), Problems of Atmospheric and Space Electricity,
388-404, American Elsevier Pub. Co., New York, 1965.
Taylor, W. L. "Detecting tornadic storms by the burst rate nature of
electromagnetic signals they produce," Ninth Conf. on Severe Local
Storms, 311-315, 1975.
Taylor, W. L., "Space-time mapping of lightning discharge processes in
thunderstorms at the NASA Kennedy Space Center," Trans. Amer. Geophys.
Union, 57, 922, 1976.
Taylor, W. L., "A VHF technique for space-mapping of lightning discharge
processes," J. Geophys. Res., 83, 3575-3584, 1978.
Taylor, W. F., "A VHF technique for space-time mapping of lightning dis
charge processes," To be published in J. Geophys. Res., Spring 1979.
Teer, T. L. and A. A. Few, "New York, Horizontal- lightning," J. Geophys.
Res., 79, 3436-3441, 1974.
Thomas, J., Statiscal Communication Theory, Wiley and Sons, Pub.,
New York, 1969.


non
21 JUNE 1979
34 5
FUNCTION DIV4SMX1.N)
** FUNCTICN SUBPROGRAM TO CALCULATE THRESHOLDt DIV4SM
DIMENSION XIDIM(4 ) ,XIOIV4(512) ,X1<20 48)
KK=512
DO 2 MK = I ,4
DO 4 I = 1 KK
4 X 1DIV4( I )=Xi ( (MK1 ) *KKF l )
2 X IDIM(MK) =UIG(X1DIV4512)
DIV4SM = SM ALL(X IDIM.4)
RETURN
END
* *


* dart LEADER H* STROKE H
I 1 1 { 1 1 1 j H
IOO 200 300 400 500 600 700 800 900
TIME IN MICROSECONDS
Figure 3.58. Logarithmic-amplitude VHF radiation during the dart leader and
the sixth return stroke.
4,
60


Figure 5.45. Three sequences of histograms, t^, t2, and t3 (1.5 msec intervals) of all the
detected sources in the PB and the stepped leader. Sequences (a), (b), and
(c) correspond to tp, t2, and t3, respectively. There are three histograms
in each sequence. The top row shows distance histograms referenced to the
weather tower. The middle row shows histograms of the elevation angle of the
sources referenced to the weather tower. The bottom row shows histograms of
- the azimuth angle of the sources referenced to the weather tower.


Figure 5.63. Simultaneous records of the logarithmic-amplitude VHF radiation detected at 9 km, and the
electric field 12 km away, during the 192356 flash. The following events in flash
are shown: R1 to R8 are the eight return strokes; J1 to J6 are the six J-changes; FR is
the activity following the first return stroke; SP is a solitary pulse during the
activity after the return strokes; and SL is the first stepped leader.


9
8
7
6
5
4-
3-
2-
1-
O'
-30C
0 1
EAST (km)
-20C
-10C


32
The initial J-change in the other two flashes formed a well defined
path. However, the noise sources occurred randomly throughout the path.
The path of the VHF noise sources during subsequent J-changes
extended to regions of high altitudes and occupied a larger volume in
space. Some of the paths of the noise sources during subsequent J-
changes were located in the same location or in the neighborhood of the
path of the previous J-change. Other subsequent J-changes developed
parallel to the path of the previous one. The fact that some previous
VHF sources remain active during subsequent J-changes (Figures 5.53 and
5.55) was previously observed by Proctor (1976). As the stroke number
increases, subsequent J-changes became less organized. In the last
J-change in the six and the eight stroke flashes the VHF sources did
not form an obvious path and were randomly located over a larger volume.
Our interpretation of the given facts about J-change processes is
as follows:
1) The J-change process makes available the negative charge needed
for subsequent strokes to ground.
2) As the number of strokes increases, this charge is being drained
from higher places in the cloud. Since there is less negative charge
available near the end of the flash, the J-changes associated with the
last strokes occupied a larger volume.
3) As it is clearly shown in this thesis in Figures 5.18, 5.48,
5.70, and 5.74, some of the subsequent stepped leaders propagated from
the lower and most concentrated region of the J-change. That is, the
negative charge made available by the J-changes is then lowered to
ground. In the remaining of the J-changes-leader paths, not shown in
the above figures, the dart leaders or the subsequent stepped leaders


157
out over a larger volume between the heights of 3,4 and 10 km. We
studied the progressing sequence of the VHF sources and searched for
any pattern in the development of the source locations. We determined
that some of the large VHF pulses during this interval had correlated
electric field changes. Every time a group of large pulses appeared,
they were at a new location. The largest variation in the VHF source
locations for consecutive pulses was about 5.4 km in the horizontal
direction and 1 km in height. During the CAFS interval the electric
field stations 3 and 19 km away showed the same sign in the slopes of
the electric field change. This is probably due to the large horizon
tal component of the VHF sources in Figure 5.35 (Malan and Schonland,
1951; Uman, 1969; Krehbiel, 1979). Using a two-point charge model
(equation (3.10)) for the X and Y locations in Figure 5.35, we found
that -13.5 Coul were lowered or raised within the cloud during this
interval.
The characteristics of the VHF noise during CAFS and its source
locations are very similar to the J1 and J2 processes. From the
characteristic of the VHF noise it is not evident that a new stepped
leader will not occur until the VHF pulse rate decreases and quiet
periods start developing at the beginning of DAFS. The VHF radiation
of all the subsequent stepped and dart leaders studied in this thesis
were preceded by a J-change VHF pulse rate of at least a pulse every
10 ysec for at least 10 msec. The CAFS has tills pulse rate but did not
produce a leader. It appears that the VHF pulse rate and duration of
VHF activity is a necessary condition for leader development but it is
not a sufficient condition.


APPENDIX A
DERIVATION OF SOURCE LOCATION FROM
DIFFERENCE OF TIME OF ARRIVAL MEASUREMENTS
Let r and r. be the distances from the desired space-location
ox r
P(X,Y,Z) to the central Q(0,0,0) and remote i's stations Q^CX^jY^.Z^)
for i = 1, 2, and 3 (Figure A.l). Since the relative elevation of the
stations is less than 2 m, and the remote stations are about 10 km from
the central station (negligible earth curvature), co-planar stations
are assumed. Then
represents the measured range difference, and
2 2 2 2 2
rQ = (PQ) = X + Y + Z
2 2 2 2 2
r. = (PQ.) = (X-X.) + (Y-Y.) + Z
l i l i
(A.l)
(A.2)
(A.3)
represent the square of the distances from the space-location to the
ground-based stations. From equation (A.l) we have
2 2 2
r, = r 2r u. + u.
I o OIL
(A.4)
Substituting equations (A.2) and (A.3) into (A.4), we get
X.2 + Y.2 2XX. 2YY. = -2u.r + u.2
11 1 1 1 O 1
(A.5)
311


91.
to the spherical azimuth angle (tj)), and the elevation angle (0),
respectively.
5.1.3 First Return Stroke
Figure 5.8 shows the VHF noise during the first return stroke.
The first return stroke was characterized by small high frequency pulses
riding on the envelope of a high amplitude pulse of about 250 ysec.
Only five VHF pulses could be correlated during the stroke, probably
because there were too many sources active and these sources were spread
over too large a volume of space. Three of the correlated sources were
located along the stepped leader channel, a fourth source was located
at the top of the highest average location of the preliminary breakdown,
and the fifth source was located 1 km above the fourth source. The
estimated total length of the return stroke channel from the tower
through the five sources was 8.8 km. Since the VHF return stroke noise
lasted about 250 ysec, we estimated that the return stroke propagated
at about 3.5 x 10^ m/sec. Since the cross-correlated location might
not be a true representation of the actual source location when a
7 8
potential wave propagates in a channel at a velocity of 10 or 10 msec,
return stroke velocities obtained from VHF source locations might be
off by axi order of magnitude.
Krehbiel (Uman et al., 1978) determined that a charge of -24 Coul
was lowered by the first return stroke using the technique described in
Section 3.5. Wc used the technique described in Section 3.6 and deter
mined that a charge of -19 Coul was lowered by the first leader-return
stroke process. Our point charge source for the transition region be
tween PB and stepped leader in the VHF record was within 1.5 km of
the location determined using multiple electric field records.


Dcte Due
^2) U£
i
3 |
rrr i
r
MAV 1 a \Mj
pr 2 8 roe
' ?-f V
. FEB 1
8 2013
-*
f>--
r-^=#E^
-


15 -
14-
13-
12-
I I-
ALTITUDE (km)
(c)
I 92


VHF RADIATION
5000
4000
3000
2000
1000
J4
J5
R6
200
J6-
R7
R8
300
400
500
TIME IN MILLISECONDS


L9
or intracloud discharge. It was reported by Proctor that the noise
from dart leaders emanated from the upper part (heights of 5 or 6.5 km
above sea level) of the channel. During the return strokes the noise
was continuous for 100 or 200 ysec. Many sources were active and few
fixes were determined along the channel. Proctor (1971) reported
activity within 250 ysec following the return stroke. This activity
was located in the previous return stroke branches. The interstroke process
reported was confined to one flash. The interstroke emitted a large
fraction of the VHF noise during the ground discharge. It was reported
to start 10 or 12 msec after the first return stroke and involved regions
between 3 and 4 km of altitude. Interstroke noise after subsequent strokes
was reported to extend the previous channel in an upward direction.
Proctor (1971) reported no information about fixes in an intracloud
discharge.
Proctor presented his next report in the 5th International Conference
in Atmospheric Electricity (Proctor, 1974a). By this time 18 flashes
(250 msec intervals) had been analyzed. This paper is the first publi
cation to discuss the location of noise sources during a cloud flash.
It is claimed that cloud flashes emit pulsed radiation during their
initial and very active (VA) phases, but only pulsed trains, less than
one millisecond width, in the final stage. These trains were also
reported in the VA phase. According to Proctor, these trains are emitted
by two kinds of events. One produces a long propagation from the
previous noise sources while the other one produces a shorter path which
moves toward the starting volume of the flash going throughout
non-previously located channels. Proctor associates these trains with
6
K-changes. The speed of the train of pulses ranged between 3 x 10 and


10
I
I
I
I
Figure 3.1. General block diagram.


ALTITUDE (km)
143


on
21 JUNE 1979
** BACK SOLUTION **
70 NY-N-1
IT=N*N
DO 80 J=1 N Y
i a=ir-j
I = N J
IC=N
DO 80 K=1 iJ
U( IU)=B(IB)-A< I A )*Ul IC)
I A = I A N
80 IC=IC-1
RETURN
END


ALTITUDE (km)
07
EAST (km)
Figure 5.57. Three-dimensional view of the cross-correlated noise
sources during J5, the dart leader and the sixth return
stroke. The location of the sixth return stroke charge
center is also shown.


273
5.6 The 181416 Flash
At 181416 UT during the thunderstorm on 8th August 1977 an intra
cloud discharge occurred. Figure 5.82 shows simultaneous records of
the logarithmic-amplitude VHF radiation and the electric field reading
at three different stations located 2.6, 7.6, and 13.7 km from the
discharge. The fact that the electric field reading at 2.6 km showed
a positive field change while the electric field at 13.7 km showed a
negative field change indicated that an upper positive and a lower
negative polarity charge center were supporting the discharge (equation
(3.10)). The electric field reversal with distance, the fact that the
field showed no evidence of leader-return stroke sequence, and the
locations of the VHF sources in the cloud combine to indicate that the
181416 flash was indeed an intracloud discharge.
5.6.1 Characteristics of the VHF Radiation
The 181416 flash lasted 114 msec and was characterized by pulses
one to 5 |_isec wide superimposed on an envelope x^hose pulse width
ranged between 50 and 600 ptsec. Figure 5.83 shows the logarithmic-
amplitude VHF radiation during the first 8.4 msec of the intracloud
discharge. The VHF radiation pattern at the beginning of the intra
cloud discharge is markedly different from the VHF radiation for the
cloud-to-ground flash studied in this thesis. Since the preliminary
breakdown phase in a cloud-to-ground flash studied in this thesis
lasted between 2 and 3 msec and was followed by a stepped leader with
significantly different VHF characteristics, we can, in the absence of
the VHF leader, uniquely identify this present radiation with an


5.3 The 181806 Flash
On 8th August 1977 at 181806 a cloud-to-ground flash was photo
graphed via a television camera (Figure 5.39) and videotape recorder
striking the 150-meter weather tower struck previously by the July, 1976
165959 flash. The VHF portion of the 181806 flash lasted 418 msec and
consisted of a six strokes to ground followed by a 216 msec continuing
current. Figure 5.40 shows the relationship between the VHF radiation
and the electric field for the entire discharge. Table 5.3 contains a
complete summary of the various phases of the flash. The upper and
lower locations, the duration of the phases, and the average velocity
if defined, of the VHF noise sources in each phase are given. Even
though the upper and lower coordinates are given for each event in
Table 5.3, only the events with velocities listed showed continuous
upwards or downwards propagation between these upper and lower coordi
nates, source locations as a function of time for the other events being
less organized. These charge regions are correlated with the VHF source
locations for each of the return strokes. The accuracy in the determi
nation of source locations for the entire flash is given in Appendix 3.
In the next sections we consider in detail what we learned from the VHF
radiation about the phases of the 181806 flash listed in Table 5.3.
5.3.1 Preliminary Breakdown (PB)
The VHF radiation started 7.8 msec prior to the first return stroke.
The first 1.9 msec of the 7.8 msec were associated with the preliminary
breakdown. The VHF noise during this 1.9 msec is characterized by high
frequency pulses riding on the envelope of pulses having between 20 and
40 psec width. Figure 5.41 shows the VHF noise during the PB, the
stepped leader, and the first return stroke. The electric field change


57
z(t) = log IP (t) I (3.5)
The z(t) signal represents the time dependent logarithmic envelope
of the VHF radiation.
From standard envelope detection treatment (e.g., Thomas, 1969;
Davenport and Root, 1958), we know that the frequency spectrum of z(f)
is concentrated in several regions as shown in Figure 3.8. The z (t)
output data is recorded on analog tape with a frequency response from
400 Hz to 1.5 MHz. Figure 3.9 shows the frequency content of the signal
that is recorded in the tape recording channels. The z^(t) signal is
composed of unipolar pulses. Since the recorder had a 400 Hz lower
cutoff frequency, the VHF radiation out of the recorder has no frequency
component below about 400 Hz and is roughly symmetrical about the center-
line through the radiation.
3.2.1 Description of Center Frequency, Bandwidth, and Magnitude Level
in the Telemetry System
3.2.1.1 Center Frequency. The choice of the 30 to 50 MHz range
for the band-pass filter was made for various reasons. First of all,
the lower limit was selected above the HF range where multiple reflec
tion of the ionosphere will occur disturbing the signal (Horner, 1964;
Pierce, 1976). Furthermore, the upper frequency limit was chosen below
the VHF band for television channels, FM radio, and other sources of
interferences. Thus the use of the 30-50 MHz range reduces the noise
level. In addition, previous work (Oetzel and Pierce, 1969; Cianos et
al., 1972) on measuring the radio emissions from lightning have proved
that the largest number of detectable radiation pulses are present
between 20 and 100 MHz. As the frequency increases above the HF range,


Figure 5.14. Cross-correlated VHF noise sources, 94 psec intervals, during the three SP's
shown in Figure 5.13.


EAST (km)
ALTITUDE (km)




ALTITUDE (km)
156
EAST (km)
Figure 5.35. Three-dimensional view of the cross-correlated VHF noise
sources during the 87.1 msec continuous VHF radiation
activity following the return stroke.


UNIVERSITY OF FLORIDA
262 08676 742 2


361
21 JUNE! 1979
DO 39 1 = 1 ,NT ICK
X N=FLO AT( I-l )*COS(ANGX)+0.2*SIN(ANGX )
Y N = FL O AT ( 1-1 )*5IN(ANGX)-0.2*COS(ANGX)
VAL=SX +FL0AT( I 1 )
CALL NUMQER(XN,YN,0.1 ,VAL DE GX,-l ,0.1.1 )
XN = FLOAT( I-l HCOS( ANGX)
YN=f-LOAT( I-l ) *SI N( ANGX )
THETA = 9 0.0+-DEGX
CALL SYMBOL{XN,YN,0.1,15,THETA,-l,0.1,1)
39 CONTINUE
CALL PLOT(0.0,0.0,3)
CALL PLOT YX=YB£*COS( ANGY ) /?. 0+ 0.4 S I N ( A NG Y )
YEY=Y8S*3 IN( ANGY )/2.0-0.4*CUS( ANGY)
CALL SYMBOL!YBX,YGY,0.15,NORTH (KM) ,DEGY. 10,0 .I 5, l)
NTI CK= YD S +1
DC 4 1 1-1 NT t CK
XN=FLOAT( l -1 )*COS{ANGY) +0.2 *51N(ANGY)
Y N = FL 0 AT ( I-l ) S 1N ( ANGY ) 0 2 £CU S ( A NGY )
Y AL~SY fFLAT ( I-t )
CALL NUMBER! XN.YN.O.i ,VAL,DEGY,-l ,0.1,1 )
XN=FLOAT!I-l)*COS(ANGY)
YN=FLOAT ( I-l ) S I N ( AN GY }
THETA=90.O+DEGY
CALL SYMBOL(XN,YN,0.1, I 5,THETA,-l ,0.1, 1 )
41 CONTINUE
CALL PLOT(0.0,0.0,3)
CALL PLOT (X2,Y23)
CALL TRNSFM!XMP,YMP,ZMP,ML,XXM,YXM.XYM,YYM,XPM,YPM,
YPPM,ANGX,ANGY)
DS-(Y2Yl)/{X2-X1)
WR ITE( 6,50)
N 1 =0
N2 = 0
DO 35 1 = 1 ,NL
D5S=YPM( I )/XPM ( I )
XINT=(DS*X1Yl)/(DS-DSS)
IF(XINT.LT.XPM(I)) GO TO 36
N 1 =N1 + 1
XPDN1 )= X P M( I)
YPH(Ml ) = YPM( I >
Y Y E(N1 )=YYM( I)
X YB(N1 ) = X YM{ I )+XBS
X X E ( N 1 ) = XXM( I )
Y X 0{Nl )=YXM( I )
YPPB(N l )=YPPM( I )
GO TU 35
36 N2=N2+ 1
XPT(N2 ) = XPM( I )
YPT(N2)=YPM(I)+ZSS
YYT( N2 ) YYM( I ) + ZBS
X Y T(N2 ) = XYM( I )
X X T(N2 )=X XM( I )
Y X T(N2) = Y X M( I ) FZOG
YPPT(N2)=YPPM(l)
3 5 C CN rI NUL
DO 33 1=1,Ml
WRITE( 6,4 7) XPIH I ) YPE3 ( D.YYOl I ) XYO ( I ) X X13 ( I ) YXO! I )
3 3 CONTINUE
W n IT E (6,50)
DO 37 1=1, N2
WR ITF ( 6,4 7) XPT( I ) YPT! I ) YYT ( I ) X Y T ( I ) X X T ( I ) YX T ( I )
37 CONTINUE
WRIT r. (6,50)
DO 46 1=1,NL


with center frequency at 50 MHz; Canos et al. (1972), bandwidth of 10 MHz
with center frequency at 30 MHz). In the work reported herein a 20 MHz
bandwidth centered at 40 MHz is used for 1976 and a 10 MHz bandwidth
centered at 45 MHz is used for 1977 data.
3.2.1.3 Amplitude. Oetzel and Pierce (1969) summarized previous
work on amplitude spectra of the radiation from lightning between
100 KHz and 10 GHz. The receiver bandwidths were normalized to 1 KHz
and to 10 km range. The various data after normalization agreed within
an order of magnitude. On the basis of those results, we have deter
mined that the signal amplitude at 40 MHz with 20 MHz bandwidth is
about 30 mV/m at a range of 10 km. The relative magnitude of the VHF
radiation signals reported herein vary between a noise level of -70 dBm
(.1 mv) and a maximum detected amplitude about -20 dBm (30 mv), a factor
of 300.
3.3. Data Pre-Processing and A/D Conversion
Analog tapes containing six randomly selected lightning flashes
recorded in the Kennedy Space Center, Florida, were sent to Eglin AFB for
digitization. Figure 3.10 shows the digitization process used at Eglin AFB.
The data pre-processing and A/D conversion consisted of four different
steps, three of which were the slow-down process, the final step was
the digitization process. The selected time intervals were first slowed
down by a factor of 4 in a direct-recording-reproduce mode. The purpose
of this step was to reduce, the upper frequency content of the data
from 1.5 MHz to 375 KHz. Using the direct mode the recorded lowest
frequency range will be multiplied by the slow-down factor, that is,
from 400 Hz to 1.6 KHz. Since the wider pulses observed in the final
processed data were in the neighborhood of 200 psec, limiting the


EAST (Km)
ALTITUDE (km)
95Z


5
techniques described in Chapter IV. Appendix D provides a listing of
the computer algorithm to display the channel locations in three
dimensions. Lastly, Appendix E presents two frequency domain tech
niques which could be used to obtain DTOA. These techniques were not
used because they do not adapt to the experimental data as well as the
selected time domain technique described in Chapter IV.


Figure 5.26. Two-dimensional views: (a) EW-NS, (b) EW-height, and (c) NS-height of all the
sources (triangles) and the cross-correlated source location (squares) during the
PB and the first stepped leader. The five circles represent the location of the
cross-correlated noise sources during the first return stroke. The circle Q1 is
the two-dimensional projection of Ql in Figure 5.25.


NORTH (km)
(A) (B) (C)
Figure 5.68. Two dimensional views: (A) top view, EW-NS, (B) elevation view, EW-height, and (C)
elevation view, NS-height of the cross-correlated sources during the third and fourth
stepped leaders. The locations A-B and C-D correspond to the initial propagation of
the fourth and third stepped leader, respectively.
61?


203
Three dart leader sources, 94 fisec intervals, are shown in Figure
5.53. As previously discussed in Section 5.3.10, the J3 process was
located east and north of the J2 process. The VHF noise from the dart
leader was emitted from a non-previously ionized region that joined the
old J2 and the new J3. Both the new J3 and the old J2 are shown in
Figure 5.53. This type of behavior was also observed in the dart
leader in the 165959 flash previously studied.
5.3.12 Fourth J-Change (J4)
The fourth return stroke was followed by a 3.8 msec quiet period
in which no VHF sources were detected. Figure 5.55 shows the cross-
correlated noise sources, 376 ysec intervals, during the J4 process.
Figure 5.55 also shows the location of the fifth return stroke spherical
charge center (Q5). The J4 process lasted 24.7 msec and was located 1.7
km east of the previous J-change. About 50% of all the noise sources
were located in a path 35 off vertical leaning toward the northeast
between the heights of 12 and 14 km. In general, the VHF noise sources
are much more dispersed than in the previous J-changes and did not
propagate in any ordered way.
Some of the noise sources in the neighborhood of J3 were still
active during J4. About 90% of all the J4 sources occurred between the
heights of 11 and 14 km. This J4 process extends higher than J3 which
extends higher than .12.
5.3.13 Dart header and Fifth Return Stroke
Figure 5.56 shows the VHF noise during the dart leader and the
fifth return stroke. Correlation with the electric field records indi
cates that the dart leader started about 80 30 ysec from the


17 3
starts about the middle of the PB interval and correlated VHP and elec
tric field pulse occur. After this point and continuing throughout the
rest of the PB and the stepped leader, large electric field pulses are
correlated with VHF pulses.
In addition to determining the cross-correlated, 94 ysec intervals,
and all the source locations using the computer algorithm described in
Chapter IV, we matched the pulses manually during the first 120 ysec of
the flash. We determined 36 locations during this interval, a location
every 3.3 ysec, about twice as many sources as determined by the compu
ter algorithm. Figure 5.42 shows a three-dimensional view of all the
VHF sources during the 120 ysec interval. The labels A to Z, and AA to
JJ show the regular progressing sequence of the noise sources. The VHF
sources formed a path 20 off vertical between the heights of 5 and 11 km.
During the PB the cross-correlated noise sources were located
between 9.5 and 6.7 km of altitude. However, all the PB noise sources
extended between the heights of 10.3 and 6.5 km. The upper and lower
cross-correlated source locations are shown as A and B in Figures 5.43
and 5.44. Even though the cross-correlated noise sources showed a pre
dominant downward propagation, the first few individual sources did not
correspond with the highest source locations. The first cross-correlated
source detected was at 7.9 km. The cross-correlated source locations,
94 ysec intervals, propagated upwards during the first 4.9 msec.
However, during the final 1.0 msec of the preliminary breakdown, that
was coincident with appreciable electric field change, the propagation
of the cross-correlated VHF sources is only downwards. All the VHF
noise sources during the entire PB interval were located with a cylinder
of 500 meter radius in the path from A to B as shown in Figures 5.43 and


n ri n n n orino o onon noonOn noon
(37
2 1 JUNE 1979
19
c
X I = X I - X2 ( 1 )-X2( l MM )
AVEM2(I-15 ) = XI/FLUAT(MM)
CALL RMEAN(AVEM02,2032.0.0)
V
C *
C *
r
LAG IS THE SUBPROGRAM THAT CALCULATES THE TIME DELAY **
TO PEAK THE CROSSCORRELAT10N FUNCTION. **
L
52 9
L A GL = L AG( AVEMO,AVEM02 ,MKN)
IF(LAGL.LE.5)GO TO 585
IF(MKN.EQ.l) L AG 1 =L A GL
IF(MKN *E Q 2) L AG2 =LA GL
IFMKN.EQ.3) GO TO 529
GO TO 530
LAG3=LAGL
DELTA 1( l)=.22978*FLOAT(LAGl)
DELTA2(1 ) = 2 2 9 7 8*FLOAT(LAG2)
DELT A3( 1 )=.229784FLOAT(LAG3)
N l N ( l ) = 1
t.
C *
C *
c *
c #*
r
HYPERM IS THE SUBROUTINE THAT FINDS THE LOCATION **
BASED ON THE DTO A IN THIS CALL ONLY THE LOCATION **
THAT CCRR ESPGNOS TO THE CROSS-CORRELATION VALUES *
IS FOUND **
v.
580
WRITE(6,580)
FORMAT( 1H0,1 OX,l 1HX IN METERS, lOX, 1 1 MY IN METERS,
* I OX,1 1HZ IN METERS)
WRITE(6,581) X(i),Y(1),Z(1)
50 1
FORMAT ( 3F 20. 3 )
WRITE(6,724)
724
r~
F ORMA T(IOX,11HX IN METERS,1 OXI 1 HY IN METERS,
* 1 OX, 1 1HZ IN METERS)
v,
c **
c **
c
c
IF THE SIGNAL LEVEL IS LOW AND BAD CORRELATION RESULTS, **
THE DATA IS ELIMINATED* 4*
IF((Z( 1 ).LE.0. ) ,CR. ((ABS(X(1 )) ).GE.40000.).OR.
* ( (AOS(Y( 1 ))).GE.40000.).OR.(Z( 1).GE.16000. ))GO TO 585
IF((LAG1 .LE.5) .OR (LAG2.LE.5).OR.
* (LAG3.LE.5)) GO TO 585
V.
702
530
c
WRITE( 8.7 02) X(l ),Y( 1 ) ,Z(1 ),ZERO
FORMAT(4F20.3)
CALL L0CMA2(MA0LM2,MM,JJ.AVE,SLPR2,SLPL2.NUMDR2.NUMDL2,
* NRROW2)
C *
c **
c
r
THE PROPERTIES OF THE LARGEST PULSE WITHIN THE **
SUBSET IS STUDIED **
DO 73 K=1,MP
IF(K.GE.2) MDIFTE=NDIFTE
v_
C **
c *
c *
s~
MABLMA IS THE ABSCISSA OF THE LOCAL MAXIMUM IN THE + *
CENTRAL, MX2GEN IS THE ABSCISSA OF THE LOCAL MAX- **
IMUM FOR THE REMOTE STATIONS **
C
160
M X 2GE N(K) -MAELMA (NNN(K) )+L AGL
I FMX2CEN(K) .GT.(N+l5) ) GO TO 7 3
NCCUNT =0
DO 70 J = 1,NP
IF ( IAf3S( MX2GEN( K ) M ADL M2 (MMM(J) ) ) .LE.( 16) )GO TO 160
GO TO 70
NC GUNT = NC 0 UN T +1
MABSC I(NCOUNT)=MMM( J)
LI(NCOUNT)=MABLM2(MMM(J))


nnn
2 1 JUNE 1979
VtJ
FUNCTION QIG(XiN)
** THIS SUBROUTINE FINDS THE LARGEST NUMBER IN THE SET
DIMENSION X ( 1 )
T = X ( 1 )
DO 570 I = 1 N
IF (T-X(I) )56 5,570,570
565 T=X( I )
570 CONTINUE
n I G= T
RETURN
END
**


Figure 5.72.
VHF noise detected at the central station (A) and
one of the remote stations (B). The (B) noise
has been shifted such that pulse 1 occurs at the
same time. Pulses 2 to 7 show the shift in the
VHF noise when the noise is emitted from a dif
ferent region.


109
EAST (km)
Figure 5.15. Cross-correlated VHP noise sourcds, 376 )isec intervals,
during the continuous VHP radiation of the J2 process.
A represents the end sources of the ,12 process. Spheres
Q2 and Q3 represent the charge center for the second
and third return stroke (Urnan et al., 1978).


nnri nono nn
135
2 1 JUNE 1979
** CONVERT TO THE ABSOLUTE TI ME **
LHCUR=16
MINU=59
LSECD=59
LMIL-LRIL + 1 000
LSEC^LSEC- 1
LSECOl-LSEC-13584
LMILD1=LMIL984
5ECO1=LSECDl
RMILD1 =LMILD t
SECD= SECD 1/32.
RM ILD 1 =RM ILD 1/32.
LSECD=SECD
R MILD =(SECDFLO A T(LSECD) )* 1 0 00 + RMILD1
M ILO=RM ILD
RMICRO = ( RMI LC-FLOAT (MILD) ) *100 0 .
M ICROT = RMICRO
MILST=8+MILD
IF( ( MILST.GE. 1000) .AND. (LSECD.GT.0 ) )GO TO 592
L SECL)= 59 tLSECD
IF(LSECD.GT.59) GO TO 592
GO TO 593
59 2 LSCCD=C
MINU-0
LHOUR= 17
M ILST=MILST-1000
593 DO 599 MN=1,6
599 WRITE!6*506)
WRITE(6.862) L hCUR.MINU.LSECD,M ILST,MICROT
862 FORMAT(l2X, UN I VERSAL TIME =* I 3, HOURS 13 'MI NUTES* ,
* 2X, 13.IX 'SECONDS' 14, lX, 'MIL I SECONDS' I 4, lX,
* MICROSECONDS' )
594 FORMAT{UNIVTRSAL TIME = .IJ,'HOURS' I 3, MI NUTES' .
* 2 X I 3 IX, 'SECONDS' 4. IX, 'MILL I SECOND S' I 4,1X,
* 'MICROSECONDS)
WRITE!0,594) LHOUR,MINU.LSECD,MILST,MICROT
** NORMALIZING THE FOUR TIME SERIES TO THE CENTRAL **
** STATION THRESHOLD LEVEL **
TIL12D-TIL1L TIL2L
IFTIL12D.EQ.O.O)GO TO 521
T IL23 = TILIL/TIL2L
DO 517 J = I .8610
5 17 X 7( J ) =TIL23tX7( J )
521 T IL13D = T IL1L-TIL3L
IF(TILI3D.EQ.0.OJGO TU 523
T IL3S=T IL IL/T IL3L
DO 519 J=1.36 1 0
519 X0(J)=TIL3S*X0(J)
523 T IL 1 4D=T IL t L-T l L4L
IFCTIL14D.E0.0i0)GQ TO 528
IIL4S=IIL1L/TIL4L
DC 526 J= 1,86 10
526 X9(J)=TIL4S+X5CJ)
** INITIALIZATION **
528 KK= 512
N-2040
M M = 1 6
T I ME 1=0.0
J J = I2e
J 1 -0


Figure 5.34. Two-dimensional views: (a) EW-NS, (b) EW-Height, and (c) NS-Height of all the sources
(triangles) and the cross-correlated source locations (squares) during the third
stepped leader. The four circles represent the location of the cross-correlated noise
sources during the third return stroke.


Figure 5.43(a).
Three-dimensional view of the cross-correlated noise sources during the first
PB-stepped leader process. Point A corresponds to the height cross-correlated
source during the PB. Point B is a similar source at the beginning of the
stepped leader. The sphere Q1 represents the source charge for the first
return stroke by Krehbiel (private com) using the techniques of Krehbiel et al.
(1979).
Figure 5.43(b).
Similar three-dimensional view for all the individual detected sources.


8
the leader to ground. Stepped leaders precede first strokes and some
subsequent strokes and move downward in about 50 meter steps with about
50 microseconds interval between steps. The velocity of the individual
steps is too fast to be determined from available streak photographs.
The stepped leader moves toward earth with a typical average velocity
of 2.0 x 10^ m/s. Dart leaders precede most subsequent strokes. Dart
leaders occur if additional charge is moved from another region of the
cloud to the top of the leader channel in a time less than about 100 msec.
A dart leader serves the same purpose as the stepped leader in that it
deposits charge along the channel and lowers cloud potential to ground.
The dart leader is less branched and has higher velocity than the
stepped leader. The elucidation of these processes is mostly credited to
Schonland and his co-workers in South Africa (1934 to .1938) who used
photographic techniques and electric field measurements. Discharges
also take place in the cloud in the time between strokes. Interstroke
electric field changes observed on the ground are termed J-changes;
interstroke impulsive electric field changes are termed K-changes
(Kitagawa and Kobayashi, 1958; Uman, 1969; Pierce, 1977).
Ground flashes can be classified as hybrid or discrete flashes
(Malan, 1954; Kitagawa et al. 1962). A lightning flash which involves
one or more continuing currents between strokes is called a hybrid flash.
A flash which involves only discrete strokes and no continuing current is
called a discrete flash. Between 29 and 46 percent of all ground flashes
have strokes followed by a continuing current (Livingston and Krider, 1978
Kitagawa et al., 1962), that is, hybrid characteristics. The J-change is
differentiated from the continuing current stroke because the J-change
has no channel luminosity and at close range the J-change electric field


Figure 5.30. Two-dimensional views: (a) EW-NS, (b) EW-Height, and (c) NS-Height of all the
sources (triangles) and the cross-correlated source location (squares) during
the second stepped leader. The three circles represent the location of the
cross-correlated noise sources during the second return stroke.


136
5.2.4 Following First Return Stroke (FR)
We have divided the interval between the first two return strokes
in three sections: (a) activity following return stroke (FR), (b) the
Jl process, and (c) the stepped leader.
The FR is the first interval after the first return stroke. The
FR interval is characterized by having large high frequency pulses riding
on the envelope of pulses of 3 to 30 ysec width. The VHF noise sources
during the FR interval were located in the neighborhood of the previous
stepped leader-return stroke channel between the heights of 3.7 and 6.5
km as shown in Figure 5.27. During the FR interval the electric field
decreased sharply at a station located 3 km away from the charge center,
while a station 19 km away showed a slight increase in field magnitude.
This field reversal indicates that during the FR interval either nega
tive charge was lowered from a region in the neighborhood of the first
return stroke charge center (as in the stepped leader), or that positive
charge (most likely from the previous return stroke) was raised to a
region above the previous charge source. We attempted to determine which
one of these situations was occurring by studying the progressing sequence
of the VHF noise sources. However, the VHF sources were unorganized and
we could not determine a direction of propagation.
5.2.5 The Jl Process
The Jl process started with a K-change and followed immediately
after the FR interval. The K-change was characterized by a change of
slope in the electric field record and a correlated large VHF pulse.
The VHF noise during the Jl process appears similar to that in the FR
interval, and is identified by the following two factors: (1) There was


Figure 5.71.
Three-dimensional view of the cross-correlated noise sources (triangles) during the
J4 process that preceded the dart leader and the sixth return stroke. The rectangles
represent the cross-correlated dart leader sources and the circles represent the
sixth return stroke cross-correlated sources. F and G show the isolated locations
of the two active regions.


EAST EAST NORTH
OJ
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ro
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00
uo
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r\)
oj
rg
oj JA
i 1
cn cn
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.£* r.
r- f,
go
if


EAST(km)


EXECUTE IN FORTRAN H OVER 800 LINES OF CODE WITH
12 SUBROUTINES ABOUT $1 CPU TIME PER I MSEC OF STORM ACTIVITY
Figure 4.4. Computer processing block diagram.


EAST EAST NORTH
NORTH
HEIGHT
HEIGHT
o
0 ro oj
Ul OI >1 d) (D
ro
oj
cn
(T>
-si
co
>>; y
e
. -j, 'V
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Hi-? v;V
V.-J
;h * *
,b> bj* / ¡H
> **Â¥ lv ih U
.-rS-uA:-* '
;j*i .'a. h
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-1-> <
<751


This dissertation was submitted to the Graduate Faculty of the
College of Engineering and to the Graduate Council, and was accepted as
partial fulfillment of the requirements for the degree of Doctor of
Philosophy.
December 1979
Dean, Graduate School


ALTITUDE (km)
278
EAST (km)
Cross-correlated VHP sources, 94 ysec intervals, during
the first 18.8 msec of the IC discharge.
Figure 5.84.


272
This phase is characterized by a pulse every few milliseconds in the
VHF record and small variation in the electric field record. Some of
the SP's during the junction phase have correlated electric field
change as can be observed in Figure 5.78. Therefore, we identify these
SP's with K-changes following the work of Brook and Kitagawa (.1960),
and Ogawa and Brook (1964).
5.5.4 Volume of the Flash
Figure 5.81 shows the 21,752 individual noise sources (triangles)
detected during the intracloud flash. The cross-correlated noise
sources are also shown with squares. The average rate of pulse loca
tion throughout the flash was a pulse every 28.9 Msec. This low rate
of source locations, compared to the typical 7 to 10 Msec for active
VHF periods, is caused by the long duration of the junction phase in
which sources were located only during the SP's. The source locations
extended from 2.5 to 7 km EW, 8 to 15 1cm NS, and 6 to 14 km in height,
3
for a total volume of 140 km .


297
with the previous return stroke channel (Section 5.1 prior to the second
return stroke, and Section 5.3 prior to the third and fourth return
strokes). In the former case the dart leader expanded from the bottom
of the path formed by the J-change noise sources. However, in the
latter case the dart leader radiation path was mainly horizontal between
4 and 6 Ion. The wide pulse at the beginning of the leader with a mag
nitude of 20 times that of the stepped leader is probably caused by a
potential wave that propagated from the previous J-change. No dart
leader VHF sources were detected in the leader path to ground.
Brook and Kitagawa (1964) and Proctor (1976) also reported strong
radiation during dart leaders. They also concluded that the dart leader
radiating sources were located in the cloud and not along the leader
channel to ground. Proctor (1976) did so using the same technique we
use; Brook and Kitagawa (1964) used arguments based on the time difference
between the electric field and the high frequency radiation.
7.1.4 Return Strokes
The VHF radiation during return strokes lasted between 92 and 859
psec and was characterized by either one large pulse of duration 92 to
250 psec or a succession of pulses between 30 and 100 psec width. VHF
radiation was absent during the fourth return stroke in Section 5.3.
Otherwise, the maximum magnitude of the VHF radiation during return
strokes was about 25 times larger than the stepped leader.
The VHF sources during return strokes preceded by stepped leaders
were located in the neighborhood of the previous stepped leader channel
and throughout the PB or J-change that preceded the leader- Return
strokes VHF sources after stepped leaders were detected between a height
of 14.5 and 0.7 km. Similarly, VHF sources during return strokes


Table B
.2. Error Analysis for the Locations in the 181806 Flash,
ascending order in z.
The locations are arranged in
Source Locations
(Meters)
-1172
-2176
-656
-1093
-593
-458
-710
-202
-372
260
-50
-257
819
1177
48
-1235
-905
1186
3959
4331
1522
4013
1313
5478
5547
2796
2671
6318
8841
8293
8937
9191
9231
9295
9372
8695
9096
11410
9320
9708
12050
12137
9704
10245
9527
10560
10426
10855
1103
10944
10654
11529
117 98
10055
12294
12710
633
1865
2966
3287
3646
4510
4915
5373
5789
6464
7033
7484
7763
7887
8237
8682
9379
9777
9953
10521
lu634
10659
12385
12658
13152
13355
13663
14864
Average e
tions in
rror
this
for loca-
flash.
Quant
Erro
dx.
50
57
56
58
60
64
65
69
70
97
83
83
133
160
94
88
89
162
561
657
195
570
191
923
932
329
341
1152
264
ization RMS
r (Meters)
dy,
Q
326
276
432
407
473
515
505
530
550
846
636
657
1058
1161
712
660
665
981
1678
1888
1107
1757
1069
2280
2321
1202
1530
2717
1033
dz.
3004
1887
747
648
657
526
461
355
357
662
309
312
650
702
302
285
271
439
1171
1392
526
1221
601
2069
2120
914
959
2719
938
Calibration RMS
Errors (Meters)
dx
106
105
133
127
143
156
153
170
171
236
204
204
311
360
231
200
210
370
1089
1271
438
1117
443
1805
1832
713
737
2281
547
dy.
710
593
936
881
1024
1112
1089
1136
1181
1841
1363
1411
2298
2523
1527
1416
1418
2106
3607
4061
2377
3779
2285
4895
4983
2563
3282
5830
2222
dz
7302
3649
1804
1565
1577
1244
1085
801
798
1473
594
591
1292
1334
467
509
391
455
1228
1566
537
1347
837
2989
3129
1463
1330
4326
1632
Total RMS Error
(Meters)
dx.
118
120
144
140
155
169
166
184
185
256
221
220
338
394
250
218
229
404
1225
1431
480
1254
482
2029
2056
785
812
2555
608
dyt
781
654
1031
971
1128
1226
1201
1253
1303
2026
1504
1557
2530
2778
1685
1562
1567
2323
3978
4479
2622
4167
2523
5400
5497
2831
3621
6432
2451
dz
7896
4108
1953
1694
1708
1351
1179
876
875
1615
670
669
1447
1507
556
584
476
633
1697
2095
752
1819
1031
3636
3780
1725
1640
5110
1882
326


nono nnnn nonn ooo
133
2 1 JUNE 1979
C
C
C
c
c
c
c
c
c
c
c
c
* * *
*
THIS algorithm determines the three-dimensional locations
OF VHF NOISE SOURCES DURING A LIGHTNING FLASH- THE PRO
GRAM IS BASED CN DETERMINING THE DIFFERENCE IN THE TIMF
OF ARRI VAL (DTOA ) OF FOUR TIME SERIES VHF RADIATION DATA.
THE DTOA IS DETERMINED BY USING PATTERN RECOGNITION AND
THE CROSS-CORRELATION FUNCTION.
A
*
*
*
*
*
*
DI MENS ION LCHAN(167 0).LREC 2,16 70),X6(361 0) ,X7{86 I 0).
* X£(86l0) AVE( 128) ORDLMA( 128 ) MABL MA( 12 6) AVEMO I 2 04 0) ,
* AVEM02(2048),MX2GEN(128),MA0LM2(12B),NUMDER(128),
* NRROWE(128).NRR0W2(128)
DIMENS ION SLPR 128) ,SLPR2( 128) SL_PL( 128) SLPL2( 128) .
* NUMDEL( 128) NUMDL2 ( I 28 ) NGOOD ( 5 ) MGCJODt b ) DELTA 1 ( 128 ) ,
* DELTA2(l23).DELTA3(128),X(128),Y(128),Z(128),NDIFB0(5),
* MAOSCI(10)Ll(10),NDSLRI(10 ) ,NDSLLE(10).PENDRI(10),
* PENOLE( 10),X9(8610) ,NSTDEV( 10 ) ,MBSC K 128),TI ME(123),
* NIN(128),NUMDR2(l28),LINT(1670)
LOGICAL*! LCHAN
INTEGE R* 2 LR EC
COMMON KK,N,MP,NP.NNN(128),MMM(12Q),X1(2048),X2(2040)
10 FORMAT(75(75A1))
ZERO=0.
W R IT E ( 6,700)
70 0 FORMAT (IH I )
WR ITE( 6,722)
722 FORMAT(33X,32H5TURM ACTIVITY ON I 9 TII JULY 1 976.//21X,
* 6OHST ART TIME = 16 HOURS 59 MINUTES 59 SECONDS
* 008 MILLISECONDS, //20X, 6 1 HE INI 3H TIME = 17 HOURS
* 00 MINUTES 01 SECONDS 009 MILLISECONDS)
** SKIP THE CALIBRATION BLOCK **
READ( l 1,1 0) ( (LCHAN( I ) (LRE C(J,I),J=l,2)),I=1.100)
** SKIP A PRE-DETERMINED TIME CORRESPONDING TO THE NOISE **
** LEVEL BEFORE THE SIGNAL IS DETECTED. **
DO 12 LK-. 1,310
12 READ(11,10)
** PROCESS THE NEXT 500 BLOCKS OF DATA. A BLOCK HAS 410 **
** DATA POINTS OF EACH OF THE FOUR SERIES. **
DO 520 I 1 M = 1 ,25
DO 20 K=1,21
R E AD( 1 1, l0)( (LCHAN(I ), (LREC(J, I ) J = 1 ,2) ) 1=1 1670)
** CONVERT THE DATA ON THE TAPE FROM *
** POP-COMPUTER FORMAT TO IBM FORMAT. **
DO 18 1=1.1670
DC 16 J=1 ,2
16 LRECJ ,1) =(LREC(J,I )-64)/256
18 L I NT ( I )=L RFC (1,1) *G>4 + LREC(2,I)
IF(K.EC.1) GO TO 805
GO TO 802
C
C ** THE FOLLOWING INFORMATION IS NEEDED TO DETERMINE **
C ** THE ABSOLUTE UNIVERSAL TIME. **
805 LSAVE1=LI NT( 1641 )


of the third stepped leader (M, Figure 5.70(a)). The main M region
extended 3 km horizontally and vertically. The fifth stepped leader
followed J3 and descended from the center of this concentrated region
(N, Figure 5.70(a)). A study of the electric field record and the VHF
source locations indicate that negative charges were lowered during the
J3 interval. The noise sources in the P region in Figure 5.70(a)
correspond to active sources in the previous A-B channel in Figure 5.69.
The fifth stepped leader (Figure 5.70(b)) lasted 30.1 msec and
continued the downward propagation of the N region sources in Figure
5.70(a). The fifth stepped leader path to ground remained between one
and two km from the previous stepped leader. The lowest detectable
cross-correlated noise source was located at a height of 3.1 km (R,
Figure 5.70(b)). The average stepped leader velocity was 5.1 x 10^
m/sec.
5.4.11 Fifth Return Stroke
The fifth return stroke lasted 450 ysec in the VHF record. Three
cross-correlated noise sources during the fifth return stroke are shown
as circles in Figure 5.70(b). Assuming a point charge model and using
the technique in Section 3.6, we estimated that -16.2 Coul were lowered
by the fifth stepped leader-return stroke.
5.4.12 The J4 Process, the Dart Leader, and the Sixth Return Stroke
The fifth return stroke was followed by a 3.7 msec quiet period
and a 26.8 msec J-chango (J4, Figure 5.64). The J4 process formed in
the neighborhood of the source charge of the third and fifth return
stroke. Figure 5.71 shows the cross-correlated noise sources during
J4. The two different regions are shown as F and G. The sources in


norm nnon n nono oOnn
.139
21 JUNE 1979
* (LKNM.EQ.2)) GO TO 491
IF(( [A ES(L1 (3)-L AGL MAB LMA(NNN(K+l ) ) ) GT.NDIFTE).AND.
* (LKNM.EQ.3)) GO TO 491
GO TQ 73
49 1 MSCH K)-Ll(LKNM)
IF((K.GE.2) .AND.(NO IFTE.GE.MDIFTE) .AND.(MB3CI(K).EQ.
* MBSCI(K-l))) GO TO 73
e4 CONTINUE
IF (MOSCI ( K ) GT .( NFl 5) ) GO TO 73
IF(MKN2) 87.89.9l
** CELT A1 DELTA2. AND DELTA3 CONTAIN THE TIME DIFFERENCE
** FOR EVERY IDENTIFIED PULSE.
87 DELTA1 (K)=(MBSCI(K)MABLMA(NNN(K)))*.22978
GO TO 73
89 DELTA2(K) = (MDSCI (K)-MABLMA(NNN(K ) > )*.22978
GO TU 73
9 1 DELTA3(K)=(MOSC I (K)-MABLMA(NNN(K) ) )*.22978
73 CONTINUE
** CHECK FOR WHAT STATION SHOULD BE READ NEXT **
IF(MKN.EQ.3)GO TO 93
IF (MKN .CQ .2 ) GO T 95
DO 503 K= 1 ,2 04 8
503 X2(K)=X8(2048*J1-448*J1+K)
GO TD 17
95 DO 50 4 K~ 1,2 04 3
504 X2(K)=X9(20484J1448*J1+K)
GO TO 17
** A REASONABLENESS TEST IS USED TO ENSURE THE TIME **
** DIFFERENCE IS WITHIN PROPER BOUNDS. **
93 DELlUD-.2 2978*FLGAT(LAGl 1+2 5.0 *.22978
DELILB = .22978*FL0AT(LAG1 1-25.0*.22978
DEL2UB=.22978* FL OAT(LAG2)+25.0*.22973
DEL2LD =.22978*FLCAT(LAG2)25.0 *.22978
DEL3UB =.22978*FLGAT(LAG3)+25 0*.22978
DEL3L8=22978*FLOAT(LAG3)-25.0*.22978
N X =0
CO 4 52 IK = I MP
IF((DELTA 1 ( IK) .GE.DELILB.AND.
* DELTA1(IK).LE.DELlUB).AND.(DELTA2(IK).GF.0EL2L0.
* AND.DELTA2( IK ) .LC.DEL 2UB) .AND.(DELTA 3( IK) .GE.DEL3LB.
* ANDD FLT A3(IK).LE.DEL3U) ) GU TO 571
GO TQ 452
7 1 NX-NX + 1
N 1 N(NX) = I K
52 CONTINUE
** CALCULATE THF LOCATIONS FOR ALL THE PULSES MATCHED **
** FOR ALL THE STATIONS *
CALL HYPE RM( DELTA1 DEL T A2 DELT A3 X Y 7. N l N NX )
WR ITE ( £.5 35)
535 FORMAT ( 1H0, tOX1 1 HX IN METERS, 10X, l lHY IN METERS,
* l OX, L 1HZ IN METERS 5X.20HTIME IN MICROSECONDS )
WR ITE( 8,706 )
DO 1 72 LK = 1 NX
T1 ME(LK)=.22978*ELOAT(J 1*2 048-J1*44 8 ) +
* .22978*FL0AT(MAOLMA(NNN(NIN(LK))))
if. t
**


stroke charge using our technique in Table 5.6(b) compares reasonably
well with the value obtained in Table 5.6(a).
5.4.4 Activity Following the First Return Stroke (FR)
The FR activity followed immediately after the first return stroke
(Figure 5.64), lasted 7.1 msec and contained five large pulses (1 to 5
in Figure 5.64) about 200 psec wide with an interval between the pulses
ranging from .4 to 1.7 msec. The VHF noise sources during each of these
pulses propagated downward in a southerly direction at a velocity be
tween 1.5 and 3.5 x 10^ m/sec. The longest of these paths extended 4.3
km vertically and 3.2 km horizontally. Figure 5.66 shows the cross-
correlated VHF sources during the FR interval. We fitted a point charge
model to the FR interval assuming a charge transfer from A to B in
Figure 5.66. A charge transfer of 4.5 2.1 Coul was determined by
using the six more distant electric field stations between 9 and 21 km
from the source. We used points other than A and B in Figure 5.66 and
obtained a charge transfer between 1.8 and 5.1 Coul. For all our charge
models the stations located closer to the source (3 to 7 km) gave
inconsistent results. It appears that the charges are not concentrated
and the point charge model is not a good approximation for close stations.
From the characteristics of the VHF radiation, the source locations,
and the point charge model, we conclude that either negative charge at
higher altitudes was lowered toward the top of the previous return stroke
channel or that positive charge from the previous return stroke con
tinued its upward propagation. A total charge of 4.5 Coul distributed
in 5 large pulses is about .9 Coul transfer per event. This number is
comparable with the .85 Coul calculated for the K-change that initiated
the J1 process in the 180710 flash.


Figure 5.1. Simultaneous records of the logarithm amplitude VHF radiation observed at 10 km,
and the electric field 13 km away, during the 165959 flash. The following events
in the flash are shown: Rl, R2, and R3 represent the three return strokes; SL is
the stepped leader before Rl; DL is the dart leader before R2; SDh is the stepped
dart leader before R3; J1 and J2 are the interstroke processes; FR is the activity
following the first return stroke, SP's are the solitary pulses; and IC is the
intracloud discharge, of which the final 99 msec is not shown.


158
5.2.11.2 Discrete VHF Activity After Third Return Stroke. The dis
crete VHF activity after return stroke (DAFS) followed the CAFS phase and
lasted 71 msec in the VHF record. Six solitary pulses (Figure 5.1) could
be observed in this final stage of the flash. Three of these SP's showed
correlated electric field changes. The last SP lasted 1.9 msec, had a
correlated rapid electric field change, and possessed the largest ampli
tude of the VHF radiation of any pulse in the flash. The VHF radiation
and the location of its cross-correlated noise sources are shown in Fig
ures 5.36 and 5.37, respectively. The first five noise sources (A to E
in Figure 5.36) corresponded to the first two wide pulses at the beginning
of the SP. These sources were located in a regular progressing sequence
and propagated 2 km south and 1 km downward at a velocity of 8.8 x 10^
m/sec. The source locations of the remaining 1.4 msec were located in
the different regions shown in Figure 5.37. The most concentrated VHF
source region, J to S, corresponded to the lowest crowded VHF source
region of Jl, J2, and CAFS, most likely a negative charge region because
that is where the stepped leaders originated. At the end of the SP some
of the noise sources, T to W, were located in the same returning path to
A. The location of these noise sources showed some evidence that this
1.9 msec SP was a K-change as described by Kitagawa and Kobayashi (1958)
4
except that Kitagawa estimated downwards velocity in the order of 10 m/sec.
By measuring the electric field changes as a function of distances,
Kitagawa and Kobayashi (1958) concluded that K-changes resulted when
charges moving downward encounter charges of the opposite sign and upward
moving return strokes occur. The noise sources- indicate this type
of effect. Positive charges located near A were lowered to the
main active negative charge region (J to S) and an upward moving


nnnn non oooo co
559
2 1 JUNE 1979
** SETTING THE VALUES INSIDE THE SCALES **
XMP( I ) =XMP( I )-3X
YMP( I)=YMP(I) -SY
23 2MP( I } -ZMP( I )-SZ
DO 45 1=1,NL
45 WRITE(6*18) XMP( I ) ,YMP( I ) ,ZMP( I)
WRITE!£,50)
PX1=0.0
** PROJECT I UN OF THE SCALE ON THE BASE EARTHS AXES. SETTING **
** UP THE CUTER PERIMETER. **
PX 2= XB S*C 03!ANGX)
PX3=YBS*CS C ANGY)
PX4=PX2+PX3
PY 1 = 0.0
PY2=XOS*5IN(ANGX)
P Y 3= YO S* SIN!ANGY >
PY 4=PY 2+P Y3
PY5=Z0S
PY6=PY5+PY2
PY7=PY5+PY4
PYfl=PY 3+PY5
X l=PX3
Y 1=PY3
X2=PX2
Y2-PY2
** SETTING UP THE GOULD PLOTTER **
CALL PLOTS!15.0,20.0,01*XSHIFT,YSHIFT)
CALL L INE WT(2)
** DRAWING THE THREE-DIMENSIONAL DOX AND DOING ALL *+
** THE PROJECTIONS. **
CALL PLOT(PXl*PY1,3)
CALL PLOT(PX1,PY5,2>
CALL PLOT !PX2,PY6,2 )
CALL PLOT(PX2 ,PY2 ,2)
CALL PLOT(PX1*PY1,2}
CALL PLOT(PX2.PY2,3)
CALL PLOT(PX4,PY4,2
CALL PLOT(PX4,PY7*2)
CALL PLOT(PX2,PY6,2)
CALL PLOT(PXI,PY5,3)
CALL PLOT(PX3,PYa,2)
CALL PLOT(PX4,PY7,2)
CALL PLOT(0.0.0.0,3)
C ALL L INEWT(0 )
SPACE= 0.25
L=Y03/SPACE
L =L/2
DO 25 1= l *L
CALL WHLREXW, YW ,XF YF )
XW=XW-FSPACE*CQS( ANGY >
Y W = Y W + SPACE 5 IN(ANGY)
CALL PLOT(XW,YW,2)
XW = XW+ SPACE*CQS(ANGY)
YW=YW + SPACE* SIN!ANGY)
2 5 CALL PLOT (XW YW 3 )
CALL WHERE!XW,YW ,XF ,YF)
X 5 5= X W
YSS=YW


78
per flash after 10 man-months of processing. However, since our data
are recorded on analog tape with a frequency response between 400 Hz and
1.5 MHz, our source locations are not as accurate as those reported
from the LDAR or Proctor (1976) systems. In the next two chapters we
described the telemetry and data processing techniques used in this
research.


non
344
21 JUNE 1979
FUNCTION SMALL( X N)
** THIS SUBROUTINE FINDS THE SMALLEST NUMBER IN THE SET
O I VENS ION X( 1 1
T=X( 1 >
DO 57S 1=1,N
IF(T-X(I))575,575,580
580 T=X( I )
575 CONTINUE
SMALL = T
RETURN
END
* *


303
VHF sources were detected in the neighborhood of some of the lower
regions of the J-change.
7.1.7 SP and K-Changes
Kitagawa et al. (1958) defined a K-change as a small, rapid field
change with accompanying pulses of luminosity. We refer to K-changes as
those small, rapid field changes with accompanying VHF radiation. In
addition, we refer to SP's (solitary pulses) as those isolated VHF
pulses with a magnitude 30 to 45 times larger than the stepped leader
and with no detectable electric field change. SP's were preceded and
followed by quiet periods and were detected during the J-change, after
the last return stroke in CG flashes, and in the junction phase of IC
discharges. The duration of the SP1s is about 1 msec and the VHF noise
is characterized by pulses 1 to 30 ysec wide superimposed in an envelope
with a pulse width between 100 and 180 ysec. Figures 5.13(a), 5.13(b),
and 5.13(c) show the VHF noise during three SP's that occurred in a quiet
period during the interstroke process. Figure 5.36 shows the VHF noise
for a K-change that occurred after the last return stroke of one of the
CG flashes.
The VHF noise sources for the SP's in the interstroke process
(Figures 5.14(a), 5.14(b), and 5.14(c)) propagated upwards 2 to 5 km
at a velocity between 1 and 4 x 10^ m/sec. A K-change initiated the J1
change in the flash discussed in Section 5.2. This K-change lasted 1.1
msec and propagated downwards about 4 km from a height of 10.6 km at a
velocity of 9.5 x 10^ m/sec. No other SP or K-changes were detected
during the J-process. Other rapid electric field changes during the


ALTITUDE (km)
<15
EAST (km)


277
intracloud discharge. The initial VHF noise of the intracloud has
similar characteristics to that of the cloud-to-ground discharge prior
to the stepped leader; that is, both appear to be due.to the PB process.
Figure 4.1 shows the first 800 ysec of the VHF radiation detected
at the central station, and at the Wl, Ml, and M3 stations. These
stations are identified in Figure 3.1. The ground distance from the
discharge to the four stations is 7.6, 4.1, and 12.4 km, respectively.
The DTOA between the central and each one of the remote stations is
shown in Figure 4.1. This data is taken directly from the digitized
tapes and corresponds to the simultaneous recorded VHF radiation. To
determine the actual DTOA needed to calculate source locations we have
to subtract the retransmission delays for the remote stations
(Appendix B).
Similar to the cloud-to-ground discharge after the last return
stroke, the VHF noise pulse repetition rate decreases toward the end
of the discharge. This decrease of the pulse rate of continuous
radiation coupled with the appearance of discrete VHF radiation of SP's
mark the end of the intracloud discharge.
The 181416 flash did not have the three previously described
phases: initial, very active, and junction phase. The VHF pulse rate
of one every 10 to 20 ysec (characteristic of the active phase) decreased
toward the end of the flash. Therefore, we could characterize the VHF
radiation in two intervals: an active phase and a junction phase as
proposed by Brook and Kitagawa (I960) for some of the flashes they
studied.
5.6.2 Locations of the VHF Noise Sources
Figure 5.84 shows the cross-correlated VHF noise sources, 94 ysec
intervals, during the first 18.8 msec of the IC discharge. The VHF


I 72


¡65
of these techniques make use of the two point measurement problem (see
Figure E.i).
Let x and y represent the discrete time series at the central
n n
(x ) and either of the three remote stations (y ).
n y n
Figure E.l. The two point measurement problem.
y = x h 4- r
a n n n
(E.l)
where is the convolution operator, h^ is the transmission path, and
r is random noise. The transmission path in this case does not
n
represent,a physical transmission path but a conceptual one which is
introduced with the purpose of illustrating a number of digital tech
niques. Now we can proceed to determine the time difference between
identifiable pulses in x and y Once this time has been determined,
n il
the procedure is repeated for the remaining two remote stations.


cross-correlated source locations, 376 ysec intervals, for the entire
discharge. During the first 4.6 msec of the VHF radiation, the average
noise sources were located within half a kilometer perpendicular dis
tance of the bottom-half of the Line joing A and B. During the next
11.2 msec the noise sources moved to the upper half of the path between
A and B. Figures 5.21(a) and 5.21(b) show histograms of the average
source locations, every 94 jisec, for the first 5.6 and 11.2 msec,
respectively. For the first 16.8 msec, 85% of all the average sources
were located within half a kilometer perpendicular distance of a line
joining A and B. During the remainder 484 msec of the IC discharge,
VHF sources traversed from the path between A and B many times, widen
ing the VHF source volume to over 1 km radius. VHF sources also extended
an additional 2 km at the ends, near A and B.
The intracloud discharge can be divided into three phases: initial,
very active, and junction, as done by previous investigators (Kitagawa and
Brook, 1960). The initial phase started with a large 10 ysec wide VHF
pulse. This phase lasted about 64 msec and consisted of a low rate of
VHF radiation, approximately one pulse every 25 ysec. In the electric
field waveform of Figure 5.1, the initial phase includes the rising part
of the IC record. The active portion of the VHF radiation lasted about
437 msec and was characterized by a faster pulse rate, about a pulse
every 10 ysec. The total of the initial and the active phase, 501 ysec,
corresponded to the portion of the IC discharge for which the VHF noise
was more or less continuous. For the next 99 msec, not shown in Figure
5.1, five solitary pulses were observed. The HP's occurred 49.3, 58.7,
70.5, 75.7, and 97.1 msec after the continuous radiation. We associate
the quiet period where the five SP's occurred with the junction phase


141
This is another example of the utility of VHF records for a clear
identification of the different events in a lightning discharge.
Figures 5.29(a) and 5.29(b) show a three-dimensional view of the
188 cross-correlated sources, 94 ysec intervals, and the 2991 individual
source locations, respectively, during the second stepped leader.
Figure 5.30 shows the two-dimensional projections of all the individual
noise sources (triangles), and cross-correlated sources (rectangles).
The stepped leader VHF noise sources started from the lower concentrated
J1 noise source volume in Figure 5.29 and descended in a near-vertical
path. The VHF noise sources were detected between a height of 6.6 and
.7 km. From the VHF source locations in Figure 5.29(a), we estimated
the ground contact point as (5.3 .5, 8.5 .5). This point is located
about 1.5 km east of the UC-7 field mill station.
From a study of the location and the sequence of the noise sources
in Figure 5.29, we estimated that the second stepped leader had at least
two detected branches labeled M and N in Figure 5.29. During the first
18.2 msec the second stepped leader propagated vertically from a height
of 6.7 to about 4.0 km, with about 3.5 km horizontal propagation.
During the remaining 10.8 msec the VHF noise sources are grouped in a
more nearly vertical channel. The stepped leader average velocity
ranged between 2.4 and 5.3 x 10^ m/sec.
5.2.7 Second Return Stroke
Figure 5.31 shows the VHF noise during the period including the
second stepped leader, the return stroke, and the beginning of the J2
process. The return stroke had a duration of 316 ysec in the VHF record.
The VHF cross-correlated source locations, 94 ysec intervals, during the
second return stroke, were located in the neighborhood of the upper part


180
charge sources to be discussed in the next section. The near-vertical
path of the PB and the stepped leader is evident from this picture.
The stepped leader velocity was 1.0 x 10^ m/sec. Photographs taken of
this flash (Figure 5.39) showed that the first channel struck the
150-meter weather tower. Figure 5.45 shows three sequences of histo
grams of all the source locations during the PB and the first 3.2 msec
of the stepped leader. These graphs are similar to those provided in
Figure 5.7 and they illustrate the propagation of noise sources for
three time sequences, every 1.5 msec.
5.3.3 First Return Stroke
The first return stroke VHF radiation lasted 475 ysec. The noise
was characterized by a low frequency envelope with a succession of
pulses between 10 and 50 ysec width. Noise sources were located during
and immediately following the return stroke. The return stroke cross-
correlated noise sources, 94 ysec intervals, are shown as circles in
Figure 5.44. The return stroke noise sources are located in the pre
liminary breakdown and stepped leader channel regions.
The charge and locations of the six return stroke charge regions
(Ql through Q6) were provided by Krehbiel (private com) and were found
using the technique of Krehbiel et al. (1979). Krehbiel's results are
summarized in Table 5.4. The Ql charge center in Table 5.4 is within
random error in source location from B (-0.9, 9.1, 6.7) which is the
point charge location of the transition in the VHF record between the
PB and the stepped leader. At a station 10.9 km from the tower, the
electric field change from the first leader-return stroke sequence was
990 volts/meter. Using location B as the charge center and the technique


Uiuan, M. A., Lightning, McGraw-Hill, New York, 1969.
Uman, M. A., W. H. Beasley, J. A. Tiller, Yung-Tao Lin, E. P. Krider,
C. D. Weidman, P. R. Krehbiel, M. Brook, A. A. Few, Jr., J. L. Bohannon,
C. L. Lennon, H. A. Poehler, W. Jafferis, J. R. Bulick and J. R. Nicholson,
"An unusual lightning flash at the NASA Kennedy Space Center," Science,
201, 9-16, 1978.
Uman, M. A., R. D. Brantley, Y. T. Lin, J. A. Tiller, E. P. Krider, and
D. K. McLain, "Correlated electric and magnetic fields from lightning
return strokes," J. Geophys. Res., 80, 373-376, 1975.
Uman, M. A. and D. K. McLain, "Lightning return stroke current from
magnetic and radiation field measurements," J. Geophys. Res., 75, 5143-
5147, 1970.
Watson-Watt, R. A. and J. F. Herd, "An instantaneous direct reading
radiogoniometer," J. Inst. Elec. Engrs., 64, 611-622, 1926.
Weinberg, H. and R. Cooper, "The recognition index: A pattern recogni
tion technique for noisy signals," Electroenceph, Clin. Neurophysiol.,
33, 608-613, 1972.
Widrow, B., "The 'Rubber Mask' technique 1 pattern measurement and
analysis," Report Stanford Univ., 1974.
Wilson, C. T. R., "On some determinations of the sign and magnitude of
electric discharges in lightning flashes," Proc. Roy. Soc, London, A92,
555-574, 1916.
Wood, L. C. and S. Treitel, "Seismic signal processing," Proc. IEEE,
63, 649-661, 1975.


Ogawa, T. and M. Brook, "The mechanism of the intracloud lightning dis
charge," J. Geophys. Res., 69, 5141-5.150, 1964.
Pierce, E. T., "Electrostatic field changes due to lightning discharges,"
Quart. J. Roy. Meteorol. Soc., 81, 211-228, 1955.
Pierce, E. T., "Atmospherics from lightning flashes with multiple strokes,
J. Geophys. Res., 65, 1867-1871, 1960.
Pierce, E. T., "Atmospherics: Their characteristics at the source and
propagation," in Progress in Radio Science 1963-1966, pt. 1, 987-1039,
International Scientific Radio Union, Berkley, Calif., 1967.
Pierce, E. T., "Source characteristics of atmospherics generated by
lightning," Proceedings of Waldorf Conference on Long-Range Geographic
Estimation of Lightning Sources, NRL Report 7763, Washington, D. C.,
64-79, 1974.
Pierce, E. T., "The thunderstorm research international program (TRIP) -
1976," Bull. Amer. Meteorol. Soc., 57, 1214-1216, 1976.
Pierce, E. T., "Atmospherics and radio noise," in R. H. Golde (ed.),
Lightning Volume 1: Physics of Lightning, 351-384, Academic Press,
London, 1977.
Pitman, G. R., Inertial Guidance, Wiley and Sons, Pub., New York, 1962.
Proctor, D. E., "A hyperbolic system for obtaining VHF radio pictures of
lightning," J. Geophys. Res., 76, 1478-1489, 1971.
Proctor, D. E., "VHF radio pictures of lightning," in H. Dolezalek and
R. Reiter (eds.), Electrical Processes in Atmospheres, 694-699, Dr.
Dietrich Steinkopff Verlag, Darmstadt, 1974a.
Proctor, D. E., "VHF radio pictures of lightning," CSIR Special Report,
TEL 118, Pretoria, South Africa, 1974b.
Proctor, D. E., "VHF radio pictures of lightning," CSIR Special Report,
TEL 119, Pretoria, South Africa, 1974c.
Proctor, D. E., "VHF radio pictures of lightning," CSIR Special Report,
TEL 120, Pretoria, South Africa, 1974d.
Proctor, D. E., "A radio study of lightning," Ph.D. Thesis, 574 pp.,
University of Witwatersrand, Johannesburg, South Africa, 1976.
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IBM Systems Journal, Vol. 14, 4, 385-406, 1975.
Roth, P. R., "Effective measurements using digital signal analysis,"
IEEE Spectrum, 62-70, 1971.
Rustan, P. L., M. A. Uman, D. G. Childers, W. H. Beasley and C. L. Lennon,
"Lightning properties for a flash at Kennedy Space Center via multiple
time series analysis," Submitted to Science, Summer, 1979.


2,17
8.9 msec after the first return stroke. During this interval the VHF
noise sources propagated upwards in the neighborhood of the previous
stepped leader-return stroke channel between the heights of 5.1 and 8
km at a velocity of 1.2 x .10^ m/sec. It appears that during this
interval either positive charges were raised or negative charges were
lowered from higher altitudes as the VHF sources moved upwards.
(5) The VHF radiation associated with the source of the second return
stroke started with an 8.1 msec J-change (Jl) or a new preliminary
breakdown (PB2). During this interval VHF noise sources propagated
downwards from a height of 14.2 to 10.5 km in a path 25 off vertical
at a velocity of 5.0 x 10"* m/sec. Using a point charge model we deter
mined that -1.8 Coulombs were lowered during this interval.
(6) Following Jl or PB2 a new stepped leader developed at about a height
of 10.5 km and propagated downwards at a velocity of 6.7 x 10J m/sec
striking the ground at a point about 1.4 km west and 0.9 km south of the
first stroke. From the path of the stepped leader and the leader-return
stroke field changes we estimated that -8.2 Coul were lowered by the
second return stroke. This result compares well with the -9.6 Coul
calculated by Krehbiel (private com). (7) The VHF radiation from the
dart leaders was detected prior to the last four return strokes. The
dart leader VHF radiation started with a pulse between 80 and 150 ysec
wide. The noise sources during dart leaders were located in the neigh
borhood of the previous J-change channel and in the region between the
last two J-change channels. (8) The VHF radiation during return strokes
was characterized by one or a succession of pulses between 10 and 100
ysec wide with the exception of the fourth return stroke which had no
detectable VHF radiation. The first return stroke had detectable VHF


Figure 5.36. Log-amplitude VHF radiation during the last solitary
pulse (K-change) in Figure 5.22.


Figure 5.82. Simultaneous record of the logarithmic-amplitude VHF radiation observed at 7 km,
and the electric field detected at 2.6, 7.6 and 13.7 km from the discharge.


283
z
t
*l2c-l + *2*t-2 +
. +

P t-p t
0lac-l
2at-2
. . a a
q t-q
(6.3)
Many test data show nonstationary behavior when models (6.1), (6.2),
or (6.3) are tested, but the data are stationary if a new series is found
which contains a higher order difference than the original series. Let
Wt = Vzt = zt zt-l = vdzt = ylzt (6-4)
where d is the number of differences in the original series. Similarly,
the first difference ARIMA model can be defined in a manner similar to
equation (6.3). That is
W = -,W + ... + cp W + a 0.a ,
t 1 t-1 Tp t-p t 1 t-1
... a 0
q t-q
(6.5)
The procedures used for the model estimate is the Box and Jenkins
(1976) approach. We used this approach for model, estimates as follows:
(1) Model identification. A total of 12 data records composed of
four sets of 5,000 samples each were selected from the noise level,
stepped leader, and J-change. For each of the four ground flashes we
selected a data record for the three identifiable processes. We deter
mined the autocorrelation and partial correlation of each set of data.
We used the Box and Jenkins (1976) selection criteria to determine the
stochastic model type (AR, MA, ARMA, or ARIMA) and order based on the
properties of the autocorrelation and partial autocorrelation functions
A model was chosen for each data record independent of the physical
process.


do not always involve the main channel. Some K-changes propagated in
channels which were not connected with the previous channels.
The velocity of the main channel in a cloud flash reported by
Proctor was 1.7 x 10^ m/sec. This value was obtained by finding the
velocity between centroids 1 msec apart and located along the channel.
The velocity determined in this manner during the propagation of the
main channel in a cloud flash seems to be associated with the P pulses.
A high velocity between 2.7 x 10^ and 3.0 x 10^ m/sec is associated with
Q noise trains.
From the five cloud flashes reported by Proctor (1976), four ex
tended near-horizontal while one was near-vertical. The vertical flash
extended between -11C and -52C (6.3 to 13.0 km MSL) while the horizon
tal flashes developed at temperatures of 0, -7, -10 and -21C. It is
worth noting that the mainly horizontal flashes extended over a height
of 5 km while the vertical flash extended over a height of 7 km. The
vertical flash was associated with upward propagation of negative charge.
The diameters of the concentrated VHF sources were between 100 and 600
meters. Even though some noise sources were located in a much wider
diameter, Proctor attributed the wide channel to multiple branching.
Additional information in ground flashes provided by Proctor (1976)
follows: (1) Dart leaders were characterized by one or more successions
of wide pulses (tens of microseconds) separated by low amplitude Q noise
trains. The VHF noise sources during the dart leader connected separate
regions that had been previously ionized, and were not located near the
dart leader path to ground. (2) There was no apparent time difference
(greater than 10 psec) between the occurrence of the electric field and
VHF for the first return stroke. However, in most cases the VHF waveform


5.1 The 165959 Flash
This flash is the most comprehensively studied single lightning
flash in the history of lightning research (Uman et al., 1978 and
Rustan et al., 1979).
The flash consisted of a three strokes to ground followed by an IC
discharge. The duration of the flash VHF radiation was 939 msec of
which the last 600 msec were part of the IC discharge. The locations
of the three charge regions for the three return strokes obtained from
measuring the return stroke electric field change at multiple ground-
based locations (Uman et al., 1978) correlate well with the VHF source
locations. Figure 5.1 shows the relationship between the VHF radiation
and the electric field for the entire discharge. Table 5.1 shows a
complete summary of the identified phases of the flash For each
phase we have provided the duration of the VHF radiation, the average
velocity of propagation of the noise sources (if applicable), and the
upper and lower location of the VHF noise sources. An error analysis
for the VHF noise source locations is given in Appendix B. Table B.l
shows a summary of the uncertainty in the determination of the locations
of the sources in this flash as a function of position. In the next
subsections we consider in detail what we learned from the study of
different phases of the flash, given in Table 5.1.
5.1.1 Preliminary Breakdown
Observation of the VHF records for one second prior to the first
stroke shows that the VHF radiation above the system noise level began
4.9 msec before the return stroke and continued until the return stroke.
The first 2.2 msec of the VHF pulses we identify with the "preliminary
breakdown," the final 2.7 msec with the stepped leader. The wideband


103
from the dart leader joins the bottom of the J1 change with the begin
ning of the preliminary breakdown as shown in Figure 5.10. Our calcu
lations of the locations of the VHF noise sources during the dart leader
are in agreement with the work of Brook and Kitagawa (1964) and Proctor
(1971), which suggested that most of the radiation during the dart
leader's trip to ground is from within the cloud rather than from the
dart leader channel. Comparing the location of the noise sources with
the correlated electric field and VHF radiation is not possible to
determine where the charge in motion during Jl entered the previous
ionized return stroke channel and descended to ground. In addition to
the BC channel, Figure 5.10 shows a continuous line from the preliminary
breakdown channel. The noise sources of the dart leader (shown as dots
in Figure 5.10) not only connected the two previous channels but also
extended horizontally over 1 km beyond the top of the preliminary
breakdown.
5.1.7 Second Return Stroke
The second return stroke lasted approximately 259 ysec in the VHF
record as shown in Figure 5.12. The four source locations identified
during the second return stroke were located within 1 km radius of the
highest cross-correlated source location of the preliminary breakdown.
These findings suggest that the preliminary breakdown has become part
of the active leader channel used by the consecutive strokes which
propagate in the defunct return stroke path to ground. No sources were
identified in the return stroke channel to ground.


NORTH (km)
Figure 5.81.
Two-dimensional views: (A)
elevation view, NS-height of
top view,
all the
EW-NS, (B) elevation view, EW-height, and
noise sources during the 180544 intracloud
(C)
discharge.


14
300 KHz the earth and the lower ionosphere create a quasi-waveguide;
between 300 KHz and 30 MHz reflections occur from the ionosphere;
above 30 MHz atmospherics penetrate the ionosphere. In the research
reported in this thesis, the atmospherics were recorded in the VHF
range (30 to 50 MHz) where at the close ranges considered there is no
appreciable ionospheric reflection.
2.3 Lightning Direction Finders
The distant electromagnetic radiation associated with lightning
is usually called spherics. Spherics have been used as lightning
direction finders in the VLF and VHF range. The standard method of
location of distant ground flashes in the VLF range uses cathode-ray
direction finders (CRDF). This method was originally developed by
Watson-Watt and Herd (1926). It consists of two or more direction finding
stations, each with two vertical loop antennas usually tuned to a VLF
frequency. The azimuth angle of the flash is usually determined by
displaying the two perpendicular antenna magnetic field outputs on the
perpendicular scope axes. Two or more stations can be used to determine
the location of the discharge from the intersection of the azimuth vectors.
For discharge distances less than 100 or 200 km from the stations, the
accuracy of this standard technique has been found to be poor. This is
caused by the fact that if return strokes are not vertical, the antennas
will be sensing not only the vertical magnetic field but also the
horizontal component. As much as 20 degrees error has been found by
Nishino et al. (1973) at a distance of 200 km from the discharge.
Uman et al. (1975) observed that even at 10 km the initial peak magnetic
fields occurs in the first 5 ysec and hence is due to the vertical
channel position near ground. VLF direction finders have been improved


of the T to W source .locations. The lowest detectable stepped leader
source was at a height of 3.4 km. It can be observed from the log-
amplitude VHF scale in Figure 5.64 that the radiation of the PB is
several orders of magnitude larger than that of the stepped leader.
In addition, the stepped leader VHF radiation decreases as it propagates
near ground. Therefore, it appears difficult to detect stepped leader
sources near ground with lower amplitude radiation and too many leader
sources active over a large volume. The stepped leader average velocity
ranged between 1.9 x 10^ and 4.3 x 10^ m/sec for heights between 5.9
and 3.4 1cm.
5.4.3 First Return Stroke
The first return stroke VHF radiation (Figure 5.64) lasted 500 ysec
The return stroke noise sources were located in the neighborhood of the
T, U, V, and W region in Figure 5.65(b). Using T (-3.9, 11.7, 5.8) in
Figure 5.65(b) as the point where the VHF noise changed characteristics
from the PB to stepped leader, and the technique described in Section
3.6, we.estimated that -20.5 Coul were lowered during the first stepped
leader return stroke process. We have correlated the VHF record and
its source locations with the New Mexico Institute of Mines and Technol
ogy (NMIMT) measured multiple electric field records and calculated
charge locations. Table 5.6(a) shows the value of the source charge and
its location for the first, second, fourth, and fifth return stroke as
provided by Krehbiel (private com) using the technique of Krehbiel et al
(1979). Table 5.6(b) shows the value of the source charge and its loca
tion for each of the stepped leader-return stroke processes obtained by
using the techniques in Section 3.6. The first stepped leader-return


APPENDIX C
COMPUTER ALGORITHM TO DETERMINE VHF SOURCE LOCATIONS
FROM THE DIFFERENCE IN THE TIME OF ARRIVAL OF VHF RADIATION DATA
In this appendix we give the Fortran computer program code used
to determine the three dimensional source locations based on the
measured difference in the time of arrival of VHF radiation. The input
of the program is a digital tape with four VHF series digitized at
4.352 MHz. There are two types of outputs: (1) a printout of all the
three dimensional source locations and their relative time of occur
rence, and (2) a digital tape where the same printout information is
stored for future access. This appendix also contains on page 355 an
example of a computer printout of the output. This output consists of
the source location for successive 376 Usee cross-correlated time
intervals and the relative time and location of each one of the
individual sources.
330


charge magnitude and locations, calculated for us by NMIMT, were corre
lated with our VHF source locations.
Previous work on three-dimensional "channel structure" during
lightning flashes was performed by Proctor in South Africa, who
pioneered the technique of VHF source locations. Proctor's determina
tion of DTOA was done manually by pulse shape identification on 253 MHz
signals. The three-dimensional source locations presented in this
thesis for the different phases of lightning discharges were obtained
using a computerized technique which allows a large amount of data to
be analyzed quickly.
The data were recorded with a wideband VHF receiver having a band
pass filter of 30-50 MHz and a logarithm envelope detector. The
detected signals from three of the stations were transmitted to the
fourth station where all were recorded on four tape channels having a
bandwidth of 400 Hz to 1.5 MHz. The analog tapes were digitized at
3 4
4.35 MHz, a sample every 229 nanoseconds. Between 20 x 10 and 25 x 10
pulses per flash were recorded during active VHF radiation. A newly
developed computer algorithm employing cross-correlation and pattern
recognition was written to determine the DTOA between the individual
pulses. Once the DTOA's were calculated, we used a three-dimensional
hyperbolic position measuring system to determine the source locations.
The significance of this research is the following: (1) We develop
an important new tool for lightning research: a computer program which,
using digital tape data from four VHF stat Lons, can determine source
locations every 7 to 10 microseconds. An average of about 20,000 loca
tions was found for each one of the studied flashes. (2) We derive
properties of the lightning flashes studied. Some of these results
vii


200
EAST (km)
Figure 5.53. Three-dimensional view of the cross-correlated noise
sources during J3, and the dart leaders. Source locations
of the previous J2 channel which continue to radiate
during J3 are also shown. The location of the fourth
stroke spherical charge center is shown as Q4.


noise:
LEVEL
k-PB-4
2. CO
4.00
6.00
8.GO
10.00
12.00
14.00
16.00
TIME IN MILLISECONDS
Figure 5.64.
Log-amplitude VHF radiation at the beginning of the 182356 flash. PB is
the preliminary breakdown, SL is the stepped leader, RS in the first return
stroke, FR is the activity following the first return stroke which contains
pulses 1 to 5, and J1 is the first J-change.
227


4
5.5 The 180644 Flash
The work reported in this thesis includes three IC flashes. The
first of these IC flashes was studied in Section 5.1 because it followed
the 165959 flash. The other two IC flashes are discussed in this section
and in Section 5.6.
The first lightning discharge during the thunderstorm on the 8th
August 1977 happened at 180644 UT. This lightning discharge was an
intracloud flash and occurred 56 sec prior to the first cloud-to-ground
flash at 180710, previously described in Section 5.2.
Figure 5.78 shows simultaneous records of the logarithmic-amplitude
VHF radiation and the electric field reading in four different stations
located 4, 15, 17.5, and 18.5 km from the discharge. The fact that the
electric field reading at 4 and 15 km showed a positive electric field
change while the stations at 17.5 and 18.5 km showed a negative field
change indicated that an upper positive and a lower negative polarity
charge center were supporting the discharge (equation (3.10)). The
electric field reversal with distance, the fact that the field shows no
evidence of leader-return stroke sequence, and the locations of the VHF
sources in the cloud combine to indicate that the 181416 flash was
indeed an intracloud discharge.
The flash lasted 360 msec and can be described as being composed
of three different phases on the basis of the relationship between the
electric field and the VHF radiation. This pattern is similar to the
one described by Kitagawa and Brook (1960) who classified the intracloud
discharge into an initial, a very active, and junction phase, and
similar to the 165959 IC flash. These events are shown in Figure 5.78
and lasted 75, 185, and 260 msec, respectively.


291
7.1.1 Preliminary Breakdown
At the beginning of the CG flashes we detected VHF noise levels
about 20 times larger than during the stepped leader. Based on the
difference of the VHF noise level we chose to name this time interval
"preliminary breakdown" (PB). The VHF noise for the four CG flashes
during the PB is shown in Figures 5.5, 5.23, 5.41, and 5.64. The dura
tion of the PB's varied between 1.9 and 2.2 msec. The VHF noise was
characterized by high frequency pulses ranging in width from 1 to 150
ysec superimposed on a lower frequency envelope. Three of the PB's
ended with a pulse 300 to 700 ysec wide (Figures 5.23, 5.41, and 5.64).
We suspect that the end portion of these wide pulses are oscillations
caused by the tape recorder's sharp low frequency cutoff.
We studied the progressing sequence of the VHF noise source loca
tions during the first few hundred microseconds of the PB, which corre
sponds to the beginning of the CG discharges. We labeled the progressing
sequence of these sources and the time of their occurrence in Figures 5.4,
5.25, 5.42, and 5.65. The initial paths formed by the VHF sources for
the four studied flashes were: (1) path length of 4.8 km at 28 off
vertical between a height of 9.9 and 6.5 km, (2) path length of 12 km at
55 off vertical between a height of 9.8 and 4.1 km, (3) path length of
7.8 km at 22 off vertical between a height of 11 and 4.9 km, and (4)
path length of 7.5 km at 26 off vertical between a height of 9.9 and
4.0 km. The PB sources initially formed a cylinder of about 500 meters.
During the period of time that these cylinders were formed there was no
correlated electric field change indicating no. significant charge trans
fer. The timing sequence of the beginning of the VHF sources is random
in the first two flashes but appears to follow an ascending then


5.5.1 The Initial Phase
267
The flash started with an initial phase characterized by a smooth
variation of the electric field and a VIIF pulse rate of one every 20
to 50 ysec. Figure 5.79 shows the VHF noise during the first 8.5 msec
of the intracloud discharge. The flash started with a 100 ysec wide
pulse, similar to the pulse that starts the PB in a cloud-to-ground
discharge. However, the lower amplitude, higher frequency VHF radiation
following the PB in a CG discharge and characteristic of the stepped
leader did not occur.
Figure 5.80 shows the location of the cross-correlated VHF noise
sources, 94 ysec intervals, during the first msec of the intracloud
discharge. Most of the VHF source activity is located between the
heights of 9.2 and 10.5 km. During the first 13 msec, a channel is
formed between the heights of 9.2 and 14.5 km in a path 40 off verti
cal. As we can see from comparing Figure 5.80 with Figure 5.81, these
initial sources become the center of the flash. We also studied the
progressing sequence of the VHF noise sources in Figure 5.80. The
most active region was at the lower altitude, 9.2 to 10.5 km, but we
could not determine the direction of propagation of the VHF sources.
We continued this analysis throughout the entire 75 msec of the initial
phase, and the only conclusion that we could derive was that at the
beginning most of the. sources were concentrated at the lower altitude
of the slanted channel while at the end of the initial phase there was
more activity at the higher altitude. In addition, the original VHF
source region became wider throughout the flash.


281


Figure 5,5.
Logarithmic-amplitude VHF radiation at the beginning of the 165959 cloud-to-ground flash.


60
only if the pulse that produced the peak has similar characteristics
in the central and on each of the remote stations.
The pulse model used to determine whether any of the pulses from
the considered peaks in the remote stations correspond to the same pulse
in the central station is a) values of ascending and descending slopes,
b) number of reversals in the ascending and descending slopes, and c.)
the total area under the pulse. Figure 4.2 illustrates a typical pulse
and how we selected the additional pulse properties to complete the
pattern recognition technique.
Using the guidelines of identifiable characteristics, we selected
15 sample points for pulse recognition, centering the individual peak
in the middle of the pulse. The description of the individual pattern
recognition features mentioned in a, b, and c were as follows: a) the
ascending and descending slopes (AS and DS) were calculated by making
straight line approximations between the peak and the value of the ex
treme of the pulse. However if the pulse increases in magnitude in
three consecutive samples before arriving to the pulse boundary (7th
sample), the slope was arbitrarily determined between the peak and the
5th data sample. b) The number of reversals is determined by counting
the number of times that there is a change of slope and dividing this
number by 2. In Figure 4.2 there are two changes of slopes to the
right of the peak (reversal to the right, RR), corresponding to one
reversal and there are four changes of slopes to the left (reversal
to the left, RL), which correspond to two reversals. c) Since all the
remote stations' data were normalized with respect to the central
station, we also calculated the area under the curve as a measurement
of the narrowness of the pulse (NAR). The tolerances allowed


71
propagation is calculated only for those events on which consecutive
cross-correlated locations were in the neighborhood of the previous
ones, and a path was formed by displaying the noise sources in the
desired process (stepped leader and some PB, K- and J-changes).
2) Determine the ^ ^ velocities using all the cross-correlated source
locations. 3) Test if these velocities were grouped at any specific
value. A velocity value is used only if a certain value or range of
value repeats for at least 50% of the test data (n(n-l)/4). For an
additional check we determined velocities using all the individual
source locations for three stepped leaders, but the procedure was quite
a bit longer and resulted in the same velocity value.
The results showed that we could determine the velocities of about
50 or 60% of the events that met conditions 1), 2), and 3) simply by
their starting and ending points. In addition, about 15% of the events
failed condition 3) and no velocity of propagation could be determined
consistently. Throughout this thesis the only velocity values found
are those that met the three conditions above.


216
in Appendix B. The flash extended east and north from the -3 to 7 km
EW, and from 7 to 17 km NS. It appears that every event in the flash
developed further toward the north and the east. The flash extended
3
throughout a volume of 450 km during a 416 msec interval.
5.3.18 Concluding Remarks About This Flash
Some of the new information about the flash derived from the VHF
noise source, its source locations, and the correlated electric field
records follows: (1) The flash lasted 418 msec and consisted of six
strokes to ground followed by a continuing current. The flash had two
stepped leaders which followed different channels to ground. (2) The
flash started with a 1.9 msec preliminary breakdown which was located
near and inside the charge source of the stepped leader. All of the
VHF noise sources for the PB were located within a cylinder of 2.8 km
vertical length and a .5 km horizontal radius. From the electric field
records we find that detectable charge motion was only associated with
the final 1.0 msec of the 1.9 msec preliminary breakdown. The average
velocity of propagation of the final millisecond of the PB was 9.2 x 10^
m/sec. (3) A 5.9 msec stepped leader followed the preliminary breakdown.
The stepped leader path to ground extended 1 km horizontally, was near
vertical, and started within .6 km horizontal distance of the 150-meter
weather tower. The stepped leader started at a height of 6.7 km and
5
propagated downwards at an average velocity of 9.2 x 10 m/sec. From
the path of the first stepped leader VHF noise sources and the leader-
return stroke field changes we estimated that -17 Coulombs were lowered
by the first return stroke. This result is comparable to the -24
Coulombs estimated by Krehbiel (private com) using the technique by
Krehbiel et al. (1979). (4) Strong VHF radiation was detected for


5.4.5 The Jl Change
The Jl change lasted 13.2 msec and followed immediately after the
FR interval in the VHF record. The Jl change was characterized by a
higher pulse rate and shorter pulse width than during the FR interval.
Throughout Jl the VHF noise amplitude decreased and the pulse rate
increased. During the Jl process the cross-correlated VHF noise sources
were located between -3 and -4 km EW, 9 and 12 km NS, and 6 to 7.5 km
in altitude.
5.4.6 The Second Stepped Leader
The beginning of the second stepped leader was selected as a point
in the transition region when the VHF radiation changed characteristics
from the slower pulse rate with higher amplitude pulses from Jl to the
shorter pulses with a faster rate during the stepped leader. As soon as
stepped leader variation in amplitude was detected in the VHF record,
the noise sources showed a vertical propagation. Correlated electric
field records for eight ground stations during the interstroke interval
showed no significant slope change as would be expected at the occurrence
of a stepped leader. However, other characteristics of stepped leaders
were observed: decrease in the VHF magnitude of the noise, an increase
in the pulse rate, and some downward propagation in the VHF sources.
Using these criteria, we suggest that the second stepped leader lasted
14.2 msec.
Figures 5.67(a) and 5.67(b) show three-dimensional views of all the
sources and of the cross-correlated sources, respectively, during the
second stepped leader. The cross-correlated VHF sources propagated
between the heights of 6.5 and 3.4 km. The stepped leader cross-corre
lated sources in Figure 5.67(b) were located in two separate regions.


propagated at an average velocity of 1.4 x 10^ m/sec connected the
bottom end of the first J-change sources with the charge region of the
previous stepped leader. (3) Continuous VHF radiation was detected in
the final 35% of the time between the second and third return strokes.
During this part of the second J-change, radiation sources propagated
both upwards and downwards for the first 15 msec, then propagated down
ward 4.7 km for 25 msec at an average velocity of 2.0 x 10^ m/sec.
The negative charge lowered during this portion of the J-change was
3.41.8 Coulombs. (4) Following the second J-change, a new stepped
leader propagated from 7 km, the bottom of the J-change VHF source
locations, downward to a height of 3.2 km, where it joined the previous
stepped leader channel, and, presumably, return stroke channel. The
stepped leader average velocity was 4.5 x 10^ m/sec. (5) During the
intracloud discharge following the third return stroke, sources of VHF
radiation covered a path from near the source charges of the return
strokes to about 14.0 km, near the cloud top. The VHF noise sources
traversed the same path many times, widening the main channel and
extending the ends. The VHF radiation during the IC discharge displayed
the three phases described in the literature for IC discharges which
were not associated with a ground discharge.


22
Proctor has estimated the amount of charge, the charge density, and
the current flow during the initial phase of a cloud flash. VHF source
locations during this phase propagated upwards in a path about 25 degrees
off vertical. The technique used consists of determining the centroid
of VHF locations every millisecond, and finding the amount of charge for
the given field change. The charge density and the current are determined
at each millisecond interval taking into consideration the field generated
by the two point charges and the leader. Using this technique, the
following parameters were determined: a) 10 Coulombs for the inital
phase of the IC (fast field change), b) 1 Coul/km charge density, and
c) a current of .2 kA every 3 msec. Since only one field meter was used
to determine the electric field and a number of assumptions had to be
used about the charge structure, these results are questionable.
The most recent work published by Proctor is his Ph.D. thesis
(Proctor, 1976). Next we will present a summary of our view of the new
ideas presented in his thesis.
Proctor classifies the VHF noise (253 MHz, 5 MHz bandwidth) pulses
in three groups: P pulses, Q noise trains, and S pulses. The P pulses
are nearly rectangular in shape with an average pulse width of 1 psec.
By comparing the same pulses with wider bandwidth (10 MHz), Proctor
claimed that P pulses were a rapid succession of very short spikes which
had been smeared into one pulse by the limited receiver bandwidth. Dur
ing a cloud flash these pulses appear at a rate of about 4.7 for groups
of 310 psec intervals. The time between groups was about 1.8 msec. The
Q noise trains consist of rapid successions of spikes. They are common
to all flashes and are more frequent in the junction phase of a cloud
flash. They appear to be related to very rapid movement of charges and


dZ
1
Z
(B.3)
316
3r
o
o 3u.
i
i
The X, Y, and Z measurements are a function of the three time delays
represented in the u.'s (u. = cT. in equation (A.9)). The u.'s are indepen-
iii i.
dent with RMS error du.. We define the RMS source location errors as
i
dX
RMS
3
3x
2
r i
l
3u.
1 y
du.
=1
1 J
dY
RMS
3
v
3Y
2
' s
i
du.
i=l
du .
1/
dZ
3 '3Z ^
RMS
I
i1
3u.
du.
(B.4)
A computer program was developed to determine the error associated
with the channel locations. Two classes of errors must be considered:
(1) the quantization error, and (2) the calibration error.
The quantization error is due to the discrete sample interval used
in digitizing the data. This sample interval limits the measurement of
the difference in the time of arrival (DTOA) to 0.23 microseconds
(du_j, = du^ = du^) The raw-data analog tape input had a frequency
response between 400 Hz and 1.5 MHz, flat response in the medium range,
3 dJ5 down at the end points, and 20 dB/decade beyond the ends. In order
to accurately reproduce this spectrum with sampling, the tapes were
digitized at 4.352 MHz, that is, sample intervals of 0.23 microseconds.
Hence the original frequency response of the data determines the quanti
zation error.


Figure 5.S5. Two-dimensional projections: (a) EW-liF, (b) EW-height, and (c) NS-height of all the
cross-correlated VHF sources, 94 psec intervals, for the IC discharge.


Table 5.5 cont.
Time
Coordinates (km)
Start
Duration
UPPER
LOWER
Velocity
(msec)
Event
(msec)
X
y
z
X
y
z
m/sec
97.0
J3 Change
21.1
-5.6
9.4
9.6
-4.7
8.2
5.8
118.1
5th Stepped Leader
30.1
-4.8
8.8
9.6
-3.3
11.6
3.1
5.1 x 10"* m/sec
148.2
5th Return Stroke
.45
148.6
Quiet Period of J4
3.7
152.3
J4 Change
26.8
0.9
11.2
12.8
0.6
10.2
5.2
179.1
Dart Leader
1.5
-5.3
7.8
8.8
-4.9
7.1
7.7
180.6
6th Return Stroke
.4
-5.0
8.2
7.8
-4.9
8.3
7.1
181.0
Quiet Period of J5
8.5
189.5
J5 Change
55.0
0.7
12.5
12.8
-4.0
7.6
5.3
1.6 x 10^ m/sec
244.5
Stepped Leader
30.6
-5.2
8.3
7.7
-4.3
9.2
3.0
2.9 x 10^ m/sec
275.1
7th Return Stroke
.38
275.5
J6 Change
60.3
-1.2
11.1
13.7
0.7
12.1
5.2
335.8
Dart Leader
1.7
337.5
8th Return Stroke
.27
337.7
Discrete Activity after
8th Return Stroke
168.7
0.2
15.1
13.2
-3.8
7.9
5.1
225


n n n n n nn
21 J UN E 1979
4 6 WR ITC( 6,4 7 ) XXM ( I) YXM ( I ),XYM( I),YYM(I ) ,XPM{I) YPM(I)
* YPPM(I)
** GETTING THE SCALES LUWER POUND *
47 FORMAT(7F15.7)
XPE(N1f1)=0.0
XPD(Ml+2)=1.0
YPPBIN t + 1 ) = 0.0
YPPU( N l -2 )= 1 .0
XP T(N2 + 1 ) =0.0
XPT Y P PT(N 2+1 )=0.0
YPPT(N 2 + 2 )=1.0
XPE ( N1 + 1 )=0.0
X P Q(Nl+2) =1.0
YPQ( N 1 M ) =0. 0
YPE(Nl*2)=1.0
XP T(N2 + 1 )=0.0
XPTN2 +2)=1 .0
YPT(N2+1)=0.0
YPT CALL LINEWT(-2)
PROJECTING THE SOURCE LOCATIONS EITHER ON THE TUP *
** PLANE(Nl) OR ON THE BOTTOM PLANEIN2). **
C ALL LIME(XPB YPPUN1,1.-1.2,0.1)
CALL L INE(XPT,YPPT,N2, 1 ,-l .2,0 1 )
CALL LINE WTI-1 )
CALL L INE(XPC.YPB,N1 t, 1 10,0.1)
CALL LINE(XPT,YPT,N2,1 .- l 10.0.1 )
CALL L INF WT( 1 )
DU 24 1=1,Nl
CALL PLOT(XPBII),YPD(1).3)
CALL PLOTIXPBI I) ,YPPB( I ) ,2)
24 CONTINUE
DO 32 1=1,N2
CALL PLOT (XPT( I ) ,YPT( I ) ,3)
CALL PLOT (XPT ( I ) ,YPPTI I ) ,2 )
32 CONTINUE
DO 30 1=1 N1
CALL PLOT(XX(I),YXO(I),3)
CALL PLOT(XPB( I ) ,YPO( l) ,2)
CALL PLOT (XYI3 ( 1 ) YYB( I ) 2)
30 CONTINUE
DO 34 1=1,N2
CALL PLOT(XXT(I),YXT(I),3)
CALL PLOT(XPT( I ) YPT< I) ,2 )
CALL PLOT(XYT(I),YYT(I),2)
34 CONTINUE
CALL PLOT(0.0.0.0,999)
STOP


167
obtaining satisfactory results. Also looking at the number of computa
tions involved, there are fewer computations in this technique than in
other frequency techniques such as the phase measurement which will be
described in the next section.
E.2. Measurement of Time Delay by Measuring the Phase of the Frequency
Response Function
We can estimate the time difference by measuring the phase of the
frequency response function. Since and y^ can be approximated by a
linear system, we have
00
y l Vn-k R=-
where h^ is the impulse response between and y Using the two point
measuring problem, we get
n
= x
, + r
-A n
(E.8)
Y (f) = exp (-j 2irf A)X (f) + R(f) (E.9)
averaging different ensembles, dividing, and calculating the phase, we
obtain
Y(f)/X(f) = H (f) = Phase (2tt A) (E.10)
xy
Therefore the time delay A is determined as
A = 2irf A/2fir (E.ll)
The question still remains as to what frequency to use in the compu
tation of (E.ll). This can be solved by using the frequency that


Figure 5.28.
Three-dimensional view of the cross-correlated VHF noise sources during the first
J-change process. Point P represents the location of the beginning of the K-change
that initiated the J-change. The arrows show the regular progressing sequence of
propagation of the VHF noise sources during the K-change. Point A is the start of
the following stepped leader shown in Figure 5.29.


82
the top and the back edge of the Ql volume and generally propagated in
a downward direction. The preliminary breakdown started at a height of
7.1 km (point A at about -18C free air temperature) and propagated a
distance of 2.3 km to a height of 5.1 km (point B at about -6C) before
the first detectable slow change of the electric field associated with
the stepped leader occurred. The cross-correlated source locations
during the preliminary breakdown interval are very much in a straight
line and exhibit an average velocity of propagation of about 1.0 x 10^
m/sec.
In addition to determining the cross-correlated and all the individ
ual source locations (Figure 5.4(b)) using the computer algorithm des
cribed in Chapter IV, we determined the individual source locations
manually during the first 537 psec of the preliminary breakdown. This
task was performed to identify any propagation of the sources on a time
scale of every 2 or 3 psec instead of every 7 or 10 psec, the limit
using the computer algorithm. These results are shown in the three-
dimensional graph in Figure 5.4. The sources A through RR are time tagged
and shown in alphabetical order A -* Z, AA -> RR. This initial stage of the
PB extends 1.5 km horizontally and 3.6 km vertically. The sequence of the
VHF sources shows that the activity started at about 9 km and there was
propagation initially upwards and downwards.
5.1.2 First Stepped Leader
The VHF radiation during the. stepped leader consists of a low
amplitude high frequency pulse train, a characteristic radiation
observed during the first leader and again prior to the third stroke,
but not in any other part of the flash. The stepped leader VHF is


LOA
5.1.8 Solitary Pulses During the Quiet Period of J2
Three solitary VHF pulses (SP's) occurred during the 84 msec quiet
period after the second return stroke (Figure 5.1). The duration of
the SP's in the timing sequence they appear was 0.78, 0.95, and 0.57 msec.
The SP's VHF amplitude and frequency content are similar to the return
stroke. Figures 5.13(a), 5.13(b), and 5.13(c) show the VHF noise for
the three SP's during the quiet portion of J2.
The SP's propagated upwards for 2 to 5 km in a near-vertical path
from tlie previous ionized region of the negative charge center on tlie
bottom of J1 and the top of the preliminary breakdown. The velocity
of propagation of the J2 SP's is between 1 and 4 x 10^ m/sec. All
three SP's started within 2 km from each other but consecutive SP's
extended over a larger volume of space. Figures 5.14(a), 5.14(b), and
5.14(c) show cross-correlated source locations, 94 ysec intervals, for
the three SP's. Even though the first source location always coincides
with the lowest source of the SP's, sources within a few hundred micro
seconds of the beginning of the SP's were located at the top of the
channel. In the last two SP's there were detected noise sources
occurring near the end of the SP's which locations occurred in the path
between the lowest and highest sources. These three SP's did not have
detectable correlated electric field changes and therefore the charge
transferred by this type of pulses must be relatively small. It is
tempting to associate the SP's with K-changes (liman, 1969), thought to
be in-cloud upward-moving mini-return strokes initiated when charge of
one sign moving downward encounters charge of opposite sign. The
absence of VHF radiation preceding the upward moving SP's and absence
of appreciable rapid electric field change associated with the SP's is
puzzling.


Table B.4. Error Analysis for the Locations in the 182357 Flash. The locations are arranged in
ascending order in z.
Source Locations
Quantization RMS
Calibration
RMS
Total RMS Error
(Meters)
Error (Meters)
Errors (Meters)
(Meters)
X
y
z
%
dyQ
dzQ
dx
C
dyc
dz
c
dx
t
dyt
dz
t
-487
5915
2219
63
99
267
62
192
630
89
216
685
-3655
12638
3332
124
239
821
144
292
1753
191
378
1936
-3940
5458
4421
76
115
243
85
206
525
114
236
579
-2933
13562
4738
123
261
667
137
310
1387
184
406
1539
-3342
12171
5050
120
225
532
133
283
1127
179
362
1247
-2986
11851
5080
112
214
493
122
275
1044
166
348
1155
-5975
9194
5144
135
187
507
180
257
1067
225
318
1182
-4718
7742
5808
106
151
326
127
233
687
166
278
761
-935
10823
6672
90
178
330
86
249
673
124
307
750
-3831
11237
6964
126
212
408
141
275
849
189
348
942
-4560
8509
7199
116
166
323
136
244
667
179
295
741
-4415
11139
7414
136
218
422
159
281
870
210
356
967
-1256
11053
7701
97
189
328
91
257
660
134
320
737
-5393
9276
7862
139
189
387
172
261
785
221
322
876
-2819
12412
8432
125
237
409
130
296
824
181
380
920
-7855
9353
8880
197
221
560
279
288
1097
342
363
1232
-551
7582
9210
136
165
342
169
247
668
217
297
750
-2262
12857
9546
124
249
410
124
308
807
176
397
906
-137
12522
9764
99
226
379
91
289
719
135
367
813
-3225
13322
10309
146
275
451
155
333
884
213
432
993
-9196
10455
11336
261
271
701
376
336
1332
458
432
1505
582
14293
12192
105
288
467
98
354
850
144
457
970
Average error for loca
tions in this flash.
125
208
444
145
276
905
193
346
1008
329


are: a) From observing the initial lightning VHF noise we can determine
whether a flash will become a cloud-to-ground or an intracloud discharge,
b) Cloud-to-ground flashes were initiated by a process we name preli
minary breakdown. The VHF sources during the preliminary breakdown
formed an inclined cylinder 5 to 12 km long and about 500 meter radius
between a height of 4 and 10 km. c) The VHF radiation of stepped
leaders and return strokes during cloud-to-ground flashes have unique
characteristics which can be used to identify these events by studying
the VHF noise alone. The stepped leader has the lowest level of
radiation of any process in the flash, but it radiates along the whole
path from the charge center to ground. d) Dart leaders do not emit VHF
radiation along their paths to ground, but rather in the neighborhood
of the previous J-changes. e) The paths of the VHF sources during
J-changes were inclined 25, 35, 45, and 55 off vertical.. The path
of the VHF sources during J-changes was well defined after the first
few strokes of a cloud-to-ground flash, but the path became less
organized as the stroke order increased. The first J-change of all the
ground flashes propagated downward toward the previous charge center
lowering negative charge.
viii


< 5
(b)


other stepped leaders. The stepped leader velocities were: 1.9 to 4.3
x 106; 2.6 x 105, 2.3 x 105, 2.9 x 105, 5.1 x 105; and 1.6 to 2.9 x 105
m/sec, respectively. The first stepped leader in this flash is shorter
in duration and propagated an order of magnitude faster than the subse
quent stepped leaders. The charge lowered by each one of the stepped
leaders was calculated by using a point charge model. We found that
-20.5, -8.2, -14.2, -3.6, -16.2, and -24.1 Coul were lowered by stepped
leader-return stroke processes. That is a total charge of about -86
Coul, considering only six of the eight return strokes. (4) The VHF
sources corresponding to the VHF radiation in the first 7.1 msec after
the first return stroke were located in a region above the previous
stepped leader-return stroke channel. By studying the VHF noise sources
of the individual VHF pulses during this interval and the correlated
electric field change, we conclude that either -4.5 Coul were lowered
into the top of the previous return stroke channel from a region at the
higher altitudes, or that 4.5 Coul were raised in the cloud from the
top of the previous return stroke. (5) All but one of the subsequent
stepped leaders and the dart leaders were preceded by J-change processes.
The exception is between the third and fourth return strokes because
sources from both the fourth stepped leader and higher location in the
cloud are detected. The VHF J-change process durations are: Jl, 13.2
msec (preceding the second*stepped leader); J2, 7.2 msec (preceding the
third stepped leader); J3, 21.1 msec (preceding the fifth stepped
leader); J4, 26.8 msec (preceding the first dart leader); J5, 55.0 msec
(preceding the sixth stepped leader); and J6, 60.3 msec (preceding the
second dart leader). Two active regions about 4 km apart were detected,
a northern and a southern region. The Jl noise sources were concentrated


signal, the time difference between different events in the same flash
is only limited to a maximum of two or three microseconds due to tape
stretching. This procedure of time conversion allows us to read
accurately the original time-of-the-day with an absolute resolution of
about 100 ysec.
The twelve seconds for the six selected lightning flashes were
expanded to 12 x 512 = 6144 seconds prior to digitization. The
6144 second data were digitized at 4.352 MHz for a total of 52.244 x 10^
sample points per channel or 208.9 x 10^ total samples for the four
channels. The digitized data were recorded using 2400 feet, 7 track,
800 bpi, digital tapes. Approximately 1.638 x 10 samples per channel
can be stored on a 7 track tape. Therefore about 52.244/1.638 = 32 tapes
were needed for processing.
The tapes containing the calibration pulses were processed in a
manner similar to the one previously described for the lightning data.
Two differences were noted: 1) there was no need to convert timing
information, and 2) the digitization rate was increased to 8 MHz, a
sample every 115 nanoseconds. Appendix B shows the uncertainties in
the three-dimensional locations due to the calibration error.
3.4 Electric Field Meters
The waveforms recorded by the electric field measuring systems of
the University of Florida (U of F) and New Mexico institute of Mines and
Technology (NMIMT) wore used for correlation with the radiation field.
The electric field measuring systems used by U of F were similar to that
described by Fisher and Uman (1972) and later by Krider and his co-workers
(Krider et al., 1975, 1977). The correlated waveforms from the U of F
electric field system for 1976 consisted of an FM channel with a frequency


and pattern recognition techniques. On the basis of Sections 4.2.2(1)
and (2), we decided to use cross-correlation functions with sample
intervals of 94 or 376 ysec, which correspond to either one or four
blocks of digital data, to determine the time delay of the envelope
signal. To comply with property 4.2.2(3), we smoothed the data before
the calculation of the time delays. The smoothing was performed by
using moving averages of 16 data samples across the cross-correlated
interval. The peaks of the cross-correlation functions were used to
determine the cross-correlated time delays and the corresponding loca
tions. The cross-correlation functions arc weighted toward the loca
tions of the envelope pulses in the sample interval. Once the cross
correlation DTOA's are known, the computer uses a pattern recognition
scheme to identify the DTOA between individual events in the envelope-
detected signal. A search over a 3.7 ysec interval around the cross-
correlated DTOA's is used. This time interval was chosen to comply with
the properties of the time-series described in Section 4.2.2(2). Next
we present a description of the cross-correlation and pattern recogni
tion techniques.
4.3.1 The Cross-Correlation Function
The cross-correlation technique we use has been applied in a variety
of fields, e.g., statistical theory of communication (Lee, 1960), geo
physics (Enochson, 1973), biomedical engineering (French and Holden, 1977),
rad a r d v t e c lion (S ko 1 n :i k, .1962).
Let x and y be two time-series. In our application y can be the
central station data while the x^ can represent any of the remote sta
tions. The discrete cross-correlation function between x and y can be
n 'n
defined as


ALTITUDE (km)
O O
o o
65?


206
beginning of Figure 5.56. The beginning of the dart leader record prior
to the fifth return stroke in Figure 5.56 is almost identical to the
beginning of the dart leader record prior to the fourth return stroke
in Figure 5.54. However, the fifth return stroke was characterized by
a sequence of large pulses with a width between 3 and 15 psec. The
pulse 40 to 100 psec wide that usually characterizes the return stroke
can be barely observed in the envelope of the VHF radiation.
The cross-correlated locations of three dart leader sources, 94
psec intervals, are shown as circles in Figure 5.55. The dart leader
sources are located near the defunct J3 channel. From a plot of the
cross-correlated locations in Figure 5.55, we cannot see if the dart
leader joins the J3 and J4 regions. However, a plot of all the dart
leader sources shows that VHF radiation was emitted from 1 km west to
1.7 km east of J3, which is the location of the J4 channel. We conclude
that radiation from the dart leader joined J3 and J4. No source loca
tions were identified with the fifth return stroke. The few isolated
VHF return stroke pulses in Figure 5.56 showed varied characteristics
in the different stations making impossible the identification of its
source locations.
5.3.14 Fifth J-Change (J5)
The VHF radiation of the fifth J-change started after a quiet
period of 7 msec in which no VHF sources were detected. As shown in
Table 5.3 this is the longest of all the quiet periods that followed
the return strokes. Figure 5.57 shows the active VHF noise sources,
376 psec intervals, during the 19.3 msec of the fifth J-change.
Figure 5.57 also shows the location of the spherical charge center of
the. sixth return stroke (Q6) The sources were located over a volume


218
radiation in the location of the previous stepped leader and prelimi
nary breakdown. However, VHF noise sources for subsequent return
strokes were located near the top of the previous J-change channel.
(9) The VHF radiation associated with the J-change (J2 to J5) processes
was detected during the last 90% of the time between the last four
return strokes. The VHF noise sources during the J2 process formed a 1
km radius cylinder between the heights of 12.7 and 5.8 km in a path 32
off vertical. Each subsequent J-change process (J3 to J5) was located
1 to 2 km further eastward, was 1 to 2 km longer, and was parallel to
the previous J-change channel. In addition, subsequent J-changes had
a less organized channel formation. Since the VHF noise sources during
the last J-change did not form an organized channel, this might be an
indication that no sufficient charge can be made available for subse
quent return strokes. (10) Continuous VHF radiation was detected during
the first 85 msec of the continuing current interval. During this
initial 23 msec the VHF noise sources formed a 14 km channel eastward
and parallel to the previous J-changes. The channel extended to a
height of 15 km. In the following 55 msec of the continuous VHF radia
tion of the first 85 msec, the VHF noise sources widened the 14 km
channel. During the last 138 msec of the continuing current interval
isolated SP's channels propagated downward merging into the main CC
channel. The longest SP during the CC lasted 11.5 msec and propagated
downward between the heights of 11.8 and 2.8 km in a path 20 off
vertical at a velocity of 6.2 x 10^ m/sec. The remaining SP's also
propagated downwards from the 10 to 14 km of altitude until they joined
the main 14 km channel. Since the lowest part of the CC channel was
located in the neighborhood of the previous leader path to ground, it
appears that the CC interval lowered negative charge to ground. This


Figure 5.37. Three-dimensional view of the cross-correlated VHF noise sources during the last
SP (K-change). The letters A through Z show the location of the progressing
sequence of the VHF noise sources.


313
*
Let
2 2 2
d = X. + Y. (A. 6)
ill
and
vi-i'L2 i2) (A-7>
Equation (A.5) becomes
XX. + YY. u.r = V. (A.8)
The time difference between a signal arriving at the central
and a remote is given by
u. =
i
cT.
i
(A. 9)
Since is known from the measurement T^, equation (A.8) represents
three equations with three unknowns (X,Y,rQ) which can be solved for
the unknowns. With this solution Z is calculated as
(A.10)
By definition the locus of equation (A.8) represents a hyperbola.
The intersection of the three hyperbolas for the three time difference
(i = 1, 2, and 3) provides a unique source location. Therefore, this
method of finding the space-location is called the three dimensional
hyperbolic system. Another method of finding space-locations based on
a spherical triangulation system is described in Holmes (1951). For
the application to our research, the hyperbolic system is used because
it provides lower random errors over a wider range of space-locations.


292
descending sequence in the remaining two PB's. The location of some
of the sequential VHF sources were not caused by the propagation of
the previous sources, since the time and distance yields a velocity
greater than the speed of light. For three of the four CG flashes the
initial electric field change occurs within a few hundred microseconds
of the final PB pulse, the tail end of which may be due to the recorder
response. Proctor (1976) claims that over 90% of the stepped leader
radiation began with a sharp burst of noise of higher amplitude. In
addition, Proctor (1976) reports that sometime the VHF noise began
suddenly before the start of the electric field records. These
characteristics observed by Proctor appear to be consistent, with our
definition of preliminary breakdown.
From a study of the VHF sources during the PB, we determined that
the path of the series of pulses riding a slowly varying envelope is
generally about 4 km. This path is probably caused by a potential wave
that propagates throughout part of the initial PB path. In addition,
breakdown regions in different parts of the path are probably the con
tributors of the high frequency pulses superimposed on the envelope.
Most of the individual pulses during the entire PB are detected within
about 1 km perpendicular radius from the initial path. Some of the
pulses are located in small isolated regions. Pulses during the PB's
appear similar to the isolated SP's studied in Chapter V and discussed
In Section 7.1.7. That is, both are probably potential waves of about
4 km length with lLttie charge transfer.
7.1.2 Stepped Leader
We studied a total of 20 leader-return stroke sequences in the
four randomly selected CG flashes. From these 20 leaders, 12 were


nnnn
21 JUNE 1979
FUNCTION STDSET(Xl.N)
** FUNCTICN SUBROUTINE TO CALCULATE THE
** DEVIATION OF SET
D I MENS ION XI ( 1 }
T S UM S = 0 0
DO 536 1=1 N
536 T S UM 5= T3UMS+-X1 ( I )
AV SET = TSU MS/FLUAT(N)
T SUMS= 0*0
DO 530 1=1 ,N
SUM5 =( X1 ( I)-AVSET)**2
530 TSUMS=TSUVSFSUVS
S TDSE T = SQR T ( T SUMS/FLOAT ( N-l ) )
RETURN
END
ST ANOARD


1.23
5.2 The 180710 Flash
On 8th August 1977 a thunderstorm moved west from the Atlantic
coast side of the Cape Canaveral AFS, Florida, and at 1810 UT the cloud
tops were reported at a height of 12.9 km. At 180710 UT the first
cloud-to-ground flash of the newly developed thunderstorm was recorded.
Details of that flash are reported in this section. Two other cloud-to-
ground flashes in this storm occurring at 181806 and 182357 UT are also
studied in this thesis (see Sections 5.3 and 5.4).
The VHF portion of the 180710 flash lasted 282 msec and consisted
of three separate strokes to ground. Figure 5.22 shows the relationship
between the VHF radiation recorded 10 km from the flash and the electric
field recorded 3 km away. It is evident from either the VHF or the elec
tric field records that there were stepped leaders associated with all
three of the return strokes in this flash. At 3 km from the. flash the
three stepped leaders were within the electric field reversal distance
(Uman, 1969, Chapter 3) and hence had initially negative-going electric
fields, while an electric field station at 19 km showed positive stepped
leaders field changes. Table 5.2 contains a complete summary of the
various phases of the flash. All the cross-correlated noise source loca
tions reported in this flash were determined by using 94 ptsec intervals.
The location of the charge region for the first return stroke was provided
by Krehbiel (private com) using the technique described by Krchbiel et al.,
(1979). An error analysis for the VHF noise source locations is given in
Appendix B. Table B.3 shows a summary of the uncertainty in determination
of the locations of the sources in this flash ms a function of position.
In the next subsection we consider in detail what we learned from the VHF
radiation about the different events that took place in the 180710 flash.


(f) (g) (li) (i) (j)
Figure 5.39. Sequence of photographs during the 131306 flash. The Julian day is 220 and the time is shown
in each photo. Sequence (a) through (h) shows the two stepped leader return stroke channels.
Sequences (a), (b), and (c) correspond to the first stroke that hit the tower while sequences
(d) through (j) show t;.ie remaining strokes in a separate channel. This photo is a courtesy of
Douglas Jordan of the University of Florida.
9 I


EAST (km)
Dooe-


n n nnn orn non non non oonono
21 J UN E 1979
153
SUBROUTINE SIMQCA,0,N,KS)
** THIS SUBROUTINE SOLVES SIMULTANEOUS EQUATIONS BY **
4* USING GAUSSIAN ELIMINATION. 44
DIMENS ION All ) E ( 1 )
44 FORWARD SOLUTION 44
T CL 0 0
KS = 0
J J=-N
DO 65 J=1 ,N
J Y = JF 1
J J = JJ + N+l
BIGA= 0
l T = J J J
DO 30 I=J,N
44 SEARCH FOR MAXIMUM COEFFICIENT IN COLUMN 44
I j = I r + i
IFIABSIBIGA)-ABS(A(IJ))) 20,30,30
20 0 IGA = A( I J )
IMAX =I
30 CONTINUE
44 TEST FOR PIVOT LESS THAN TOLERANCE (SINGULAR MATRIX)
IF(ABS(DIGA)-TOL) 35,35,40
35 KS-1
RETURN
44 INTERCHANGE ROWS IF NECESSARY 44
40 I I= J+N4(J-2)
I T = I M A X J
DO GO K=J,N
I I = I I + N
12=11+ IT
SAVE = A( I I )
A( I I )=A( I 2)
A ( 12 ) = SAV E
44 DIVIDE EQUATION BY LEADING COEFFICIENT 44
50 A{ II ) = A( l I)/BIGA
S AVE= B( IMAX )
( I MAX )=U(J)
13 ( J) = SAVE /!3 IGA
+4 ELIMINATE NEXT VARIABLE 4*
1 F ( J N ) 5 5,7 0,55
55 S=N*(J-l>
DO 65 IX= J Y,N
I XJ=IQS + IX
I T = J I X
DO 60 JX=JY,N
I X JX=N4( JX-1 ) FIX
J JX= I X JXF I T
60 A ( IXJX ) = A( I X JX ) 1 A( IXJ ) A( J JX ) )
05 B ( IX) =B( I X) ( 0 ( J ) *A ( IX.J > )
* 4


208
of 4 km in the east and north direction and 8 km in height starting less
than 1 km east of J4. The noise sources extended between a height of
7.5 and 15.0 km. These locations did not form an organized channel,
rather they occurred over the entire volume. It appears that the lack
of organization in the location of the V11F noise sources might be an
indicative factor of the termination of the flash. That is, as long as
the noise sources appear along some organized formation, sufficient
charge is available for a consecutive return stroke. It is also worth
noting that only the VHF noise sources from Jl showed a well-organized
propagation pattern. This was the case for the two J-changes in the
165959 flash previously described.
5.3.15 Dart Leader and Sixth Return Stroke
Figure 5.58 shows the VHF noise during the dart leader and the
sixth return stroke. The return stroke lasted about 180 ysec and was
preceded by a 470 ysec dart leader. The VHF noise in Figure 5.58 are
similar to the dart leader and third return stroke in Figure 5.52.
Two noise sources for the dart leader and one for the sixth return
stroke, 94 ysec intervals, are shown as circles and squares, respective
ly, in Figure 5.57. There was no identifiable pattern detected when
relating all the locations of the dart leader, the return stroke, and
the previous J-change. The non-existence of a J-change channel across
which charges could propagate coupled with the continuing decrease in
the field change for consecutive return strokes (Figure. 5.40) have
indicated the termination of additional strokes to ground during this
fla sh.


Figure 4.1. Four channel VHF radiation directly from the
recorder for the beginning of the intracloud
flash occurring at 181416 UT on 8th August 1977.
(A) is the VHF radia tion at the central station
7.6 km from the discharge. (B), (C) and (D) are
the VHF noise for the remote stations, 7.4, 4.1,
and 12.4 km from the discharge, respectively.


L 84
described in Section 3.6, we found that -17.2 Coulombs were lowered by
the first return stroke.
5.3.4 Following First Return Stroke (FR)
Figure 5.46 shows the VHF noise during the FR period. Strong VHF
radiation with a pulse every 3 ysec was detected during the first 8.9
msec after the first return stroke. Two large pulses were detected
4.4 and 8.7 msec after the beginning of the FR. These pulses were 250
and 100 ysec wide, respectively, and had the largest amplitude of any
VHF pulses in the entire flash. These wide pulses contained superimposed
pulses that propagated upwards at a velocity of 1.2 x 10^ m/sec.
About 90% of the VHF noise sources during the FR were located in
the previous stepped leader-return stroke channel between the heights
of 5 and 8 km. The remaining 10% of the sources were located between
the heights of 3 and 5 km and above 8 km. Figure 5.47 shows the cross-
correlated locations, 376 ysec intervals, for the FR period. The loca
tions are labeled to indicate the sequence on which the events occurred.
The noise sources propagated upwards between the heights of 5 and 8 km.
By correlating the VHF radiation sources with the electric field record
during this time period, we conclude that either positive charges were
raised by the FR interval or that negative charges were lowered from
higher altitudes as the VHF sources move upward.
5.3.5 Semi-Quiet Period (SQP) Following the FR
The VHF activity continued for 7.5 msec after the first FR at an
average rate of a pulse every 25 ysec. This 'time interval appears to
be a transition between the high pulse rate from the FR and the quiet
period with almost absent VHF radiation that followed the SQP. About


331
DEFINITION OF VARIABLES USED IN THE COMPUTER ALGORITHM DESCRIBED IN
THIS APPENDIX:
LCHAN
- Digital tape channel number (0, 1, 2, 3)
LREC
- Six bit byte of data read from seven track digital tape
LINT
- Value of the VHF radiation reconstructed from the bytes
X6, X7, X8, X9 Value of the VHF radiation for the central and the
three remote stations, respectively
X1ME, X2ME, X3ME, X4ME Average value of the VHF radiation in the
selected data window for the central and the
three remote stations
Till, TI21, TI31, TI41 Value of the VHF radiation for the channels
(without a mean value)
LHOUR,
LSEC, LMIN, LMIL Converting time code value on digital tape to
hour, minute, second, and millisecond
TIL2S,
TIL3S, TIL4S Normalization factor for VHF radiation of remote
stations versus central station
XI, X2, X3, X4 Subsections of the value of the VHF radiation for the
central and the three remote stations
AVEMO
- Moving average of the' VHF radiation in the central station
AVEM02
- Moving average of the VHF radiation for the remote station
AVE
- Average value of a section of the VHF data
LAG1, LAG2, LAG3 Amount of samples needed to maximize the cross
correlation function
DELTA1, DELTA2, DELTA3 Time corresponding to the cross-correlation
intervals
X, Y, Z Three-dimensional locations
MABLMA
- Sample value for local maximum for the central station
MX2GEN
- Estimation of the cross-correlation value for local maximum
SLPR2
- Slope to the right of local maximum
SLPL2
- Slope to the left of local maximum >.
NDSLRI
- Number of reversals on descending slopes to the right of
local maximum
NDSLLE
- Number of reversals on descending slopes to the left of
local maximum
NDSLLE


Figure 5.4. Three-dimensional view of the VHF noise sources
during the first 537 ysec of the preliminary
breakdown. The sources A through RR are time
tagged (in microseconds) and shown in alphabeti
cal order A -* Z, AA -* RR.


L37
3 4 5 6 c>
EAST (km)
Figure 5.27. Three-dimensional view of the cross-correlated noise
sources during the 8.4 msec FR interval.


CHAPTER III
DATA ACQUISITION AND PROCESSING
Figure 3.1 shows a general block diagram of the data acquisition
and processing used in this research. The VHF radiation generated by
lightning flashes during thunderclouds was detected at four selected
ground receivers (RX), and recorded simultaneously at one station
(recorder). Four VHF radiation channels were simultaneously slowed
down (data pre-processing) and then digitized (A/D converter) at a
rate greater than twice the bandwidth of the recorded signal. A com
puter algorithm, to be described in Chapter IV, was developed to deter
mine the VHF source locations from the difference in the time of arrival
(DTOA) of the four time series VHF data. The results were interpreted
and related to other correlated data. In this chapter we describe
the technique used for data recording, the properties of the telemetry
system, the data pre-processing and A/D conversion, and other
correlated measurements used to supplement this research.
3.1. Data Recording
The LDAR system used to obtain the original data consisted of
a central and six remote stations forming two Y configurations, with
the central station at the center of the Y. Figure 3.2 shows the
station geometry. The detected VHF radiation at the remote stations was
retransmitted to the central station and recorded. There were two
methods of retransmission: microwave and wideband cables. Signals from
29


1.6
to determine elevation angles. His 1978 system used a vertical and a
horizontal antenna, 13.7 meters apart, at each of two stations separated
by 17.8 km. The horizontally and vertically spaced antennas were used to
measure azimuth and elevation, respectively. Time measurements were
performed to 0.4 nsec with angle accuracy of 0.5 degree.
In addition to the VLF magnetic field ratio techniques and the VHF
time of arrival direction finders previously described, Lewis (1960)
used a VLF direction finder with DTOA techniques. Lewis used four
stations in a Y configuration with the central station at the intersec
tion of the Y. The distance between the central and the remote stations
(at the three ends of the Y) ranged between 100 and 120 km. This system
was used in relation to a system implemented in England to detect
spherics over the Atlantic Ocean and Western Europe. The waveforms
from the four stations were photographed on continuously moving 35-mm
film. Only three stations were needed for direction finders. The
remaining two stations were used for redundancy. The reported accuracy
for this system was about 0.5 degree of latitude and of longitude.
2.4 Review of Proctor's Work
In addition to the previously described direction finders, channel
locations have been reported by other means, such as, thunder measure
ments (e.g., Holmes et al., 1971; Nakano, 1973; and Teer and Few, 1974),
and radar studies based on the appearance and decay of ionized channels
(Hewitt, 1953, 1957). However the most relevant work to date is a DTOA
hyperbolic system that uses a minimum of four stations to determine the
three-dimensional channel locations (Proctor, .1976; Lennon, 1975).
By the time Oetzel and Pierce (1969) had suggested in print that
spherics locations could be determined by measurements of DTOA in the VHF


115
We used the technique described in Section 3.6 choosing (A) in
Figure 5.15 as the point charge source and determined that -6 Coul were
lowered by the third leader-return stroke process. This result is com
parable to the -9 Coul determined by Uman et al. (1978).
5.1.12 Solitary Pulse Between the Cloud-to-Ground and the Intracloud
Discharge
Thirty milliseconds after the last and final return stroke of the CG
discharge, a large SP was observed. The SP lasted about 625 ysec and
started with an 80 ysec wide pulse very similar to the first SP between
the second and third return stroke.
The sources of the SP propagated upwards to the NE in a path 35
off vertical starting about an altitude of 4 km. This SP VHF amplitude
and the propagation of its source locations were larger than the SP's
between R2 and R3. The vertical inclination of this SP and the source
of its upper region coincided with the intracloud discharge that followed.
5.1.13 The Intracloud Discharge
The continuous VHF radiation from the intracloud discharge follow
ing the cloud-to-ground discharge began 12.8 msec before the first sharp
increase in the IC electric field (Figure 5.1). Figure 5.19 shows the
VHF radiation during the beginning of the IC discharge. There is a
remarkable difference between the beginning of the IC and the beginning
of the CG in Figure 5.4, which suggests that we can distinguish these
flashes after only 3 msec of VHF radiation. The first three sources
during the IC were located near (3.1, 12.1, 11,2), in the middle of the
path to be eventually covered by the intracloud discharge. The entire
discharge extended about 10 km in a path 35 off vertical between A
(6.0, 13.6, 14.0) and B (1.7, 9.5, 5.9) of Figure 5.20 which shows the


EAST (km) EAST(km)
ALTITUDE(km)
ALTITUDE (km)
351


I 49
(UJ>1)1SV3
|
ALTITUDE (km)


317
The RMS quantization error was obtained by using du_. = cdT_. =
300. .23 = 68.93 meters in equation (B.4) and solving for dX ,
RMS
dYn.._, and dZ for any specified DTOA. The relative location of the
VHF source with respect to the ground-based station is an important
factor in the solution of equation (B.4). The X and Y error increases
as we get away from the VHF ground-based network. Since only discrete
measurements of time differences are available, we get only discrete
locations for X, Y, and Z. These locations are generally within 100
meters for X, and 500 meters for Y and Z for the VHF sources studied in
this thesis. The Z error measurement increases for VHF locations near
the ground and for Z larger than 10 km. Figure 3.1 shows the source
locations of every sample, corresponding to variations along
T^, T^, and T^. This graph illustrates the effect of the quantization
error in any of the three DTOA. Figure 3.2 shows a mapping of all the
55,171 three dimensional locations obtained within the range of the
graph axis for 50 iterations of T^, T^, and T^ every sampling interval
(.230 ysec). The remaining 69,829 locations of the possible 125,000
fell outside the boundaries of the graph. Figure B.2 also shows the
discrete pattern of the locations of the hyperbolic equations which is
obtained for the discrete sample intervals. Figure B.3 shows a mapping
of 49,581 three-dimensional locations obtained within the range of the
graph axis for 50 iterations of T^, T^, and T taken every 0.1 ysec.
Since the quantization error is smaller, the pattern in Figure B.3 is
less evident.
In addition to the uncertainties produced by the quantization
error, the calibration error must be considered. The calibration error
is determined by the uncertainties in the retransmission delay, the


198
though the VHF noise sources do not appear in a regular progressing
sequence throughout the channel, about 80% of all the source locations
are located within 1 km perpendicular distance of a line 32 off verti
cal leading toward the northeast. It appears that the VHF radiation
during the latter part of the J-change joins previous regions from an
earlier part of the J-change. In addition, during the last 7.2 msec of
the J-change all the VHF noise sources were located in the lower half
of the channel between the heights of 5.7 and 9 km.
5.3.9 Dart Leader and the Third Return Stroke
Figure 5.52 shows the VHF radiation during the dart leader and the
third return stroke. The dart leader lasted 495 psec and was followed
by a 92 psec return stroke.
The VHF sources of the dart leader were located between the heights
of 7.5 and 8.5 km, in the neighborhood of the previous J-change. Three
dart leader's cross-correlated locations, 94 psec intervals, are shown
as circles in Figure 5.51. The third return stroke VHF noise sources
were located near the top of the J2 channel. Three return stroke
sources, 94 psec intervals, are shown as squares in Figure 5.51. It is
worth noting that while the VHF noise of the dart leader was located in
the bottom half of the previous J-change, the return stroke sources were
located near the top of the previous channel.
5.3.10 Third J-Change (J3)
Figure 5.53 shows the cross-correlated VHF noise sources, 376 psec
intervals, during the third J-change process.. Figure 5.53 also shows
the location of the fourth return stroke spherical change center (Q4).
There was a 1.1 msec quiet period between the previous return stroke


Figure 5.47.
Three-dimensional view of the cross-correlated
noise sources, 94 ysec intervals, during the FR
interval. The labels A to U show the progres
sing sequence of occurrence of the sources.


Figure 5.76. Three-dimensional view of the cross-correlated locations of the VHF noise sources
during the SP shown in Figure 5.63. The labels A to N show the regular progressing
sequence of the noise sources.


197
Figure 5.51. Three-dimensional view of the cross-correlated noise
sources during J2, the dart leader, and the third return
stroke. The location of the third stroke spherical
charge center is shown as Q3.


EAST (km) EAST (km)
ALTITUDE (km)
Li I


of the intracloud discharge. The V1IF noise for these SP's closely
resembles the SP' s during the J-changes of the cloud-to-ground discharge.
The V1IF locations for these SP's propagated upwards for about 6 to 8 km
starting in a region one to three km east of B. None of the SP's prop
agated along the primary AB path of the intracloud discharge. Their
starting location was as noted arid their path was either vertical or
northwest, instead of the 35 northeast path of the IC discharge. We
attempted to fit a point charge model, equation (3.10), to the multiple
stations electric field records, for the location of the continuous
radiation of the IC discharge but could obtain no reasonable results.
On the other hand, because of the polarity of the IC field and its
reversal with distance (Uman, 1978), it is clear that the bulk of the
charge motion was either negative upwards or positive downwards.
5.1.14 Concluding Remarks About This Flash
Some of the new information about the flash derived from the VHF
noise, its source locations, and the correlated wideband electric field
records follows: (1) The first stepped leader was preceded by a 2.2 msec
preliminary breakdown located near and inside the charge source of the
stepped leader. The stepped leader had an average velocity which
6 6
increased from 1.3 x 10 m/sec at 5.1 km height to 7.0 x 10 m/sec at
2.2 km, the lowest height for which average source locations were
obtained. (2) Continuous VHF radiation was detected in the final 65%
of the time between the first two return strokes. During this portion
of the first J-change, radiation sources and negative charge propagated
downward 5.7 km in a path 35 off vertical at an average velocity of
1.5 x 10J m/sec. The negative charge lowered during this portion of
the J-change was 2.40.7 Coulombs. A 4 km near-horizontal channel which


L99
EAST (km)


e.g., stepped leader branches, and (2) Active sources which still
radiate at higher altitudes in the neighborhood of the PB-stepped leader
junction while the leader propagates to ground.
The fact that the VHF pulses appear to be associated with the
stepped leader steps and that correlated electric field change is
detected up to about 1 msec prior to the stepped leader pulses suggests
the following sequence of events in the formation of a CG flash:
(1) The path of the PB sources becomes an ionized channel or arc;
(2) Current starts to flow through the channel providing correlated
electric, field change from the motion of the electric charges; and
(3) The steps of the stepped leader formation start and stepped leader
propagation continues from the cloud charge.
We found the VHF source locations during the PB-stepped leader
transition. A source which corresponds to the locations in the
transition between the PB and the stepped leader VHF noise is chosen
as the beginning of the stepped leader. The VHF sources are detected
throughout the leader path to near-ground. In addition to the poor
accuracy of our detection system for altitude locations near-ground,
we found two other limitations in trying to obtain stepped leader source
locations. First, stepped leader sources, most likely from leader
branches or leader path enhancement, are simultaneously active over a
large volume. Second, the VHF noise for sources near the ground usually
decreases prior to the return stroke. The stepped leader velocity that
we calculated from the beginning source of the stepped leader VHF
radiation to the last detectable stepped leader source ranged from 9.2
x 10J m/sec to about 4.3 x 1.0 m/sec. These initial stepped leader
velocities are about a factor of 10 larger than those reported from
optical measurements by Schonland and his co-workers and by Proctor (1976).


'7
N-l
R
xy
(J) = l
n=0
x
n
n+j
(4.1)
where N is the number of data samples. Since the signal at the central
station (y ) always arrives first (property 4.2. 1(1)), we have to delay
the y signal by a certain amount T. In addition, a noise term r is used
n n
to account for properties 4.2.1(2), (3), and (4), and different
background noise. Therefore
x
n
n+x
+ r
n
(4.2)
Substituting equation (4.2) into (4.1), we get
N-l
R
xy
(i) = I (y
n=0
n+T
+ r
n
N-l N-l
) V y + y r y
L n n+T n+1 L- n^n+i
n=0 n=0 J
(4.3)
or
R
xy
(j)
= R (j
yy
T) +
R (j)
ny J
(4.4)
Depending on the cross-correlated value of the noise R (j), the
peak value of R ( j) will occur in the neighborhood of j = T. Our task
is to find the maximum value of R and see what the lag T is for a maxi-
xy
mum. If data from ensemble averages of x^ and y^ are processed, the
cross-correlated noise term can be averaged out and a more accurate
value of R can be determined. However each selected interval of the
xy
multiple series has different time delays and additional data for
averaging is not available. In addition, the VHP radiation properties
4.2.1(2) to (4) indicated that there might be substantial differences
between the data recorded in the different stations.


delay error. Next we present a solution for a ,w, o _w, and a w_ for
QRMS cRMS tRMS
the four main flashes studied in this thesis.
B.1. Error Analysis for the Locations of the 165959 Flash on 19th
July 1976
The remote stations selected to determine channel locations were
Wl, Ml, and W3 (Figure 4.1). The RMS uncertainties in the calibration
error for Wl, Ml, and W3 were .62, .25, and .41 microseconds. The flash
extended between -2 and 6 km EW, 9 and 16 km NS and up to 16 km in
altitude. Table B.l shows the quantization, calibration, and total
error for the three-dimensional channel locations over the entire range
of the flash.
B.2. Error Analysis for the Locations of the 181806 Flash on 8th
August 1977
The remote stations selected to determine channel locations were
Wl, Ml, and M3 (Figure 4.1). The RMS uncertainties in the calibration
error for Wl, Ml, and M3 were .56, .19, and .57 microseconds. The flash
extended between -3 and 9 km EW, 7 and 17 km NS and up to 15.5 km of
altitude. Table B.2 shows the quantized, calibration, and total error
for the three-dimensional VHF sources over the entire range of the flash.
B.3. Error Analysis for the 180710 and 182357 Flashes on 8th August 1977
The remote stations selected to determine channel locations were Ml,
M2, and M3. The RMS uncertainties in the calibration error for Ml, M2,
and M3 were .19, .38, and .57 microseconds. The 180710 flash developed
in the NE of the central station, 3 to 7 km EW, 8 to 15 km NS, and up to
10 km of altitude. The 182357 flash developed in the NW of the central
station, -8 to 1 km EW, 5 to 14 km NS, and up to 13 km of altitude.


TABLE OF CONTENTS
Page
ACKNOWLEDGEMENTS ii
ABSTRACT vi
CHAPTER
IINTRODUCTION 1
IIGENERAL REVIEW OF LIGHTNING AND PREVIOUS LIGHTNING
VHF TOA RESEARCH 6
2.1 Description of Cloud-to-Ground and Intracloud
Lightning 6
2.2 Description of Electromagnetic Radiation Emitted
by Intracloud and Cloud-to-Ground Flashes 10
2.3 Lightning Direction Finders 14
2.4 Review of Proctor's Work 16
2.5 Review of Lennon's Work 25
IIIDATA ACQUISITION AND PROCESSING 29
3.1 Data Recording 29
3.2 Telemetry System 33
3.3 Data Pre-Processing and A/D Conversion 40
3.4 Electric Field Meters 43
3.5 Charge Locations Derived from Electric Field
Stations 44
3.6Charge Locations Derived from VHF Noise Sources ... 47
IVCOMPUTER ALGORITHM FOR LOCATION OF LIGHTNING
CHANNELS 49
4.1 General 49
iii


APPENDIX D
COMPUTER ALGORITHM TO DISPLAY A
THREE-DIMENSIONAL DRAWING OF VHF NOISE SOUNDS
This appendix contains the computer algorithm we wrote to display
the VHF noise sources in three-dimensions. The input of the algorithm
is the three-dimensional sources stored in digital tape which are pro
duced by the algorithm given in Appendix C. The output of the algorithm
is an isometric view of either the cross-correlated (94 or 376 ysec
intervals) or the individual VHF noise sources. Examples of the output
of this program are shown several times in Chapter V.
356


i4
(a)


30.1
stepped leaders cannot propagate unless they are immediately preceded
by active VHF radiation from the J-change process. As we shall see in
this section, the physical reason for the J-change-leader sequence is
that the J-change makes available the charges which are lowered by the
dart or subsequent stepped leader.
Two of the studied flashes (Sections 5.1 and 5.3) had VHF radiation
emitted during J-changes which originated at a height near 14 km. The
path of these two flashes were more vertically inclined and we refer to
them as vertical flashes. The other two flashes only extended to a
height of about 12 km and we refer to them as horizontal flashes.
The VHF sources for the first J-change in the two vertical flashes
followed a regular progressing sequence from a height of 13.7 and 14.2
km, and propagated downwards in paths of 35 and 25 off vertical,
respectively. These two J-changes lasted 44.3 and 8.1 msec and the VHF
sources propagated at a velocity of 1.5 x 10^ m/sec and 5.0 x 10> m/sec,
respectively. We fitted a point charge model that lowered negative
charge along the regular progressing sequence of the path and found that
-2.4 and -1.8 Coul were lowered by these processes. From al.1 the J-
change in the four flashes, these two J-changes were the only ones that
exhibit a regular progressing sequence of the noise sources. It is
interesting to note that these J-changes were the first ones in these
two flashes and they were preceded by 16 and 16.5 msec quiet periods.
d
Quiet periods are those time intervals in the flash which have electric
field change buL no VHF radiation. We do not know If the quiet period
had any effect in the sequence of propagation ,of the noise sources, or
if it was a coincidence.


ELECTRIC FIELD
LOG AMPLITUDE
VHF RADIATION


Figure 5.60. Three-dimensional view of the cross-correlated
noise sources during a SP in the CC interval.
The arrows indicate the regular progressing
sequence of the noise sources during the SP.




2
In this introductory chapter we shall briefly survey the organiza
tional aspects of this thesis as well as some of the information pre
sented. Chapter II presents a general review of lightning and previous
lightning VHF time of arrival (TOA) research. Systematic lightning
research started in the middle of the eighteenth century with the work
of Benjamin Franklin. Modern lightning, however, did not start until
the early part of the twentieth century with the electric field measure
ments of C. T. R. Wilson published in 1916. Within ten years, cathode-
ray-oscillography and high speed photography were introduced to the
study of thunderstorm electricity. The first published suggestion that
VHF radiation might be used to determine source locations in three
dimensions appears to be due to Oetzel and Pierce (1969). The pioneer
ing work in the determination of source locations by calculating the
difference in the time of arrival was published by Proctor (1971).
Proctor's original work was performed manually and provided new infor
mation about the different phases of a lightning discharge.
Chapter III presents a description of the system used to perform
the VHF measurements. In addition, this chapter presents a brief
discussion of the measuring system used for the electric field measure
ments and of the point charge models which are used to interpret the
results. The original VHF data are analog (400 Hz to 1.5 MHz) tape
recordings of the output of envelope detectors of four ground-based VHF
(30 to 50 MHz) receivers located at the Kennedy Space Center. The
amplitude scale of the VIII radiation was made logarithmic to provide
80 dB dynamic range for the input signal. The VHF analog data for the
four stations were subsequently digitized at a sampling rate of 4.35 MHz.


l6
40 MHz
(b)
Figure 3.6(a). Input spectra. Figure 3.6(b). Spectra after
the VHF receiver.
Output (volts)
.03 .1 .3 I 3 10 Millivolts
Figure 3.7 Log IF input-output characteristics.
Table 3.1. Log IF Test Values
Input (dBm)
Output (volts)
-80
.255
-70
.542
-60
.798
-50
1090
-40
1.394
-30
1.675


61
Figure 4.2. Pulse model.


'308
toward the end of the discharge, starting with a pulse about every 5
msec and ending with a pulse every 30 or 50 msec. The only correlated
electric field change, during this phase, was directly related to the
detected K-changes.
The V1 IF sources of these SP's or K-changes were located in the
neighborhood of the previous IC path. These pulses extended the previous
ends of the paths widening the volume of the discharge.


4
University of Florida station and at a network of eight electric field
stations designed and operated by the New Mexico Institute of Mines
and Technology (NMIMT). In addition, for two of the ground flashes, we
correlated our results with photographs of the lightning channels to
ground obtained from the KSC TV network.
Chapter VI presents a statistical model for the VHF radiation data.
This model was derived with the purpose of classifying the properties of
the time-series data. The Box and Jenkins (1976) techique was used to
identify a time-series model and to estimate the parameters of the model.
Chapter VII summarizes the properties of the different phases of
cloud-to-ground and intracloud lightning derived from the flashes
studied in Chapters V and VI. The main properties of the different
phases studied were the characteristics of the VHF radiation, the length,
direction and velocity of propagation of the various lightning paths
associated with different discharge phases, the charge transfer associated
with each of the lightning phases, and the total volume occupied by the
flashes.
Finally, Chapter VIII provides some concluding remarks and suggests
some of the areas for future research.
Appendices A through E are provided to present mathematical deri
vations or computer listings which were not appropriate for the text.
Appendix A gives the derivation of three-dimensional locations obtained
from the difference in the time of arrival. Appendix B provides the
error analysis in the determination of the three-dimensional locations.
Appendix B also shows four tables with tabulated RMS errors associated
with channel locations as a function of position. Appendix C gives a
Fortran computer listing used to determine DTOA in accordance with the


(km)
Figure 5.69. Three-dimensional view of the cross-correlated noise
sources during the third and fourth stepped leaders.
The sources A-B and C-D correspond to the initial propa
gation of the fourth and third stepped leader, respectively.


131
sources every 2 or 3 )isec (if active VHF radiation was recorded), instead
of every 7 to 10 ysec, the limiting using the computer algorithm. These
results are shown in the three-dimensional graph in Figure 5.25. The
sources A through EE are time tagged and shown in alphabetical order
A -* Z, AA DD. This initial stage of the PB extends 8 km horizontally
and 7 km vertically. The sequence of the VHF sources shows that the
activity started at 7.4 km and there was propagation initially horizon
tally and then vertically.
5.2.2 First Stepped Leader
The last 7.9 msec prior to the first return stroke are associated
with the stepped leader in the VHF noise record. Figure 5.24(a) and
Figure 5.24(b) show the cross-correlated, and all the individual detected
noise sources respectively, during the PB-stepped leader process. Figures
5.26(a), 5.26(b), and 5.26(c) show two-dimensional projections of all the
sources in Figure 5.24. The noise sources extended north-northeast 10
km in the horizontal direction from a height of 6.1 km at the beginning
of the stepped leader to a height of 1.9 km. It is worth noting that
the leader extended 5 km over water and away from the most eastern end
of the KSC which is located at (5.3, 8.3). This large horizontal prop
agation of the stepped leader may be related to the fact that the leader
propagated over water. The velocity of the stepped leader ranged between
.8 and 10'> and 1.7 x 10^ m/sec.
5.2.3 First Return Stroke
The first return stroke VHF radiation lasted 400 ysec. The noise
was characterized by high frequency pulses riding on the envelope of a
low frequency pulse as shown in Figure 5.23.


Table 5.5. Events in the 182356 Flash.
Universal Time at the Start
of the VHF
Radiation: 18 23 56
.267, 8th August 1977
Start
Coordinates (km)
Time
Duration
UPPER
LOWER
Velocity
(msec)
Event
(msec)
X
y
z
X
y
z
m/sec
0
Preliminary Breakdown
1.8
-5.2
8.3
9.8
-4.2
7.9
4.6
1.8
First Stepped Leader
5.9
-4.0
11.1
5.9
-4.1
10.6
3.4
1.9 x 106 to
4.3 x 10^ m/sec
7.7
First Return Stroke
.500
-4.2
10.7
6.0
-4.1
10.5
4.5
8.2
Following First Return
Stroke
7.1
-5.5
11.7
9.5
-4.7
8.2
4.9
15.3
J1 Change
13.2
-3.1
12.2
7.5
-4.1
8.9
6.0
28.5
2nd- Stepped Leader
14.2
-4.5
12.6
6.7
3.8
9.7
4.0
2.6 x 10"* m/sec
42.7
2nd Return Stroke
.81
-3.6
12.1
6.5
-4.3
12.7
5.1
43.5
Quiet Period of J2
5.7
49.2
J2 Change
7.2
-5.2
9.1
9.0
-4.0
8.0
5.2
56.4
3rd Stepped Leader
35.0
-4.2
11.2
7.9
-3.5
12.6
1.8
2.3 x 10^ m/sec
91.4
3rd Return Stroke
.2
91.6
4th Stepped Leader
5.2
-5.2
9.1
8.9
-6.0
7.8
3.7
2.9 x 10^ m/sec
96.8
4th Return Stroke
.25
224


231
Table 5.6(a). Return Stroke Charge Value and Location as determined
by Krehbiel (private com) using the technique of
Krehbiel et al. (1976). R3 is missing because the
beginning of the field change was not easily distin
guishable. R7 and R8 are missing because most electric
field stations were saturated.
Return Stroke
Charge (Coulombs)
Location (km)
R1
-21.4
Q1 (-4.0, 7.4, 7.5)
R2
- 9.5
Q2 (-3.5, 8.0, 7.6)
R4
- 2.9
Q4 (-4.6, 6.7, 7.6)
R5
-10.2
Q5 (-3.5, 8.1, 6.8)
R6
- 6.2
Q6 (-2.6, 7.5, 6.8)
Table 5.6(b). Stepped Leader-Return Stroke Charge Value and Location for
Each of the Return Strokes Preceded by Stepped Leaders as
determined from the VHF source locations and one electric
field record using the technique described in Section 3.6.
R6 and R8 are missing because the return stroke was pre
ceded by dart leaders.
Return Stroke
Charge (Coulombs)
Location (km)
R1
-20.5
(-3.9, 11.7, 5.8)
R2
- 8.2
(-3.7, 11.7, 5.9)
R3
-14.4
(-4.4, 12.8, 6.2)
R4
- 3.6
(-4.1, 7.8, 6.1)
R5
-16.2
(-4.2, 11.2, 6.9)
R7
-24.1
(-5.3, 8.3, 6.9)


5.1.9 Second J-Change
Significant VHF radiation was measured during the last 47 msec of
the second J-change (J2, Figure 5.1). The VHF noise sources started at
(1.2, 12.5, 11.2), that is, about 2.1 km below and 4 km southeast of
the starting point of Jl. During the first 19 msec there was activity
taking place one or two kilometers upwards and downwards, but in the
last 25 msec the noise sources propagated primarily downwards, ending
at (0.1, 11.8, 8.5). Figure 5.14 shows a three-dimensional view of the
cross-correlated VHF noise sources, 376 ysec intervals, active during
J2. Figure 5.15 also shows the charge center for the last two return
strokes (Q2 and Q3) and the location (A) of the end of J2.
We modeled the field change during the VHF portion of J2 with
equation (3.10) and derived a charge for the E-field at each of the stations.
For the J2 process, starting and ending points chosen were (1.2, 12.5,
11.2) and (0.1, 11.8, 8.5), a path 32 off vertical. We found a nega
tive charge lowered of 3.4 Coul, with a standard deviation of 1.8 Coul,
representing a charge moment of 16.2 + 8.5 Coul-km. The velocity of
propagation during the final 25 msec was 2.0 x 10^ m/sec. The model
fit is not as good as for the first J-change as might be expected in
view of the fact that the second J-change originally propagated both
upwards and downwards.
5.1.10 Stepped-Dart Leader (SDL) Before Third Return Stroke
For 2.2 msec after the second J-change, the VHF radiation waveforms
showed a high frequency pulse train without any low frequency envelope,
very similar to the radiation observed during the first stepped leader.
The electric field records verify a stepped leader was occurring.
Figure 5.16 shows the VHF radiation during the stepped leader.


69
The value of computer graphics should not be underestimated. Any
attempt to represent the locations by hand was tedious and resulted in
large errors. All the graphics for the VHF noise and its source loca
tions were displayed on the Gould Electrostatic Plotter of the Univer
sity of Florida Computer System.
Figure 4.4 shows a computer processing block diagram. This diagram
shows the procedure that we followed to process and interpret the digital
input data.
4.6 Velocity of Propagation of Noise Sources
We determined the velocity of propagation of the noise sources by
using the three-dimensional locations and their time of occurrence. We
chose only those lightning events on which the location of the noise
sources formed a channel following a regular progressing sequence. To
determine whether the events followed a progressing sequence we calcu
lated the value of the velocity of propagation using all the cross-
correlated locations.
Let p1(x1y1z1) > P2('X2y2,Z2') pn(xnyn,Zn^ be the locations
of cross-correlated sources at time t^, t^, ..., t^, respectively. Then
velocities of propagation can be calculated by determining the distance
P and dividing it by the time interval t where m and n are anv two
sources (m < n). A total of T~^- velocities can be calculated from n
locations. Only about 50 or 60% of all the velocities that we obtained
during the specific -lightning events that we studied using the above
techniques showed a velocity of propagation the same as would be found
by taking the starting and ending point. Therefore, we decided to use
the following procedure to determine channel velocities. 1) Determine
whether the VHF sources followed a progressing sequence. A velocity of


18
and the triggering signal might not detect the beginning of the flash,
only limited information is recorded. The records are read by operators
who first identify the same pulse in all the stations and then measure
the DTOA between the four remotes and the central station. The records
are enlarged to .36 cm/ysec for reading purposes. Using a transparent
graticule, DTOA can be measured to .1 Usee. Redundant sets of readings
are obtained by using the additional station. The by-hand DTOA for
every pulse are fed into a computer which is programmed to solve the
hyperbolic equations and print the three dimensional locations. This
tedious technique required 8 man-months to determine the locations of
one 250 msec sample. The reported accuracy of the locations for a 20 km
range is 25 meters for X arid Y, and 140 meters for Z. Proctor (1971)
states that a limited number of 250 msec intervals had been processed.
Actually, from studying the article, we reasonably infer that only one
250 msec interval was completely processed.
The results reported by Proctor (1971) for the different phases of
the discharge are as follows. One stepped leader was processed with 225
locations. The radiation started at a height of 5 to 6.5 km above sea
level (ground level 1.5 km). The noise sources extended upward and
downward but the median height moved downward at 3 x 10'' m/sec for 7 msec.
The active region became greater by the end of the leader and extended
from near ground to a height of 6.5 km above mean sea level (MSL). Poor
height resolution at low heights does not permit the determination of
accurate channels. The noise emitted by dart leaders was reported to be
similar to stepped leaders. This information is in conflict with the
work presented in this thesis. We claim that stepped leaders have
unique, identifiable pulses not seen anywhere else in a cloud-to-ground


1.1
(D,t) =
2ire
z0 2-3sin 0. t
I 2 T1' / 1
z, R."
1 J
Z,T -
dxdz
z 2-3sin^0.
+ / i
z, cR
z,t -
R.
J
dz
z sin 0 .
-2 3 di
-1 2
z c R.
1 J
9t
r "J]
dz
l c
(2.1)
where the subindex j represents the contribution due to one of the
current elements. The pertinent geometry, distance, and angles are
defined in Figure 2.1.
A spark channel carrying a transient current, usually referred to
as current element, acts as a radio antenna and emits electromagnetic
radiation. The radiation field from a current element is the term that
contains the time derivative of the current in equation (2.1). That is
ERad
(D,t)
1
2
2Tre c
o
sin 0. .
J. 9i
R. 9t
J
r
z, t
R.
-i ->
^ dz a
c J z
(2.2)
Halan (1958, 1963) first obtained correlation between the low
frequency electric fields and the radiation fields produced by intracloud
and cloud-to-ground lightning flashes in the 1 KHz to 10 MHz range.
Brook and Kitagawa (1964) measured radiation fields at frequencies of
420 and 850 MHz from lightning flashes 10 to 30 km away. Horner (1964),
Kimpara (1965), Pierce (1967), Oetzel and Pierce (1969), and Pierce
(1974) provided good reviews of correlated eleotric and radiation fields
extending from 1 KHz to 100 MHz. These reports showed that at frequencies
less than 300 KHz few current elements are active during the flash.
Isolated radiation pulses were obtained primarily during return strokes


CHAPTER V
ANALYSIS OF RESULTS
This chapter presents a detailed description of six lightning
flashes that occurred during the summers of 1976 and 1977 at the
Kennedy Space Center. We have correlated the three-dimensional loca
tions with other storm and lightning parameters measured (see Chapter
III), primarily the electric field. We have studied four cloud-to-
ground (CG)flashes and two intracloud (IC) flashes. The six lightning
flashes are identified by their time of occurrence and type below:
(5.1) 165959, a three stroke CG flash to the .150 meter weather
tower on 19th July 1976 followed by an IC discharge.
(5.2) 180710, a three stroke CG flash on 8th August 1977.
(5.3) .181806, a six stroke CG flash on 8th August 1977 followed
by continuing current.
(5.4) 182356, an eight stroke CG flash on 8th August 1977.
(5.5) 180644, an IC discharge at the beginning of the storm on
8th August 1977.
(5.6) 181416, a small IC discharge on 8th August 1977.
All of the above flashes were at relatively close range, 3 to .17 km
from the central station. The coordinates given throughout this thesis
are referenced to the central station whose absolute coordinate in the
Florida grid system is (187023,466021) meters. The three coordinate
parameters given always correspond to the East-West location, North-South
location, and altitude, respectively.
72


289
1 2 3 4 5 6 7 8
TIME IN MILLISECONDS


PROPERTIES OF LIGHTNING DERIVED FROM
TIME SERIES ANALYSIS OF VHF RADIATION DATA
By
PEDRO L. RUSTAN, JR.
A DISSERTATION PRESENTED TO THE GRADUATE COUNCIL OF
THE UNIVERSITY OF FLORIDA
IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE
DEGREE OF DOCTOR OF PHILOSOPHY
UNIVERSITY OF FLORIDA
1979

UNIVERSITY OF FLORIDA
262 08676 742 2

oo
o*

o
r
ACKNOWLEDGEMENTS
I gratefully express my appreciation to the members of my super
visory committee for their support and cooperation. In particular, I
thank Dr. M. A. Uman for his guidance, enthusiasm, and professional
expertise, and Dr. D. G. Childers for his probing questions and con
stant support of this research. Special thanks are due to Dr. J. McClave
(Statistics) for providing programs for data modeling. I am also thank
ful to Mr. Paul Krehbiel at the New Mexico Institute of Mines and Tech
nology, and Mr. Carl L. Lennon and Mr. William E. Jafferis at the
Kennedy Space Center for their generous help in providing data, the main
ingredients of this work. I acknowledge the work of Mr. Ronald Jacobs
from Eglin AFB in digitizing the analog tapes. A special note of appre
ciation for the continuing help of Dr. W. H. Beasley and Mr. W. G. Baker
and many other colleagues working in the University of Florida Lightning
Research Laboratory. The author especially thanks his wife, Alexandra,
without whose love, patience, and understanding this work could not have
been completed.
This investigation was made possible by the Air Force Institute of
Technology. The research reported here was jointly supported by
NASA KSC Contract NAS10-9378; NSF Grant ATM-76-01454; and ONR Contract
N0001475C0153.
11

TABLE OF CONTENTS
Page
ACKNOWLEDGEMENTS ii
ABSTRACT vi
CHAPTER
IINTRODUCTION 1
IIGENERAL REVIEW OF LIGHTNING AND PREVIOUS LIGHTNING
VHF TOA RESEARCH 6
2.1 Description of Cloud-to-Ground and Intracloud
Lightning 6
2.2 Description of Electromagnetic Radiation Emitted
by Intracloud and Cloud-to-Ground Flashes 10
2.3 Lightning Direction Finders 14
2.4 Review of Proctor's Work 16
2.5 Review of Lennon's Work 25
IIIDATA ACQUISITION AND PROCESSING 29
3.1 Data Recording 29
3.2 Telemetry System 33
3.3 Data Pre-Processing and A/D Conversion 40
3.4 Electric Field Meters 43
3.5 Charge Locations Derived from Electric Field
Stations 44
3.6Charge Locations Derived from VHF Noise Sources ... 47
IVCOMPUTER ALGORITHM FOR LOCATION OF LIGHTNING
CHANNELS 49
4.1 General 49
iii

Page
4.2 Data Characteristics ....... 50
4.3 Technique for Determining Delays Based on the
Data Characteristics 55
4.4 Algorithm Flow Chart 62
4.5 Display of Three-Dimensional Locations and
Their Time of Occurrence 68
VANALYSIS OF RESULTS 72
5.1 The 165959 Flash 73
5.2 The 180710 Flash 123
5.3 The 181806 Flash 166
5.4 The 182356 Flash 220
5.5 The 180644 Flash 264
5.6 The 181416 Flash 27 3
VIDATA MODEL 281
6.1 Noise Level 284
6.2 Stepped Leader 284
6.3 J-Change 285
6.4 Characteristics of VHF Radiation 286
VIICHARACTERISTICS OF THE VHF RADIATION DURING THE
DIFFERENT PHASES OF LIGHTNING 287
7.1 Cloud-to-Ground Lightning 290
7.2 Intracloud Lightning 305
VIIICONCLUDING COMMENTS AND SUGGESTIONS FOR FUTURE
RESEARCH 309
APPENDIX
A DERIVATION OF SOURCE LOCATION FROM DIFFERENCE
OF TIME OF ARRIVAL MEASUREMENTS 311
B ACCURACY OF THE LOCATION OF LIGHTNING SOURCES
USING THE HYPERBOLIC EQUATIONS 315
xv

Page
B.l Error Analysis for the Locations of the 165959
Flash on 19th July 1976 324
B.2 Error Analysis for the Locations of the 181806
Flash on 8th August 1977 324
B.3 Error Analysis for the 180710 and 182357 Flashes
on 8th August 1977 324
C COMPUTER ALGORITHM TO DETERMINE VHF SOURCE LOCATIONS
FROM THE DIFFERENCE IN THE TIME OF ARRIVAL OF VHF
RADIATION DATA 330
D COMPUTER ALGORITHM TO DISPLAY A THREE-DIMENSIONAL
DRAWING OF VHF NOISE SOURCES 356
E FREQUENCY DOMAIN APPROACH TO DETERMINE DIFFERENCE
IN THE TIME OF ARRIVAL 364
E.l Measurement of Time Delay by Determining the
Peak of the Impulse Function 366
E.2 Measurement of Time Delay by Measuring the
Phase of the Frequency Response Function 367
REFERENCES 369
BIOGRAPHICAL SKETCH 376
v

Abstract of Dissertation Presented to the Graduate Council
of the University of Florida in Partial Fulfillment of the Requirements
for the Degree of Doctor of Philosophy
PROPERTIES OF LIGHTNING DERIVED FROM
TIME SERIES ANALYSIS OF VHF RADIATION DATA
By
Pedro L. Rustan, Jr.
December 1979
Chairman: Martin A. Uman
Co-Chairman: Donald G. Childers
Major Department: Electrical Engineering
The purpose of this research is to derive lightning properties by
correlating three-dimensional VHF source locations, characteristics of
the VHF (30 to 50 MHz) radiation, and electric field intensity (0.1 Hz
to 1.5 MHz). We study the discharge initiation, propagation, overall
geometry, and charge magnitude and location for the various phases of
both cloud-to-ground and intracloud lightning. We analyze in detail
four cloud-to-ground and three intracloud flashes, all selected
randomly. The experimental data were recorded during the summers of
1976 and 1977 at the Kennedy Space Center (KSC). The VHF radiation was
recorded using the multiple VHF stations of the KSC Lightning Detection
and Ranging (LDAR) system. We located the VHF noise sources from the
difference in the time of arrival (DTOA) between the pulses received at
the multiple VHF stations using a hyperbolic geometry. The electric
field data were recorded by the New Mexico Institute of Mines and
Technology (NMIMT) and the University of Florida. Leader-return strokes
vi

charge magnitude and locations, calculated for us by NMIMT, were corre
lated with our VHF source locations.
Previous work on three-dimensional "channel structure" during
lightning flashes was performed by Proctor in South Africa, who
pioneered the technique of VHF source locations. Proctor's determina
tion of DTOA was done manually by pulse shape identification on 253 MHz
signals. The three-dimensional source locations presented in this
thesis for the different phases of lightning discharges were obtained
using a computerized technique which allows a large amount of data to
be analyzed quickly.
The data were recorded with a wideband VHF receiver having a band
pass filter of 30-50 MHz and a logarithm envelope detector. The
detected signals from three of the stations were transmitted to the
fourth station where all were recorded on four tape channels having a
bandwidth of 400 Hz to 1.5 MHz. The analog tapes were digitized at
3 4
4.35 MHz, a sample every 229 nanoseconds. Between 20 x 10 and 25 x 10
pulses per flash were recorded during active VHF radiation. A newly
developed computer algorithm employing cross-correlation and pattern
recognition was written to determine the DTOA between the individual
pulses. Once the DTOA's were calculated, we used a three-dimensional
hyperbolic position measuring system to determine the source locations.
The significance of this research is the following: (1) We develop
an important new tool for lightning research: a computer program which,
using digital tape data from four VHF stat Lons, can determine source
locations every 7 to 10 microseconds. An average of about 20,000 loca
tions was found for each one of the studied flashes. (2) We derive
properties of the lightning flashes studied. Some of these results
vii

are: a) From observing the initial lightning VHF noise we can determine
whether a flash will become a cloud-to-ground or an intracloud discharge,
b) Cloud-to-ground flashes were initiated by a process we name preli
minary breakdown. The VHF sources during the preliminary breakdown
formed an inclined cylinder 5 to 12 km long and about 500 meter radius
between a height of 4 and 10 km. c) The VHF radiation of stepped
leaders and return strokes during cloud-to-ground flashes have unique
characteristics which can be used to identify these events by studying
the VHF noise alone. The stepped leader has the lowest level of
radiation of any process in the flash, but it radiates along the whole
path from the charge center to ground. d) Dart leaders do not emit VHF
radiation along their paths to ground, but rather in the neighborhood
of the previous J-changes. e) The paths of the VHF sources during
J-changes were inclined 25, 35, 45, and 55 off vertical.. The path
of the VHF sources during J-changes was well defined after the first
few strokes of a cloud-to-ground flash, but the path became less
organized as the stroke order increased. The first J-change of all the
ground flashes propagated downward toward the previous charge center
lowering negative charge.
viii

CHAPTER I
INTRODUCTION
The main purpose of this research is to determine VHF lightning
source locations in three dimensions and to relate these results to
other simultaneously recorded data, notably the dc to 1.5 MHz wideband
electric field, in order to obtain a better understanding of the physics
of the lightning discharge. The VHF radiation data were recorded during
the summers of 1976 and 1977 at the Kennedy Space Center (KSC) using
the KSC Lightning Detection and Ranging (LDAR) system. The VHF locations
were determined from the difference in the time of arrival of the VHF
radiation pulses at four LDAR ground stations. This study was part
of the Thunderstorm Research International Project (TRIP). TRIP brought
together a group of outstanding scientists in atmospheric electricity
from the USA and foreign countries with the purpose of performing
coordinated measurements during thunderstorms. The work reported in
this thesis represents an important new dimension in lightning research.
For the first time the use of a fully computerized algorithm has made
it possible to understand in more detail the different phases of a
lightning flash. We now have a much fuller understanding of the electrical
activity inside a thundercloud and we are better able to describe the
generation and propagation of the different phases of both cloud and
ground lightning flashes. It is to be hoped that the new techniques
developed as a part of this study will facilitate future research in the
field of atmospheric electricity.
1

2
In this introductory chapter we shall briefly survey the organiza
tional aspects of this thesis as well as some of the information pre
sented. Chapter II presents a general review of lightning and previous
lightning VHF time of arrival (TOA) research. Systematic lightning
research started in the middle of the eighteenth century with the work
of Benjamin Franklin. Modern lightning, however, did not start until
the early part of the twentieth century with the electric field measure
ments of C. T. R. Wilson published in 1916. Within ten years, cathode-
ray-oscillography and high speed photography were introduced to the
study of thunderstorm electricity. The first published suggestion that
VHF radiation might be used to determine source locations in three
dimensions appears to be due to Oetzel and Pierce (1969). The pioneer
ing work in the determination of source locations by calculating the
difference in the time of arrival was published by Proctor (1971).
Proctor's original work was performed manually and provided new infor
mation about the different phases of a lightning discharge.
Chapter III presents a description of the system used to perform
the VHF measurements. In addition, this chapter presents a brief
discussion of the measuring system used for the electric field measure
ments and of the point charge models which are used to interpret the
results. The original VHF data are analog (400 Hz to 1.5 MHz) tape
recordings of the output of envelope detectors of four ground-based VHF
(30 to 50 MHz) receivers located at the Kennedy Space Center. The
amplitude scale of the VIII radiation was made logarithmic to provide
80 dB dynamic range for the input signal. The VHF analog data for the
four stations were subsequently digitized at a sampling rate of 4.35 MHz.

3
Chapter IV describes the computer algorithm used for the location
of lightning VHF sources. Digital tapes containing VHF time-series
data from four stations were processed with the purpose of determining
the differences in the time of arrival (DTOA) between pulses in one
reference station and the remaining three stations. The computer
algorithm to determine DTOA was based on cross-correlation and pattern
recognition techniques. The cross-correlation function was optimized
to determine DTOA between the central and each one of the remote
stations every 94 ysec. For long processes when there was little
variation from one DTOA to the next by using 94 ysec intervals, a
longer sampling interval of 376 ysec was used. Even though the cross
correlation provides the DTOA for the 94 ysec intervals, it does not
determine the DTOA for individual pulses with a width much less than
94 ysec. Therefore, we used pattern recognition to determine DTOA
between individual pulses which were within 3.7 ysec of the cross-
correlated DTOA result. Using this technique we obtained a source
location every 7 to 10 microseconds.
Chapter V gives the lightning source locations and other derived
physical properties for the selected flashes. We randomly selected
four cloud-to-ground and two intracloud flashes from a group of about
1,000 which had correlated electric fields. The six flashes are referred
to in this thesis by the Universal Time of occurrence of the flash.
Except for the first flash at 165959 on 19th July .1976, all of the
remaining flashes were recorded on 8th August 1977. The cloud-to-ground
flashes are presented in sections 5.1 through 5.4, followed by the two
intracloud flashes in sections 5.5 and 5.6. We correlated the different
phases of each lightning flash with the electric field record at a

4
University of Florida station and at a network of eight electric field
stations designed and operated by the New Mexico Institute of Mines
and Technology (NMIMT). In addition, for two of the ground flashes, we
correlated our results with photographs of the lightning channels to
ground obtained from the KSC TV network.
Chapter VI presents a statistical model for the VHF radiation data.
This model was derived with the purpose of classifying the properties of
the time-series data. The Box and Jenkins (1976) techique was used to
identify a time-series model and to estimate the parameters of the model.
Chapter VII summarizes the properties of the different phases of
cloud-to-ground and intracloud lightning derived from the flashes
studied in Chapters V and VI. The main properties of the different
phases studied were the characteristics of the VHF radiation, the length,
direction and velocity of propagation of the various lightning paths
associated with different discharge phases, the charge transfer associated
with each of the lightning phases, and the total volume occupied by the
flashes.
Finally, Chapter VIII provides some concluding remarks and suggests
some of the areas for future research.
Appendices A through E are provided to present mathematical deri
vations or computer listings which were not appropriate for the text.
Appendix A gives the derivation of three-dimensional locations obtained
from the difference in the time of arrival. Appendix B provides the
error analysis in the determination of the three-dimensional locations.
Appendix B also shows four tables with tabulated RMS errors associated
with channel locations as a function of position. Appendix C gives a
Fortran computer listing used to determine DTOA in accordance with the

5
techniques described in Chapter IV. Appendix D provides a listing of
the computer algorithm to display the channel locations in three
dimensions. Lastly, Appendix E presents two frequency domain tech
niques which could be used to obtain DTOA. These techniques were not
used because they do not adapt to the experimental data as well as the
selected time domain technique described in Chapter IV.

CHAPTER TI
GENERAL REVIEW OF LIGHTNING AND PREVIOUS LIGHTNING VHP TOA RESEARCH
2.1 Description of Cloud-to-Ground and Intracloud Lightning
This section contains an introduction to the basic terminology of
the physics of lightning. Lightning is a transient, high current
electric discharge whose path length is measured in kilometers. A
lightning discharge starts when the electric field in some region of
the cloud exceeds the breakdown strength of air, that is, equal to or
6
less than 3 x 10 V/m, depending on pressure, temperature, and the
presence of precipitation. The most common source of lightning and the
only one considered in this thesis is the thundercloud. A typical Florida
thundercloud has a top between 9 and 15 km above sea level (Jacobson and
Krider, 1976).
The lightning produced by the thundercloud can take place within
a cloud (intracloud), between cloud and earth, between clouds, or
between the cloud and the surrounding air. Our study includes the
intracloud and the cloud-to-earth lightning usually called cloud-to-
ground or ground discharge. A complete discharge is called a flash.
Either discharge, the intracloud or the cloud-to-ground flash, typically
lasts 0.5 seconds.
Regardless of the type of flash being studied, one of the most im
portant factors in thunderclouds is the location and size of the charge
regions. The simplest and most accepted model of a thundercloud was
given by Wilson (1916). He assumed that the center of electric charges
6

7
within a thundercloud might be considered as point charges if the
dimension of the charge region was small compared to the ground distance
to the ground observation point. Under these assumptions the thunder
cloud charge was treated as an electric dipole with an upper part that
carried a positive charge and a lower part that carried a negative
charge. Electric field measurements performed by Malan (1963), and
balloon tests made by Simpson and Robinson (1941), and Gish and Wait
(1950) yielded an average value of 40 coulombs for each of the charge
regions. However, measurements of charge neutralization of the order of
40 coulombs or larger in single ground flashes made by Brook et al. (1962),
Uman et al. (1978), and Krehbiel et al. (1979) make us suspect that 40
coulombs is too low an estimate for cloud charge. In addition, Malan
(1952) estimated that about half of the cloud negative charge was
neutralized during the lightning flash. Since the external electric
field often used to compute the cloud's static charge is due to the net
of the thundercloud charge and the surrounding space charge, the actual
value of the thundercloud charge is larger than reported values. In our
study we used the difference in the electric field during the different
phases of a lightning flash to determine the charge being transferred or
destroyed in a thundercloud, so the actual value of static charge is not
important to our work.
A ground flash is composed of one or more separate strokes in the
same or separate channels. Each stroke lasts for milliseconds and the
time interval between strokes is roughly 50 msec.. A stroke is composed
of a downward propagating leader, which lowers cloud charge and cloud
potential toward ground level, followed by a return stroke, an earth-
potential wave, which propagates back up the leader channel, discharging

8
the leader to ground. Stepped leaders precede first strokes and some
subsequent strokes and move downward in about 50 meter steps with about
50 microseconds interval between steps. The velocity of the individual
steps is too fast to be determined from available streak photographs.
The stepped leader moves toward earth with a typical average velocity
of 2.0 x 10^ m/s. Dart leaders precede most subsequent strokes. Dart
leaders occur if additional charge is moved from another region of the
cloud to the top of the leader channel in a time less than about 100 msec.
A dart leader serves the same purpose as the stepped leader in that it
deposits charge along the channel and lowers cloud potential to ground.
The dart leader is less branched and has higher velocity than the
stepped leader. The elucidation of these processes is mostly credited to
Schonland and his co-workers in South Africa (1934 to .1938) who used
photographic techniques and electric field measurements. Discharges
also take place in the cloud in the time between strokes. Interstroke
electric field changes observed on the ground are termed J-changes;
interstroke impulsive electric field changes are termed K-changes
(Kitagawa and Kobayashi, 1958; Uman, 1969; Pierce, 1977).
Ground flashes can be classified as hybrid or discrete flashes
(Malan, 1954; Kitagawa et al. 1962). A lightning flash which involves
one or more continuing currents between strokes is called a hybrid flash.
A flash which involves only discrete strokes and no continuing current is
called a discrete flash. Between 29 and 46 percent of all ground flashes
have strokes followed by a continuing current (Livingston and Krider, 1978
Kitagawa et al., 1962), that is, hybrid characteristics. The J-change is
differentiated from the continuing current stroke because the J-change
has no channel luminosity and at close range the J-change electric field

9
has different polarity. The work on cloud-to-ground discharges presented
in this thesis will provide the VHF noise source locations for each
phase of hybrid and discrete flashes. Whenever wideband electric field
measurements were available, we attempted to calculate the charge
involved along the radiating paths. These findings provide additional
insights into the mechanisms of ground flashes.
The intracloud discharge is not as thoroughly investigated as the
ground discharge. On the basis of electric field waveforms, Kitagawa
and Brook (1960) studied the nature of electrical discharges inside
thunderclouds. They included the cloud to cloud, cloud to the surrounding
air, and the intracloud discharge, treated them as identical, and referred
to them as cloud flashes. Three phases of the cloud flash were classified:
initial, very active, and junction phase. The initial phase was charac
terized by a large number of small impulses. The active phase had larger
and more regular impulses. The final phase had a number of rapid regular
impulses. Ogawa and Brook (.1964) studied the variations of the electric
field with time and distance during the initial and junction phases of
intracloud discharges. They claimed that positive charge was lowered during
the initial phase by downward positive streamers, and that negative recoil
streamers occurred during the junction phase. This viewpoint is partially
shared by Takagi (1961) who proposed a mid-gap streamer where positive
streamers propagate downwards into the negative charges and negative
streamers propagate upwards into the positive charges. However, earlier
work by Pierce (1955) and Smith (1957) suggested that the intracioud
discharge raised negative charges. Khastgir and Saha (1972), using
questionable models attempted to prove analytically that the experimental
electric field curves of Ogawa and Brook (1964) could be interpreted as

10
either positive descending streamers, negative ascending streamers, or a
combination of both of these processes. The work in intracloud discharges
presented in this thesis will provide the VHF noise source locations in
three-dimensional space and in time. These findings should provide
additional information to help understand the mechanisms of the intra
cloud discharge.
2.2 Description of Electromagnetic Radiation Emitted by Intracloud
and Cloud-to-Ground Flashes
The most recent comprehensive study of the electromagnetic radia
tion produced by lightning discharges is given by Pierce (1977).
Briefly, this section presents a review of the radiation fields due to
the intracloud and cloud-to-ground flashes over the frequency range
from 1 KHz to 1 GHz.
One means of learning about discharge processes associated with
cloud-to-ground and intracloud lightning discharges is by measuring
the resultant electromagnetic radiation. Numerous investigators
(e.g., Malan, 1958; Brook and Kitagawa, 1964; Takagi and Takeuti, 1963;
Pierce, 1960; Kimpara, 1965; Uman, 1969; Proctor, 1971; Takagi, 1975;
Krider et al., 1977, 1979; Taylor, 1978; LeVine and Krider, 1977;
Serhan et al., 1979) have studied the electromagnetic radiation of
lightning in various frequency ranges with the purpose of deriving some
conclusions about the lightning discharge.
The electric field due to a small straight vertical conducting
element above a conducting plane can be calculated exactly at any distance.
These results are found in Uman and McLain (1970), and McLain and Uman
(1971).

1.1
(D,t) =
2ire
z0 2-3sin 0. t
I 2 T1' / 1
z, R."
1 J
Z,T -
dxdz
z 2-3sin^0.
+ / i
z, cR
z,t -
R.
J
dz
z sin 0 .
-2 3 di
-1 2
z c R.
1 J
9t
r "J]
dz
l c
(2.1)
where the subindex j represents the contribution due to one of the
current elements. The pertinent geometry, distance, and angles are
defined in Figure 2.1.
A spark channel carrying a transient current, usually referred to
as current element, acts as a radio antenna and emits electromagnetic
radiation. The radiation field from a current element is the term that
contains the time derivative of the current in equation (2.1). That is
ERad
(D,t)
1
2
2Tre c
o
sin 0. .
J. 9i
R. 9t
J
r
z, t
R.
-i ->
^ dz a
c J z
(2.2)
Halan (1958, 1963) first obtained correlation between the low
frequency electric fields and the radiation fields produced by intracloud
and cloud-to-ground lightning flashes in the 1 KHz to 10 MHz range.
Brook and Kitagawa (1964) measured radiation fields at frequencies of
420 and 850 MHz from lightning flashes 10 to 30 km away. Horner (1964),
Kimpara (1965), Pierce (1967), Oetzel and Pierce (1969), and Pierce
(1974) provided good reviews of correlated eleotric and radiation fields
extending from 1 KHz to 100 MHz. These reports showed that at frequencies
less than 300 KHz few current elements are active during the flash.
Isolated radiation pulses were obtained primarily during return strokes

Figure 2.1. Radiation field of a small current element.

and K-changes. The maximum energy of the radiation spectrum is at VLF.
The average source spectrum has a maximum at about 5 KHz and decreases
inversely proportional to frequency above 10 KHz. In the frequency
range from 300 KHz to 30 MHz the number of current elements increases
but the magnitude of the return stroke radiation pulse decreases. As
the frequency increases above 30 MHz the number of current elements
increases with a peak at 50 MHz, and then decreases (Oetzel and Pierce,
1969). Above 30 MHz the magnitude of the pulses decreases with increasing
frequency. At LF and VLF the length of the return stroke channel and the
K-change channel are of the order of magnitude of these wavelengths,
since the radiation half cycle time is the channel length divided by the
propagating velocity and this is the only radiation that exists. As
frequency increases into the HF and MF range, there are more current
elements with length comparable to the wavelength. We expect that most
current elements active during lightning discharges have lengths of the
order of tens of meters which will be detected with a center frequency
of tens of MHz.
Another important variable to consider in the study of atmospherics
is the effect of the propagation medium between the current elements and
the group receiving stations. Excellent reviews of the propagation
conditions of atmospherics can be found in Horner and Bradley (1964),
Oetzel and Pierce (1969), Harth (1974), and Pierce (1977). The charac
teristics are a function of the frequency of the emitting source, the
propagating distance, and the reflective properties of the earth and the
ionosphere. The ionosphere has complex reflection properties as a
function of frequency. According to Pierce (1977), the propagating
conditions of atmospherics can be separated into three groups. Below

14
300 KHz the earth and the lower ionosphere create a quasi-waveguide;
between 300 KHz and 30 MHz reflections occur from the ionosphere;
above 30 MHz atmospherics penetrate the ionosphere. In the research
reported in this thesis, the atmospherics were recorded in the VHF
range (30 to 50 MHz) where at the close ranges considered there is no
appreciable ionospheric reflection.
2.3 Lightning Direction Finders
The distant electromagnetic radiation associated with lightning
is usually called spherics. Spherics have been used as lightning
direction finders in the VLF and VHF range. The standard method of
location of distant ground flashes in the VLF range uses cathode-ray
direction finders (CRDF). This method was originally developed by
Watson-Watt and Herd (1926). It consists of two or more direction finding
stations, each with two vertical loop antennas usually tuned to a VLF
frequency. The azimuth angle of the flash is usually determined by
displaying the two perpendicular antenna magnetic field outputs on the
perpendicular scope axes. Two or more stations can be used to determine
the location of the discharge from the intersection of the azimuth vectors.
For discharge distances less than 100 or 200 km from the stations, the
accuracy of this standard technique has been found to be poor. This is
caused by the fact that if return strokes are not vertical, the antennas
will be sensing not only the vertical magnetic field but also the
horizontal component. As much as 20 degrees error has been found by
Nishino et al. (1973) at a distance of 200 km from the discharge.
Uman et al. (1975) observed that even at 10 km the initial peak magnetic
fields occurs in the first 5 ysec and hence is due to the vertical
channel position near ground. VLF direction finders have been improved

L5
considerably by Krider et al. (1976) using the properties of the magnetic
field previously observed by Uman et al. (1975). The improved VLF
direction finder has been successfully tested to detect the location
of ground flashes within 200 km of the stations (Krider et al. (1976)).
Oetzel and Pierce (1969) suggested that time-of-arrival techniques
could be used for line--of-sight direction finding in the VHF (30-100
MHz) range. VHF direction finders were developed along these lines by
Cianos et al. (1972) ; Murty and MacClement (1973) ; MacClement and Murty
(1978); and Taylor (1976, 1978). These VHF direction finders made it
possible to locate lightning discharges within a range of 100 or 200
km from the stations. Cianos et al. (1972) used two VHF stations
(25 to 35 MHz) separated by 122 meters. Using this system the difference
in the time of arrival (DTOA) was measured with an accuracy of 10 nsec,
and the azimuth angle of about 2000 impulses per flash was located.
The Cianos VHF direction finder operated in real-time for distances up
to about 150 km. The VHF direction finder described by Murty and
MacClement (1973) operated in the 82-88 MHz range and used difference
in the time of arrival (DTOA) to determine the azimuth angle of atmo
spherics up to 160 km apart. DTOA within 25 nsec were measured from
the scope traces. The latter system was improved by MacClement and
Murty (1.978) to include a third station. The third station permitted
measurement of elevation in addition to the azimuth angle. The system
operated in the 66-72 MHz range and D'IOA were measured with an accuracy
of 10 nsec. This system operated in real-time and located the azimuth
and elevation angles of about 300 impulses per flash. A two station VHF
(20-80 MHz) direction finder was also reported by Taylor (1975). This
system was later improved by Taylor (1978) to include a third station

1.6
to determine elevation angles. His 1978 system used a vertical and a
horizontal antenna, 13.7 meters apart, at each of two stations separated
by 17.8 km. The horizontally and vertically spaced antennas were used to
measure azimuth and elevation, respectively. Time measurements were
performed to 0.4 nsec with angle accuracy of 0.5 degree.
In addition to the VLF magnetic field ratio techniques and the VHF
time of arrival direction finders previously described, Lewis (1960)
used a VLF direction finder with DTOA techniques. Lewis used four
stations in a Y configuration with the central station at the intersec
tion of the Y. The distance between the central and the remote stations
(at the three ends of the Y) ranged between 100 and 120 km. This system
was used in relation to a system implemented in England to detect
spherics over the Atlantic Ocean and Western Europe. The waveforms
from the four stations were photographed on continuously moving 35-mm
film. Only three stations were needed for direction finders. The
remaining two stations were used for redundancy. The reported accuracy
for this system was about 0.5 degree of latitude and of longitude.
2.4 Review of Proctor's Work
In addition to the previously described direction finders, channel
locations have been reported by other means, such as, thunder measure
ments (e.g., Holmes et al., 1971; Nakano, 1973; and Teer and Few, 1974),
and radar studies based on the appearance and decay of ionized channels
(Hewitt, 1953, 1957). However the most relevant work to date is a DTOA
hyperbolic system that uses a minimum of four stations to determine the
three-dimensional channel locations (Proctor, .1976; Lennon, 1975).
By the time Oetzel and Pierce (1969) had suggested in print that
spherics locations could be determined by measurements of DTOA in the VHF

range, Proctor, working in South Africa, had built and tested a five
station system to measure noise impulses in the VHP range. Proctor
has written only a Ph.D. thesis and a limited number of papers and
reports about his work in South Africa. Next we will present a summary
of Proctor's work (Proctor, 1971, 1974a, 1974b, 1974c, 1974d, and 1976)
and its relationship to the work presented in this thesis.
Proctor (1971) describes his telemetry system and gives some
preliminary results. The system consists of four 253 MHz crystal-
controlled receivers located at the ends of a cross (the remote stations),
and a fifth station (the central station) at the center of the cross.
The distance from the central to the remote stations ranged between 10.7
and 26.7 km. All stations consisted of a 10 MHz bandwidth VHF receiver
centered at 253 MHz and progression detection i.f. amplifiers to give
the receiver a logarithm response near 80 dB. This detection technique
is very similar to the band-pass filter and logarithm envelope detector
used in the telemetry of the work reported in this thesis. The remote
station spherics were retransmitted to the central station by frequency
modulated 10 GHz links with 5 MHz bandwidth. Therefore the overall
bandwidth was 5 MHz for the remote stations and 10 MHz for the central
station. All five signals together with 5-ysec timing markers were
displayed on cathode ray tubes (CRT's) and they were photographed by
35-mm rotating drum cameras. The film moved with a velocity of 8 m/sec.
CRT's were also used to display electric field change and time markers.
When the operator had decided that the storm was sufficiently close for
channel reconstruction (usually less than 20 km') a trigger signal
selected a threshold level to start the film. The maximum continuous
film time is 250 msec. Since most flashes last more than 250 msec

18
and the triggering signal might not detect the beginning of the flash,
only limited information is recorded. The records are read by operators
who first identify the same pulse in all the stations and then measure
the DTOA between the four remotes and the central station. The records
are enlarged to .36 cm/ysec for reading purposes. Using a transparent
graticule, DTOA can be measured to .1 Usee. Redundant sets of readings
are obtained by using the additional station. The by-hand DTOA for
every pulse are fed into a computer which is programmed to solve the
hyperbolic equations and print the three dimensional locations. This
tedious technique required 8 man-months to determine the locations of
one 250 msec sample. The reported accuracy of the locations for a 20 km
range is 25 meters for X arid Y, and 140 meters for Z. Proctor (1971)
states that a limited number of 250 msec intervals had been processed.
Actually, from studying the article, we reasonably infer that only one
250 msec interval was completely processed.
The results reported by Proctor (1971) for the different phases of
the discharge are as follows. One stepped leader was processed with 225
locations. The radiation started at a height of 5 to 6.5 km above sea
level (ground level 1.5 km). The noise sources extended upward and
downward but the median height moved downward at 3 x 10'' m/sec for 7 msec.
The active region became greater by the end of the leader and extended
from near ground to a height of 6.5 km above mean sea level (MSL). Poor
height resolution at low heights does not permit the determination of
accurate channels. The noise emitted by dart leaders was reported to be
similar to stepped leaders. This information is in conflict with the
work presented in this thesis. We claim that stepped leaders have
unique, identifiable pulses not seen anywhere else in a cloud-to-ground

L9
or intracloud discharge. It was reported by Proctor that the noise
from dart leaders emanated from the upper part (heights of 5 or 6.5 km
above sea level) of the channel. During the return strokes the noise
was continuous for 100 or 200 ysec. Many sources were active and few
fixes were determined along the channel. Proctor (1971) reported
activity within 250 ysec following the return stroke. This activity
was located in the previous return stroke branches. The interstroke process
reported was confined to one flash. The interstroke emitted a large
fraction of the VHF noise during the ground discharge. It was reported
to start 10 or 12 msec after the first return stroke and involved regions
between 3 and 4 km of altitude. Interstroke noise after subsequent strokes
was reported to extend the previous channel in an upward direction.
Proctor (1971) reported no information about fixes in an intracloud
discharge.
Proctor presented his next report in the 5th International Conference
in Atmospheric Electricity (Proctor, 1974a). By this time 18 flashes
(250 msec intervals) had been analyzed. This paper is the first publi
cation to discuss the location of noise sources during a cloud flash.
It is claimed that cloud flashes emit pulsed radiation during their
initial and very active (VA) phases, but only pulsed trains, less than
one millisecond width, in the final stage. These trains were also
reported in the VA phase. According to Proctor, these trains are emitted
by two kinds of events. One produces a long propagation from the
previous noise sources while the other one produces a shorter path which
moves toward the starting volume of the flash going throughout
non-previously located channels. Proctor associates these trains with
6
K-changes. The speed of the train of pulses ranged between 3 x 10 and

:'.o
3 x 10 m/sec. The manner in which the sources form appeared erratic.
During the initial stage they seem to be confined to a volume less than
3
1 km ; then the channel emerged. The emerging channel is accompanied
with a sharp change of electric field during the beginning of the
discharge. The propagating streamer during a cloud flash, according to
Proctor, emits radiation from near the tip of the advancing leader, in
contrast to the stepped leader which radiates from both extremities as
well as in the intervening channels. Four isolated regions were presented
in the horizontal projections of the source locations. It is reasonable
to assume that these sources would in some way be connected if all the
VHF noises were identified.
Proctor classifies two types of cloud flashes in accordance with the
pulse rate of the emitting cloud. The low pulse repetition frequency (prf)
flash emits about 2000 pulses/sec while the high prf flash emits about
30,000 pulses/sec.
Proctor (1974a) correlates VHF noise source locations with the
weather radar precipitation echoes. Some flashes were contained almost
entirely in the regions of heavy precipitation. Some of the streamers
terminated at the end of the precipitation echoes. Some other flashes
followed the path of highest reflectivity gradients. The radar corre
lation reported was performed using a constant altitude plan position
indicator (CARPI).
Proctor (1974b, 1974c, and 1974d) consist of three special reports
published by the Council for Scientific and Industrial Research (CSIR)
in Johannesburg, South Africa. These reports d'eal with the sources of
cloud-flash spherics, instantaneous spectra of spherics, and VHF radio
pictures of lightning. Next we give our views of the significant findings
in these reports which have not been discussed previously.

?.l
Simultaneous recordings of the radiation field of lightning flashes
were performed at one site. The selected frequencies were 30, 250, 600,
and 1430 MHz. This experiment shows that pulses were emitted at all these
frequencies for the low prf cloud flashes but were not the same, in gen
eral, for the high prf cloud flashes. This is an important result which
has also been studied in recent years by Krider et al. (1979). Krider et
al. compared the wideband electric field (1 KHz to 2 MHz) and the 300 KHz
bandwidth RF receivers at 3, 69, 139, and 295 MHz for a distant storm
(50 km away). These results illustrate that pulses were simultaneous in
all these frequencies and a wideband (dc to 1.5 MHz) electric field pulse
(radiation term) also occurred at the same time. Proctor determined the
DTOA between the leading and trailing edges within single pulses and con
secutive pulses. He could find no definite relationship between the
direction of the vectors and the direction of the channel. But most
vectors, either between the leading and trailing edge of the same pulse
or between the trailing edge of one pulse and the leading edge of the
next pulse, had a component in the direction of the channel tip.
From the study of the pulse width during cloud flashes, Proctor con
cluded that the average extent of the active source was about 240 meters.
He claimed that channels are formed in a stepped information. This view
point was first proposed by Schonland et al. (1938) and later reported by
Pierce (1955), Ishikawa (1960), Takagi (1961), and Krider et al. (1979).
Proctor noted that the return stroke had differences in the pulse
width (in the tens of microseconds) between the different stations. He
related the difference in the pulse width to the velocity of the propa
gating potential wave via a Doppler-type effect. Pulse width differences
in the order of a few ysec were found in all wide pulses (over 50 ysec).

22
Proctor has estimated the amount of charge, the charge density, and
the current flow during the initial phase of a cloud flash. VHF source
locations during this phase propagated upwards in a path about 25 degrees
off vertical. The technique used consists of determining the centroid
of VHF locations every millisecond, and finding the amount of charge for
the given field change. The charge density and the current are determined
at each millisecond interval taking into consideration the field generated
by the two point charges and the leader. Using this technique, the
following parameters were determined: a) 10 Coulombs for the inital
phase of the IC (fast field change), b) 1 Coul/km charge density, and
c) a current of .2 kA every 3 msec. Since only one field meter was used
to determine the electric field and a number of assumptions had to be
used about the charge structure, these results are questionable.
The most recent work published by Proctor is his Ph.D. thesis
(Proctor, 1976). Next we will present a summary of our view of the new
ideas presented in his thesis.
Proctor classifies the VHF noise (253 MHz, 5 MHz bandwidth) pulses
in three groups: P pulses, Q noise trains, and S pulses. The P pulses
are nearly rectangular in shape with an average pulse width of 1 psec.
By comparing the same pulses with wider bandwidth (10 MHz), Proctor
claimed that P pulses were a rapid succession of very short spikes which
had been smeared into one pulse by the limited receiver bandwidth. Dur
ing a cloud flash these pulses appear at a rate of about 4.7 for groups
of 310 psec intervals. The time between groups was about 1.8 msec. The
Q noise trains consist of rapid successions of spikes. They are common
to all flashes and are more frequent in the junction phase of a cloud
flash. They appear to be related to very rapid movement of charges and

23
often accompany a K-change. S pulses are those that do not fit the two
categories previously described. In addition, Proctor often refers to
R noise as the abrupt (starting noise) pulse which is characteristic of
most return strokes.
The P-type of pulse has been the subject of additional analysis.
In general, it was reported that the rate of electric field change was
directly related to the frequency of P pulses. That is, a sequence of
P pulses indicated fast E field change while their absence indicated a
reduction in the slope of the field change. P pulses seem to be emitted
from regions near the advancing tip. By determining a fix at the
leading and trailing edge of the pulse, propagation vectors have been
found. The sources appeared to form at very high velocities near the
speed of light. The directions of the vectors grouped in cones whose
axes appeared to lie in similar directions for any one storm. Proctor
speculated that the geomagnetic field might have some influence in the
direction of the sources.
The Q noise trains and K-changes were also studied further by
Proctor (1976). Of 26 Q noise trains reported in one flash, only eight
had detectable K-changes and six of these were associated with positive
streamers. Proctor attributed this difference to the low gain of the
field meters. Contrary to Proctor, the work reported in the present
finds that more than 50 percent of the Q noise trains did not show any field
meter change. Our equipment was sufficiently sensitive to detect a
2 volt/meter change. The Q noise that Proctor reported was weak and
only 5 out of 26 channel locations were studied. These Q noises were
emitted from regions below the lower extremity of the flash. K-changes

do not always involve the main channel. Some K-changes propagated in
channels which were not connected with the previous channels.
The velocity of the main channel in a cloud flash reported by
Proctor was 1.7 x 10^ m/sec. This value was obtained by finding the
velocity between centroids 1 msec apart and located along the channel.
The velocity determined in this manner during the propagation of the
main channel in a cloud flash seems to be associated with the P pulses.
A high velocity between 2.7 x 10^ and 3.0 x 10^ m/sec is associated with
Q noise trains.
From the five cloud flashes reported by Proctor (1976), four ex
tended near-horizontal while one was near-vertical. The vertical flash
extended between -11C and -52C (6.3 to 13.0 km MSL) while the horizon
tal flashes developed at temperatures of 0, -7, -10 and -21C. It is
worth noting that the mainly horizontal flashes extended over a height
of 5 km while the vertical flash extended over a height of 7 km. The
vertical flash was associated with upward propagation of negative charge.
The diameters of the concentrated VHF sources were between 100 and 600
meters. Even though some noise sources were located in a much wider
diameter, Proctor attributed the wide channel to multiple branching.
Additional information in ground flashes provided by Proctor (1976)
follows: (1) Dart leaders were characterized by one or more successions
of wide pulses (tens of microseconds) separated by low amplitude Q noise
trains. The VHF noise sources during the dart leader connected separate
regions that had been previously ionized, and were not located near the
dart leader path to ground. (2) There was no apparent time difference
(greater than 10 psec) between the occurrence of the electric field and
VHF for the first return stroke. However, in most cases the VHF waveform

during consecutive return strokes either preceded or followed the electric
field waveforms by as much as a few hundred microseconds. In two
reported cases the VHF was absent during consecutive return strokes.
The locations of the beginning of the return stroke were usually found
near the top of the previous leader channel. The locations at the end
of the return stroke were usually found 1 or 2 km above the previous
return stroke sources. Very few locations were found near the previous
leader channel to ground. (3) Proctor reported that the largest amount
of VHF noise sources occurred during J-changes, but very little effort
was spent analyzing the process. He reported near-horizontal and near
vertical J-changes and that some VHF noise sources active during J-changes
occurred in sequence.
2.5 Review of Lennon's Work
Lennon (1976) described a VHF (30-50 MHz) DTOA Lightning Detection
and Ranging (LDAR) "real-time" system operated at the Kennedy Space
Center during the 1974-1975 period. Originally the system consisted
of four remote and one central stations. During 1977 the system was
extended to include six remote and one central station. Even though
only three remote and one central station are needed for DTOA measurements,
the additional stations provided redundancy. The remote stations were
located an average of 10 km from the central station forming two Y
configurations which share the central station. The system was designed
to sense the log of the envelope detected VHF radiation from atmospherics
in all the stations and retransmit the information from the remotes to
the central station. The signals from three of the remote stations were
retransmitted to the central station using 10 MHz bandwidth microwave

2ft
links (around 7.4 GHz). The signals from the other three remote stations
used 5 Miz bandwidth cables. At the central station a Biomation 1010
was assigned to each of the VHF signals. Biomation 1010 s were used to
digitize 2048 consecutive samples with a sample every 50 nanoseconds.
The output from the Biomation is transferred to the preprocessor. The
preprocessor has several functions. First, it performs a reasonableness
check by determining the largest signal in all the stations and by checking
if the DTOA of the largest signal is within the limitations of the
physical geometry. In addition, for this test to succeed, the central
station largest peak has to occur first. If these conditions are met,
the preprocessor is used to measure the DTOA between the largest signal
in the central and each one of the remote stations. Using the hyperbolic
system equations described by Holmes et al. (1951), Appendix A, two sets
of three-dimensional locations are calculated. If the values of the two
sets of stations do not agree within a few hundred meters, the data are
rejected. Otherwise the data are stored in digital tape and displayed in
a Plan Position Indicator (PPI) and a Range Height Indicator (RHI) CRT
screen. Since this process takes less than 100 msec, the output locations
are represented in near "real-time." Two milliseconds after the first
sample, the Biomation 1010's are ready to receive a new set of data and
repeat the same process.
This technique can provide very accurate fixes whenever only one
large VHF pulse is detected in all the stations. Since the data bandwidth
is 5 MHz and the sampling frequency is 20 MHz, this is a highly accurate
system. The system accuracy is within tens of meters for X and Y, and
150 meters for Z. For a study of lightning channels, however, this
processing is not adequate because a maximum of one location is determined

27
every 2 msec.. In practical applications reasonable locations are only
obtained every 5 or 10 msec. In addition, using only amplitude thresholds
the LDAR system can match the wrong pulses and pass the redundancy
test. Let us illustrate this problem with an example. Assume that
there are two active VHF regions emitting radiation of the same magnitude,
and these regions are located at any height and are a few kilometers on
the opposite side of the central station. Pulses, received from the A
and B regions in an interval of a few tens of microseconds, will be
tested simultaneously in the Biomation. The pulse from A will be larger
in the station closer to A, whereas the pulse from B will be larger in the
station closer to B. Regardless of redundancy, there will be a consistent
matching of pulses from A and B and meaningless results will be obtained.
The work described in this dissertation used some of the components
of the LDAR system. These components were the sensors and the telemetry
for the four stations. Instead of the Biomations, we recorded the
4-station (3 remotes and 1 central) VHF data on analog tape. The VHF
noise from the analog tape was later digitized and processed to recon
struct the lightning VHF sources. By using a computer implemented algo
rithm to process the data and display the output, our technique can pro
vide source locations every 5 or 10 ysec. For any given flash we determine
about 500 locations for every location of the original LDAR system. This
abundant information permits us to study the lightning channels inside
a thundercloud, not visible to any type of photography. Our computerized
data processing provides tens of thousands of locations per flash after
two hours of computer processing, thus far surpassing the by-hand
technique used by Proctor (1976), which can determine about 1000 locations

78
per flash after 10 man-months of processing. However, since our data
are recorded on analog tape with a frequency response between 400 Hz and
1.5 MHz, our source locations are not as accurate as those reported
from the LDAR or Proctor (1976) systems. In the next two chapters we
described the telemetry and data processing techniques used in this
research.

CHAPTER III
DATA ACQUISITION AND PROCESSING
Figure 3.1 shows a general block diagram of the data acquisition
and processing used in this research. The VHF radiation generated by
lightning flashes during thunderclouds was detected at four selected
ground receivers (RX), and recorded simultaneously at one station
(recorder). Four VHF radiation channels were simultaneously slowed
down (data pre-processing) and then digitized (A/D converter) at a
rate greater than twice the bandwidth of the recorded signal. A com
puter algorithm, to be described in Chapter IV, was developed to deter
mine the VHF source locations from the difference in the time of arrival
(DTOA) of the four time series VHF data. The results were interpreted
and related to other correlated data. In this chapter we describe
the technique used for data recording, the properties of the telemetry
system, the data pre-processing and A/D conversion, and other
correlated measurements used to supplement this research.
3.1. Data Recording
The LDAR system used to obtain the original data consisted of
a central and six remote stations forming two Y configurations, with
the central station at the center of the Y. Figure 3.2 shows the
station geometry. The detected VHF radiation at the remote stations was
retransmitted to the central station and recorded. There were two
methods of retransmission: microwave and wideband cables. Signals from
29

10
I
I
I
I
Figure 3.1. General block diagram.


32
the three remote stations in one of the Y configurations (Ml, M2, and
M3, Figure 3.2) were retransmitted to the central station using 10 MHz
bandwidth microwave links. Signals from the other three stations (Wl, W2,
and W3, Figure 3.2) forming the second Y were retransmitted to the central
station using 5 MHz bandwidth A-2A cables. All seven VHF radiation
signals were recorded at 120 ips on a 14 channel analog recorder operating
in a direct mode with a frequency response from 400 Hz to 1.5 MHz.
Timing information in IRIG B format (accuracy to fractions of milli
seconds) was recorded on one of the remaining tape recorder channels.
A minimum,, of four _recei.,yi.n,gi._st,ations i^ne^d^_..t-o_abt,a4n,^he_J\/HI^ radia
tion used for the determination of thTOe^dimensional-J.aca.tions.^Ololmes
and Reedy, 1951). Appendix A contains a derivation of the three-
dimensional locations obtained from the measurement of the difference of
the time of arrival between the remotes and the central station. The
baseline between the remotes and the central station in Figure 3.2 is
approximately 10 km. The 10 km choice was made by KSC personnel to
obtain accuracy in the order of 100 meters using a real time system for
source locations within the KSC geographical area. Figure 3.2 also
shows the location of the Vertical Assembly Building calibration signal
(VAB CAL) used to obtain the calibration error in the measurement of
source locations. An error analysis for the three-dimensional locations
is shown in Appendix B. During this research there were some variations
in the selection of the three remote stations for different flashes.
Appendix B also shows the selected remote stations for the different
flashes analyzed in this thesis.

33
3.2 Telemetry System
Figure 3.3 shows the telemetry system used at each receiving sta
tion. The signal w^(t) is received by a 5 meter-high linear antenna
array that detects the electric field. The signal is passed through
a 30-50 MHz bandpass filter (30-50 MHz for 1976 data, 40-50 MHz for
1977 data), included in the VHF receiver. Then the logarithm of the
magnitude of the envelope signal is obtained using an envelope detec
tor .
Figure 3.3 is redrawn in Figure 3.4 to show the operation of the
receiving system. Here, f = 40 MHz, and the bandwidth, 2B, is equal
to 20 MHz. Figure 3.5(a) shows an approximation to the squared band
pass filter. The g^(f) filter has gain N^. Figure 3.5(b) shows the
corresponding time domain function, g^(t), of the wideband VHF receiver.
gx(t) = 2 NlB cos(2TTtfq) (3.1)
Equation (3.1) can be obtained from Figure 3.5(a) by doing the
inverse Fourier Transform of g^(t). The g^(t) term consists of a slow
varying waveform of the form sint/t which constitutes the envelope of
the waveform cos(27rtf ) which has been modulated. The output u.(t) can
o l
be written as
U(t) = w.(t) 2NXB cos(2?rfot) (3.2)
where is the convolution operator.
The spectra of atmospherics from nearby lightning discharges has
been studied by various investigators (e.g., Takagi and Takeuti, 1963).

V ANTENNA
W; (t)
BANDPASS
FILTER
ENVELOPE
DETECTOR
Figure 3.3. VHF receiver and envelope detector.
Figure 3.4. Description of VHF receiver and envelope detector.
9|(f)
(a)
9|(t)
Figure 3.5. Approximation for band-pass filter:
and (b) time domain.
(a) frequency domain,

35
The general characteristics are shown in Figure 3.6(a). Figure 3.6(b)
shows an approximation of the frequency domain of the signal after the
VHF receiver.
The rectifier part of the envelope detector from u.(t) to
z^(t) is a log IF device designed by RHG Lab with center frequency at
40 MHz for the 1976 data and 45 MHz for the 1977 data. The IF device
has a 3 dB bandwidth which corresponds to the bandwidth of the VHF
receiver. The device risetime is better than .05 microseconds and its
dynamic range is about 80 dB. The input-output characteristic of the
log IF is given in Figure 3.7. The actual values are tabulated in
Table 3.1. It should be noted that the use of the log IF device is
quite convenient in this application because it permits an input range
4
from 30 microvolts (-80 dBm) to 300 millivolts (0 dBm), a factor of 10 ,
for an output range from .255 to 2.5 volts, a factor of 10.
Assuming that W (f) is constant over the frequency range of interest
(30 to 50 MHz), the u^(t) can be represented as a time dependent
modulation P(t) multiplied by a phase displacement, i.e.,
u.(t) = P(t)cos(w t + 0) (3.3)
i o
Therefore
z(t) = logjP(t)cos(wQt + 0)| = log|P(t)|
+ log|cos(w t + 0)| (3.4)
The second term will be filtered out by the envelope detector
because it is at a frequency higher than 50 MHz. The log|P(t)| will
be recovered at the output.

l6
40 MHz
(b)
Figure 3.6(a). Input spectra. Figure 3.6(b). Spectra after
the VHF receiver.
Output (volts)
.03 .1 .3 I 3 10 Millivolts
Figure 3.7 Log IF input-output characteristics.
Table 3.1. Log IF Test Values
Input (dBm)
Output (volts)
-80
.255
-70
.542
-60
.798
-50
1090
-40
1.394
-30
1.675

57
z(t) = log IP (t) I (3.5)
The z(t) signal represents the time dependent logarithmic envelope
of the VHF radiation.
From standard envelope detection treatment (e.g., Thomas, 1969;
Davenport and Root, 1958), we know that the frequency spectrum of z(f)
is concentrated in several regions as shown in Figure 3.8. The z (t)
output data is recorded on analog tape with a frequency response from
400 Hz to 1.5 MHz. Figure 3.9 shows the frequency content of the signal
that is recorded in the tape recording channels. The z^(t) signal is
composed of unipolar pulses. Since the recorder had a 400 Hz lower
cutoff frequency, the VHF radiation out of the recorder has no frequency
component below about 400 Hz and is roughly symmetrical about the center-
line through the radiation.
3.2.1 Description of Center Frequency, Bandwidth, and Magnitude Level
in the Telemetry System
3.2.1.1 Center Frequency. The choice of the 30 to 50 MHz range
for the band-pass filter was made for various reasons. First of all,
the lower limit was selected above the HF range where multiple reflec
tion of the ionosphere will occur disturbing the signal (Horner, 1964;
Pierce, 1976). Furthermore, the upper frequency limit was chosen below
the VHF band for television channels, FM radio, and other sources of
interferences. Thus the use of the 30-50 MHz range reduces the noise
level. In addition, previous work (Oetzel and Pierce, 1969; Cianos et
al., 1972) on measuring the radio emissions from lightning have proved
that the largest number of detectable radiation pulses are present
between 20 and 100 MHz. As the frequency increases above the HF range,

38
t z (f )
/
/
/\ /
>S(f )
A
/\A/2
2fo
-80MHz
K-2B-H
20 MHz
2f0
80 MHz
Figure 3.8. Frequency spectrum at the output of the envelope detector.
Figure 3.9. Frequency spectrum at the recorder.

39
the number of pulses and their magnitude decreases. Oetzel and Pierce
(1969) claimed that the maximum signal-to-noise ratio is obtained
between 20 and 100 MHz. Probably the lower part of the VHF range,
around 30 MHz, is the ideal center frequency to study lightning
radiation channels.
3.2.1.2 Bandwidth. The receiver bandwidth is an important fac
tor in determining the pulse characteristics. It is desirable to use
wideband receivers, since if narrow bandwidths are used, the detected
radiation pulses will appear almost identical making cross-correlation
difficult. The minimum pulse width detected in a telemetry system is
inversely proportional to the receiver bandwidth and the minimum rise
time is the reciprocal of the bandwidth. Therefore, a VHF receiver with
a narrow bandwidth of 1 KHz will only detect pulses equal or greater
than 1 msec. Studies performed by Oetzel and Pierce (1969), Pierce
(1977), and Proctor (1976) have shown that the maximum number of VHF
lightning radiation pulses ranged between 10,000 and 500,000 pulses per
second. That is a maximum pulse repetition rate of a pulse every 20
ysec. In order to measure time difference between the individual
pulses, resolution of about one microsecond is needed, which requires
a bandwidth of 1 MHz. However to determine lightning source locations
to an accuracy of hundreds of meters, time differences must be measured to
a fraction of a microsecond (Appendix B). With the exception of Lewis (1960),
who used a bandwidth of 41 KHz with center frequency in the VLF range,
all the recent researchers who have measured the difference in the time
of arrival on radiation from lightning have used a wideband system and
a center frequency in the VHF range (e.g., Proctor (1971), bandwidth
5 MHz with center frequency at 253 MHz; Taylor (1973), bandwidth 60 MHz

with center frequency at 50 MHz; Canos et al. (1972), bandwidth of 10 MHz
with center frequency at 30 MHz). In the work reported herein a 20 MHz
bandwidth centered at 40 MHz is used for 1976 and a 10 MHz bandwidth
centered at 45 MHz is used for 1977 data.
3.2.1.3 Amplitude. Oetzel and Pierce (1969) summarized previous
work on amplitude spectra of the radiation from lightning between
100 KHz and 10 GHz. The receiver bandwidths were normalized to 1 KHz
and to 10 km range. The various data after normalization agreed within
an order of magnitude. On the basis of those results, we have deter
mined that the signal amplitude at 40 MHz with 20 MHz bandwidth is
about 30 mV/m at a range of 10 km. The relative magnitude of the VHF
radiation signals reported herein vary between a noise level of -70 dBm
(.1 mv) and a maximum detected amplitude about -20 dBm (30 mv), a factor
of 300.
3.3. Data Pre-Processing and A/D Conversion
Analog tapes containing six randomly selected lightning flashes
recorded in the Kennedy Space Center, Florida, were sent to Eglin AFB for
digitization. Figure 3.10 shows the digitization process used at Eglin AFB.
The data pre-processing and A/D conversion consisted of four different
steps, three of which were the slow-down process, the final step was
the digitization process. The selected time intervals were first slowed
down by a factor of 4 in a direct-recording-reproduce mode. The purpose
of this step was to reduce, the upper frequency content of the data
from 1.5 MHz to 375 KHz. Using the direct mode the recorded lowest
frequency range will be multiplied by the slow-down factor, that is,
from 400 Hz to 1.6 KHz. Since the wider pulses observed in the final
processed data were in the neighborhood of 200 psec, limiting the

EGLIN AFB
ADTC/ADUA (MATH LAB)
ANALOG TAPE KSC
DIGITAL
400Hz 1.5 MHz
TAPES
I
ft
SLOW DOWN BY 4
K
SLOW- DOWN
SLOW- DOWN
N
DIGITIZE AT
8.5 KHz
4 CHANNELS
DIRECT-RECORDING
V^]
BY 16 FM MODE
V'H
BY 8 FM MODE
^
TIME COR.
PDP-15
SLOW-DOWN RATE-4 X 16 X 8 = 512
REAL TIME SAMPLE RATE1 8.5 KHz X 512 = 4.352 MHz
2F = 3MHz (MEET NYQUIST RATE)
MAX
(SAMPLE EVERY .229 MICROSECONDS)
3.10.
Slow-down and digitization
technique used at Eglin AFB.
Figure

42
pulse risetime to 1/1.6 KHz = 625 ysec did not reduce the information
content. The significant aspect of this step was to reduce the band
width of the analog data to within 500 KHz, the maximum available band
width for FM modules. The remaining two slow down processes used FM
modules, first a factor of 16, then by a factor of 8. The FM modules
were used because they maintain the low frequency content of the data.
As part of the latter slow-down process, the four channels containing
the desired information were digitized simultaneously at a rate of 8.5
KHz. Since the total slow-down rate was 4 x 16 x 8 = 512, the real
time sample rate became 8.5 KHz x 512 = 4.352 MHz. This sample frequency
is well beyond the Nyquist rate of two times the maximum tape frequency.
Using this high sampling rate, digitized points can be linearly inter
polated with straight lines without significant loss of characteristics
(Jerri, 1977).
Time correlation is an important factor of the slowing down and
digitization process. The original IRIG B recorded in the tape is still
readable during the first factor of 4 slow-down. At this stage a
different IRIG A (ten times faster than IRIG B) is recorded on a
different channel and the initial desired processing time is converted
to the new IRIG A code. In the next slow-down (a factor of 16), the
previous IRIG A is still readable and a new IRIG A is introduced. The
desired starting time is converted from the previous IRIG A to the new
IRIG A. During the final slow-down process (a factor of 8), a time code
generator automatically reads the initial converted starting time, which
is typed in as part of the program, and starts 'digitizing when this time
is reached. Although the initial absolute time can only be read in
millisecond or a fraction thereof, from the original IRIG B timing

signal, the time difference between different events in the same flash
is only limited to a maximum of two or three microseconds due to tape
stretching. This procedure of time conversion allows us to read
accurately the original time-of-the-day with an absolute resolution of
about 100 ysec.
The twelve seconds for the six selected lightning flashes were
expanded to 12 x 512 = 6144 seconds prior to digitization. The
6144 second data were digitized at 4.352 MHz for a total of 52.244 x 10^
sample points per channel or 208.9 x 10^ total samples for the four
channels. The digitized data were recorded using 2400 feet, 7 track,
800 bpi, digital tapes. Approximately 1.638 x 10 samples per channel
can be stored on a 7 track tape. Therefore about 52.244/1.638 = 32 tapes
were needed for processing.
The tapes containing the calibration pulses were processed in a
manner similar to the one previously described for the lightning data.
Two differences were noted: 1) there was no need to convert timing
information, and 2) the digitization rate was increased to 8 MHz, a
sample every 115 nanoseconds. Appendix B shows the uncertainties in
the three-dimensional locations due to the calibration error.
3.4 Electric Field Meters
The waveforms recorded by the electric field measuring systems of
the University of Florida (U of F) and New Mexico institute of Mines and
Technology (NMIMT) wore used for correlation with the radiation field.
The electric field measuring systems used by U of F were similar to that
described by Fisher and Uman (1972) and later by Krider and his co-workers
(Krider et al., 1975, 1977). The correlated waveforms from the U of F
electric field system for 1976 consisted of an FM channel with a frequency

44
response from DC to 20 KHz and a direct recording channel with frequency
response from 300 Hz to 300 KHz. The electric field input to the
recorder had a response from 0.2 Hz to 1.5 MHz. In 1977 the recording
system was improved such that the analog data was recorded with a FM
frequency response from DC to 500 KHz, and a direct recording with a
frequency response from 400 Hz to 1.5 MHz.
The correlated waveforms from the NMIMT electric field stations
consisted of a network of nine stations spread out over the KSC area
(Krehbiel et al., 1974). The electric field sensed at eight remote
sites was retransmitted as amplitude modulation over a microwave telemetry
link to the central station (station nine). At the central station the
electric field from all the stations was recorded on analog tape. The
NIMIT electric field meter had a system decay of 10 sec and a frequency
response from 0.1 Hz to 5 KHz.
KSC IRIG B time code information was stored in all the analog tapes
containing electric field information. Time correlation between any of
the electric field stations and the four LDAR VHF radiation data was
accurate to one hundred microseconds.
3.5. Charge Locations Derived from Electric Field Stations
The electric field (E) detected at a horizontal distance d from a
charge Q at a height z from a perfectly conducting ground plane is given
by Uman, 1969, pp. 48-49.
E =
2 Q z
2 2
4tte (z + d )
o
3/2
(3.6)
where e is the permittivity of free space. The term d can be expressed

4 5
as
2 2 2
d = (x-xjL) + (y-y^)
(3.7)
where (x ,y.) is the ground coordinate at the electric field station,
t S
Therefore the electric field at any station can be expressed as
E.
i
2 Q z
4tt£ ((x-x.)^ + (y-y.)^ + z^)
o x 1
3/2
(3.8)
Assuming a one point charge model where the charge Q at (x,y,z) is
removed producing a field change E., four electric field measurements are
L- i
needed to determine the four unknowns Q, x, y, and z. Fitzgerald (1957)
obtained an analytical solution for this equation when the ground-based
electric field stations were located at the vertices of a parallelepiped.
Krehbiel et al. (1974) derived an analytical solution to equation (3.8)
without limiting conditions, assuming that a solution does exists. The
solutions obtained from a set of four stations using this technique were
1 to 3 km away from each other because the electric fields at each
station were slightly in error. However when several solutions of a
group of four stations were used, about 75% of the solutions fell in a
3
volume of 1 or 2 km This is a reasonable technique for finding the
charge center neutralized by return strokes whenever d z. When d
is comparable to z, the point charge model is not a reasonable approxi
mation to finding the value of Q and its location, and a solution
using this model usually does not exist.
Jacobson and Kridcr (1976) improved the analytical solution derived by
Krehbiel et al. (1974) using a nonlinear least square iteration technique
where all the electric field stations are considered. Iterations are

performed to determine Q, x, y, and z which minimizes C in
, N E E .
y mi ci
-
1=1 l
(3.9)
where E and E are the measured and calculated field, N is the number
mi ci
of measurements, and 0. is the measurement error. The values of the
i
charge centers presented in this thesis, unless specified otherwise,
have been obtained using the least square technique as described by
Krehbiel et al. (1979).
A reasonable model for the charge neutralized during some
lightning phases, especially J-changes and the intracloud discharge,
consists of a point charge which we move from height h^ and horizontal
distance d^ to a height h^ and horizontal distance d^. The change of
electric field is (Uman, 1969, p. 70),
+ d,
3/2
(3.10)
where Q is the charge moved and is the permittivity of free air. The
values of d^ and d^ are expressed as
d2 = ^x2 xi') + (y2 yi') ^
2JS
1
((*, x) + (yx yp )
(3.11)
Seven parameters are needed to solve equation (3.1/3), namely, the
coordinates of each of the ends and the charge involved. Jacobson
and Krider (1976) extended their application of the nonlinear least
square fit to solve equation (3.10).

3.6 Charge Locations Derived from VHF Noise Sources
The VHF radiation during initial and subsequent stepped leaders
has unique properties. The stepped leader VHF radiation has lower
amplitude and higher frequency than any other event during a lightning
flash. Initial stepped leaders are preceded by lower frequency pulses
with higher magnitude that we have called the preliminary breakdown (PB).
Similarly, stepped leaders before subsequent strokes are preceded by higher
magnitude pulses which characterize the J-process. In addition, the
beginning of subsequent stepped leader VHF radiation is often accompanied
by correlated change of slope in the electric field record. During
the entire first stepped leader VHF radiation, significant correlated
electric field change is detected. However, stepped leader electric field
change has been detected as much as 1.2 msec prior to the first stepped
leader VHF radiation which corresponds to about 2 km change in the VHF
sources. These properties are discussed in detail in Chapters V and VI.
In this section we discuss the use of VHF noise sources to determine
the charge value and its location.
On the basis of the above statements, we have chosen the noise
source location where the VHF radiation changes characteristics from PB
or J-change to stepped leader. The location of this point charge which
will be lowered to ground by the stepped leader-return stroke process.
This is a reasonable assumption since stepped leader VHF sources are
detected from this point on and throughout most of its path to ground.
We have proceeded to solve equation (3.8) for the value of the point
charge (Q). The value of (x,y,z) in (3.8) corresponds to the VHF source
for the beginning of the stepped leader in the VHF record; the value
of (x^,y^,) and E_^ are the ground coordinates and electric field change

48
during the correlated electric field change. Since the electric field
records from at least eight ground stations in the KSC area were provided
by Krehbiel (private comm.), we could verify our results by using differ
ent electric field stations. We found that as long as the horizontal dis
tance from the electric field station to the point charge source was
further than the height of the source, our charge calculation was within
20% for the E-field at each station. Throughout this work, we selected
an electric field station which gave results in the middle of the 20%
deviation. The fact that we obtained inconsistent results for a
horizontal distance less than the height is an indication that a point
charge is not a good approximation within this range. For all the
stepped leader-return stroke studied in this thesis, we have calculated
the value of its charge source using this technique and whenever available
we have compared this result with the values obtained by Krehbiel
(private comm.) using the technique described by Krehbiel et al., (1979).
As we shall see, our results compare well with those of Krehbiel for
charge magnitude and location.

CHAPTER IV
COMPUTER ALGORITHM FOR LOCATION OF LIGHTNING CHANNELS
One important task of this research is the development of an
algorithm to measure time delays between every "identifiable" pulse
detected at the central and at the three remote stations. From the
measured time delays, the three-dimensional locations of the VHF
radiation sources are determined by using hyperbolic equations (Holmes
and Reedy, 1951). In this chapter, we review the available techniques
for determining time delays, and then we describe the technique chosen
for the present study.
4.1 General
Two types of computer processing are performed as part of this
thesis: First, we determine and display locations as calculated from
the measured time delays. Second, we determine a data model for the
VHF radiation time series data. The first task is described in this
chapter whereas the second task is studied in Chapter VI.
Since the Second World War the measurement of time delays has been
an important aspect of engineering work. Some important applications
of time delay measurements over the last 30 years include:
a) Radar technology based on the measurement of time delay between
a transmitted and a received pulse (Skolnik, 1962). Some of
the applications required estimating the distance to other
planets.
49

50
b) Navigation (Aircraft, Missile, Vessel). Time delays are widely
used in the field of aircraft and missile navigation to deter
mine a location update (Holmes and Reedy, 1951). The LORAN
worldwide system presently used for civilian and military air
craft navigation update is based on the measurement of time
delay between signals at known positions to determine the air
craft position (Pitman, 1962).
c.) Seismic signal processing for oil and gas (Wood and Treitel,
1975). Time differences between reflected seismic signals map
structural deformation and provide the locations of oil and
natural gas layers.
d) Ground response to earthquake conditions (Enochson, 1973).
The time difference at two separate ground locations is used
to determine the transit time of particle velocity waves
through soil when activated with earthquake loading conditions.
e) Digital signal processing. Measurement of time delays between
a stimulus and a response to a system or between two time series
has wide applications in the field of communication (Roth, 1971).
f) Determination of lightning channels. Oetzel and Pierce (1969)
proposed the determination of lightning channels by measuring
the time delays between four stations. A similar technique
was independently implemented in South Africa in 1968 and
described by Proctor (1971). In the USA a real-time system was
developed by Lennon (1975) .
4.2 Data Characteristics
In order to find a systematic technique for measuring the difference
in the time of arrival between four data channels, it is necessary to study

51
the properties of the multiple channel VHF radiation and the properties
of the time-series data.
4.2.1 Properties of the Multiple Channel VHF Radiation
Some of the important properties of multiple channel VHF radiation
are as follows:
1. The VHF radiation received at the three remote stations was
retransmitted to the fourth station (central). Since VHF radiation was
also recorded at the central station, any radiation pulse, from anywhere
in space, identified at the central station will arrive before the
arrival of the same pulse retransmitted from the remote stations.
Figure 4.1 shows an example of the four channel VHF radiation. The
signal from the central station (A) arrives before the signal from the
three remote stations (B, C, and D).
2. Since the radiation field is inversely proportional to the
distance from the space source location to the ground receiving stations,
there are differences in the magnitude of the radiation at each of the
stations. For ease of comparison the four channels are normalized with
respect to the central station. The amplitude normalization has no
effect in the shape of the pulses and provides a more effective compari
son between the four stations' data.
3. From equation (2.1) we know that the radiation field is propor
tional to the sine square of the angle between the center line of the
radiating element and the line to the ground station. Therefore, some
high amplitude pulses in a ground station with an angle near 90 might
fall within the noise level in another station 20 km away with an angle
near 180. This will be the case for a near-vertical radiating source
located immediately above a ground based station. In this case 0 = 180

Figure 4.1. Four channel VHF radiation directly from the
recorder for the beginning of the intracloud
flash occurring at 181416 UT on 8th August 1977.
(A) is the VHF radia tion at the central station
7.6 km from the discharge. (B), (C) and (D) are
the VHF noise for the remote stations, 7.4, 4.1,
and 12.4 km from the discharge, respectively.

53

for that station and no VHF radiation is detected whereas significant
radiation is located at the other stations.
4. Since the analog tape direct recording follows a Butterworth
response with a 3 dB drop-off at 400 Hz and 1.5 MHz, only pulses with
an original period between 2.5 msec and 0.66 ysec could be properly
measured with this recorder bandwidth. The largest pulse width measured
was about 500 visee; therefore,the lowest recorder frequency did not
limit the characteristic of the data pulses. In addition, we studied
the characteristics of the VHF pulses obtained with a 5 MHz bandwidth
using the Biomation 1010 in the LDAR real-time system. We determined
that about 5% of the VHF pulses had a width between 0.2 and 0.6 ysec.
These pulses and any shorter ones were lost in our analysis.
4.2.2 Properties of the Multiple Time-Series Data
We displayed some selected data with a 10 dB signal-to-noise ratio,
from the four channels, with a resolution of 1 ysec per cm for the pur
pose of studying the characteristics of the pulses in the series. From
this display we manually determined the DTOA between identifiable pulses
Some of the important characteristics that we identified are listed
below:
1. With the exception of the stepped leader radiation discussed
in Chapters V and VI, the time-series data contained an envelope with
pulse widths between 5 and 500 ysec. In addition, there were higher fre
quency pulses of a pulse width usually less than 3 ysec superimposed on
the envelope.
2. To identify uniquely the same pulse on any two of the time-
series, two selection criteria were used. First, we matched the lower
frequency envelope on which the pulses were superimposed. Second, we

identified the corresponding pulses within the envelope. When we per
formed our manual matching of pulses, we attempted to determine a
minimum time interval, needed for a unique identification of the envelope.
After studying different sections of the data, we determined that the
minimum sample interval to uniquely characterize the envelope was about
100 ysec. In addition, we attempted to determine a time interval
required to uniquely identify the duration of the individual pulses
which are superimposed in a selected time interval of 100 ysec. Our
results indicated that a maximum interval of about 3 ysec was required.
3. An additional test that we performed was to pass the time-series
data through a low pass filter that eliminated all pulses wider than 10
ysec. When we attempted to match the individual pulses manually, we
were only 20% successful. On the other hand, when we smoothed the data,
getting rid of the high frequency pulses, we were 100% successful on
matching the envelope for a sample interval of about 100 ysec. In the
latter test, we have lost information on the individual high frequency
pulses.
4. To determine some additional characteristics of the time-series,
we measured the time delays of 185 consecutive individual pulses between
the central and each one of the remote stations in one flash and 50 pulses
in another flash. We learned that time delays for over 95% of the con
secutive pulses are within a 2.5 ysec interval.
4.3 Technique for Determining _Delays Based on the Data Characteristics
Our next step was to develop a computer algorithm to determine time
delays based on the data characteristics of our time-series. To meet
the data properties in Section 4.2.2, we chose to use cross-correlation

and pattern recognition techniques. On the basis of Sections 4.2.2(1)
and (2), we decided to use cross-correlation functions with sample
intervals of 94 or 376 ysec, which correspond to either one or four
blocks of digital data, to determine the time delay of the envelope
signal. To comply with property 4.2.2(3), we smoothed the data before
the calculation of the time delays. The smoothing was performed by
using moving averages of 16 data samples across the cross-correlated
interval. The peaks of the cross-correlation functions were used to
determine the cross-correlated time delays and the corresponding loca
tions. The cross-correlation functions arc weighted toward the loca
tions of the envelope pulses in the sample interval. Once the cross
correlation DTOA's are known, the computer uses a pattern recognition
scheme to identify the DTOA between individual events in the envelope-
detected signal. A search over a 3.7 ysec interval around the cross-
correlated DTOA's is used. This time interval was chosen to comply with
the properties of the time-series described in Section 4.2.2(2). Next
we present a description of the cross-correlation and pattern recogni
tion techniques.
4.3.1 The Cross-Correlation Function
The cross-correlation technique we use has been applied in a variety
of fields, e.g., statistical theory of communication (Lee, 1960), geo
physics (Enochson, 1973), biomedical engineering (French and Holden, 1977),
rad a r d v t e c lion (S ko 1 n :i k, .1962).
Let x and y be two time-series. In our application y can be the
central station data while the x^ can represent any of the remote sta
tions. The discrete cross-correlation function between x and y can be
n 'n
defined as

'7
N-l
R
xy
(J) = l
n=0
x
n
n+j
(4.1)
where N is the number of data samples. Since the signal at the central
station (y ) always arrives first (property 4.2. 1(1)), we have to delay
the y signal by a certain amount T. In addition, a noise term r is used
n n
to account for properties 4.2.1(2), (3), and (4), and different
background noise. Therefore
x
n
n+x
+ r
n
(4.2)
Substituting equation (4.2) into (4.1), we get
N-l
R
xy
(i) = I (y
n=0
n+T
+ r
n
N-l N-l
) V y + y r y
L n n+T n+1 L- n^n+i
n=0 n=0 J
(4.3)
or
R
xy
(j)
= R (j
yy
T) +
R (j)
ny J
(4.4)
Depending on the cross-correlated value of the noise R (j), the
peak value of R ( j) will occur in the neighborhood of j = T. Our task
is to find the maximum value of R and see what the lag T is for a maxi-
xy
mum. If data from ensemble averages of x^ and y^ are processed, the
cross-correlated noise term can be averaged out and a more accurate
value of R can be determined. However each selected interval of the
xy
multiple series has different time delays and additional data for
averaging is not available. In addition, the VHP radiation properties
4.2.1(2) to (4) indicated that there might be substantial differences
between the data recorded in the different stations.

The cross-correlation function R (i) was normalized as
xy J
r (j) = R (j)/
xy J xy J
N-l _
c
r1
1
53
'T.
y x_2
l yn
- 1 r (j) 1
(4.5)
1! [
O
n=0
xy
To prevent any error due to ambiguous selection of r (j) when the
xy
function flattens out near maximum, four decimal digits are used for
comparison. For S/N greater or equal to 10 dB the optimum value of
r (j) ranged between 0.9300 and 0.9850. Once the four station time-
xy
series data are cross-correlated for a selected time interval of either
94 or 376 ysec, the procedure is continued for the next interval. For
the cross-correlation function to be applied the signal level must be
greater than the noise level. Before the beginning of the flash, the
noise threshold level is calculated and the data is not processed if
the S/N is equal to or less than 0 dB.
Once we have determined the cross-correlated time delays, we need
to calculate the time delays of the higher frequency pulses superimposed
on the envelope (see properties 4.2.2(1) and (2)). To achieve this task
we used pattern recognition techniques.
4.3.2 The Pattern Recognition Technique
Widrow (1974) has divided the field of pattern recognition into
two broad schools: the first group classifies the data by comparing
individual features with a pattern recognition list, the other group
attempts to fit the data to some type of template matching. Gottman
and Gloor (1976) working in electroencephalogram and Weinberg and
Cooper (1972) working in neurophysiology applied the first and second
pattern recognition techniques, respectively, obtaining successful
results. Additional pattern recognition applications include

59
ehromotograms (Widrow, 1974), speech (Boudry and Dupeyrat, 1974), and
picture rasters (Erich and Foith, 1976)* We classified our data with a
pattern recognition list similar to those described by Gottman and
Gloor (1976). Before we could apply the pattern recognition list to
match the individual pulses around the cross-correlation time delay,
we had to define a pulse model. Next we provide our pulse model defini
tion.
4.3.2.1 Pulse Model. We divided the four time-series in subsets
of 3.7 psec (16 samples), roughly the maximum pulse rate for which the
data could have the identifiable characteristics needed for pattern
recognition. Then, the sample value which corresponds to the peak of
the data subset is determined. This sample value is needed to perform
peak recognition of the time-series. The peak recognition is performed
as follows: 1) We determine the time delay for the cross-correlated
interval of either 94 or 376 psec between the central and each of the
remote stations. 2) We determine the time at which peak values occurred
for each data subset within the 94 or 376 psec interval for all the time-
series. 3) We add the time value of (1) and (2) above to obtain the.
corresponding cross-correlated value in the remote stations for the
peak of the pulses. 4) Finally, we determine how many peaks in the
remote station are within the 3.7 psec search interval. This proce
dure limits the number of peaks to be considered to a maximum of 3.
At this time in the algorithm the peak recognition is completed; now we
have to determine which pulse at the remote stations that produced the
peaks which met (4) above, is similar to the pulse at the central sta
tion. One of these peaks within the search interval will be selected

60
only if the pulse that produced the peak has similar characteristics
in the central and on each of the remote stations.
The pulse model used to determine whether any of the pulses from
the considered peaks in the remote stations correspond to the same pulse
in the central station is a) values of ascending and descending slopes,
b) number of reversals in the ascending and descending slopes, and c.)
the total area under the pulse. Figure 4.2 illustrates a typical pulse
and how we selected the additional pulse properties to complete the
pattern recognition technique.
Using the guidelines of identifiable characteristics, we selected
15 sample points for pulse recognition, centering the individual peak
in the middle of the pulse. The description of the individual pattern
recognition features mentioned in a, b, and c were as follows: a) the
ascending and descending slopes (AS and DS) were calculated by making
straight line approximations between the peak and the value of the ex
treme of the pulse. However if the pulse increases in magnitude in
three consecutive samples before arriving to the pulse boundary (7th
sample), the slope was arbitrarily determined between the peak and the
5th data sample. b) The number of reversals is determined by counting
the number of times that there is a change of slope and dividing this
number by 2. In Figure 4.2 there are two changes of slopes to the
right of the peak (reversal to the right, RR), corresponding to one
reversal and there are four changes of slopes to the left (reversal
to the left, RL), which correspond to two reversals. c) Since all the
remote stations' data were normalized with respect to the central
station, we also calculated the area under the curve as a measurement
of the narrowness of the pulse (NAR). The tolerances allowed

61
Figure 4.2. Pulse model.

62
in matching pulses were: a 20 difference of slope was allowed for AS
and DS, one difference in reversals was allowed for RR and LR, and a 25%
variation was allowed for the area under the pulse (NAR). We refer to
the five additional requirements needed for selecting the individual
pulses as AS, DS, RR, LR, and NAR. We weighted these factors to match
the individual peaks as a function of the time interval away from the
cross-correlation time delay. If peaks were selected within 0.92 Usee (4
data samples) from the cross-correlation time delay, the pulse that
generated the peak was required to meet at least two of the five require
ments. Stricter requirements of 3 out of 5, 4 out of 5, and 5 out of 5 were
needed to match peaks between 0.92 and 1.84 Usee (4 to 8 data samples),
1.84 to 2.76 Usee (8 to 12 data samples), and 2.76 to 3.7 Usee
(12 to 16 data samples), respectively, from the cross-correlation time
delay. It is worth noting that an identifiable pulse in the central
station has to pass a separate test at each of the three remote stations
before a location is calculated. A failure of the pattern recognition
at any of the stations will, prevent the determination of a source
location.
4.4 Algorithm Flow Chart
A simplified algorithm flow chart is shown in this section. This
algorithm has been developed using the techniques discussed in Section
4.3. Only those most general steps are Included In the flow chart.
This algorithm was written in FORTRAN language using a structured pro
gramming sequence (Rogers, 1975) for execution in the AMDAHL 470-VI.
For a detailed description of the procedure used, reference is made to
the LITMAT program in Appendix C. In the next flow chart (Figure 4.3)
a set of data is defined as the time interval for which the

Figure 4.3. Block diagram of the LITMAT algorithm to obtain
the cross-correlated and all the noise sources
based on the calculation of time delays.

i4
(a)

< 5
(b)

( 6
REPEAT THE PROCEDURE FOR
THE NEXT TIME INTERVAL
(c)

67
cross-correlation is calculated, either 94 or 376 ysec. The graph is
expanded in Figures 4.3(a), 4.3(b), and 4.3(c). Figure 4.3(a) shows the
algorithm initialization and the characterization of the central station.
Figure 4.3(b) shows a similar technique for the remote station and its
relationship with the central station to determine the time delays.
Finally, Figure 4.3(c) concludes the algorithm with a determination of
the three-dimensional locations. If additional data are desired, the
algorithm is repeated.
4.4.1 The Algorithm Limitations
The principal limitations in the development of this algorithm are
the time interval selected for the cross-correlation function and the
selected features for pattern recognition. Next we provide some argu
ments about these limiting factors.
The longest time delay between the central and a remote station is
determined for source locations near the ground and on the opposite side
of the line joining the central and the remote stations. For a 10 km
baseline between central and remote stations, the search for appropriate
time delays should include 33 ysec from the central station data.
From the test described in Section 4.2.2(3), we could have several
pulses which met any given tolerances for AS, DS, RR, RL, and NAR with
in the 33 ysec interval. This argument implies that pattern recogni
tion alone is not a sufficient factor for the determination of time
delays. Also from Section 4.2.2(3) we learned that we were 100%
successful matching the envelope of the time-series data. Therefore,
the use of the cross-correlation function is an essential part of the
algorithm. The cross-correlation time interval of 94 or 376 ysec was
chosen on the basis of the data properties and this is one of the

68
limiting factors of the algorithm development. If the individual pulses
within the cross-correlated interval originate from the same source
or from closely scattered sources, the cross-correlation locations
represent a true representation of the source locations. For example,
a spark channel which propagates at a velocity of 5 x lO'* m/sec will
cover 47 meters during a 94 ysec cross-correlated interval. Therefore,
consecutive cross-correlation locations represent a true representation
of the locations of the spark channel. We successfully determined the
location of the noise sources because 95% of the DTOA's measured in
consecutive pulses were about 2.5 ysec from the cross-correlated value,
which represents 2 or 3 km apart. However, if there were several
channels located several kilometers apart or if there was at least one chan-
g
nel propagating at a velocity in the order of 1.0 m/sec, our locations may
not represent the true location of the originating source.
4.5 Display of Three-Dimensional Locations and Their Time of Occurrence
All the VHF source locations and their time of occurrence were
stored in digital tapes. The time was needed to differentiate between
the different phases of a lightning flash. We developed three computer
programs to display the source locations. 1) An algorithm was written
to display the data in a three-dimensional isometric view. The computer
code for this program is included in Appendix D. 2) The source loca
tions were displayed in two-dimensional projections. These projections
were: (a) EW-NS, (b) EW-hcight, and (c) NS-hcight. 3) Fixed histograms
are generated to show the relative radius, azimuth, and elevation of the
noise sources with respect to a reference point. All these visual aids are
used to display the results derived in Chapter V.

69
The value of computer graphics should not be underestimated. Any
attempt to represent the locations by hand was tedious and resulted in
large errors. All the graphics for the VHF noise and its source loca
tions were displayed on the Gould Electrostatic Plotter of the Univer
sity of Florida Computer System.
Figure 4.4 shows a computer processing block diagram. This diagram
shows the procedure that we followed to process and interpret the digital
input data.
4.6 Velocity of Propagation of Noise Sources
We determined the velocity of propagation of the noise sources by
using the three-dimensional locations and their time of occurrence. We
chose only those lightning events on which the location of the noise
sources formed a channel following a regular progressing sequence. To
determine whether the events followed a progressing sequence we calcu
lated the value of the velocity of propagation using all the cross-
correlated locations.
Let p1(x1y1z1) > P2('X2y2,Z2') pn(xnyn,Zn^ be the locations
of cross-correlated sources at time t^, t^, ..., t^, respectively. Then
velocities of propagation can be calculated by determining the distance
P and dividing it by the time interval t where m and n are anv two
sources (m < n). A total of T~^- velocities can be calculated from n
locations. Only about 50 or 60% of all the velocities that we obtained
during the specific -lightning events that we studied using the above
techniques showed a velocity of propagation the same as would be found
by taking the starting and ending point. Therefore, we decided to use
the following procedure to determine channel velocities. 1) Determine
whether the VHF sources followed a progressing sequence. A velocity of

EXECUTE IN FORTRAN H OVER 800 LINES OF CODE WITH
12 SUBROUTINES ABOUT $1 CPU TIME PER I MSEC OF STORM ACTIVITY
Figure 4.4. Computer processing block diagram.

71
propagation is calculated only for those events on which consecutive
cross-correlated locations were in the neighborhood of the previous
ones, and a path was formed by displaying the noise sources in the
desired process (stepped leader and some PB, K- and J-changes).
2) Determine the ^ ^ velocities using all the cross-correlated source
locations. 3) Test if these velocities were grouped at any specific
value. A velocity value is used only if a certain value or range of
value repeats for at least 50% of the test data (n(n-l)/4). For an
additional check we determined velocities using all the individual
source locations for three stepped leaders, but the procedure was quite
a bit longer and resulted in the same velocity value.
The results showed that we could determine the velocities of about
50 or 60% of the events that met conditions 1), 2), and 3) simply by
their starting and ending points. In addition, about 15% of the events
failed condition 3) and no velocity of propagation could be determined
consistently. Throughout this thesis the only velocity values found
are those that met the three conditions above.

CHAPTER V
ANALYSIS OF RESULTS
This chapter presents a detailed description of six lightning
flashes that occurred during the summers of 1976 and 1977 at the
Kennedy Space Center. We have correlated the three-dimensional loca
tions with other storm and lightning parameters measured (see Chapter
III), primarily the electric field. We have studied four cloud-to-
ground (CG)flashes and two intracloud (IC) flashes. The six lightning
flashes are identified by their time of occurrence and type below:
(5.1) 165959, a three stroke CG flash to the .150 meter weather
tower on 19th July 1976 followed by an IC discharge.
(5.2) 180710, a three stroke CG flash on 8th August 1977.
(5.3) .181806, a six stroke CG flash on 8th August 1977 followed
by continuing current.
(5.4) 182356, an eight stroke CG flash on 8th August 1977.
(5.5) 180644, an IC discharge at the beginning of the storm on
8th August 1977.
(5.6) 181416, a small IC discharge on 8th August 1977.
All of the above flashes were at relatively close range, 3 to .17 km
from the central station. The coordinates given throughout this thesis
are referenced to the central station whose absolute coordinate in the
Florida grid system is (187023,466021) meters. The three coordinate
parameters given always correspond to the East-West location, North-South
location, and altitude, respectively.
72

5.1 The 165959 Flash
This flash is the most comprehensively studied single lightning
flash in the history of lightning research (Uman et al., 1978 and
Rustan et al., 1979).
The flash consisted of a three strokes to ground followed by an IC
discharge. The duration of the flash VHF radiation was 939 msec of
which the last 600 msec were part of the IC discharge. The locations
of the three charge regions for the three return strokes obtained from
measuring the return stroke electric field change at multiple ground-
based locations (Uman et al., 1978) correlate well with the VHF source
locations. Figure 5.1 shows the relationship between the VHF radiation
and the electric field for the entire discharge. Table 5.1 shows a
complete summary of the identified phases of the flash For each
phase we have provided the duration of the VHF radiation, the average
velocity of propagation of the noise sources (if applicable), and the
upper and lower location of the VHF noise sources. An error analysis
for the VHF noise source locations is given in Appendix B. Table B.l
shows a summary of the uncertainty in the determination of the locations
of the sources in this flash as a function of position. In the next
subsections we consider in detail what we learned from the study of
different phases of the flash, given in Table 5.1.
5.1.1 Preliminary Breakdown
Observation of the VHF records for one second prior to the first
stroke shows that the VHF radiation above the system noise level began
4.9 msec before the return stroke and continued until the return stroke.
The first 2.2 msec of the VHF pulses we identify with the "preliminary
breakdown," the final 2.7 msec with the stepped leader. The wideband

Figure 5.1. Simultaneous records of the logarithm amplitude VHF radiation observed at 10 km,
and the electric field 13 km away, during the 165959 flash. The following events
in the flash are shown: Rl, R2, and R3 represent the three return strokes; SL is
the stepped leader before Rl; DL is the dart leader before R2; SDh is the stepped
dart leader before R3; J1 and J2 are the interstroke processes; FR is the activity
following the first return stroke, SP's are the solitary pulses; and IC is the
intracloud discharge, of which the final 99 msec is not shown.

NOISE
LEVEL

Table 5.1. Time-Table for the VHF Activity in the 165959 Flash.
Start
Time
(msec)
Event
Duration
(msec)
Average Velocity
m/sec
Coordinates (km)
UPPER
LOWER
X
y
Z
X
y
Z
0.0
Preliminary Breakdown (PB
2.2
1.0 x 106
0.3
11.6
7.1
.2
10.8
5.1
2.2
Stepped Leader (SL)
2.7
1.3 to 7.0 x 106
0.2
10.8
5.1
-1.3
9.7
2.2
4.9
First Return Stroke (Rl)
0.25
5.15
Quiet Period
2.4
7.55
Follow Return Stroke (FR)
4.27
0.5
12.2
7.0
1.1
10.2
1.3
11.82
Quiet Period
15.5
27.37
VHF Portion of J1
43.27
1.5 x 105
0.0
16.0
13.7
-0.2
12.3
7.9
70.59 .
Dart Leader (DL)
.35
1.8 to 2.6 x 106
-0.1
12.0
7.8
0.3
11.2
6.6
70.94
Second Return Stroke (R2)
.26
71.20
1st Quiet Period of J2
11.52
82.72
SP No. 1 (SP1)
.775
1 to 4 x 107
83.50
2nd Quiet Period of J2
3.2
86.7
SP No. 2 (SP2)
.95
1 to 4 x 107
87.65
3rd Quiet Period of J2
7.78
95.43
SP No. 3 (SP3)
.57
1 to 4 x 107

Table 5.1 cont.
Start
Time
(msec)
Event
Duration
(msec)
Average Velocity
m/sec
Coordinates (km)
UPPER
LOWER
X
y
z
X
y
Z
96.00
4th Quiet Period of J2
52.45
148.45
VHF Portion of J2
47.0
2.0 x 105
3.6
16.2
13.1
0.1
11.8
8.5
195.45
Stepped Portion of SDL
2.2
4.5 x 106
0.4
12.2
8.0
-1.0
11.7
3.3
198.65
Dart Leader Portion of SDL
1.1
199.75
Third Return Stroke (R3)
.13
199.88
Quiet Period
29.82
229.70
SP No. 4 (SP4)
.625
230.32
Quiet Period
108.82
339.20
IC (Continuous Part)
501.00
7.5 x 105
6.0
13.6
14.0
1.7
9.5
5.9
889.5, 898.9, 910.7, 915.9,
and 937.3
msec Solitary Pulses after the
IC.

78
electric field records indicate that there is a small electric field
pulse of 2 ysec width at about the time of the initial VHF radiation,
but a clear correlation between VHF and electric field does not exist
until the final .8 msec of the preliminary breakdown which corresponds
to, a steady electric field change.
Figure 5.2 shows simultaneous records of VHF radiation during 117
ysec of the preliminary breakdown that preceded the initial stepped
leader. During the preliminary breakdown the log amplitude of the
envelope-detected VHF noise is characterized by large pulses having a
duration of 40 to 150 ysec. Superimposed on these slow pulses are
pulses of 1 to 5 ysec width. Pulses 1, 2, 3, and 4 of
Figure 5.2 illustrate the difference in the time of arrival of typical
pulses at the four stations. The "r" value shown in the figure repre
sents an approximate distance between the VHF source and the individual
ground-based stations. The computer algorithm when applied to the data
in Figure 5.2, generated source locations for pulses 1 through 4 and for
10 additional pulses.
Figure 5.3(a) shows all the 150 source locations identified during
the preliminary breakdown which occurred between locations A and B.
It is worth noting that most of the sources are concentrated within a
cylinder of 500 meter radius and many are inside the volume, source
of the first return stroke charge (Figure 5.3(b)). Figure 5.3(b) shows
the cross-correlated noise sources, 94 ysec intervals, associated with
the preliminary breakdown. The cross-correlated locations are weighted
toward the location of the larger pulses in the 94 ysec interval because
it is these that play the dominant role in maximizing the cross
correlation function.
The cross-correlated noise sources started near

i 9
Figure 5.2. Simultaneous records of the logarithm VHF radiation at
four different ground-based stations. Pulses 1, 2, 3, and
4 are identified as examples of pulses arriving at differ
ent times at different stations. The parameter "r" repre
sents the actual distance from the stations to the cloud
source.

Figure 5.3(a).
All of the 422 VHF noise sources detected for both the preliminary breakdown
(A to B) and the stepped leader (below B) during the first 4.5 msec of the
4.9 msec before the first return stroke.
Cross-correlated VHF noise sources, 94 ysec intervals during the preliminary
breakdown (A to B) and during the stepped leader (below B). The sphere Q1
represents an estimate of the volume enclosing the charge source for the first
return stroke as derived from electric field records (Uman et al., 1978).
Figure 5.3(b).

--20C
-IOC
-oc
2-10 1
EAST (km)
(a)
EAST (km)
(b)

82
the top and the back edge of the Ql volume and generally propagated in
a downward direction. The preliminary breakdown started at a height of
7.1 km (point A at about -18C free air temperature) and propagated a
distance of 2.3 km to a height of 5.1 km (point B at about -6C) before
the first detectable slow change of the electric field associated with
the stepped leader occurred. The cross-correlated source locations
during the preliminary breakdown interval are very much in a straight
line and exhibit an average velocity of propagation of about 1.0 x 10^
m/sec.
In addition to determining the cross-correlated and all the individ
ual source locations (Figure 5.4(b)) using the computer algorithm des
cribed in Chapter IV, we determined the individual source locations
manually during the first 537 psec of the preliminary breakdown. This
task was performed to identify any propagation of the sources on a time
scale of every 2 or 3 psec instead of every 7 or 10 psec, the limit
using the computer algorithm. These results are shown in the three-
dimensional graph in Figure 5.4. The sources A through RR are time tagged
and shown in alphabetical order A -* Z, AA -> RR. This initial stage of the
PB extends 1.5 km horizontally and 3.6 km vertically. The sequence of the
VHF sources shows that the activity started at about 9 km and there was
propagation initially upwards and downwards.
5.1.2 First Stepped Leader
The VHF radiation during the. stepped leader consists of a low
amplitude high frequency pulse train, a characteristic radiation
observed during the first leader and again prior to the third stroke,
but not in any other part of the flash. The stepped leader VHF is

Figure 5.4. Three-dimensional view of the VHF noise sources
during the first 537 ysec of the preliminary
breakdown. The sources A through RR are time
tagged (in microseconds) and shown in alphabeti
cal order A -* Z, AA -* RR.

9
8
7
6
5
4-
3-
2-
1-
O'
-30C
0 1
EAST (km)
-20C
-10C

8 5
markedly different from the preliminary breakdown VHF which precedes it.
Figure 5.5 shows the VHF noise during the stepped leader.. By comparing
the VHF noise during the preliminary breakdown shown in Figure 5.2 with
Figure 5.5 we can see the remarkable difference between the two processes.
The stepped leader pulses in Figure 5.5 have a pulse width less than one
microsecond and an interpulse interval which decreases with increasing
time, starting at about 11 ysec and decreasing to about 1 ysec. The
characteristic leader pulses start about 0.8 msec after initial electric
field change of the flash. The leader pulses are probably related to
the electrical breakdown associated with leader steps. As the leader
progresses downward it generates more branches and hence more steps and
pulses per unit time. If a normal interstep time is assumed to be 50
ysec (Uman, 1969), then at least four steps are simultaneously active
during the beginning of the leader, increasing to about 50 simultaneous
steps. Figure 5.3(a) shows all the 272 identified stepped leader radia
tion sources while Figure 5.3(b) shows the cross-correlated, 94 ysec
intervals, locations. Even though the VHF noise changed characteristics
between the preliminary breakdown and the stepped leader, the source
locations of the stepped leader appear continuous with that of the pre
liminary breakdown channel. In addition, the stepped leader, sources
spread horizontally as the leader moves downward, most likely due to
the stepped leader branches. The individual and the cross-correlated
stepped leader source locations of Figure 5.3 did not occur in a regular
ly progressing sequence. The channel shape shown in Figure 5.3(b) is
our best estimate from an overall view of the individual locations, the
cross-correlated locations, and the sequences of occurrence of the
locations.

Figure 5,5.
Logarithmic-amplitude VHF radiation at the beginning of the 165959 cloud-to-ground flash.

87
A two-dimensional view with all the detected preliminary breakdown
and stepped leader sources is shown in Figure 5.6. Figure 5.6(a) shows
the plan view while Figures 5.6(b) and 5.6(c) show the elevation views
of all the located stepped leader sources. In both graphs, Figures
5.3 and 5.6, the 150-meter weather tower struck by the flash is shown.
The weather tower is located at (-1.1,9.5). Figure 5.6 also shows the
cross-correlated locations represented with circles. It is worth noting
that these cross-correlated locations form a narrow channel during the
preliminary breakdown, but this channel is widened at a later stage
during the stepped leader process.
The velocity during the first 700 microseconds of the stepped
leader ranged between 1.3 and 3.8 x 10^ m/sec and during the next 1.8
msec showed a nearly linear increase from about 1.5 x 10 m/sec at about
5 km altitude to about 7.0 x 10^ m/sec at 2.2 km. Although there was
strong VHF radiation during the last 0.4 msec of the stepped leader, no
sources were located during this time. It is probable that the pulses
on the four channels could not be correlated because too many VHF
sources, leader steps, were simultaneously active over a large volume.
Figure 5.7 shows three sequences of histograms of all the source
locations from the beginning of the preliminary breakdown to the last
detectable source in the stepped leader. The time sequences t^, t^,
and t^ in Figure 5.7 correspond to 1.5 msec intervals from the beginning
of the preliminary breakdown to the end of the detected VHF sources
from the stepped leader. Figure 5.7(a) is a distance histogram
referenced to the weather tower, as the time'progresses the radiation
sources approach the 150 meter weather tower. Figure 5.7(b) and Figure
5.7(c) show polar histograms of all the radiation sources with reference

NORTH (km)
13-
12-
11
10-
9t
8
-3
EAST (km) EAST (km) NORTH (km)
(a) (b) (c)
Two-dimensional views: (a) top view, EU-NS, (b) elevation view, EW-height, and (c) elevation
view, IiS-height of all the sources (triangles) and the cross-correlated source locations
(squares), 376 usee intervals, during the PB and first stepped leader. The circle Q1 is the
two-dimensional projection of Q1 in Figure 5.3.
cc
Figure 5.6.

Figure 5.7. Three sequences of histograms, t]_, t2, and t^ (1.5 msec intervals) of all the
detected sources in the PB and stepped leader. Sequences (a), (b), and (c)
correspond to t^, t2, and t3, respectively. There are three histograms in each
sequence. The top row shows distance histograms referenced to the weather
tower. The middle row shows histograms of the elevation angle of the sources
referenced to the weather tower. The bottom row shows histograms of the azimuth
angle of the sources referenced to the weather tower.

O)

91.
to the spherical azimuth angle (tj)), and the elevation angle (0),
respectively.
5.1.3 First Return Stroke
Figure 5.8 shows the VHF noise during the first return stroke.
The first return stroke was characterized by small high frequency pulses
riding on the envelope of a high amplitude pulse of about 250 ysec.
Only five VHF pulses could be correlated during the stroke, probably
because there were too many sources active and these sources were spread
over too large a volume of space. Three of the correlated sources were
located along the stepped leader channel, a fourth source was located
at the top of the highest average location of the preliminary breakdown,
and the fifth source was located 1 km above the fourth source. The
estimated total length of the return stroke channel from the tower
through the five sources was 8.8 km. Since the VHF return stroke noise
lasted about 250 ysec, we estimated that the return stroke propagated
at about 3.5 x 10^ m/sec. Since the cross-correlated location might
not be a true representation of the actual source location when a
7 8
potential wave propagates in a channel at a velocity of 10 or 10 msec,
return stroke velocities obtained from VHF source locations might be
off by axi order of magnitude.
Krehbiel (Uman et al., 1978) determined that a charge of -24 Coul
was lowered by the first return stroke using the technique described in
Section 3.5. Wc used the technique described in Section 3.6 and deter
mined that a charge of -19 Coul was lowered by the first leader-return
stroke process. Our point charge source for the transition region be
tween PB and stepped leader in the VHF record was within 1.5 km of
the location determined using multiple electric field records.

!
RETURN STROKE
3
1 1 1 1 1 1 1 |
40 80 120 160 200 240 280 320
TIME IN MICROSECONDS
360
400
Figure 58. Logarithmic-amplitude VHF radiation during the first return
stroke.

5.1.4 Activity Following the First Return Stroke (FR)
For 2.4 msec after the first return stroke there was a quiet period.
No VHF sources were identified during this period. The VHF radiation
after the quiet period was significant, lasting 4.3 msec with a pulse
about every 4 fisec. This activity is shown by FR (following return
stroke) in Figure 5.1. The source locations of the FR period propagated
upward between 2 and 7 km in height. The lower sources were located in
the neighborhood of the eastern locations of the stepped leader sources
in Figure 5.3(a). However, most of the radiation originated at a height
between 4.5 and 5.8 km, that is, in the lower portion of the preliminary
breakdown and upper portion of the stepped leader. Figure 5.9 shows
the location of the cross-correlated VHF noise sources, 94 ysec inter
vals, during the FR interval. We have labeled A through Q the progressing
sequence of the sources. Figure 5.8 also shows the location of the
previous return stroke charge source. The FR activity terminated with
a large low frequency pulse similar to the characteristic return stroke
pulses. The electric field records indicate that either negative charge
was lowered or positive charge was raised or both during the 4.3 msec of
VHF activity. Taking into account the locations of the VHF noise it
appears that the FR activity raised positive charges.
5.1.5 First J-Change (Jl)
Even though the FR activity is in the interstroke process, its
properties seemed to be related to the previous return stroke. The Jl

Figure 5.9.
Cross-correlated VHF noise sources, 94 ysec
intervals, during the FR period. The sources
are labeled A through S to indicate the pro
gressing sequence of their occurrence. Each
label is repeated three times. No time
sequence is given for each repeated letter.
The sphere Q1 is described in Figure 5.3.

ALTITUDE (km)
<15
EAST (km)

%
change reported in this section started with the 15.5 msec quiet period
in the VHF noise record following the FR activity. Quiet periods after
return strokes have been the subject of considerable study. Malan (1958)
first reported quiet periods of 5 to 20 msec after the return stroke.
A summary of quiet period studies has recently been published by Clegg
and Thomson (1979). It is not possible to determine the location of
noise sources, if they exist, during this quiet period because the VHF
radiation is comparable with the system noise level. However, during
the quiet period there is a steady electric field change and hence
charge motion is taking place. For the final 43.3 msec of the inter
stroke interval there is significant VHF radiation with the initial
pulse repetition rate nearly doubling in the 21 msec prior to the dart
leader.
Figure 5.10 shows a three-dimensional view of the lightning channels
active during the J-change between the first and second return stroke
(Jl, Figure 5.1). The sources start near the top of the cloud and prop
agate downward in a path 35 off vertical into the region associated
with the stroke charge. The motion (in km) is approximately from
A (0.0, 16.0, 13.7) to B (-0.2, 12.3, 7.9). Eighty-two cross-correlated
source locations, 376 ysec intervals, are displayed in Figure 5.10.
The arrows indicate the direction of burst of sources occurring during
the overall propagation from A to B which took place at an average
5
velocity of about 1.5 x 10 m/sec.
The change in electric field during Jl was measured at eight
separate ground stations at distances from 2 to 20 km from the noise
source locations. The experimental J-change fields during the VHF
radiation can be remarkably well modeled by equation (3.10) if we assume

Figure 5.10. Cross-correlated VHF noise sources, 376 ysec
intervals, during the first J-change. Parts A
and B represent the beginning and the end of the
J-change region, respectively. The arrows indi
cate the direction of propagation of groups of
sources which occurred in bursts. During the
dart leader following the J-change, a 4 km near
horizontal channel joint B with C (shown as
circles), a region near the previous leader
channel. Also shown as a continuous line in the
neighborhood of Q1 is the upper part of the pre
liminary breakdown which preceded the first
return stroke. Both first and second stroke
charge volumes are shown.

ALTITUDE (km)
o
o
o
o
o

99
a negative point charge moves downward from A to B (Figure 5.10).
Deriving a charge value from the E-field at each station yields 2.4
Coulombs with a standard deviation of 0.7 Coulombs, representing a charge
moment of 13.4 4,0 Coul-km. This value of charge moment is an order
of magnitude larger than previous estimates of the maximum charge moment
during the J-process (Brook et al., 1962). The experimental data do
not fit nearly as well if points other than A and B along the VHF radia
tion path are chosen as the starting and ending points of the negative
charge motion.
Figure 5.11 shows two-dimensional graphs of all the 3377 noise
sources detected during the VHF portion of the J1 change. Figure 5.11(a)
shows the plan view while Figure 5.11(b) and Figure 5.11(c) show the two
corresponding elevated views. The VHF sources are spread out at the
beginning of Jl (near the 14 km height) occupying a radius of 1.5 km or
2 km, but as the VHF sources propagated downward to near the 02 source
region, the channel narrows down in the east direction to about 1 km
radius. It appears that negative charge flow is detected from a region
about 2 km below the cloud tops.
5.1.6 Dart Leader Before the Second Return Stroke
The VHF dart leader radiation started about 350 ysec before the
second return stroke. The beginning of the dart leader was character
ized by a high amplitude, 110 ysec wide pulse. The remaining 240 ysec
width with about 7 ysec between pulses. Figure. 5.12 shows the VHF noise
during the dart leader and subsequent return stroke.
The VHF dart leader sources are located in a 4 km near-horizontal
channel connecting B to C in Figure 5.10. The velocity of propagation
of the BC channel is between 1.8 and 2.6 x 10^ m/sec. The radiation

Figure 5.11. Two dimensional views: (a) top view, EW-NS, (b) elevation view, EW-height, and
(c) elevation view, NS-height of all the 'hill noise sources detected during the
J1 process.

0) > n
in
NORTH
12 13
-v 1
,7- y .v> *
HEIGHT
10
m
Q >
CT c/)
HEIGHT
10
^ o
O 3)
V ;,*:<. ** ,. ,., ,.
n" *T fc*Yi-Va-^i->'* * *<"
, ->y/i £ !/*
, V #v"V <'.' ?
\7, - V
h
TOi

VHF RADIATION
Logarithmic-amplitude VHF radiation during the dart leader and the second return stroke.
Figure
5.12
ZO I

103
from the dart leader joins the bottom of the J1 change with the begin
ning of the preliminary breakdown as shown in Figure 5.10. Our calcu
lations of the locations of the VHF noise sources during the dart leader
are in agreement with the work of Brook and Kitagawa (1964) and Proctor
(1971), which suggested that most of the radiation during the dart
leader's trip to ground is from within the cloud rather than from the
dart leader channel. Comparing the location of the noise sources with
the correlated electric field and VHF radiation is not possible to
determine where the charge in motion during Jl entered the previous
ionized return stroke channel and descended to ground. In addition to
the BC channel, Figure 5.10 shows a continuous line from the preliminary
breakdown channel. The noise sources of the dart leader (shown as dots
in Figure 5.10) not only connected the two previous channels but also
extended horizontally over 1 km beyond the top of the preliminary
breakdown.
5.1.7 Second Return Stroke
The second return stroke lasted approximately 259 ysec in the VHF
record as shown in Figure 5.12. The four source locations identified
during the second return stroke were located within 1 km radius of the
highest cross-correlated source location of the preliminary breakdown.
These findings suggest that the preliminary breakdown has become part
of the active leader channel used by the consecutive strokes which
propagate in the defunct return stroke path to ground. No sources were
identified in the return stroke channel to ground.

LOA
5.1.8 Solitary Pulses During the Quiet Period of J2
Three solitary VHF pulses (SP's) occurred during the 84 msec quiet
period after the second return stroke (Figure 5.1). The duration of
the SP's in the timing sequence they appear was 0.78, 0.95, and 0.57 msec.
The SP's VHF amplitude and frequency content are similar to the return
stroke. Figures 5.13(a), 5.13(b), and 5.13(c) show the VHF noise for
the three SP's during the quiet portion of J2.
The SP's propagated upwards for 2 to 5 km in a near-vertical path
from tlie previous ionized region of the negative charge center on tlie
bottom of J1 and the top of the preliminary breakdown. The velocity
of propagation of the J2 SP's is between 1 and 4 x 10^ m/sec. All
three SP's started within 2 km from each other but consecutive SP's
extended over a larger volume of space. Figures 5.14(a), 5.14(b), and
5.14(c) show cross-correlated source locations, 94 ysec intervals, for
the three SP's. Even though the first source location always coincides
with the lowest source of the SP's, sources within a few hundred micro
seconds of the beginning of the SP's were located at the top of the
channel. In the last two SP's there were detected noise sources
occurring near the end of the SP's which locations occurred in the path
between the lowest and highest sources. These three SP's did not have
detectable correlated electric field changes and therefore the charge
transferred by this type of pulses must be relatively small. It is
tempting to associate the SP's with K-changes (liman, 1969), thought to
be in-cloud upward-moving mini-return strokes initiated when charge of
one sign moving downward encounters charge of opposite sign. The
absence of VHF radiation preceding the upward moving SP's and absence
of appreciable rapid electric field change associated with the SP's is
puzzling.

O 40 80 120 60 200 240 280 320 3G0 400 440 480 520 560 600 640 680 720 70 800 840 880 920 960
TIME IN MICROSECONDS
Figure 5.13. Logarithmic-amplitude VHF radiation during the three
solitary pulses (SP's) in the J2 process.

Figure 5.14. Cross-correlated VHF noise sources, 94 psec intervals, during the three SP's
shown in Figure 5.13.

ALTITUDE (km)
(c)

5.1.9 Second J-Change
Significant VHF radiation was measured during the last 47 msec of
the second J-change (J2, Figure 5.1). The VHF noise sources started at
(1.2, 12.5, 11.2), that is, about 2.1 km below and 4 km southeast of
the starting point of Jl. During the first 19 msec there was activity
taking place one or two kilometers upwards and downwards, but in the
last 25 msec the noise sources propagated primarily downwards, ending
at (0.1, 11.8, 8.5). Figure 5.14 shows a three-dimensional view of the
cross-correlated VHF noise sources, 376 ysec intervals, active during
J2. Figure 5.15 also shows the charge center for the last two return
strokes (Q2 and Q3) and the location (A) of the end of J2.
We modeled the field change during the VHF portion of J2 with
equation (3.10) and derived a charge for the E-field at each of the stations.
For the J2 process, starting and ending points chosen were (1.2, 12.5,
11.2) and (0.1, 11.8, 8.5), a path 32 off vertical. We found a nega
tive charge lowered of 3.4 Coul, with a standard deviation of 1.8 Coul,
representing a charge moment of 16.2 + 8.5 Coul-km. The velocity of
propagation during the final 25 msec was 2.0 x 10^ m/sec. The model
fit is not as good as for the first J-change as might be expected in
view of the fact that the second J-change originally propagated both
upwards and downwards.
5.1.10 Stepped-Dart Leader (SDL) Before Third Return Stroke
For 2.2 msec after the second J-change, the VHF radiation waveforms
showed a high frequency pulse train without any low frequency envelope,
very similar to the radiation observed during the first stepped leader.
The electric field records verify a stepped leader was occurring.
Figure 5.16 shows the VHF radiation during the stepped leader.

109
EAST (km)
Figure 5.15. Cross-correlated VHP noise sourcds, 376 )isec intervals,
during the continuous VHP radiation of the J2 process.
A represents the end sources of the ,12 process. Spheres
Q2 and Q3 represent the charge center for the second
and third return stroke (Urnan et al., 1978).

100
200
300 400 500 600
700
800
TIME IN MICROSECONDS
Figure 5.16. Logarithmic-amplitude VHF radiation during the stepped portion of
the SDL preceding R3.

Ill
Figure 5.17 shows a histogram of the interval between VHF pulses. If
we associate the high frequency VHF pulses with leader steps, the aver
age time interval between leader steps was 8.2 ysec (Figure 5.17) with
a standard deviation of 3.5 ysec. If there was a typical value of 50
ysec between leader steps, about 5 branches were simultaneously active.
The location of the VHF noise sources during the stepped leader
extended the path of the previous J-change as shown in Figure 5.18.
The VHF sources propagated from an altitude of about 8 km, the end of
J2, to a height of 3.3 km below which no radiation sources were located.
The bottom of the stepped leader nearly coincides with the previous
channel. The stepped leader velocity determined from the cross-correlated
source locations was about 4.5 x 10^ m/sec. After the last stepped
leader location and for 1.1 msec, the electric field showed a more
rapid variation of slope than previously and the VHF radiation indicated
the long-duration pulse characteristic of dart leader, return strokes,
and SPTs. The noise sources were located around an altitude of 3.5 km,
that is, near the bottom of the stepped leader channel. In view of the
above it is reasonable to assume that the stepped leader contacted the
previous stroke channel and at that point became a dart leader, making
the whole leader process a stepped-dart leader.
5.1.11 Third Return Stroke
The third return stroke lasted about 130 ysec in the VHF record.
The beginning of the return stroke VHF record shows a wide 80 ysec pulse
which seems to be an indication of the propagation of a potential wave.
All the four cross-correlated noise sources detected during the third
return stroke were located near the top of the stepped-dart leader
channel, which coincided with the end of J2.

20
18
16
14
!2
10
8
6
4
2
e 5.
Averc5ge-8.2yU.sec.
Std. Dev.; 3.5 /xsec.
Time (/xsec)
7. Histogram of the interval between VHF pulses during the stepped portion of the stepped
dart leader preceding the third return stroke.

Figure 5.18.
Cross-correlated VHF noise sources, 94 ysec
intervals, during the 2.2 msec of the stepped
portion of the stepped-dart leader that preceded
the third return stroke. A corresponds to the
location at the end of the J2 process as shown
in Figure 5.15. Q3 is the charge center for the
third return stroke from Uman et al., (1978).

EAST (km)
ALTITUDE (km)

115
We used the technique described in Section 3.6 choosing (A) in
Figure 5.15 as the point charge source and determined that -6 Coul were
lowered by the third leader-return stroke process. This result is com
parable to the -9 Coul determined by Uman et al. (1978).
5.1.12 Solitary Pulse Between the Cloud-to-Ground and the Intracloud
Discharge
Thirty milliseconds after the last and final return stroke of the CG
discharge, a large SP was observed. The SP lasted about 625 ysec and
started with an 80 ysec wide pulse very similar to the first SP between
the second and third return stroke.
The sources of the SP propagated upwards to the NE in a path 35
off vertical starting about an altitude of 4 km. This SP VHF amplitude
and the propagation of its source locations were larger than the SP's
between R2 and R3. The vertical inclination of this SP and the source
of its upper region coincided with the intracloud discharge that followed.
5.1.13 The Intracloud Discharge
The continuous VHF radiation from the intracloud discharge follow
ing the cloud-to-ground discharge began 12.8 msec before the first sharp
increase in the IC electric field (Figure 5.1). Figure 5.19 shows the
VHF radiation during the beginning of the IC discharge. There is a
remarkable difference between the beginning of the IC and the beginning
of the CG in Figure 5.4, which suggests that we can distinguish these
flashes after only 3 msec of VHF radiation. The first three sources
during the IC were located near (3.1, 12.1, 11,2), in the middle of the
path to be eventually covered by the intracloud discharge. The entire
discharge extended about 10 km in a path 35 off vertical between A
(6.0, 13.6, 14.0) and B (1.7, 9.5, 5.9) of Figure 5.20 which shows the

Figure 5.19. Logarithmic-amplitude VHF radiation during the beginning of the intracloud discharge.

I I 7
EAST (km)
Figure 5.20. Cross-correlated VHF noise sources, 376 psec intervals,
during the initial and active phase of the intracloud dis
charge. Points A and B represent the termination regions
of the main 10 km intracloud discharge channel. Charge
volumes for all three return strokes are shown (Ql, Q2,
and Q3).

cross-correlated source locations, 376 ysec intervals, for the entire
discharge. During the first 4.6 msec of the VHF radiation, the average
noise sources were located within half a kilometer perpendicular dis
tance of the bottom-half of the Line joing A and B. During the next
11.2 msec the noise sources moved to the upper half of the path between
A and B. Figures 5.21(a) and 5.21(b) show histograms of the average
source locations, every 94 jisec, for the first 5.6 and 11.2 msec,
respectively. For the first 16.8 msec, 85% of all the average sources
were located within half a kilometer perpendicular distance of a line
joining A and B. During the remainder 484 msec of the IC discharge,
VHF sources traversed from the path between A and B many times, widen
ing the VHF source volume to over 1 km radius. VHF sources also extended
an additional 2 km at the ends, near A and B.
The intracloud discharge can be divided into three phases: initial,
very active, and junction, as done by previous investigators (Kitagawa and
Brook, 1960). The initial phase started with a large 10 ysec wide VHF
pulse. This phase lasted about 64 msec and consisted of a low rate of
VHF radiation, approximately one pulse every 25 ysec. In the electric
field waveform of Figure 5.1, the initial phase includes the rising part
of the IC record. The active portion of the VHF radiation lasted about
437 msec and was characterized by a faster pulse rate, about a pulse
every 10 ysec. The total of the initial and the active phase, 501 ysec,
corresponded to the portion of the IC discharge for which the VHF noise
was more or less continuous. For the next 99 msec, not shown in Figure
5.1, five solitary pulses were observed. The HP's occurred 49.3, 58.7,
70.5, 75.7, and 97.1 msec after the continuous radiation. We associate
the quiet period where the five SP's occurred with the junction phase

Figure 5.21. Histograms of the altitude of the source loca
tions during (a) the first 5.6 msec, and (b)
the next 11.2 msec of the intracloud discharge.

Number of Source Locations
Number of Source Locations
ho-^cn cd oro.£> ao

of the intracloud discharge. The V1IF noise for these SP's closely
resembles the SP' s during the J-changes of the cloud-to-ground discharge.
The V1IF locations for these SP's propagated upwards for about 6 to 8 km
starting in a region one to three km east of B. None of the SP's prop
agated along the primary AB path of the intracloud discharge. Their
starting location was as noted arid their path was either vertical or
northwest, instead of the 35 northeast path of the IC discharge. We
attempted to fit a point charge model, equation (3.10), to the multiple
stations electric field records, for the location of the continuous
radiation of the IC discharge but could obtain no reasonable results.
On the other hand, because of the polarity of the IC field and its
reversal with distance (Uman, 1978), it is clear that the bulk of the
charge motion was either negative upwards or positive downwards.
5.1.14 Concluding Remarks About This Flash
Some of the new information about the flash derived from the VHF
noise, its source locations, and the correlated wideband electric field
records follows: (1) The first stepped leader was preceded by a 2.2 msec
preliminary breakdown located near and inside the charge source of the
stepped leader. The stepped leader had an average velocity which
6 6
increased from 1.3 x 10 m/sec at 5.1 km height to 7.0 x 10 m/sec at
2.2 km, the lowest height for which average source locations were
obtained. (2) Continuous VHF radiation was detected in the final 65%
of the time between the first two return strokes. During this portion
of the first J-change, radiation sources and negative charge propagated
downward 5.7 km in a path 35 off vertical at an average velocity of
1.5 x 10J m/sec. The negative charge lowered during this portion of
the J-change was 2.40.7 Coulombs. A 4 km near-horizontal channel which

propagated at an average velocity of 1.4 x 10^ m/sec connected the
bottom end of the first J-change sources with the charge region of the
previous stepped leader. (3) Continuous VHF radiation was detected in
the final 35% of the time between the second and third return strokes.
During this part of the second J-change, radiation sources propagated
both upwards and downwards for the first 15 msec, then propagated down
ward 4.7 km for 25 msec at an average velocity of 2.0 x 10^ m/sec.
The negative charge lowered during this portion of the J-change was
3.41.8 Coulombs. (4) Following the second J-change, a new stepped
leader propagated from 7 km, the bottom of the J-change VHF source
locations, downward to a height of 3.2 km, where it joined the previous
stepped leader channel, and, presumably, return stroke channel. The
stepped leader average velocity was 4.5 x 10^ m/sec. (5) During the
intracloud discharge following the third return stroke, sources of VHF
radiation covered a path from near the source charges of the return
strokes to about 14.0 km, near the cloud top. The VHF noise sources
traversed the same path many times, widening the main channel and
extending the ends. The VHF radiation during the IC discharge displayed
the three phases described in the literature for IC discharges which
were not associated with a ground discharge.

1.23
5.2 The 180710 Flash
On 8th August 1977 a thunderstorm moved west from the Atlantic
coast side of the Cape Canaveral AFS, Florida, and at 1810 UT the cloud
tops were reported at a height of 12.9 km. At 180710 UT the first
cloud-to-ground flash of the newly developed thunderstorm was recorded.
Details of that flash are reported in this section. Two other cloud-to-
ground flashes in this storm occurring at 181806 and 182357 UT are also
studied in this thesis (see Sections 5.3 and 5.4).
The VHF portion of the 180710 flash lasted 282 msec and consisted
of three separate strokes to ground. Figure 5.22 shows the relationship
between the VHF radiation recorded 10 km from the flash and the electric
field recorded 3 km away. It is evident from either the VHF or the elec
tric field records that there were stepped leaders associated with all
three of the return strokes in this flash. At 3 km from the. flash the
three stepped leaders were within the electric field reversal distance
(Uman, 1969, Chapter 3) and hence had initially negative-going electric
fields, while an electric field station at 19 km showed positive stepped
leaders field changes. Table 5.2 contains a complete summary of the
various phases of the flash. All the cross-correlated noise source loca
tions reported in this flash were determined by using 94 ptsec intervals.
The location of the charge region for the first return stroke was provided
by Krehbiel (private com) using the technique described by Krchbiel et al.,
(1979). An error analysis for the VHF noise source locations is given in
Appendix B. Table B.3 shows a summary of the uncertainty in determination
of the locations of the sources in this flash ms a function of position.
In the next subsection we consider in detail what we learned from the VHF
radiation about the different events that took place in the 180710 flash.

Figure 5.22. Simultaneous records of the logarithm of the amplitude of the VHF radiation observed
at 9 km, and the electric field 3 km away, during the 180710 flash. The following
events in the flash are shown: Rl, R2, and R3 correspond to the three return strokes
SL1, SL2, and SL3 are the three stepped leaders; J1 and J2 are the J-change processes
PB is the preliminary breakdown; FR is the activity after the first return stroke; K
is the K-change pulse that initiated the J1 process; CAFS and DAFS are the continuous
, and discrete activity after the return stroke; last SP corresponds to the last soli
tary pulse during the DAFS process.


Table 5.2. Events in the 180710 Flash.
Universal Time at the Start of the VHF Radiation:
18 hr 07ml0s 743.5 msec, 8th August 1977
Start
Coordinates (km)
Time
(msec)
Duration
UPPER
LOWER
Velocity
Event
(msec)
X
y
z
X
y
z
m/sec
0
Preliminary Breakdown (PB)
2.1
4.6
10.8
7.1
5.1
11.7
6.1
2.1
First Stepped Leader (SL1)
7.9
5.1
11.7
6.1
6.8
16.7
1.9
Between 0.8 x 10^
and 1.7 x 10 m/sec
10.0
First Return Stroke (Rl)
.4
4.8
10.9
4.5
5.7
12.8
0.8
10.4
Following First Return
Stroke (FR)
8.4
4.7
10.9
6.5
4.0
9.9
3.7
18.7
First J-Change (Jl)
28.4
7.6
13.4
10.6
3.9
10.00
5.7
9.5 x 10^ m/sec during
initial K-change
47.1
Second Stepped Leader
(SL2)
29.0
4.5
10.6
6.6
5.6
8.3
0.7
Between 2.4 and 5.3 x
10^ m/sec
76.1
Second Return Stroke (R2)
0.5
4.8
8.9
7.1
4.7
8.8
6.3
76.6
Second J-Change (J2)
31.2
6.5
10.3
9.3
4.0
8.7
4.9
107.8
Third Stepped Leader (SL3)
15.5
4.9
11.2
6.8
7.7
15.7
.7
Between 7.6 x 10^
and 1.1 x 10^ m/sec
123.3
Third Return Stroke (R3)
.6
5.1
11.2
6.8
4.8
11.2
6.4
123.9
Continuous VHF Activity
after R3
87.1
7.9
14.2
10.0
4.1
8.0
3.4
211.0
Discrete VHF Activity
after R3
71.0
5.3
14.6
9.4
4.1
9.8
5.6
1 26

127
5.2.1 Preliminary Breakdown (PB)
The VHF radiation started 10.0 msec prior to the first return
stroke. The first 2.1 msec of the 10.0 msec was associated with the
preliminary breakdown. The VHF noise characteristics of the PB are
shown in Figure 5.23 along with the VHF noise during the stepped leader,
first return stroke, and some of the activity after the return stroke.
Correlation with the electric field record was only possible to within
750 psec. At a distance of 3 km there was detectable field change
9.0 0.75 msec prior to the first return stroke, that is, about half
way through the preliminary breakdown. Thus the electric field change
started about 1.0 msec after the initial preliminary breakdown pulse
shown at 2.0 msec in Figure 5.23.
The first cross-correlated noise source was located at A (4.6,
10.8, 7.1) in Figure 5.24(a) and corresponded to the highest detectable
cross-correlated source of the preliminary breakdown-stepped leader
process. The noise sources,during the preliminary breakdown as found by
the computer did not occur in a regularly progressing sequence. Attempts
to determine a preliminary breakdown velocity did not produce consistent
results. At the end of the preliminary breakdown the noise sources were
at B (5.1, 11.7, 6.1). The cross-correlated noise sources during the PB
extended between 4.2 and 5.3 km EW, 9.8 and 13.0 km NS, and between 4.9
and 7.1 in altitude.
In addition to determining the cross-correlated and all the indi
vidual source locations (Figure 5.24(b)) using the computer algorithm
described in Chapter IV, we determined the individual source locations
manually during the first 600 psec of the preliminary breakdown. This
task was performed to show the progressing sequence of the initial

0
" T ' "1 1 1
2 4 6 8
TIME IN
10 12
MILLISECONDS
f
14
16
18
Figure 5,23. Log-amplitude VHF radiat
cloud-to-ground flash.
ion at the beginning of
the 180710
1 28

Figure 5.24(a).
Three-dimensional view of the cross-correlated noise sources during the first
PB-stepped leader process. Point A is the location of the first cross-correlated
source during the PB. Point B is a similar source at the beginning of the
stepped leader. The sphere Q1 represents the source charge for the first return
stroke provided by Krehbiel (private com) using the techniques of Krehbiel et al.,
(1979).
Figure 5.24(b).
Similar three-dimensional view for all the individual detected sources.

EAST (km) EAST (km)
on

131
sources every 2 or 3 )isec (if active VHF radiation was recorded), instead
of every 7 to 10 ysec, the limiting using the computer algorithm. These
results are shown in the three-dimensional graph in Figure 5.25. The
sources A through EE are time tagged and shown in alphabetical order
A -* Z, AA DD. This initial stage of the PB extends 8 km horizontally
and 7 km vertically. The sequence of the VHF sources shows that the
activity started at 7.4 km and there was propagation initially horizon
tally and then vertically.
5.2.2 First Stepped Leader
The last 7.9 msec prior to the first return stroke are associated
with the stepped leader in the VHF noise record. Figure 5.24(a) and
Figure 5.24(b) show the cross-correlated, and all the individual detected
noise sources respectively, during the PB-stepped leader process. Figures
5.26(a), 5.26(b), and 5.26(c) show two-dimensional projections of all the
sources in Figure 5.24. The noise sources extended north-northeast 10
km in the horizontal direction from a height of 6.1 km at the beginning
of the stepped leader to a height of 1.9 km. It is worth noting that
the leader extended 5 km over water and away from the most eastern end
of the KSC which is located at (5.3, 8.3). This large horizontal prop
agation of the stepped leader may be related to the fact that the leader
propagated over water. The velocity of the stepped leader ranged between
.8 and 10'> and 1.7 x 10^ m/sec.
5.2.3 First Return Stroke
The first return stroke VHF radiation lasted 400 ysec. The noise
was characterized by high frequency pulses riding on the envelope of a
low frequency pulse as shown in Figure 5.23.

EAST(km)
Figure 5.25. Three-dimensional view of the VHF noise sources during the
first 600 ysec of the preliminary breakdown.

Figure 5.26. Two-dimensional views: (a) EW-NS, (b) EW-height, and (c) NS-height of all the
sources (triangles) and the cross-correlated source location (squares) during the
PB and the first stepped leader. The five circles represent the location of the
cross-correlated noise sources during the first return stroke. The circle Q1 is
the two-dimensional projection of Ql in Figure 5.25.

CO CD
OJ1
NORTH
W OJ -t> U1 O) >J
HEIGHT
fCT

The five return stroke cross-correlated noise sources, 94 ysec
intervals, are shown as circles in Figure 5.26. The noise sources during
the return stroke occurred in ascending order between a height of 0.8
and 4.5 km at a velocity of 1.2 x 10^ m/sec. This return stroke veloc
ity, calculated by determining the cross-correlated VHF noise source
locations at the beginning and at the end of the return stroke and
dividing by the duration of the VHF record, can have large errors. These
errors are caused by two main factors: (1) In a 94 ysec interval the return
stroke upward propagating wave will extend several kilometers and a cross
correlation location might not be a true representation of the source.
(2) It appears that the return stroke VHF radiation is only obtained by
extensions of the previously ionized stepped leader channels, and there
fore return stroke source locations may not be a true representation of
the actual extent of the return stroke channel.
Krehbiel (private com), using the method of Krehbiel et al. (1979),
calculated that -21.1 Coul were lowered by the first return stroke from
a charge center located at Q1 (6.2, 11.1, 4.4). Figures 5.24 and 5.26
show the location of the return stroke charge source. Assuming s source
location at point B (this is the source location for the transition
between P3 and stepped leader in the VHF noise) and using the technique
described in Section 3.6, we calculated that -13.4 Coul were lowered by
the leader-return stroke process. The difference between our assumed
charge calculation source location at B (5.1, 11.7, 6.1) and Krehbiel's
calculated first return stroke charge is significant. However, Krehbiel
(private com) has indicated large uncertainty in the determination of
the locations of Ql.

136
5.2.4 Following First Return Stroke (FR)
We have divided the interval between the first two return strokes
in three sections: (a) activity following return stroke (FR), (b) the
Jl process, and (c) the stepped leader.
The FR is the first interval after the first return stroke. The
FR interval is characterized by having large high frequency pulses riding
on the envelope of pulses of 3 to 30 ysec width. The VHF noise sources
during the FR interval were located in the neighborhood of the previous
stepped leader-return stroke channel between the heights of 3.7 and 6.5
km as shown in Figure 5.27. During the FR interval the electric field
decreased sharply at a station located 3 km away from the charge center,
while a station 19 km away showed a slight increase in field magnitude.
This field reversal indicates that during the FR interval either nega
tive charge was lowered from a region in the neighborhood of the first
return stroke charge center (as in the stepped leader), or that positive
charge (most likely from the previous return stroke) was raised to a
region above the previous charge source. We attempted to determine which
one of these situations was occurring by studying the progressing sequence
of the VHF noise sources. However, the VHF sources were unorganized and
we could not determine a direction of propagation.
5.2.5 The Jl Process
The Jl process started with a K-change and followed immediately
after the FR interval. The K-change was characterized by a change of
slope in the electric field record and a correlated large VHF pulse.
The VHF noise during the Jl process appears similar to that in the FR
interval, and is identified by the following two factors: (1) There was

L37
3 4 5 6 c>
EAST (km)
Figure 5.27. Three-dimensional view of the cross-correlated noise
sources during the 8.4 msec FR interval.

138
a change of slope in the electric field record at the beginning of the
J1 process (K-change, Figure 5.22), and (2) The VHF noise sources were
located in a different region from the FR.
Figure 5.28 shows the cross-correlated VHF noise sources during
the J1 process. The K-change starting the J-process propagated from
point P in Figure 5.28, at a height of 10.6 km and descended into a
lower region between the heights of 5.7 and 7.5 km. The arrows in
Figure 5.28 show the initial sequence of the progressing of the K-change.
The K-change lasted 1.1 msec for an average velocity of 9.5 x 10 m/sec
and showed a descending path of the VHF noise sources from P to near the
center of the lower crowded region in Figure 5.28. By measuring the
electric field change and applying equation (3.10) between the end points
of the propagation path, we determined the K-change lowered .9 Coulombs.
During the remaining 27.3 msec of the J1 process the VHF noise sources
did not show any regular progressing sequence. The bulk of the VHF
sources during the Jl process are located about 2 km above the FR sources
as can be seen by comparing Figures 5.28 and 5.27.
5.2.6 Second Stepped Leader
The second stepped leader had a VHF duration of 29 msec and started
immediately after the end of the VHF associated with the first J-change
process. From an analysis of only the electric field record shown in
Figure 5.22 it is not clear whether the second stepped leader started at
the end of Jl or at the time of the faster changing slope prior to the
second return stroke. However, since stepped leaders have been shown in
this thesis to exhibit low amplitude and high frequency VHF radiation,
the comparison of the electric field with the VHF record in Figure 5.22
shows clearly the point of the beginning of the stepped leader process.

Figure 5.28.
Three-dimensional view of the cross-correlated VHF noise sources during the first
J-change process. Point P represents the location of the beginning of the K-change
that initiated the J-change. The arrows show the regular progressing sequence of
propagation of the VHF noise sources during the K-change. Point A is the start of
the following stepped leader shown in Figure 5.29.

EAST (km)
ALTITUDE (km)
0*71

141
This is another example of the utility of VHF records for a clear
identification of the different events in a lightning discharge.
Figures 5.29(a) and 5.29(b) show a three-dimensional view of the
188 cross-correlated sources, 94 ysec intervals, and the 2991 individual
source locations, respectively, during the second stepped leader.
Figure 5.30 shows the two-dimensional projections of all the individual
noise sources (triangles), and cross-correlated sources (rectangles).
The stepped leader VHF noise sources started from the lower concentrated
J1 noise source volume in Figure 5.29 and descended in a near-vertical
path. The VHF noise sources were detected between a height of 6.6 and
.7 km. From the VHF source locations in Figure 5.29(a), we estimated
the ground contact point as (5.3 .5, 8.5 .5). This point is located
about 1.5 km east of the UC-7 field mill station.
From a study of the location and the sequence of the noise sources
in Figure 5.29, we estimated that the second stepped leader had at least
two detected branches labeled M and N in Figure 5.29. During the first
18.2 msec the second stepped leader propagated vertically from a height
of 6.7 to about 4.0 km, with about 3.5 km horizontal propagation.
During the remaining 10.8 msec the VHF noise sources are grouped in a
more nearly vertical channel. The stepped leader average velocity
ranged between 2.4 and 5.3 x 10^ m/sec.
5.2.7 Second Return Stroke
Figure 5.31 shows the VHF noise during the period including the
second stepped leader, the return stroke, and the beginning of the J2
process. The return stroke had a duration of 316 ysec in the VHF record.
The VHF cross-correlated source locations, 94 ysec intervals, during the
second return stroke, were located in the neighborhood of the upper part

Figure 5.29(a). Three-dimensional view of the cross-correlated noise sources during the second
stepped leader. Point A is the location of the first stepped leader cross-
correlated source.
Figure 5.29(b). Similar three-dimensional view for all the individual dectected sources.

ALTITUDE (km)
143

Figure 5.30. Two-dimensional views: (a) EW-NS, (b) EW-Height, and (c) NS-Height of all the
sources (triangles) and the cross-correlated source location (squares) during
the second stepped leader. The three circles represent the location of the
cross-correlated noise sources during the second return stroke.

EAST EAST NORTH
OJ
-fA
cn
CD
-J
Osl
NORTH
go
(D
£-
rg
-fA
1
CD (?)
OJ
4A
cn
cn
-\!
O -
ro
HEIGHT
OJ
cn
or
-si go co
*
HEIGHT
00
uo
o
r\)
oj
rg
oj JA
i 1
cn cn
i 1
-g
1 1. i- '
.£* r.
r- f,
go
if

Figure 5.31.
Log-amplitude VHF radiation during the second stepped leader, the second return
stroke, and the beginning of the J2 process. Cross-correlated source locations
for pulses A through E at the beginning of the J2 process are shown in Figure 5.32,
146

147
of the previous stepped leader channel. Figure 5.30 shows the three
return stroke sources (circles).
Assuming point A in Figure 5.29 and Figure 5.30 as the point charge
for the second leader-return stroke and using the technique described in
Section 3.6, we determined that -11.5 Coul were lowered by the leader-
return stroke process. A charge value and location for the second or the
third return stroke using the technique of Krehbiel et al. (1979) was
not available for comparison of our results because the electric field
records at some of the stations were saturated.
5.2.8 Second J-Change (J2)
Figure 5.32 shows the VHF noise sources, 94 ysec intervals, during
the second J-change. The J2 VHF noise lasted 31.2 msec of which the
first 12.4 msec are shown in Figure 5.31 along with the VHF of the
previous stepped leader and return stroke. The J2 noise sources extended
about 5.3 km in a path 45 off-vertical. The location of the J2 process
was nearly coincident with the previous J1 process, but the J2 process
extended an additional 2 km in a northerly direction and was located
about .6 km higher than Jl. In addition, the J2 noise sources were more
spread out than Jl.
We studied the progressing sequence of the VHF noise pulses and
their source locations during the J2 interval with the purpose of improv
ing our understanding of the properties of this process. The first six
VHF pulses are labeled alphabetically A to E in Figure 5.31. The source
locations, 94 ysec intervals, for each of these pulses are also labeled
in a regular progressing sequence. The process started with pulse A
which generated locations Al to A5, followed by pulse B that generated
locations B1 to B7. The first two pulses, A and B, were located furthest

Figure 5.32. Cross-correlated source locations during the J2 process. The regular progressing
sequence of occurrence of the source locations at the beginning of J2 is as follows
A1 to A5, B1 to B7, Cl and C2, D1 to D3, and El to E7.

I 49
(UJ>1)1SV3
|
ALTITUDE (km)

150
away to the NE and SW sides, respectively, in Figure 5.32. The next
three VHF pulses (C, D, and E) were also located in the outer region.
We continued this analysis throughout the entire J2 process to determine
whether the VHF noise sources were grouped along any specific pattern
when the third stepped leader developed. The main result of this
analysis was that as the J2 process progressed the VHF sources formed
along the outside of a cylinder, but near the end of the process the J2
sources filled most of the internal regions of this cylinder. The third
stepped leader developed from Q (4.9, 11.2, 6.8) in Figure 5.32, which
is located inside the cylinder.
5.2.9 Third stepped leader
Figure 5.33(a) and Figure 5.33(b) show the cross-correlated and all
the individual noise sources, respectively, during the third stepped
leader. Figure 5.34 shows two-dimensional projections of the cross-
correlated (squares), and all the detectable sources (triangles). Both
first and third stepped leaders propagated downwards about 4 km and
horizontally about 3.5 km in the first 5.5 msec. The channel of the
respective VHF sources remained at least 1 km apart. The third stepped
leader lasted 15.5 msec and propagated from a region inside the J2
process source volume. The VHF source for the stepped leader propagated
off the Atlantic coast in the north-northeast direction about 10 km,
descending from 6.8 km to a height of 0.7 1cm. The stepped leader veloc
ity ranged between 7.6 x 10* m/sec and 1.1 x 10^ m/sec.
It is significant to note that the three stepped leaders propagated
from a common volume that can be approximated as a sphere with a 1 km
radius. It appears that the location of the charge volume is not the
principal factor determining whether subsequent return strokes will be

Figure 5.33(a). Three-dimensional view of the cross-correlated noise sources during the third
stepped leader. Point A is the location of the first stepped leader cross-
correlated source.
Figure 5.33(b). Similar three-dimensional view for all the individual detected sources.

Figure 5.34. Two-dimensional views: (a) EW-NS, (b) EW-Height, and (c) NS-Height of all the sources
(triangles) and the cross-correlated source locations (squares) during the third
stepped leader. The four circles represent the location of the cross-correlated noise
sources during the third return stroke.

EAST (km) EAST(km)
ALTITUDE(km)
ALTITUDE (km)
351

EAST EAST NORTH
NORTH
HEIGHT
HEIGHT
o
0 ro oj
Ul OI >1 d) (D
ro
oj
cn
(T>
-si
co
>>; y
e
. -j, 'V
*./ V",.
Hi-? v;V
V.-J
;h * *
,b> bj* / ¡H
> **Â¥ lv ih U
.-rS-uA:-* '
;j*i .'a. h
H t
* '*ia! > .
*t _a i> &
> *1 ,<* i
-1-> <
<751

L55
preceded by stepped or by dart leaders. In addition, the amount of
charge lowered by the subsequent stepped leaders was larger than the
charge lowered by dart leaders. It is apparent in this flash that there
are other factors such as the wind which might destroy the old return
stroke channel and necessitate the formation of a new stepped leader.
5.2.10 Third Return Stroke
The VHF noise for the third stroke lasted 540 ysec. The five
return stroke VHF cross-correlated sources, 94 ysec intervals, were
located in the neighborhood of the previous stepped leader as shown in
Figure 5.34. Assuming A (4.9, 11.2, 6.8), the highest detectable noise
source at the beginning of the leader to be the point charge of the
stepped leader and using the technique described in Section 3.6, we
estimated that -9.3 Coul were lowered by the third stepped leader-return
stroke process.
5.2.11 VHF Activity After Third Return Stroke
We have divided the VHF radiation that followed the final return
stroke in two intervals. The first interval is described in this sec
tion as the continuous VHF radiation activity following the final
return stroke (CAFS). The second interval is designated as the discrete
VHF activity following the final return stroke (DAFS).
5.2.11.1 Continuous VHF Activity After Third Return Stroke. The
CAFS followed immediately after the third return stroke and lasted 87.1
msec. Figure 5.35 shows the cross-correlated noise sources, 94 ysec
intervals, during this interval. The noise sources were located in the
neighborhood of the previous J-changes but their path extended 2 km
further toward the north. In addition the source locations were spread

ALTITUDE (km)
156
EAST (km)
Figure 5.35. Three-dimensional view of the cross-correlated VHF noise
sources during the 87.1 msec continuous VHF radiation
activity following the return stroke.

157
out over a larger volume between the heights of 3,4 and 10 km. We
studied the progressing sequence of the VHF sources and searched for
any pattern in the development of the source locations. We determined
that some of the large VHF pulses during this interval had correlated
electric field changes. Every time a group of large pulses appeared,
they were at a new location. The largest variation in the VHF source
locations for consecutive pulses was about 5.4 km in the horizontal
direction and 1 km in height. During the CAFS interval the electric
field stations 3 and 19 km away showed the same sign in the slopes of
the electric field change. This is probably due to the large horizon
tal component of the VHF sources in Figure 5.35 (Malan and Schonland,
1951; Uman, 1969; Krehbiel, 1979). Using a two-point charge model
(equation (3.10)) for the X and Y locations in Figure 5.35, we found
that -13.5 Coul were lowered or raised within the cloud during this
interval.
The characteristics of the VHF noise during CAFS and its source
locations are very similar to the J1 and J2 processes. From the
characteristic of the VHF noise it is not evident that a new stepped
leader will not occur until the VHF pulse rate decreases and quiet
periods start developing at the beginning of DAFS. The VHF radiation
of all the subsequent stepped and dart leaders studied in this thesis
were preceded by a J-change VHF pulse rate of at least a pulse every
10 ysec for at least 10 msec. The CAFS has tills pulse rate but did not
produce a leader. It appears that the VHF pulse rate and duration of
VHF activity is a necessary condition for leader development but it is
not a sufficient condition.

158
5.2.11.2 Discrete VHF Activity After Third Return Stroke. The dis
crete VHF activity after return stroke (DAFS) followed the CAFS phase and
lasted 71 msec in the VHF record. Six solitary pulses (Figure 5.1) could
be observed in this final stage of the flash. Three of these SP's showed
correlated electric field changes. The last SP lasted 1.9 msec, had a
correlated rapid electric field change, and possessed the largest ampli
tude of the VHF radiation of any pulse in the flash. The VHF radiation
and the location of its cross-correlated noise sources are shown in Fig
ures 5.36 and 5.37, respectively. The first five noise sources (A to E
in Figure 5.36) corresponded to the first two wide pulses at the beginning
of the SP. These sources were located in a regular progressing sequence
and propagated 2 km south and 1 km downward at a velocity of 8.8 x 10^
m/sec. The source locations of the remaining 1.4 msec were located in
the different regions shown in Figure 5.37. The most concentrated VHF
source region, J to S, corresponded to the lowest crowded VHF source
region of Jl, J2, and CAFS, most likely a negative charge region because
that is where the stepped leaders originated. At the end of the SP some
of the noise sources, T to W, were located in the same returning path to
A. The location of these noise sources showed some evidence that this
1.9 msec SP was a K-change as described by Kitagawa and Kobayashi (1958)
4
except that Kitagawa estimated downwards velocity in the order of 10 m/sec.
By measuring the electric field changes as a function of distances,
Kitagawa and Kobayashi (1958) concluded that K-changes resulted when
charges moving downward encounter charges of the opposite sign and upward
moving return strokes occur. The noise sources- indicate this type
of effect. Positive charges located near A were lowered to the
main active negative charge region (J to S) and an upward moving

Figure 5.36. Log-amplitude VHF radiation during the last solitary
pulse (K-change) in Figure 5.22.

Figure 5.37. Three-dimensional view of the cross-correlated VHF noise sources during the last
SP (K-change). The letters A through Z show the location of the progressing
sequence of the VHF noise sources.

EAST (km)
ALTITUDE (km)
CD CD n) 'CO CD O
O o O
non
T91

162
propagation ended the process. The regions F, G, X, Y, Z and H, I
correspond to the outer region of the previous Jl, J2, and CAFS volume.
Finally it is worth noting that the initial horizontal and downward
propagation velocity of 3.8 x 10^ m/sec (A to E) is comparable to the
upward propagation of 9.1 x 10^ m/sec (S to W).
5.2.12 Volume of the Flash
Figures 5.38(a), 5.38(b), and 5.38(c) show two-dimensional projec
tions of the 34,478 noise sources located during the flash. The average
rate of pulses is about one every 8 psec. The pattern evident in Figure
5.37 is explained in Appendix B. The flash occurred near the coast of
the Atlantic Ocean in the central part of the Cape Canaveral AFS, from
3 to 8 km EW, 7 to 17 km NS, and up to 12 km in height. With the excep
tion of the three stepped leaders most of the flash concentrated between
4 and 7 km EW, 9 to 12 km NS, and 4 to 8 km in height. The flash
1 3
extended throughout a volume of about 500 km during a time of 282 msec.
5.2.13 Concluding Remarks About the Flash
We now provide a summary of what we have learned about this flash.
(1) The flash lasted 282 msec and consisted of three return strokes each
preceded by a separate stepped leader to ground. (2) The flash started
with a PB that lasted 2.1 msec. During the first 600 msec of the PB
the VHF sources propagated upwards and horizontally and there was no
detectable correlated electric field change. During the last msec of
the PB the noise sources filled a path in an unorganized way f 1 km in
both the horizontal and vertical direction. (3) The three stepped
leaders lasted 7.9, 29.0, and 15.5 msec, respectively. All three
stepped leader paths to ground started within 2 km of each other and

Figure 5.38. Two-dimensional views: (a) EW-NS, (b) EW-Height, and (c) NS-Height of all the 34,478 noise
sources (triangles) during the 282 msec flash. The cross-correlated VHF sources are also
shown (squares).

16 A
between a height of 6 and 7 km. The first and third stepped leaders
propagated over water and had large horizontal components. The second
stepped leader had a large horizontal component during the first 18.2
msec, then was propagated vertically making a ground contact near the
coast. The three stepped leader velocities were: 0.8 x 10"* to
1.7 x 10^* m/sec, 2.4 to 5.3 x 10"* m/sec, and 7.6 x 10"* to 1.1 x 10^
m/sec, respectively. The charge lowered by each one of the three
leader-return stroke processes was calculated by using a point charge
model: -13.4, -11.5, and -9.3 Coulombs, respectively, were lowered by
these processes. (4) The VHF sources corresponding to the VHF radiation
in the first 8.8 msec after the first return stroke were located in the
upper part of the previous stepped leader-return stroke process. By
correlating with the electric field we determined that either positive
charges were raised or negative charges were lowered from higher regions
in the cloud. (5) The second and third stepped leaders were preceded
by J-change processes that lasted 28.4 and 31.2 msec, respectively.
During these processes the bulk of the VHF noise sources were located
in overlapping cloud regions between the heights of 6 and 9 km. The
first J-change started with a K-change that propagated for about 6 km
lowering 0.85 Coulombs. The progressing sequence of the VHF locations
during the second J-change formed along the surface of a cylinder and
as the process continued the sources filled the inside of the cylinder.
(6) Two types of VHF radiation, continuous and discrete, occurred on
sequence after the third return stroke. The V1IF sources during the
87.1 msec of continuous VHF activity were loqated in the neighborhood
of the previous J-change. The discrete activity consisted of 5 solitary
pulses. The second, third, and last pulse had identifiable rapid

165
electric field change. Therefore we associated these pulses with
K-changes. At the beginning of the last K-change the VHF sources prop
agated downward about 4 km into the main negative charge region. At
the end of the K-change there was some upward propagation. Except by
the velocity of the downward propagation, this behavior is in agreement
with a model proposed by Kitagawa et al. (1958). That is, the lowering
of positive charges within the cloud is followed by mini-return strokes.
(7) A total of 34,478 noise sources, an average of one every 8 ysec, were
detected during the flash. The flash extended a volume of about 500 km^.

5.3 The 181806 Flash
On 8th August 1977 at 181806 a cloud-to-ground flash was photo
graphed via a television camera (Figure 5.39) and videotape recorder
striking the 150-meter weather tower struck previously by the July, 1976
165959 flash. The VHF portion of the 181806 flash lasted 418 msec and
consisted of a six strokes to ground followed by a 216 msec continuing
current. Figure 5.40 shows the relationship between the VHF radiation
and the electric field for the entire discharge. Table 5.3 contains a
complete summary of the various phases of the flash. The upper and
lower locations, the duration of the phases, and the average velocity
if defined, of the VHF noise sources in each phase are given. Even
though the upper and lower coordinates are given for each event in
Table 5.3, only the events with velocities listed showed continuous
upwards or downwards propagation between these upper and lower coordi
nates, source locations as a function of time for the other events being
less organized. These charge regions are correlated with the VHF source
locations for each of the return strokes. The accuracy in the determi
nation of source locations for the entire flash is given in Appendix 3.
In the next sections we consider in detail what we learned from the VHF
radiation about the phases of the 181806 flash listed in Table 5.3.
5.3.1 Preliminary Breakdown (PB)
The VHF radiation started 7.8 msec prior to the first return stroke.
The first 1.9 msec of the 7.8 msec were associated with the preliminary
breakdown. The VHF noise during this 1.9 msec is characterized by high
frequency pulses riding on the envelope of pulses having between 20 and
40 psec width. Figure 5.41 shows the VHF noise during the PB, the
stepped leader, and the first return stroke. The electric field change

(f) (g) (li) (i) (j)
Figure 5.39. Sequence of photographs during the 131306 flash. The Julian day is 220 and the time is shown
in each photo. Sequence (a) through (h) shows the two stepped leader return stroke channels.
Sequences (a), (b), and (c) correspond to the first stroke that hit the tower while sequences
(d) through (j) show t;.ie remaining strokes in a separate channel. This photo is a courtesy of
Douglas Jordan of the University of Florida.
9 I

Figure 5.40. Simultaneous record of the logarithmic-amplitude VHF radiation observed at 10 km,
and the electric field 14 km away, during the 181806 flash. The following events
in the flash are shown: R1 to R6 represents the six return strokes; SL1 and SL2
are the two stepped leaders; J1 to J5 are the interstroke processes; FR is the
activity following the first return stroke; and CC is the continuous current
interval.

69 !

Table 5.3. Events in the 181806 Flash.
Universal Time at the Start of the VHF
Radiation: 18
18 06
266.13,
8th August 1977
Start
Time
(msec)
Event
Duration
(msec)
Coordinates (km)
Velocity
m/sec
UPPER
LOWER
X
y
z
X
y
z
0
Preliminary Breakdown
1.9
-0.08
9.2
9.5
-.86
9.1
6.7
(*) 9.2 x 105
1.9
First Stepped Leader
5.9
-0.86
9.1
6.7
-.82
8.7
2.7
1.0 x 106
7.8
Return Stroke (Rl)
0.475
0.1
9.6
10.2
-1.5
9.7
2.9
8.2
Following 1st Return Stroke
8.86
-0.4
9.0
8.4
-1.5
8.8
5.1
1.2 x 107
17.0
Semi-Quiet Period
7.5
-0.3
9.1
9.5
-0.8
9.0
6.5
24.5
Quiet Period
16.5
41.0
First J-Change
8.1
1.8
11.4
14.2
0.7
9.2
10.5
5.0 x 105
49.1
New Stepped Leader
17.5
0.7
9.2
10.5
-2.4
8.9
2.8
6.7 x 105
66.6
Return Stroke (R2)
.859
1.8
11.1
14.5
-1.0
8.3
6.5
67.5
Quiet Period
.5
68.2
J-Change (J2)
36.2
1.9
10.08
12.7
-0.4
8.9
5.8
104.4
Dart Leader
.495
0.3
9.8
8.5
-0.6
9.7
7.5
104.9
Return Stroke (R3)
.092
0.8
11.8
12.6
-1.4
11.8
12.2
105.0
Quiet Period
1.1
l 70

Table 5.3 cont
Start
Time
(msec)
Event
Duration
(msec)
Coordinates (km)
Velocity
m/sec
UPPER
LOWER
X
y
z
X
y
z
106.1
J-Change (J3)
37.7
3.1
11.8
13.0
0.6
8.8
5.7
143.8
Dart Leader
.488
2.0
12.2
12.0
-1.0
9.7
8.2
144.3
Quiet Period
3.8
148.1
J-Change (J4)
24.75
5.5
14.0
15.5
2.2
10.1
7.4
172.8
Dart Leader
.45
2.7
12.4
13.3
1.8
11.0
11.5
173.2
Return Stroke (R5)
.22
173.4
Quiet Period
7.09
180.5
J-Change (J5)
19.33
5.7
14.3
15.0
1.4
10.08
7.5
199.8
Dart Leader
.47
0.6
9.5
9.6
0.4
8.9
9.1
200.3
Return Stroke (R6)
.16
1.5
10.1
11.7
1.3
9.8
10.8
200.5
Quiet Period
1.5
202.0
Continuing Current
216.0
7.8
14.1
15.3
0.3
8.9
2.8
(*) Final msec
] 71

I 72

17 3
starts about the middle of the PB interval and correlated VHP and elec
tric field pulse occur. After this point and continuing throughout the
rest of the PB and the stepped leader, large electric field pulses are
correlated with VHF pulses.
In addition to determining the cross-correlated, 94 ysec intervals,
and all the source locations using the computer algorithm described in
Chapter IV, we matched the pulses manually during the first 120 ysec of
the flash. We determined 36 locations during this interval, a location
every 3.3 ysec, about twice as many sources as determined by the compu
ter algorithm. Figure 5.42 shows a three-dimensional view of all the
VHF sources during the 120 ysec interval. The labels A to Z, and AA to
JJ show the regular progressing sequence of the noise sources. The VHF
sources formed a path 20 off vertical between the heights of 5 and 11 km.
During the PB the cross-correlated noise sources were located
between 9.5 and 6.7 km of altitude. However, all the PB noise sources
extended between the heights of 10.3 and 6.5 km. The upper and lower
cross-correlated source locations are shown as A and B in Figures 5.43
and 5.44. Even though the cross-correlated noise sources showed a pre
dominant downward propagation, the first few individual sources did not
correspond with the highest source locations. The first cross-correlated
source detected was at 7.9 km. The cross-correlated source locations,
94 ysec intervals, propagated upwards during the first 4.9 msec.
However, during the final 1.0 msec of the preliminary breakdown, that
was coincident with appreciable electric field change, the propagation
of the cross-correlated VHF sources is only downwards. All the VHF
noise sources during the entire PB interval were located with a cylinder
of 500 meter radius in the path from A to B as shown in Figures 5.43 and

Figure 5.42. Three-dimensional view of all the VHF noise
sources during the first 120 usee interval
at the beginning of the 181806 cloud-to-ground
flash.

175
EAST(km)

Figure 5.43(a).
Three-dimensional view of the cross-correlated noise sources during the first
PB-stepped leader process. Point A corresponds to the height cross-correlated
source during the PB. Point B is a similar source at the beginning of the
stepped leader. The sphere Q1 represents the source charge for the first
return stroke by Krehbiel (private com) using the techniques of Krehbiel et al.
(1979).
Figure 5.43(b).
Similar three-dimensional view for all the individual detected sources.

EAST (km) EAST (km)
ALTITUDE (km)
Li I

NORTH (km)
Figure 5.44. Two-dimensional views: (a) NS-EW, (b) EW-height, and (c) NS-height of all the sources
(triangles) and the cross-correlated source locations (squares) during the PB and the first
stepped leader. The five circles represent the location of the cross-correlated noise
sources during the first return stroke. The circle Q1 is the two-dimensional projection of
Q1 in Figure 5.43.

179
5.44. The average velocity of propagation during the final msec of the
PB was 9.2 x lO' m/sec.
5.3.2 First Stepped Leader
The first stepped leader immediately followed the preliminary
breakdown and lasted 5.9 msec. The VHF noise during the stepped leader
was characterized by high-frequency low-amplitude radiation. As we shall
show from an examination of all the flashes in this thesis, these high
frequency pulses are typical of stepped leaders and hence we can with
confidence associated them with the stepped leader process. The VHF
noise sources could be correlated during the first 3.5 msec of the
leader. During the last 2.4 msec the pulse rate becomes faster than a
pulse every 2 ysec and the pulses could not be correlated because too
many VHF sources were simultaneously active over a large volume. In
addition, the magnitude of the VHF stepped leader pulses decreased.
The stepped leader followed a near-vertical path from the PB to the
tower. Figure 5.43 shows the VHF noise sources during the PB and the
stepped leader. Figure 5.43(a) shows the 416 detected individual
sources. Figure 5.43(b) shows the cross-correlated sources (94 ysec
intervals) and the location of the tower struck by the flash. The
stepped leader cross-correlated sources were detected between a height
of 6.7 and 2.7 km. Point B shows the source location around the
transition point between the two different characteristics of the VHF
noise representing the PB and the SL. Figure 5.44 shows the two-
dimensional projections of all the PB and stepped leader sources. The
cross-correlated values, 376 ysec intervals, are shown as a square of
larger size than the actual source locations which are shown as tri
angles. The circles in Figure 5.44 correspond to the return stroke

180
charge sources to be discussed in the next section. The near-vertical
path of the PB and the stepped leader is evident from this picture.
The stepped leader velocity was 1.0 x 10^ m/sec. Photographs taken of
this flash (Figure 5.39) showed that the first channel struck the
150-meter weather tower. Figure 5.45 shows three sequences of histo
grams of all the source locations during the PB and the first 3.2 msec
of the stepped leader. These graphs are similar to those provided in
Figure 5.7 and they illustrate the propagation of noise sources for
three time sequences, every 1.5 msec.
5.3.3 First Return Stroke
The first return stroke VHF radiation lasted 475 ysec. The noise
was characterized by a low frequency envelope with a succession of
pulses between 10 and 50 ysec width. Noise sources were located during
and immediately following the return stroke. The return stroke cross-
correlated noise sources, 94 ysec intervals, are shown as circles in
Figure 5.44. The return stroke noise sources are located in the pre
liminary breakdown and stepped leader channel regions.
The charge and locations of the six return stroke charge regions
(Ql through Q6) were provided by Krehbiel (private com) and were found
using the technique of Krehbiel et al. (1979). Krehbiel's results are
summarized in Table 5.4. The Ql charge center in Table 5.4 is within
random error in source location from B (-0.9, 9.1, 6.7) which is the
point charge location of the transition in the VHF record between the
PB and the stepped leader. At a station 10.9 km from the tower, the
electric field change from the first leader-return stroke sequence was
990 volts/meter. Using location B as the charge center and the technique

Figure 5.45. Three sequences of histograms, t^, t2, and t3 (1.5 msec intervals) of all the
detected sources in the PB and the stepped leader. Sequences (a), (b), and
(c) correspond to tp, t2, and t3, respectively. There are three histograms
in each sequence. The top row shows distance histograms referenced to the
weather tower. The middle row shows histograms of the elevation angle of the
sources referenced to the weather tower. The bottom row shows histograms of
- the azimuth angle of the sources referenced to the weather tower.

281

183
Table 5.4. Charge and Locations of the Six Return Strokes as provided
by Krehbiel (private com) using the technique described by
Krehbiel et al. (1979).
Return Stroke
Charge (Coulombs)
Location (km)
Ql
-25.7
(-0.1, 9.1, 6.9)
Q2
- 9.6
(0.2, 11.2, 8.1)
Q3
-10.0
(-0.4, 9.2, 7.4)
Q4
- 4.9
(1.4, 11.9, 7.4)
Q5
- 2.9
(1.6, 11.1, 7.0)
Q6
- 3.4
(1.6, 11.3, 6.9)

L 84
described in Section 3.6, we found that -17.2 Coulombs were lowered by
the first return stroke.
5.3.4 Following First Return Stroke (FR)
Figure 5.46 shows the VHF noise during the FR period. Strong VHF
radiation with a pulse every 3 ysec was detected during the first 8.9
msec after the first return stroke. Two large pulses were detected
4.4 and 8.7 msec after the beginning of the FR. These pulses were 250
and 100 ysec wide, respectively, and had the largest amplitude of any
VHF pulses in the entire flash. These wide pulses contained superimposed
pulses that propagated upwards at a velocity of 1.2 x 10^ m/sec.
About 90% of the VHF noise sources during the FR were located in
the previous stepped leader-return stroke channel between the heights
of 5 and 8 km. The remaining 10% of the sources were located between
the heights of 3 and 5 km and above 8 km. Figure 5.47 shows the cross-
correlated locations, 376 ysec intervals, for the FR period. The loca
tions are labeled to indicate the sequence on which the events occurred.
The noise sources propagated upwards between the heights of 5 and 8 km.
By correlating the VHF radiation sources with the electric field record
during this time period, we conclude that either positive charges were
raised by the FR interval or that negative charges were lowered from
higher altitudes as the VHF sources move upward.
5.3.5 Semi-Quiet Period (SQP) Following the FR
The VHF activity continued for 7.5 msec after the first FR at an
average rate of a pulse every 25 ysec. This 'time interval appears to
be a transition between the high pulse rate from the FR and the quiet
period with almost absent VHF radiation that followed the SQP. About

I I ... I I 11 I ,
00 1.00 2.00 3.00 y.00 5.00 5.00 7 00 5 00
TIME IN MILLISECONDS
Figure 5.46. Logarithmic-amplitude VHF radiation during the FR interval.
185

Figure 5.47.
Three-dimensional view of the cross-correlated
noise sources, 94 ysec intervals, during the FR
interval. The labels A to U show the progres
sing sequence of occurrence of the sources.

EAST(km)

188
85% of all the VHF sources during this period were located between the
altitudes of 6.5 and 9.5 km. The remaining 15% of the sources were
located near the altitude of 2 km in the neighborhood of the previous
channel. The SQP interval extended the upward propagation of the
sources during the previous FR interval. The end of the SQP interval
coincides with the highest detectable sources during the previous PB.
5.3.6 First J-Change Process and Second Stepped Leader
For 16.5 msec after the SQP interval there was a quiet period in
which no VHF noise sources were detected. After this period the VHF
portion of the interstroke interval started. The VHF noise during the
interstroke interval would normally be called a J-change. However,
this J-change is identical to the VHF noise during the PB that preceded
the first stepped leader as if an entirely new flash were beginning.
The only difference is that the PB's that precede first stepped leaders
studied in this thesis range between 1 and 3 msec and the J-change or
PB VHF noise that preceded the second stepped leader lasted 8.1 msec.
After the first 8.1 msec we detected the high-frequency low-amplitude
waveform which is typical of stepped leader.
Figure 5.48 shows a three-dimensional view of the cross-correlated
sources, 376 ysec intervals, detected during the J-change (Jl) or PB2
and subsequent stepped leader. Figure 5.49 shows two-dimensional pro
jections of the 1897 noise sources detected during these processes.
The fact that the source locations at the high altitudes are oriented
in patterns, either near-vertical for the east-height plot or near
horizontal for the north-height plot, is attributed to the quantization
error in the determination of the coordinates. Appendix B shows a

Figure 5.48.
Three-dimensional view of the cross-correlated
VHF sources, 94 ysec intervals, during the J1
or PB2 and the second stepped leader. The labels
A, B, C, and E, F, G show different regions of
propagation of the VHF noise sources. Q2 is the
source charge for the second return stroke
obtained from electric field records.

L99
EAST (km)

Figure 5.49. Two-dimensional views: (a) top view, EW-NS, (b) elevation view, EW-height, and
(c) elevation view, NS-height of all the sources (triangles) and the cross-
correlated source locations (squares), 376 psec intervals, during the Jl or PB2
and the second stepped leader. The labels A, B, C and E, F, G show different
- regions of propagation. The circles are the cross-correlated sources, 94 psec
intervals, of the second return stroke. The circle Q2 is the projection of Q2
in Figure 5.48.

15 -
14-
13-
12-
I I-
ALTITUDE (km)
(c)
I 92

193
derivation of the quantization and calibration RMS error in the deter
mination of the three dimensional coordinates.
The noise sources during the J-change or PB2 started at a height
of about 14.2 km (point A, Figures 5.48 and 5.49) and propagated down
ward in a path 25 off-vertical to a height of 10.5 km (point B,
Figures 5.48 and 5.49). The velocity of propagation was 5.0 x 10"*
m/sec. Even though the VHF noise changed characteristics at point B,
the noise sources continued their downward propagation. Applying the
dipole model of equation (3.10) to the 8.1 msec Jl or PB2 for an electric
field station located 12 km from the tower, we find that 1.8 Coul were
transferred between A (1.8, 11.4, 14.2) and B (0.7, 9.2, 10.5). The Jl
or PB2 process apparently made available some of the negative charge
lowered by the new stepped leader. The stepped leader duration was
17.5 msec. The stepped leader propagated from point B to C in about
2.6 msec. At this time and for the next 8.7 msec two active regions
D and E (Figures 5.48 and 5.49) started emitting VHF radiation. The D
region is in the neighborhood of the Q2 charge center while the E region
appears to extend the leader path toward the lower altitudes. The VHF
radiation was only detected during the first 3.4 msec of the remaining
6.2 msec of the 17.5 msec stepped leader. In this time interval all
the VHF noise sources were located below a height of 6.5 km. From a
study of all the noise sources during the 3.4 msec (Figures 5.49(b) and
5.49(c)), it appears that the VHF radiation between the height of 5 and
1.5 km was emitted by two separate channels. We labeled these channels
as F and G in Figures 5.49(b) and 5.49(c). From the location of the
first return striking the 150-meter weather tower and from the locations
of other objects on the ground in Figure 5.39, we estimated the ground

contact about (-2.5, 8.4). This is 1.4 km west and .9 km south of the
150-meter weather tower struck by the first return stroke channel.
Channel F corresponds to a vertical extension of the location of the
stepped leader-second return stroke luminosity while the G channel
locations are in the neighborhood of the first stepped leader channel.
The average velocity for the stepped leader was 6.7 x 10^ m/sec.
From the VHF source locations and the sequence of photographs it
is clear that the second stepped leader developed in a separate channel
to ground as shown in the sequence of pictures in Figure 5.39. The four
succeeding strokes to ground traversed the second stepped leader-return
stroke channel. It is possible that the Jl or PB2 process is not
directly related to the first leader return stroke sequence. In that
case we have two separate flashes: a single stroke flash and a five
stroke flash with continuing current. However, the longer duration of
the preliminary breakdown of the second flash compared to the duration
of the PB's for the other flashes described in this thesis, and the fact
that the VHF noise sources at the beginning of the second flash were
located at much higher altitudes than other PB's sources in this thesis
tend to indicate that the second stepped leader had different character
istics from usual first stroke PB's. Further, the time between the
first two strokes was 58 msec, a typical interstroke time, indicating
that there probably was a connection between the two strokes.
5.3.7 Second Return Stroke
The second return stroke had a duration of 859 ysec in the VHF
record as shown in Figure 5.50. The return stroke radiation was
characterized by a succession of low frequency pulses between 10 and
100 psec wide with superimposed high frequency pulses. Seven average

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END OF
STEPPED
LEADER
>K-
4-
R2
H
0.10
0.20
0.30 0.40 0.50
TIME IN MILLISECONDS
0.60
0.70
0.80
Figure 5.50. Logarithmic-amplitude VHF radiation during the second return stroke.

196
return stroke locations, 94 Msec intervals, are shown as circles in
Figure 5.49. The return stroke channel locations extended from 6.5 to
14.5 km of altitude. The return stroke channel propagated not only
throughout the previous leader but also in the previous J-change (J1)
or preliminary breakdown (PB2). This is a reasonable result since the
entire channel was apparently negative charged and the return stroke
neutralized part of this charge. Three of the seven return stroke
source locations were between 9 and 10 km. It was at about this loca
tion (point B, Figures 5.48 and 5.49) that the VHF noise changed
characteristics from J1 or PB2 to stepped leader. Taking point B
(0.7, 9.2, 10.5) as the point source of the second return stroke and
using the techniques described in Section 3.6, we calculated that -8.2
Coulombs were lowered by the second leader-return stroke sequence.
This number compares reasonably well with the -9.6 Coul shown in Table
5.6.
5.3.8 Second J-Change Process
Figure 5.51 shows the cross-correlated VHF noise sources, 376 ysec
intervals, during the second J-change (J2). The J2 process started
after a quiet period of ,5 msec, lasted 36.2 msec, and extended in a
path 32 off vertical between the heights of 5.8 and 12.7 km. Figure
5.51 also shows the Q3 location given in Table 5.6. The VHF noise
sources during the first millisecond were located at the bottom, the
middle, and the top of the J2 channel. These sources do not appear to
propagate upward in the channel, rather the noise sources are located
along isolated volumes along the path that joins these locations.
During the remaining 35 msec, 78% of the VHF noise sources are located
between the heights of 7.5 and 11.5 km. It is worth noting that even

197
Figure 5.51. Three-dimensional view of the cross-correlated noise
sources during J2, the dart leader, and the third return
stroke. The location of the third stroke spherical
charge center is shown as Q3.

198
though the VHF noise sources do not appear in a regular progressing
sequence throughout the channel, about 80% of all the source locations
are located within 1 km perpendicular distance of a line 32 off verti
cal leading toward the northeast. It appears that the VHF radiation
during the latter part of the J-change joins previous regions from an
earlier part of the J-change. In addition, during the last 7.2 msec of
the J-change all the VHF noise sources were located in the lower half
of the channel between the heights of 5.7 and 9 km.
5.3.9 Dart Leader and the Third Return Stroke
Figure 5.52 shows the VHF radiation during the dart leader and the
third return stroke. The dart leader lasted 495 psec and was followed
by a 92 psec return stroke.
The VHF sources of the dart leader were located between the heights
of 7.5 and 8.5 km, in the neighborhood of the previous J-change. Three
dart leader's cross-correlated locations, 94 psec intervals, are shown
as circles in Figure 5.51. The third return stroke VHF noise sources
were located near the top of the J2 channel. Three return stroke
sources, 94 psec intervals, are shown as squares in Figure 5.51. It is
worth noting that while the VHF noise of the dart leader was located in
the bottom half of the previous J-change, the return stroke sources were
located near the top of the previous channel.
5.3.10 Third J-Change (J3)
Figure 5.53 shows the cross-correlated VHF noise sources, 376 psec
intervals, during the third J-change process.. Figure 5.53 also shows
the location of the fourth return stroke spherical change center (Q4).
There was a 1.1 msec quiet period between the previous return stroke

i+i
* M'ii* -
-i
DART JRETURNJ
LEADER I STROKE*!
IOO 200 300 400 500 600 700 800 900
TIME IN MICROSECONDS
Figure 5.52. Logarithmic-amplitude VHF radiation during the dart leader and
the third return stroke.

200
EAST (km)
Figure 5.53. Three-dimensional view of the cross-correlated noise
sources during J3, and the dart leaders. Source locations
of the previous J2 channel which continue to radiate
during J3 are also shown. The location of the fourth
stroke spherical charge center is shown as Q4.

201
and J3. The third J-change lasted 37.7 msec and extended in a path 35
off vertical between the heights of 5.7 and 13.0 km. The channel was
located 1.5 km east and .5 km north of the previous J-change channel.
As with J2, the locations of the VHF sources did not follow any regular
sequence along the channel. About 70% of all the sources were located
between the heights of 9 and 12 km in a path 35 off vertical. Some of
the VHF sources from J2 were still active during J3. These sources are
located west and north of the J3 channel as can be seen in Figure 5.53.
The VHF sources during the J3 process spread out over similar and
parallel paths, but at higher altitude than J2. The overall radiation
region during J3 becomes wider because active sources from the previous
J-change radiate again or continue to radiate.
5.3.11 Dart Leader and the Fourth Return Stroke
Figure 5.54 shows the VHF noise at the end of the J3 process and
during the dart leader preceding the fourth return stroke. Correlation
with the electric field records indicate that the dart leader started
at 20 30 psec from the beginning of Figure 5.54. We studied the VHF
records for 2 msec following the two 80 psec pulses that marked the
beginning of the dart leader but we did not detect any large pulses.
Since return strokes are characterized by wide pulses of large amplitude
and the multiple electric field stations showed an abrupt field change
characteristic of return stroke, we concluded that the fourth stroke
did not produce any VHF radiation. It appears that the VHF radiation
from consecutive return strokes is due to the extension of the previous
channel in a non-previously ionized region. Probably the fourth return
stroke propagated only throughout a previously ionized channel, con
sequently produced no VHF radiation.

DART LEADER
-H
100
200
300 400 500
TIME IN MICROSECONDS
600
700
800
900
Figure 5.54. Logarithmic-amplitude VHF radiation during the dart leader that
preceded the fourth return stroke.
202

203
Three dart leader sources, 94 fisec intervals, are shown in Figure
5.53. As previously discussed in Section 5.3.10, the J3 process was
located east and north of the J2 process. The VHF noise from the dart
leader was emitted from a non-previously ionized region that joined the
old J2 and the new J3. Both the new J3 and the old J2 are shown in
Figure 5.53. This type of behavior was also observed in the dart
leader in the 165959 flash previously studied.
5.3.12 Fourth J-Change (J4)
The fourth return stroke was followed by a 3.8 msec quiet period
in which no VHF sources were detected. Figure 5.55 shows the cross-
correlated noise sources, 376 ysec intervals, during the J4 process.
Figure 5.55 also shows the location of the fifth return stroke spherical
charge center (Q5). The J4 process lasted 24.7 msec and was located 1.7
km east of the previous J-change. About 50% of all the noise sources
were located in a path 35 off vertical leaning toward the northeast
between the heights of 12 and 14 km. In general, the VHF noise sources
are much more dispersed than in the previous J-changes and did not
propagate in any ordered way.
Some of the noise sources in the neighborhood of J3 were still
active during J4. About 90% of all the J4 sources occurred between the
heights of 11 and 14 km. This J4 process extends higher than J3 which
extends higher than .12.
5.3.13 Dart header and Fifth Return Stroke
Figure 5.56 shows the VHF noise during the dart leader and the
fifth return stroke. Correlation with the electric field records indi
cates that the dart leader started about 80 30 ysec from the

ALTITUDE (km)
204
EAST (km)
Figure 5.55. Threedimensional view of the crosscorrelated noise
sources during J4, and the dart leader. Source locations
of the previous J3 channel which continues to radiate
during J4 are also shown. The location of the fifth
stroke spherical charge center is also shown.

DART '
>
RETURN
* LEADER
STROKE
-J
1 1 ¡
>[<
I
|
|
>j
I
1
IOO 200 300
j
400
1
500
600
700
1
800
1
900
TIME
IN
MICROSECONDS
Figure 5.56. Logarithmic-amplitude
VHF
radiation during
the
dart leader and
the
fifth return stroke.

206
beginning of Figure 5.56. The beginning of the dart leader record prior
to the fifth return stroke in Figure 5.56 is almost identical to the
beginning of the dart leader record prior to the fourth return stroke
in Figure 5.54. However, the fifth return stroke was characterized by
a sequence of large pulses with a width between 3 and 15 psec. The
pulse 40 to 100 psec wide that usually characterizes the return stroke
can be barely observed in the envelope of the VHF radiation.
The cross-correlated locations of three dart leader sources, 94
psec intervals, are shown as circles in Figure 5.55. The dart leader
sources are located near the defunct J3 channel. From a plot of the
cross-correlated locations in Figure 5.55, we cannot see if the dart
leader joins the J3 and J4 regions. However, a plot of all the dart
leader sources shows that VHF radiation was emitted from 1 km west to
1.7 km east of J3, which is the location of the J4 channel. We conclude
that radiation from the dart leader joined J3 and J4. No source loca
tions were identified with the fifth return stroke. The few isolated
VHF return stroke pulses in Figure 5.56 showed varied characteristics
in the different stations making impossible the identification of its
source locations.
5.3.14 Fifth J-Change (J5)
The VHF radiation of the fifth J-change started after a quiet
period of 7 msec in which no VHF sources were detected. As shown in
Table 5.3 this is the longest of all the quiet periods that followed
the return strokes. Figure 5.57 shows the active VHF noise sources,
376 psec intervals, during the 19.3 msec of the fifth J-change.
Figure 5.57 also shows the location of the spherical charge center of
the. sixth return stroke (Q6) The sources were located over a volume

ALTITUDE (km)
07
EAST (km)
Figure 5.57. Three-dimensional view of the cross-correlated noise
sources during J5, the dart leader and the sixth return
stroke. The location of the sixth return stroke charge
center is also shown.

208
of 4 km in the east and north direction and 8 km in height starting less
than 1 km east of J4. The noise sources extended between a height of
7.5 and 15.0 km. These locations did not form an organized channel,
rather they occurred over the entire volume. It appears that the lack
of organization in the location of the V11F noise sources might be an
indicative factor of the termination of the flash. That is, as long as
the noise sources appear along some organized formation, sufficient
charge is available for a consecutive return stroke. It is also worth
noting that only the VHF noise sources from Jl showed a well-organized
propagation pattern. This was the case for the two J-changes in the
165959 flash previously described.
5.3.15 Dart Leader and Sixth Return Stroke
Figure 5.58 shows the VHF noise during the dart leader and the
sixth return stroke. The return stroke lasted about 180 ysec and was
preceded by a 470 ysec dart leader. The VHF noise in Figure 5.58 are
similar to the dart leader and third return stroke in Figure 5.52.
Two noise sources for the dart leader and one for the sixth return
stroke, 94 ysec intervals, are shown as circles and squares, respective
ly, in Figure 5.57. There was no identifiable pattern detected when
relating all the locations of the dart leader, the return stroke, and
the previous J-change. The non-existence of a J-change channel across
which charges could propagate coupled with the continuing decrease in
the field change for consecutive return strokes (Figure. 5.40) have
indicated the termination of additional strokes to ground during this
fla sh.

* dart LEADER H* STROKE H
I 1 1 { 1 1 1 j H
IOO 200 300 400 500 600 700 800 900
TIME IN MICROSECONDS
Figure 3.58. Logarithmic-amplitude VHF radiation during the dart leader and
the sixth return stroke.
4,
60

210
5.3.16 Continuing Current
The six-stroke cloud-to-ground flash was followed by a 1.5 quiet
period and then a 216 msec continuing current. The reason we deter
mined that this period of time was a continuing current is as follows:
(1) The electric field variation in stations located 2 to 21 km away
from the discharge rose steadily during this time interval. Distant
intracloud discharges with significant vertical components should
exhibit a falling electric field as in the 165959 flash. (2) The
luminosity following the last return stroke was observed on TV and com
pared to that following a stroke with no steady field change. We
determined that the last return stroke channel had some luminosity for
195 msec, a time about 100 msec longer than the luminosity observed in
a similar flash without a following field change indicative of contin
uing current.
The VHF noise sources during the continuing current (CC) interval
developed in a 14 km channel 40 off vertical between height of 2.8 and
15 km. The western tip of the channel was located in the neighborhood
of the western part of J3, but the channel extended 4 km further toward
the northeast at the higher altitudes. Similar to the first few J-
changes, the noise sources were organized into a relatively well defined
channel. Figure 5.59 shows the cross-correlated noise sources, 94 ysec
intervals, during the first 23 msec of the CC interval. It appears
that negative charges propagated throughout the CC channel to the return
stroke channel. Since VHF radiation is not emitted by channels carrying
relatively steady currents, most of the VHF1source locations were
detected above a height of 4 km. The noise sources in Figure 5.59 did
not occur sequentially in a downward path but were located randomly

211
Figure 5.59. Three-dimensional view of the cross-correlated noise
sources during the first 23 msec of the CC interval.
The location of a spherical charge center for the sixth
return stroke and the first 23 msec of the CC interval
is shown as Q6-CC.

212
along the path during these 23 msec. For the remaining 193 msec of the
CC interval, VHF sources were located along the previous path for the
first 62 msec, and in a newly developed channel during the last 138 msec.
After the first 85 msec of the CC interval most of the VHF radiation was
concentrated in solitary pulses (SP's), similar to those previously de
scribed in this thesis during the study of the 165959 flash. The source
locations during the SP's developed in a downward propagating path which
merged with the CC channel between the heights of 4 and 10 km. The
longest of these SP's lasted 11.5 msec and propagated downward between
the heights of 11.8 and 2.8 km in a path 20 off vertical at a velocity
of 6.2 x 10^ m/sec. Figure 5.60 shows the cross-correlated noise
sources, 94 |isec intervals, during this SP. The arrows indicate the
regular progressing sequence during the SP. The VHF noise sources
during the 11.5 msec SP were located further west than the other SP's
and furthest away from the main CC channel. The VHF noise for this SP
is shown in Figure 5.40 and corresponds to the third SP from the end of
the CC interval. The SP's during the CC interval have opposite direc
tion and lower velocities than the SP's of the IC discharge in the
165959 flash. It appears that negative charges propagated in the SP's
during the CC interval. Probably SP's during the CC interval developed
new paths for negative charges to propagate down the channel.
5.3.17 Volume of the Flash
Figures 5.61(a), 5.61(b), and 5.61(c) show the two-dimensional
projections of the 18,887 noise sources located during the flash. The
average rate of a pulse .location is one every 22 psec. The pattern
evident in Figure 5.61 results from the quantization error for finding
locations with a discrete time interval of 229 nanoseconds as explained

Figure 5.60. Three-dimensional view of the cross-correlated
noise sources during a SP in the CC interval.
The arrows indicate the regular progressing
sequence of the noise sources during the SP.

ALTITUDE (km)

NORTH (km)
. Two-dimensional views: (a) NS-EW, (b) EW-height, and (c) NS-height of all the sources
(triangles) and the cross-correlated sources (squares) during the entire flash.
Figure 5.61

216
in Appendix B. The flash extended east and north from the -3 to 7 km
EW, and from 7 to 17 km NS. It appears that every event in the flash
developed further toward the north and the east. The flash extended
3
throughout a volume of 450 km during a 416 msec interval.
5.3.18 Concluding Remarks About This Flash
Some of the new information about the flash derived from the VHF
noise source, its source locations, and the correlated electric field
records follows: (1) The flash lasted 418 msec and consisted of six
strokes to ground followed by a continuing current. The flash had two
stepped leaders which followed different channels to ground. (2) The
flash started with a 1.9 msec preliminary breakdown which was located
near and inside the charge source of the stepped leader. All of the
VHF noise sources for the PB were located within a cylinder of 2.8 km
vertical length and a .5 km horizontal radius. From the electric field
records we find that detectable charge motion was only associated with
the final 1.0 msec of the 1.9 msec preliminary breakdown. The average
velocity of propagation of the final millisecond of the PB was 9.2 x 10^
m/sec. (3) A 5.9 msec stepped leader followed the preliminary breakdown.
The stepped leader path to ground extended 1 km horizontally, was near
vertical, and started within .6 km horizontal distance of the 150-meter
weather tower. The stepped leader started at a height of 6.7 km and
5
propagated downwards at an average velocity of 9.2 x 10 m/sec. From
the path of the first stepped leader VHF noise sources and the leader-
return stroke field changes we estimated that -17 Coulombs were lowered
by the first return stroke. This result is comparable to the -24
Coulombs estimated by Krehbiel (private com) using the technique by
Krehbiel et al. (1979). (4) Strong VHF radiation was detected for

2,17
8.9 msec after the first return stroke. During this interval the VHF
noise sources propagated upwards in the neighborhood of the previous
stepped leader-return stroke channel between the heights of 5.1 and 8
km at a velocity of 1.2 x .10^ m/sec. It appears that during this
interval either positive charges were raised or negative charges were
lowered from higher altitudes as the VHF sources moved upwards.
(5) The VHF radiation associated with the source of the second return
stroke started with an 8.1 msec J-change (Jl) or a new preliminary
breakdown (PB2). During this interval VHF noise sources propagated
downwards from a height of 14.2 to 10.5 km in a path 25 off vertical
at a velocity of 5.0 x 10"* m/sec. Using a point charge model we deter
mined that -1.8 Coulombs were lowered during this interval.
(6) Following Jl or PB2 a new stepped leader developed at about a height
of 10.5 km and propagated downwards at a velocity of 6.7 x 10J m/sec
striking the ground at a point about 1.4 km west and 0.9 km south of the
first stroke. From the path of the stepped leader and the leader-return
stroke field changes we estimated that -8.2 Coul were lowered by the
second return stroke. This result compares well with the -9.6 Coul
calculated by Krehbiel (private com). (7) The VHF radiation from the
dart leaders was detected prior to the last four return strokes. The
dart leader VHF radiation started with a pulse between 80 and 150 ysec
wide. The noise sources during dart leaders were located in the neigh
borhood of the previous J-change channel and in the region between the
last two J-change channels. (8) The VHF radiation during return strokes
was characterized by one or a succession of pulses between 10 and 100
ysec wide with the exception of the fourth return stroke which had no
detectable VHF radiation. The first return stroke had detectable VHF

218
radiation in the location of the previous stepped leader and prelimi
nary breakdown. However, VHF noise sources for subsequent return
strokes were located near the top of the previous J-change channel.
(9) The VHF radiation associated with the J-change (J2 to J5) processes
was detected during the last 90% of the time between the last four
return strokes. The VHF noise sources during the J2 process formed a 1
km radius cylinder between the heights of 12.7 and 5.8 km in a path 32
off vertical. Each subsequent J-change process (J3 to J5) was located
1 to 2 km further eastward, was 1 to 2 km longer, and was parallel to
the previous J-change channel. In addition, subsequent J-changes had
a less organized channel formation. Since the VHF noise sources during
the last J-change did not form an organized channel, this might be an
indication that no sufficient charge can be made available for subse
quent return strokes. (10) Continuous VHF radiation was detected during
the first 85 msec of the continuing current interval. During this
initial 23 msec the VHF noise sources formed a 14 km channel eastward
and parallel to the previous J-changes. The channel extended to a
height of 15 km. In the following 55 msec of the continuous VHF radia
tion of the first 85 msec, the VHF noise sources widened the 14 km
channel. During the last 138 msec of the continuing current interval
isolated SP's channels propagated downward merging into the main CC
channel. The longest SP during the CC lasted 11.5 msec and propagated
downward between the heights of 11.8 and 2.8 km in a path 20 off
vertical at a velocity of 6.2 x 10^ m/sec. The remaining SP's also
propagated downwards from the 10 to 14 km of altitude until they joined
the main 14 km channel. Since the lowest part of the CC channel was
located in the neighborhood of the previous leader path to ground, it
appears that the CC interval lowered negative charge to ground. This

charge was located eastward to the previous J-changes and extended from
a height of 15 to 2.8 km. (11) We located 18,877 noise sources during
this flash, an average of a VHF source location every 22.1 psec.
However, there were some quiet periods with no detectable VHF radiation
and periods in which the pulse rate was less than a pulse every 22 psec
During active VHF radiation we detected a pulse every 9 psec. The
flash extended from 7 to 17 km in the north direction, -3 to 7 km in
the east direction, and up to a height of 16 km. The space volume
, 3
covered by this flash exceeded 450 km .

2 20
5.4 The 182356 Flash
On 8th August 1977 at 182356 UT a multiple channel cloud-to-ground
flash was photographed (Figure 5.62) via a television camera and video
tape recorder. The VHF portion of the flash lasted 506 msec and con
sisted of eight return strokes, six of which were preceded by stepped
leaders. Figure 5.62 a, b, c, d, f, and h shows all six different
return stroke channels to ground. Figure 5.63 show the relationship
between the VHF radiation and the electric field for the entire dis
charge. Return strokes Rl, R2, R3, R4, R5, and R7 in Figure 5.63 were
preceded by stepped leaders. The stepped leaders preceding R3 and R4
developed simultaneously about 4 km apart. The fourth stepped leader
began first in the cloud, but the third stepped leader made ground con
tact first, 5.4 msec prior to the fourth stepped.leader. We have corre
lated the VHF record and its source locations with the New Mexico
Institute of Mines and Technology (NMIMT) measured multiple electric
field records and calculated charge locations. Table 5.5 contains a
complete summary of the various phases of the flash: the upper and
lower locations, the duration of the phases, and the average velocity
if defined, of the VHF noise sources. The accuracy in the determination
of source locations as a function of position is considered in Appendix
B, Table B.4. All the cross-correlated noise sources presented for this
flash are calculated using 94 ysec sample intervals. In the next sec
tions wo. consider in detail what we learned from the VHF radiation about
the various phases of the 182356 flash listed in Table 5.4.
5.4.1 Preliminary Breakdown
The VHF radiation started 7.7 msec prior to the first return stroke.
The first 1.8 msec of the 7.7 msec was associated with the preliminary

Figure 5.62. Sequence of photographs during the 182356 flash. The Julian date (220) and the time is shown
in each photo. Sequences a, b, c, d, f, and h show the six different stepped leader-return
stroke channels to ground. This photo is a courtesy of Douglas Jordan of the University of
Florida.

Figure 5.63. Simultaneous records of the logarithmic-amplitude VHF radiation detected at 9 km, and the
electric field 12 km away, during the 192356 flash. The following events in flash
are shown: R1 to R8 are the eight return strokes; J1 to J6 are the six J-changes; FR is
the activity following the first return stroke; SP is a solitary pulse during the
activity after the return strokes; and SL is the first stepped leader.

VHF RADIATION
5000
4000
3000
2000
1000
J4
J5
R6
200
J6-
R7
R8
300
400
500
TIME IN MILLISECONDS

Table 5.5. Events in the 182356 Flash.
Universal Time at the Start
of the VHF
Radiation: 18 23 56
.267, 8th August 1977
Start
Coordinates (km)
Time
Duration
UPPER
LOWER
Velocity
(msec)
Event
(msec)
X
y
z
X
y
z
m/sec
0
Preliminary Breakdown
1.8
-5.2
8.3
9.8
-4.2
7.9
4.6
1.8
First Stepped Leader
5.9
-4.0
11.1
5.9
-4.1
10.6
3.4
1.9 x 106 to
4.3 x 10^ m/sec
7.7
First Return Stroke
.500
-4.2
10.7
6.0
-4.1
10.5
4.5
8.2
Following First Return
Stroke
7.1
-5.5
11.7
9.5
-4.7
8.2
4.9
15.3
J1 Change
13.2
-3.1
12.2
7.5
-4.1
8.9
6.0
28.5
2nd- Stepped Leader
14.2
-4.5
12.6
6.7
3.8
9.7
4.0
2.6 x 10"* m/sec
42.7
2nd Return Stroke
.81
-3.6
12.1
6.5
-4.3
12.7
5.1
43.5
Quiet Period of J2
5.7
49.2
J2 Change
7.2
-5.2
9.1
9.0
-4.0
8.0
5.2
56.4
3rd Stepped Leader
35.0
-4.2
11.2
7.9
-3.5
12.6
1.8
2.3 x 10^ m/sec
91.4
3rd Return Stroke
.2
91.6
4th Stepped Leader
5.2
-5.2
9.1
8.9
-6.0
7.8
3.7
2.9 x 10^ m/sec
96.8
4th Return Stroke
.25
224

Table 5.5 cont.
Time
Coordinates (km)
Start
Duration
UPPER
LOWER
Velocity
(msec)
Event
(msec)
X
y
z
X
y
z
m/sec
97.0
J3 Change
21.1
-5.6
9.4
9.6
-4.7
8.2
5.8
118.1
5th Stepped Leader
30.1
-4.8
8.8
9.6
-3.3
11.6
3.1
5.1 x 10"* m/sec
148.2
5th Return Stroke
.45
148.6
Quiet Period of J4
3.7
152.3
J4 Change
26.8
0.9
11.2
12.8
0.6
10.2
5.2
179.1
Dart Leader
1.5
-5.3
7.8
8.8
-4.9
7.1
7.7
180.6
6th Return Stroke
.4
-5.0
8.2
7.8
-4.9
8.3
7.1
181.0
Quiet Period of J5
8.5
189.5
J5 Change
55.0
0.7
12.5
12.8
-4.0
7.6
5.3
1.6 x 10^ m/sec
244.5
Stepped Leader
30.6
-5.2
8.3
7.7
-4.3
9.2
3.0
2.9 x 10^ m/sec
275.1
7th Return Stroke
.38
275.5
J6 Change
60.3
-1.2
11.1
13.7
0.7
12.1
5.2
335.8
Dart Leader
1.7
337.5
8th Return Stroke
.27
337.7
Discrete Activity after
8th Return Stroke
168.7
0.2
15.1
13.2
-3.8
7.9
5.1
225

7.26
breakdown (PB). The VHP PB radiation consisted of a succession of six
pulses with widths between 80 and 150 ysec superimposed on a more slowly
varying envelope. Figure 5.64 shows the VHP radiation during the PB,
the stepped leader, first return stroke, and the activity following the
first return stroke. We can divide the 1.8 msec PB in three sections of
.6 msec each. Detectable electric field change started following the
first .6 msec period. During this first .6 msec interval the cross-
correlated source locations showed an ascending motion between the
heights of 5.5 and 9.8 km. During the second .6 msec interval, the VHF
noise sources propagated downward in a path that lies within 500 meters
of the previous ascending path. During the last .6 msec the noise
sources propagated for the most part horizontally in a northerly direc
tion.
Figures 5.65(a) and 5.65(b) show a three-dimensional graph of all
the sources and the cross-correlated sources, respectively, during the
PB and the stepped leader. The PB sources are located in the southern
part of the NS axis, and at an altitude between 5.5 and 9.8 km. We
have progressively lettered the first 23 cross-correlated noise sources
in Figure 5.65(b). Sources A through T correspond to the PB, and
sources U to W mark the initial portion of the stepped leader VHF noise.
The unlettered points occurred after W and are associated with the
stepped leader.
5.4.2 First Stopped Leader
The first stepped leader electric field change was detected at the
time the VHP sources were located in the D through J region in Figure
5.65, about 0.6 msec into the discharge. The stepped leader shown in
the VHF noise record propagated downward from a region in the neighborhood

noise:
LEVEL
k-PB-4
2. CO
4.00
6.00
8.GO
10.00
12.00
14.00
16.00
TIME IN MILLISECONDS
Figure 5.64.
Log-amplitude VHF radiation at the beginning of the 182356 flash. PB is
the preliminary breakdown, SL is the stepped leader, RS in the first return
stroke, FR is the activity following the first return stroke which contains
pulses 1 to 5, and J1 is the first J-change.
227

Figure 5.65. Three-dimensional view of the noise sources during the first preliminary breakdown
and stepped leader. Figure 5.65(a) shows all the individual noise sources. Figure
5.65(b) shows the cross-correlated noise sources. The letters in Figure 5.65(b)
show the progressing sequence of the noise sources. Letters A to T correspond to
the PB, letters U to W to the beginning of the stepped leader, and all the unlabeled
sources that occurred after W.

EAST (km) EAST (km)
ALTITUDE (km)
,o->r\j(Jj.fcicna>'sicocDO
ALTITUDE (km)
6ZZ

of the T to W source .locations. The lowest detectable stepped leader
source was at a height of 3.4 km. It can be observed from the log-
amplitude VHF scale in Figure 5.64 that the radiation of the PB is
several orders of magnitude larger than that of the stepped leader.
In addition, the stepped leader VHF radiation decreases as it propagates
near ground. Therefore, it appears difficult to detect stepped leader
sources near ground with lower amplitude radiation and too many leader
sources active over a large volume. The stepped leader average velocity
ranged between 1.9 x 10^ and 4.3 x 10^ m/sec for heights between 5.9
and 3.4 1cm.
5.4.3 First Return Stroke
The first return stroke VHF radiation (Figure 5.64) lasted 500 ysec
The return stroke noise sources were located in the neighborhood of the
T, U, V, and W region in Figure 5.65(b). Using T (-3.9, 11.7, 5.8) in
Figure 5.65(b) as the point where the VHF noise changed characteristics
from the PB to stepped leader, and the technique described in Section
3.6, we.estimated that -20.5 Coul were lowered during the first stepped
leader return stroke process. We have correlated the VHF record and
its source locations with the New Mexico Institute of Mines and Technol
ogy (NMIMT) measured multiple electric field records and calculated
charge locations. Table 5.6(a) shows the value of the source charge and
its location for the first, second, fourth, and fifth return stroke as
provided by Krehbiel (private com) using the technique of Krehbiel et al
(1979). Table 5.6(b) shows the value of the source charge and its loca
tion for each of the stepped leader-return stroke processes obtained by
using the techniques in Section 3.6. The first stepped leader-return

231
Table 5.6(a). Return Stroke Charge Value and Location as determined
by Krehbiel (private com) using the technique of
Krehbiel et al. (1976). R3 is missing because the
beginning of the field change was not easily distin
guishable. R7 and R8 are missing because most electric
field stations were saturated.
Return Stroke
Charge (Coulombs)
Location (km)
R1
-21.4
Q1 (-4.0, 7.4, 7.5)
R2
- 9.5
Q2 (-3.5, 8.0, 7.6)
R4
- 2.9
Q4 (-4.6, 6.7, 7.6)
R5
-10.2
Q5 (-3.5, 8.1, 6.8)
R6
- 6.2
Q6 (-2.6, 7.5, 6.8)
Table 5.6(b). Stepped Leader-Return Stroke Charge Value and Location for
Each of the Return Strokes Preceded by Stepped Leaders as
determined from the VHF source locations and one electric
field record using the technique described in Section 3.6.
R6 and R8 are missing because the return stroke was pre
ceded by dart leaders.
Return Stroke
Charge (Coulombs)
Location (km)
R1
-20.5
(-3.9, 11.7, 5.8)
R2
- 8.2
(-3.7, 11.7, 5.9)
R3
-14.4
(-4.4, 12.8, 6.2)
R4
- 3.6
(-4.1, 7.8, 6.1)
R5
-16.2
(-4.2, 11.2, 6.9)
R7
-24.1
(-5.3, 8.3, 6.9)

stroke charge using our technique in Table 5.6(b) compares reasonably
well with the value obtained in Table 5.6(a).
5.4.4 Activity Following the First Return Stroke (FR)
The FR activity followed immediately after the first return stroke
(Figure 5.64), lasted 7.1 msec and contained five large pulses (1 to 5
in Figure 5.64) about 200 psec wide with an interval between the pulses
ranging from .4 to 1.7 msec. The VHF noise sources during each of these
pulses propagated downward in a southerly direction at a velocity be
tween 1.5 and 3.5 x 10^ m/sec. The longest of these paths extended 4.3
km vertically and 3.2 km horizontally. Figure 5.66 shows the cross-
correlated VHF sources during the FR interval. We fitted a point charge
model to the FR interval assuming a charge transfer from A to B in
Figure 5.66. A charge transfer of 4.5 2.1 Coul was determined by
using the six more distant electric field stations between 9 and 21 km
from the source. We used points other than A and B in Figure 5.66 and
obtained a charge transfer between 1.8 and 5.1 Coul. For all our charge
models the stations located closer to the source (3 to 7 km) gave
inconsistent results. It appears that the charges are not concentrated
and the point charge model is not a good approximation for close stations.
From the characteristics of the VHF radiation, the source locations,
and the point charge model, we conclude that either negative charge at
higher altitudes was lowered toward the top of the previous return stroke
channel or that positive charge from the previous return stroke con
tinued its upward propagation. A total charge of 4.5 Coul distributed
in 5 large pulses is about .9 Coul transfer per event. This number is
comparable with the .85 Coul calculated for the K-change that initiated
the J1 process in the 180710 flash.

>33
E
L
Q
3
I
-30C
'-20C
10C
EAST (km)
Figure 5.66. Three-dimensional view of the noise sources during the FR
interval. The sources A and B represent arbitrary loca
tions which were chosen to perform a point charge model.

5.4.5 The Jl Change
The Jl change lasted 13.2 msec and followed immediately after the
FR interval in the VHF record. The Jl change was characterized by a
higher pulse rate and shorter pulse width than during the FR interval.
Throughout Jl the VHF noise amplitude decreased and the pulse rate
increased. During the Jl process the cross-correlated VHF noise sources
were located between -3 and -4 km EW, 9 and 12 km NS, and 6 to 7.5 km
in altitude.
5.4.6 The Second Stepped Leader
The beginning of the second stepped leader was selected as a point
in the transition region when the VHF radiation changed characteristics
from the slower pulse rate with higher amplitude pulses from Jl to the
shorter pulses with a faster rate during the stepped leader. As soon as
stepped leader variation in amplitude was detected in the VHF record,
the noise sources showed a vertical propagation. Correlated electric
field records for eight ground stations during the interstroke interval
showed no significant slope change as would be expected at the occurrence
of a stepped leader. However, other characteristics of stepped leaders
were observed: decrease in the VHF magnitude of the noise, an increase
in the pulse rate, and some downward propagation in the VHF sources.
Using these criteria, we suggest that the second stepped leader lasted
14.2 msec.
Figures 5.67(a) and 5.67(b) show three-dimensional views of all the
sources and of the cross-correlated sources, respectively, during the
second stepped leader. The cross-correlated VHF sources propagated
between the heights of 6.5 and 3.4 km. The stepped leader cross-corre
lated sources in Figure 5.67(b) were located in two separate regions.

Figure 5.67. Three-dimensional view of the noise sources during the second stepped leader.
Figure 5.67(a) shows all the individual noise sources. Figure 5.67(b) shows
the cross-correlated sources.

-20C
-10C
0C
5 -4 -3 "1
EAST (km)
(a)
-5 -4 -3 1
EAST (km)
(b)
2 36

237
It appears from Figure 5.67 that these two regions merged together and
that the stepped leader had a large horizontal component in the NS
direction. The stepped leader velocity was about 2.6 x 105 m/sec.
5.4.7 Second Return Stroke
The second return stroke lasted 810 ysec in the VHF noise record.
Four cross-correlated noise sources are shown in Figure 5.67 (circles).
All these sources were located in the northern group between the heights
of 5 and 6.5 km. Using point P (-3.7, 11.7, 5.9) as the transition
point to stepped leader waveform, and the technique described in Section
3.6, we calculated that the second stepped leader-return stroke lowered
-8.2 Coul (Table 5.6(b)). This number is comparable to the -9.5 Coul
shown for Q2 in Table 5.6(a), however, our source location is about 3.7
km north and 1.7 km lower in altitude than Ql.
5.4.8 The J2 Change
The J2 change lasted 7.2 msec and started after the 5.7 msec quiet
period that followed the second return stroke. The noise sources during
the J2 change started 0.5 km West and 2.0 km South of Jl. During the
first 1.5 msec of the Jl. period the noise sources propagated upwards
between the heights of 5.2 and 8.0 km. This upward propagation appears
to be related to additional breakdown caused by extensions of the
previous return stroke channel. For the remaining 5.7 msec the VHF
noise sources extended between -6.0 and -4.5 km EW, 8.3 and 10.1 km NS,
and between the heights of 6.0 and 9.0 km.
5.4.9 Third andFourth Stepped Leaders and Return Strokes
We studied the electric field change measured at ten different
electric field stations but we could not clearly determine any slope

change that indicated the beginning of the leader preceding the third
return stroke. However, the VHF noise decreased in amplitude and
increased in rate about 35 msec prior to the third return stroke. As
discussed in this thesis, this characteristic is typical of stepped
leaders. Therefore, we suggest that a stepped leader started 35 msec
prior to the third return stroke.
Figures 5.68(a), 5.68(b), and 5.68(c) show two-dimensional graphs
of the cross-correlated source locations during the leaders that pre
ceded the third and fourth return strokes. Figure 5.69 shows a three-
dimensional view of the same noise sources. The locations A (-5.4, 8.9,
7.9), B (-4.1, 7.8, 6.1), C (-4.6, 12.1, 7.3), and D (-4.4, 12.8, 6.3)
shown in these figures are related to the propagation path of the third
and fourth stepped leaders.
The sequence of events leading to the third and fourth return
strokes is as follows: 1) The fourth stepped leader sources began
first and were located in the A region in Figures 5.68 and 5.69. During
the beginning of the fourth stepped leader the VHF noise sources were
located in the same region of the J2 change. For the first 10.1 msec
the noise sources propagated in the A-B region at an average velocity
of 2.9 x 10^ m/sec. 2) About 10.1 msec after the initiation of the
fourth stepped leader, the third stepped leader started in the C region in
Figures 5.68 and 5.69. The G location is 3.4 km from A. For the fol
lowing 5.6 msec the noise sources propagated in the C-D region at an
5
average velocity of 2.3 x 10 m/sec. 3) For the remaining 19.3 msec
prior to the third return stroke, the VHF sources propagated mainly
downwards from the A-B and C-D regions. 4) About 3.5 msec prior to the
third return stroke, the stepped leader that propagated from the C-D
region was detected at a height of 1.8 km. This stepped leader appears

NORTH (km)
(A) (B) (C)
Figure 5.68. Two dimensional views: (A) top view, EW-NS, (B) elevation view, EW-height, and (C)
elevation view, NS-height of the cross-correlated sources during the third and fourth
stepped leaders. The locations A-B and C-D correspond to the initial propagation of
the fourth and third stepped leader, respectively.
61?

(km)
Figure 5.69. Three-dimensional view of the cross-correlated noise
sources during the third and fourth stepped leaders.
The sources A-B and C-D correspond to the initial propa
gation of the fourth and third stepped leader, respectively.

to contact the ground first and produce the third return stroke.
5) After the third return stroke, most of the VHF sources were detected
below the A-B channel. About 3.9 msec prior to the fourth return
stroke, the lowest detectable source from the fourth stepped leader was
detected at a height of 3.7 km. It appears that the stepped leader
from the A-B region contacted ground 5.4 msec after the third return
stroke.
It is worth noting that the sources detected in the neighborhood
of C did not propagate from the B region, but there were two different
electrified regions. This claim is made from determining the source
location in the last pulse of the B region and the first pulse of the C
region, and calculating a velocity larger than the speed of light
between these sources. The sources that appeared between the A-B and
C-D regions in Figures 5.68 and 5.69 appeared in a random sequence
during the propagation of the third and fourth stepped leaders.
Table 5.6(a) does not show a charge location for the third return
stroke because it was not possible to determine the beginning of the
stepped leader by analyzing the electric field records. The Q4 charge
location for the fourth return stroke is in the region of the A-B path
that generated the fourth return stroke. Using the techniques described
in Section 3.6, we estimated that the third and fourth stepped leader-
return strokes lowered -14.4 and -3.6 Coni, respectively.
5.4.10 The J3 process and the Fifth Stepped Leader
The. J3 process lasted 21.1 msec and followed immediately after the
fourth return stroke. Figure 5.70(a) shows the location of the cross-
correlated VHF sources during the J3 process. Most of the activity was
concentrated in a region 1 1cm east and .6 km south of the source origin

Figure 5.70(A).
Three-dimensional view of the cross-
correlated noise sources during the J3
process that preceded the fifth stepped
leader. The labels M and N represent
the beginning and the end of J3 while P
indicates a region in the neighborhood
of the fourth stepped leader that radiates
again or continues to radiate.
Figure 5.70(B). Three-dimensional view of the cross-
correlated noise sources during the fifth
stepped leader. The sources N and R
indicate the region at the end of J3 and
the last detectable cross-correlated
location, respectively.

EAST (km)
Dooe-

of the third stepped leader (M, Figure 5.70(a)). The main M region
extended 3 km horizontally and vertically. The fifth stepped leader
followed J3 and descended from the center of this concentrated region
(N, Figure 5.70(a)). A study of the electric field record and the VHF
source locations indicate that negative charges were lowered during the
J3 interval. The noise sources in the P region in Figure 5.70(a)
correspond to active sources in the previous A-B channel in Figure 5.69.
The fifth stepped leader (Figure 5.70(b)) lasted 30.1 msec and
continued the downward propagation of the N region sources in Figure
5.70(a). The fifth stepped leader path to ground remained between one
and two km from the previous stepped leader. The lowest detectable
cross-correlated noise source was located at a height of 3.1 km (R,
Figure 5.70(b)). The average stepped leader velocity was 5.1 x 10^
m/sec.
5.4.11 Fifth Return Stroke
The fifth return stroke lasted 450 ysec in the VHF record. Three
cross-correlated noise sources during the fifth return stroke are shown
as circles in Figure 5.70(b). Assuming a point charge model and using
the technique in Section 3.6, we estimated that -16.2 Coul were lowered
by the fifth stepped leader-return stroke.
5.4.12 The J4 Process, the Dart Leader, and the Sixth Return Stroke
The fifth return stroke was followed by a 3.7 msec quiet period
and a 26.8 msec J-chango (J4, Figure 5.64). The J4 process formed in
the neighborhood of the source charge of the third and fifth return
stroke. Figure 5.71 shows the cross-correlated noise sources during
J4. The two different regions are shown as F and G. The sources in

Figure 5.71.
Three-dimensional view of the cross-correlated noise sources (triangles) during the
J4 process that preceded the dart leader and the sixth return stroke. The rectangles
represent the cross-correlated dart leader sources and the circles represent the
sixth return stroke cross-correlated sources. F and G show the isolated locations
of the two active regions.

EAST (km)
ALTITUDE (km)
,cno)'vjoo(DO-r\jw
9 Vi'

the F region extended between a height of 5.6 and 12.8 km while the
sources in the G region extended between a height of 5.2 and 9.9 km.
The J4 noise sources did not follow a regular progressing sequence.
We studied the VHF radiation at the central and the remote stations
whenever there was a shift in source locations between the F and G
regions. The purpose of this study was to determine whether there was
propagation between these regions or whether sources were active simul
taneously. Figure 5.72 shows the VHF radiation at the central (a) and
one of the remote stations during a transition from F to G. We have
displayed the graph such that pulse 1 which corresponded to the F region
is lined up in both stations. Some of the subsequent pulses (e.g., 2
through 7) shown in Figure 5.72 were located in the neighborhood of G
and the DTOA in these pulses is less than 2 ysec. When we account for
the absolute difference in the time of occurrence of 1 and 2 in stations,
it was clear that a source in F producing pulse 1 cannot propagate to
G to produce pulse 2 at a speed less :than the speed of light. There
fore, the F and G regions are independent. Even though an argument
could not be invoked for the source regions of the third and fourth
stepped leaders previously described, it provides an example of a pro
cess in which two different return strokes could occur almost simultane
ously.
I
A dart leader characteristic was evident from the VLF and VHF |
record after the J4 process. As shown in this thesis, the dart leader
does not radiate in its path to ground along the previous return stroke
channel. The noise sources just prior to the 'dart leader, the dart
leader, and the return strokes were located in the G region. Figure
5.71 shows six cross-correlated noise sources during the dart leader

Figure 5.72.
VHF noise detected at the central station (A) and
one of the remote stations (B). The (B) noise
has been shifted such that pulse 1 occurs at the
same time. Pulses 2 to 7 show the shift in the
VHF noise when the noise is emitted from a dif
ferent region.

TIME IN MICROSECONDS
VHF RADIATION

250
(squares) and four cross-correlated locations for the sixth return
stroke (circles).
Figure 5.73 shows the VHF noise during the last 5.8 msec of the
J4 process, the 1.7 msec dart leader, the 810 ysec return stroke, and
the first 8 msec of the quiet period following the return stroke. The
fact that there is a quiet period after the sixth return stroke is
interesting. It appears from our results that the dart leader lowered
the negative charge from one of the isolated regions, most likely the
G region. Therefore, we would have expected the charges in the remain
ing region to cause additional breakdown and not be affected by the
return stroke of the other region, as occurred in the third and fourth
return strokes.
5.4.13 The J5 Process, the Stepped Leader Preceding the Seventh Return
Stroke and the Seventh Return Stroke
Active VHF radiation for the next J process (J5) started after the
8.5 msec quiet period that followed the sixth return stroke. The J5
process lasted 55 msec and initiated a new stepped leader. Similar to
J4, the cross-correlated VHF noise sources were detected in the neighbor
hood of the F and G regions in an unorganized sequence. Figure 5.74(a)
shows the cross-correlated VHF sources during the J5 process. The cross-
correlated sources in the F region extended a horizontal distance of 4
km and between the heights of 5.4 and 10.6 km. Simultaneously, the
sources in the C region extended a horizontal distance of 7 km and
between the height of 5.3 and 12.8 km. Even though, the cross-correlated
noise sources did not follow any regular progressing sequence, most of
the sources detected near the beginning of the J5 process were located
at the higher altitudes and the sources located near the end of J5 were


Figure 5.74(A).
Three-dimensional view of the cross-
correlated noise sources during the J5
process that preceded the sixth and last
stepped leader. F and G are the locations
of the active regions during J4.
Three-dimensional view of the cross-
correlated noise sources during the sixth
stepped leader. The label S represents the
first stepped leader cross-correlated source.
Figure 5.74(B).

EAST (km)
D.OC-

254
at the lower altitudes. Therefore, it appears that the J5 process
lowered a net negative charge in the F-G regions.
A new stepped leader which lasted 30.6 msec immediately followed
J5. From the six available electric field records which were not
saturated during the stepped leader-seventh return stroke field change,
only one of the records (9 km away from the discharge) shows the change
of slope corresponding to the beginning of the stepped leader electric
field. This electric field change of slope was correlated with the
decrease of magnitude of the VHF record, 30.6 msec prior to R7 in the
VHF record of Figure 5.63. Figure 5.74(b) shows the cross-correlated
noise sources during the stepped leader. For ease of comparison the
stepped leader and the previous J-change noise sources are lined up
vertically in Figure 5.74. The horizontal projections are the same for
both graphs, but the height range of the stepped leader graph is 0 to
10 km while the J5 is 5 to 13 km. The stepped leader progressed from
the G region as shown in Figure 5.74(b). The stepped leader velocity
ranged between 1.6 and 2.9 x 10^ m/sec. Assuming S (-5.3, 8.4, 6.9) to
be a point charge representation for the stepped leader-seventh return
stroke charge center and the technique described in Section 3.6, we
determined that -24.1 Coul were lowered by this process. This is the
largest estimate of the charge lowered by any of the return strokes of
this flash.
5.4.14 The J6 Process, the Dart Leader, and the Eighth Return Stroke
The J6 process followed immediately after the seventh return stroke
and lasted 60.3 msec. Figure 5.75 shows the locations of the cross-
correlated VHF noise sources during the J6 process. These sources are
3
spread out over a volume of about 1450 km between the heights of 5.2

Figure 5.75.
Three-dimensional view of the cross-correlated noise sources (triangles) during
the J6 process. The location of four cross-correlated dart leader sources are
shown with squares near the center of the picture.

EAST (Km)
ALTITUDE (km)
95Z

257
and 13.7 km. The progressing sequence of the noise sources do not
follow any specific channel. This J-change is less organized than the
previous one. This lack of organization, concentration, and channel
formation of the noise sources during this last J-change was previously
observed in the last J-change of the 181806 flash. It appears to be
an indication that sufficient charge is not available to be lowered to
ground in additional subsequent strokes.
During the dart leader that followed the J6 process, the VHF noise
sources were located between the heights of 12.5 and 7.7 km. Four
cross-correlated dart leader sources are shown as squares in Figure
5.75. No cross-correlation VHF sources were detected during the eighth
return stroke.
5.4.15 Discrete Activity Following the Eighth and Last Return Stroke
(DAFS)
Solitary pulses were detected in the VHF radiation for 168.7 msec
after the eighth return stroke. The pulse repetition rate during DAFS
started with a pulse every 800 ysec and decreased to a pulse every
10 msec toward the end of the flash. This is the same way that all the
flashes studied in this thesis have terminated, that is, a decrease in
the rate of SP's. We studied the cross-correlated source locations
during the SP shown in Figure 5.63. These results are shown in Figure
5.76. This SP started at a height of 8.2 km and propagated downward in
a path 50 off vertical. The noise source during this SP, which corre
sponds to the final VHF pulse of the flash, extended 5 km at a velocity
of 2.2 x 10^ m/sec.

Figure 5.76. Three-dimensional view of the cross-correlated locations of the VHF noise sources
during the SP shown in Figure 5.63. The labels A to N show the regular progressing
sequence of the noise sources.

ALTITUDE (km)
O O
o o
65?

260
5.4.16 Volume of the Flash
Figure 5.77 shows all the 33,947 individual VHF noise sources
(triangles) detected during the 506 msec flash. All the cross-correlated
noise sources are also shown as squares. The average rate of pulse loca
tion throughout the flash was one every 14.9 psec. During the 337 msec
period preceding the DAFS the detected rate was a source every 9.5 msec.
This rate decreased considerably during the 169 msec DAFS interval. The
flash extended about 15 km in the EW direction, 14 km in the NS direc
tion, and up to 14 km in altitude. The volume occupied by the flash
3
was about 1500 km .
5.4.17 Concluding Remarks About the Flash
Now we provide a summary of what we learned about this flash.
(1) The flash lasted 506 msec and consisted of eight return strokes and,
six separate stepped leader channels to ground. (2) The flash started
with a PB that lasted 1.8 msec. During the first .6 msec of the PB the
VHF sources propagated upwards and there was no detectable electric
field change. For the next .6 msec the VIIF sources propagated down
wards within 500 meters of the previous ascending channel. In the
remaining .6 msec of the PB most of the propagation was horizontal at a
height of 6.5 km. (3) This flash had stepped leaders preceding return
strokes 1 to 5, and 7 and lasting 5.9, 14.2, 35.0, 5.2, 30.1, and 30.6
msec, respectively. The third and fourth stepped leader developed
simultaneously about 4 km apart and the 5.2 msec of the fourth stepped
leader is only the time of stepped leader propagation that occurred
after the third return stroke. Stepped leaders preceding Rl, R2, R3,
and R5 started within 2 km of each other while stepped leaders preceding
R4 and R7 were also 2 km apart but about 4 km from the region of the

Figure 5.77.
Two-dimnsional views: (a) top view, EW-NS, (b) elevation view, EW-height,
elevation view, NS-height of all the noise sources during the 182356 flash.
and (c)

other stepped leaders. The stepped leader velocities were: 1.9 to 4.3
x 106; 2.6 x 105, 2.3 x 105, 2.9 x 105, 5.1 x 105; and 1.6 to 2.9 x 105
m/sec, respectively. The first stepped leader in this flash is shorter
in duration and propagated an order of magnitude faster than the subse
quent stepped leaders. The charge lowered by each one of the stepped
leaders was calculated by using a point charge model. We found that
-20.5, -8.2, -14.2, -3.6, -16.2, and -24.1 Coul were lowered by stepped
leader-return stroke processes. That is a total charge of about -86
Coul, considering only six of the eight return strokes. (4) The VHF
sources corresponding to the VHF radiation in the first 7.1 msec after
the first return stroke were located in a region above the previous
stepped leader-return stroke channel. By studying the VHF noise sources
of the individual VHF pulses during this interval and the correlated
electric field change, we conclude that either -4.5 Coul were lowered
into the top of the previous return stroke channel from a region at the
higher altitudes, or that 4.5 Coul were raised in the cloud from the
top of the previous return stroke. (5) All but one of the subsequent
stepped leaders and the dart leaders were preceded by J-change processes.
The exception is between the third and fourth return strokes because
sources from both the fourth stepped leader and higher location in the
cloud are detected. The VHF J-change process durations are: Jl, 13.2
msec (preceding the second*stepped leader); J2, 7.2 msec (preceding the
third stepped leader); J3, 21.1 msec (preceding the fifth stepped
leader); J4, 26.8 msec (preceding the first dart leader); J5, 55.0 msec
(preceding the sixth stepped leader); and J6, 60.3 msec (preceding the
second dart leader). Two active regions about 4 km apart were detected,
a northern and a southern region. The Jl noise sources were concentrated

26 3
in the northern region and the second stepped leader discended from
that region. About 80% of the J2 noise sources were concentrated in
the southern region which initiated the fourth stepped leader. The
remaining 20% of the J2 sources were located in the northern region
and initiated the third stepped leader. Most of the J3 noise sources
were located in the northern region and the fifth stepped leader
descended from that region. The J4 noise sources were spread in both
regions and the dart leader appeared to descend from the southern
region. The J5 noise sources were located in both regions and the
sixth stepped leader descended from the southern region. Finally the
J6 noise sources were spread everywhere and from the dart leader sources
it appears to be located in the northern region. All the subsequent
J-changes extended higher in altitudes and were less organized. (6) A
discrete VHF activity interval was observed for 168 msec after the last
return stroke. The pulse repetition rate continuously decreased during
this interval. The last solitary pulse in the flash was 21.6 msec from
the previous pulse. The noise sources during this SP propagated down
wards 50 off vertical in a 5 km path.

4
5.5 The 180644 Flash
The work reported in this thesis includes three IC flashes. The
first of these IC flashes was studied in Section 5.1 because it followed
the 165959 flash. The other two IC flashes are discussed in this section
and in Section 5.6.
The first lightning discharge during the thunderstorm on the 8th
August 1977 happened at 180644 UT. This lightning discharge was an
intracloud flash and occurred 56 sec prior to the first cloud-to-ground
flash at 180710, previously described in Section 5.2.
Figure 5.78 shows simultaneous records of the logarithmic-amplitude
VHF radiation and the electric field reading in four different stations
located 4, 15, 17.5, and 18.5 km from the discharge. The fact that the
electric field reading at 4 and 15 km showed a positive electric field
change while the stations at 17.5 and 18.5 km showed a negative field
change indicated that an upper positive and a lower negative polarity
charge center were supporting the discharge (equation (3.10)). The
electric field reversal with distance, the fact that the field shows no
evidence of leader-return stroke sequence, and the locations of the VHF
sources in the cloud combine to indicate that the 181416 flash was
indeed an intracloud discharge.
The flash lasted 360 msec and can be described as being composed
of three different phases on the basis of the relationship between the
electric field and the VHF radiation. This pattern is similar to the
one described by Kitagawa and Brook (1960) who classified the intracloud
discharge into an initial, a very active, and junction phase, and
similar to the 165959 IC flash. These events are shown in Figure 5.78
and lasted 75, 185, and 260 msec, respectively.

Figure 5.78. Simultaneous record of the logarithmic-amplitude VHF radiation observed at 12 km,
and the electric field detected at 4, 15, 17.5 and 18.5 km from the discharge.
The three active regions of the IC discharge are shown: initial, active and
junction phase.

E FIELD (volts/meter) VHF RADIATION
997

5.5.1 The Initial Phase
267
The flash started with an initial phase characterized by a smooth
variation of the electric field and a VIIF pulse rate of one every 20
to 50 ysec. Figure 5.79 shows the VHF noise during the first 8.5 msec
of the intracloud discharge. The flash started with a 100 ysec wide
pulse, similar to the pulse that starts the PB in a cloud-to-ground
discharge. However, the lower amplitude, higher frequency VHF radiation
following the PB in a CG discharge and characteristic of the stepped
leader did not occur.
Figure 5.80 shows the location of the cross-correlated VHF noise
sources, 94 ysec intervals, during the first msec of the intracloud
discharge. Most of the VHF source activity is located between the
heights of 9.2 and 10.5 km. During the first 13 msec, a channel is
formed between the heights of 9.2 and 14.5 km in a path 40 off verti
cal. As we can see from comparing Figure 5.80 with Figure 5.81, these
initial sources become the center of the flash. We also studied the
progressing sequence of the VHF noise sources in Figure 5.80. The
most active region was at the lower altitude, 9.2 to 10.5 km, but we
could not determine the direction of propagation of the VHF sources.
We continued this analysis throughout the entire 75 msec of the initial
phase, and the only conclusion that we could derive was that at the
beginning most of the. sources were concentrated at the lower altitude
of the slanted channel while at the end of the initial phase there was
more activity at the higher altitude. In addition, the original VHF
source region became wider throughout the flash.

BEGINNING OF I.C.
1 !
00 1.00 2.00 3.00
| 1 1 1 1
9.00 5.00 6.00 7.00 3.00
9
TIME IN
MILLISECONDS
Figure 5.79. Logarithmic-amplitude
VHF radiation during the first 7.3 msec of
the IC discharge.
H9'<:

3 4 5 6
EAST (km)
Figure 5.80. Three-dimensional view of the cross-correlated noise
sources, 94 )Jsec intervals, during the first 13 msec,
of the intracloud discharge.

NORTH (km)
Figure 5.81.
Two-dimensional views: (A)
elevation view, NS-height of
top view,
all the
EW-NS, (B) elevation view, EW-height, and
noise sources during the 180544 intracloud
(C)
discharge.

271
5.5.2 The Very Active Phase
The very active portion of the discharge is characterized by a
faster rate of change of the electric field than in the initial phase
as shown in Figure 5.78. In addition, the VHF noise pulse repetition
rate increased from a pulse every 20 to 50 psec to a pulse every 5 to
10 psec.
A study of the electric field variation with distance in Figure
5.78 suggests that an electric field station about 16 km away from the
flash will detect zero field change. Solving the two point charge
model in equation (3.10) for zero electric field change, we have
(5.1)
From a study of the VHF sources during the first 13 msec in Figure
5.80 and all the VHF sources in Figure 5.82, it is reasonable to select
the height of the charge centers at 9.5 and 13.5 km along the slanted
dipole. For these values of h^ and h^ we fitted equation (5.1) and
determined that the left and right side agreed within 10%. We also
selected other values of heights along the slanted dipole between the
heights of 9 and 14 km, but we could not obtain a better fit. There
fore, we conclude that a point charge model of this IC discharge will
have charge center at 9.5 and 13.5 km.
5.5.3 The Junction Phase
The junction or final phase of the intracloud discharge has
characteristics similar to the discrete activity after return strokes
(DAFS), (see, for example, Section 5.2.11.2) in the cloud-to-ground
flash and the final part of the IC in the 165959 flash (Section 5.1.13).

272
This phase is characterized by a pulse every few milliseconds in the
VHF record and small variation in the electric field record. Some of
the SP's during the junction phase have correlated electric field
change as can be observed in Figure 5.78. Therefore, we identify these
SP's with K-changes following the work of Brook and Kitagawa (.1960),
and Ogawa and Brook (1964).
5.5.4 Volume of the Flash
Figure 5.81 shows the 21,752 individual noise sources (triangles)
detected during the intracloud flash. The cross-correlated noise
sources are also shown with squares. The average rate of pulse loca
tion throughout the flash was a pulse every 28.9 Msec. This low rate
of source locations, compared to the typical 7 to 10 Msec for active
VHF periods, is caused by the long duration of the junction phase in
which sources were located only during the SP's. The source locations
extended from 2.5 to 7 km EW, 8 to 15 1cm NS, and 6 to 14 km in height,
3
for a total volume of 140 km .

273
5.6 The 181416 Flash
At 181416 UT during the thunderstorm on 8th August 1977 an intra
cloud discharge occurred. Figure 5.82 shows simultaneous records of
the logarithmic-amplitude VHF radiation and the electric field reading
at three different stations located 2.6, 7.6, and 13.7 km from the
discharge. The fact that the electric field reading at 2.6 km showed
a positive field change while the electric field at 13.7 km showed a
negative field change indicated that an upper positive and a lower
negative polarity charge center were supporting the discharge (equation
(3.10)). The electric field reversal with distance, the fact that the
field showed no evidence of leader-return stroke sequence, and the
locations of the VHF sources in the cloud combine to indicate that the
181416 flash was indeed an intracloud discharge.
5.6.1 Characteristics of the VHF Radiation
The 181416 flash lasted 114 msec and was characterized by pulses
one to 5 |_isec wide superimposed on an envelope x^hose pulse width
ranged between 50 and 600 ptsec. Figure 5.83 shows the logarithmic-
amplitude VHF radiation during the first 8.4 msec of the intracloud
discharge. The VHF radiation pattern at the beginning of the intra
cloud discharge is markedly different from the VHF radiation for the
cloud-to-ground flash studied in this thesis. Since the preliminary
breakdown phase in a cloud-to-ground flash studied in this thesis
lasted between 2 and 3 msec and was followed by a stepped leader with
significantly different VHF characteristics, we can, in the absence of
the VHF leader, uniquely identify this present radiation with an

Figure 5.82. Simultaneous record of the logarithmic-amplitude VHF radiation observed at 7 km,
and the electric field detected at 2.6, 7.6 and 13.7 km from the discharge.

ELECTRIC FIELD
LOG AMPLITUDE
VHF RADIATION

BEGINNING OF I.C.
1 1 1 1 1 1 1 1
00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00 9
TIME IN MILLISECONDS
Figure 5.83. Logarithmic-amplitude VHF radiation during the first 6.5 msec of
the intracloud discharge.

277
intracloud discharge. The initial VHF noise of the intracloud has
similar characteristics to that of the cloud-to-ground discharge prior
to the stepped leader; that is, both appear to be due.to the PB process.
Figure 4.1 shows the first 800 ysec of the VHF radiation detected
at the central station, and at the Wl, Ml, and M3 stations. These
stations are identified in Figure 3.1. The ground distance from the
discharge to the four stations is 7.6, 4.1, and 12.4 km, respectively.
The DTOA between the central and each one of the remote stations is
shown in Figure 4.1. This data is taken directly from the digitized
tapes and corresponds to the simultaneous recorded VHF radiation. To
determine the actual DTOA needed to calculate source locations we have
to subtract the retransmission delays for the remote stations
(Appendix B).
Similar to the cloud-to-ground discharge after the last return
stroke, the VHF noise pulse repetition rate decreases toward the end
of the discharge. This decrease of the pulse rate of continuous
radiation coupled with the appearance of discrete VHF radiation of SP's
mark the end of the intracloud discharge.
The 181416 flash did not have the three previously described
phases: initial, very active, and junction phase. The VHF pulse rate
of one every 10 to 20 ysec (characteristic of the active phase) decreased
toward the end of the flash. Therefore, we could characterize the VHF
radiation in two intervals: an active phase and a junction phase as
proposed by Brook and Kitagawa (I960) for some of the flashes they
studied.
5.6.2 Locations of the VHF Noise Sources
Figure 5.84 shows the cross-correlated VHF noise sources, 94 ysec
intervals, during the first 18.8 msec of the IC discharge. The VHF

ALTITUDE (km)
278
EAST (km)
Cross-correlated VHP sources, 94 ysec intervals, during
the first 18.8 msec of the IC discharge.
Figure 5.84.

279
noise sources formed a near vertical channel between the heights of
8.5 and 13.5 km. About 90% of the cross-correlated noise sources were
located within a cylinder of 0.5 km radius and 5 km length. During the
first 18.8 msec the VHF noise sources did not follow a progressing
sequence either upwards or downwards. However, in the first 4.5 msec,
about 80% of the VHF sources were located in the bottom half of the
cylinder.
Figure 5.85 shows a two-dimensional view of all the cross-correlated
noise sources, 94 psec intervals, during the entire IC discharge. The
VHF sources spread radially with increasing height forming an inverted
cone about 9 km in height.

Figure 5.S5. Two-dimensional projections: (a) EW-liF, (b) EW-height, and (c) NS-height of all the
cross-correlated VHF sources, 94 psec intervals, for the IC discharge.

CHAPTER VI
DATA MODEL
This chapter is an attempt to use a stochastic model to describe
the behavior of some of the different phases of the VHF radiation during
lightning discharges. We have attempted data models for the basic
noise level, the stepped leader, and the J-change process. The noise
level is used for reference and is assumed to be the VHF background
noise without a nearby lightning VHF radiation. The stepped leader is
characterized by a unique high frequency pulse rate, the properties of
which are important to study. The characteristics of the VHF noise
during the J-change process accounts for most of the CG radiation.
It is not possible to predict the exact magnitude of the VHF radia
tion during these phases because the exact physical laws that describe
these processes are not known and these processes are not deterministic.
Our goal is to derive a stochastic model of the phenomenon, that is, to
predict the probability that a future value of the radiation will lie
within certain limits. These models in turn can be used to improve the
understanding of the physics underlying the activity. To arrive at
the models we have identified the parts of the VHF radiation data
corresponding to different phases of the lightning on the correlated
electric field records. A model can be derived whenever the time series
of the VHF radiation z. z. ..., z, ,, z, behaves in such a manner that
1 2 k-1 k
given k-1 samples z^, z^, .., zk_x t*ie value the Z¡ 281

282
For a model to be valid it should fit the specific physical process
regardless of the selected flash. Therefore, we selected data from the
stepped leader, J-changes, and noise levels for all the flashes, deter
mined their respective models, and then compared the results. If con
sistent results were obtained, then we can claim that the physical pro
cess fits a specific data model.
For a data range larger than 500 microseconds all the analyzed
processes present some type of equilibrium because the larger pulses
determined in the VHF radiation have a width of the order of 240 micro
seconds. Each process studied has a constant mean for data records
larger than about 2.3 msec (about 10,000 samples) and can be treated as
stationary.
Four types of stochastic models are tested. The autoregressive
(AR), the moving average models (MA), the autoregressive-moving average
(ARMA), and the autoregressive-integrated-moving average models (ARIMA),
(Box and Jenkins, 1976). We will identify not only the type of model
that reproduces the data, but also the order and properties of such a
model. In the AR model a VHF radiation value of the output z^ is defined
as
z
t
>lZt-l + Vt-2 +
) z + a
P t~P t
(6.1)
where is a white noise representation of the VHF noise input and p is
the order of the AR model order. In the MA model is defined as
z
t
a
t
iat-i
2at-2
0 a,
q t-q
(6.2)
where q is the order of the moving average model. A more general data
model, the ARMA, includes both previous values of the output and (z^'s)
and the input (a 's):

283
z
t
*l2c-l + *2*t-2 +
. +

P t-p t
0lac-l
2at-2
. . a a
q t-q
(6.3)
Many test data show nonstationary behavior when models (6.1), (6.2),
or (6.3) are tested, but the data are stationary if a new series is found
which contains a higher order difference than the original series. Let
Wt = Vzt = zt zt-l = vdzt = ylzt (6-4)
where d is the number of differences in the original series. Similarly,
the first difference ARIMA model can be defined in a manner similar to
equation (6.3). That is
W = -,W + ... + cp W + a 0.a ,
t 1 t-1 Tp t-p t 1 t-1
... a 0
q t-q
(6.5)
The procedures used for the model estimate is the Box and Jenkins
(1976) approach. We used this approach for model, estimates as follows:
(1) Model identification. A total of 12 data records composed of
four sets of 5,000 samples each were selected from the noise level,
stepped leader, and J-change. For each of the four ground flashes we
selected a data record for the three identifiable processes. We deter
mined the autocorrelation and partial correlation of each set of data.
We used the Box and Jenkins (1976) selection criteria to determine the
stochastic model type (AR, MA, ARMA, or ARIMA) and order based on the
properties of the autocorrelation and partial autocorrelation functions
A model was chosen for each data record independent of the physical
process.

284
(2) Parameter estimation. Initial estimates of the coefficients of
the original series (d=0) or for the first difference (d=l) were chosen
to ensure convergence of the individual parameters to fit the previously
identified model. Next we discuss the results of the data models for
the three physical processes.
6.1 Noise Level
For reference purposes we identified the best model for the back
ground noise level of the four flashes. These models were chosen from
testing AR, MA, ARMA, and ARIMA for d=0 and d=l. The results obtained
are as follows: (1) Flash 165959, MA, order 3, d=l, = 0.108, 02 =
-0.431, 03 = -0.086; (2) Flash 180710, AR, order 3, d=0, (p1 = -0.1011,
2 = 0.5315, = -0.1797 ; (3) Flash 181806, AR, order 4, <|> = -0.1332,
= -0.5598, = 0.1687; (4) Flash 182356, AR, order 3,
d=0, 4)x = 0.0137, (p2 = 0.0237, cp3 = 0.0243.
The 165959 flash produced a better model for the first difference
MA of the 3rd order, however, the original 165959 series (d=0) for the
noise level also fits an AR 3rd order level. The standard deviation of
the above parameters is less than 10%. The fact that this process can
be represented as an AR of order 3 or 4 indicates that the VHF radiation
dies out quickly as a function.of the p r e v iou s.. v.a 1.ues oi the output.
6.2 Stepped Leader
We determined the best model for the initial stepped leader for
each of the four CG flashes. These models were chosen from testing AR,
MA, ARMA, and ARIMA for d=0 and d=l. The results obtained are as
follows: (1) Flash 165959, AR, order 5, d=0, (f>3 = -1.084, 4>3 = -0.4453, 4 = 0.2141, (j) = -0.1105; (2) Flash 180710, AR, order 3,

285
d-0, ^ = 1.326, c¡52 = 0.7613, (J>3 = -0.247; (3) Flash 181806, AR, order
4, d=0, 1 = -1.624, = 1.395, $ = -0.8503,

182356, AR, order 3, cj^ = -0.1875, cj>2 = 0.5632, <|> = -0.3164.
The best model for the stepped leader was AR, order 3 to 5. There
were some minor differences between the different stepped leader pro
cesses. The standard deviation in the determination of the parameters
is about 10%. The characteristics of the stepped leader are similar to
those of the basic noise level, that is, an AR process that dies out
quickly as a function of the previous values of the output.
6.3 J-Change
During the J-change process and most of the VHF radiation, other
than the stepped leader, the magnitude of the VHF radiation is heavily
dependent upon the level of the radiation. Pulses 50 to 240 Usec wide
contain a low frequency data envelope and a model for d=0 was nonstation
ary. Once we obtained the first difference, we obtained consistent
results in all the four flashes' J-changes. The results obtained are as
follows: (1) Flash 165959, MA, order 3, d=.l, 6^ = 0.212, 6^ = 0.397,
03
0.108; (2)
Flash
180710,
MA,
order
3,
i-H
II
XJ
0 = -0.466,
0 2 = 0.361,
CD
LO
II
0.327; (3)
Flash
181806,
MA,
order
3,
d=l,
61 = -0.452,
e2 = 0.268,
CD
LO
II
0.223; (4)
Flash
182356,
MA,
order
3,
d=l,
ei = -0.487,
e2 = 0.381,
03 = 0.358.
The standard deviation of the above parameters is less than 3 0%.
The model described in this section indicates that the VHF radiation can
be described as a model with a pole at the origin which corresponds to
the first difference and three separate zeros from the moving average.

286
6.4 Characteristics of VHF Radiation
The VHF radiation pulse model presented in this chapter provides
fairly consistent results for the three selected processes in four
different flashes. The basic conclusion of this analysis is that the
properties of the sources underlying the physical process are very
common from flash to flash. Even though the process is not determinis
tic, we can predict that any future value of the output will fall between
any specified limits. In addition, the consistency of the results
allows us to characterize the VHF radiation for the different phases of
the lightning discharge, without need of other measurements, e.g.,
electric field from a study of the variations of the poles and the
zeros for the different phases of lightning flashes we can determine
properties of the pulse shape emanated by the VHF source.

CHAPTER VII
CHARACTERISTICS OF THE VI1F RADIATION DURING
THE DIFFERENT PHASES OF LIGHTNING
This chapter provides a description of the properties of the indi
vidual phases of the cloud-to-ground and intracloud flashes studied in
Chapters V and VI. In this description we use the characteristics of
the 30-50 MHz VHF radiation, the location of the VHF noise sources, and
the correlated electric field measurements (0.1 Hz to 1.5 MHz). Although
our study and conclusions are based on a limited sample of four cloud-to-
ground and three intracloud flashes, we feel that the results presented
are sufficiently consistent that they may be considered valid.
Before we proceed to study the properties of each of the discharge
phases, we note that we can tell whether a CG or an IC lightning flash
will occur from the first 3 msec of the VHF noise. Figures 7.1(A),
7.1(B), 7.1(C), and 7.1(D) represent the beginning of the VHF radiation
in the four CG flashes studied in Sections 5.1 through 5.4, respectively,
whereas Figures 7.1(E), 7.1(F), and 7.1(G) represent the three IC flashes
studied in Sections 5.1.13, 5.5, and 5.6. The IC discharge that followed
140 msec after the 165959 flash discussed in Section 5.1 is shown
separately because its properties are similar to the other two IC
discharges. Both CG and IC radiation started with high frequency pulses
superimposed on the envelope of a slower varying signal. The CG VHF
noise after the first 2 or 3 msec changes to high frequency and uniform
low-magnitude pulses, which, in this thesis, are identified with the
287

Figure 7.1. VHF radiation during the beginning of the four
CG and three IC flashes studied in this thesis.
(A) 165959 CG flash, the arrow indicates the
first return stroke; (B) 1807.10 CG flash, the
first return stroke occurs off the drawing;
(C) 181806 CG flash, the first return stroke
occurs off the drawing; (D) 182356 CG flash, the
arrow .indicates the location of the first return
stroke; (E) 165959 IC flash; (F) 180644 IC flash;
(G) 181416 IC flash.

289
1 2 3 4 5 6 7 8
TIME IN MILLISECONDS

90
stepped leader. In the IC flash, however, the VHF noise level remains
large and it has additional low frequency pulses. These features can
be seen in Figure 7.1. The observation that the two types of flashes
can be identified early supports the work of Kitagawa and Brook (1960),
who studied the characteristics of the electric field during CG and IC
flashes, and claimed that from the initial electric field pulse rate the
two types of discharges could be uniquely identified. Proctor (1976)
and Hewitt (1962) working at 253 MHz and 600 MHz, respectively, claim
that they could not differentiate between CG and IC flashes from their
noise records. From observing the electric field record, we know that
the presence of a stepped leader-return stroke sequence differentiates
CG flashes from IC flashes, but the return strokes do not occur in our
records until about 5 to 12 msec. The characteristics of the VHF radia
tion reported here are evident at the beginning of the discharge, that
is, during the formation of the VHF sources for the PB-stepped leader
process. Next we look at the characteristics of the different phases of
the CG and the IC flashes.
7.1 Cloud-to-Ground Lightning
The VHF noise, the VHF source locations, and the correlated electric
field records of eight basically different processes were studied in
this thesis. These eight processes are: (1) preliminary breakdown
(PB) (2) stepped leader (SL), (3) dart leader (DL), (4) return stroke
(RS), (5) activity following the first return stroke (FR), (6) J-change
processes, (7) solitary pulses (SP) and K-changes, and (8) continuing
current.

291
7.1.1 Preliminary Breakdown
At the beginning of the CG flashes we detected VHF noise levels
about 20 times larger than during the stepped leader. Based on the
difference of the VHF noise level we chose to name this time interval
"preliminary breakdown" (PB). The VHF noise for the four CG flashes
during the PB is shown in Figures 5.5, 5.23, 5.41, and 5.64. The dura
tion of the PB's varied between 1.9 and 2.2 msec. The VHF noise was
characterized by high frequency pulses ranging in width from 1 to 150
ysec superimposed on a lower frequency envelope. Three of the PB's
ended with a pulse 300 to 700 ysec wide (Figures 5.23, 5.41, and 5.64).
We suspect that the end portion of these wide pulses are oscillations
caused by the tape recorder's sharp low frequency cutoff.
We studied the progressing sequence of the VHF noise source loca
tions during the first few hundred microseconds of the PB, which corre
sponds to the beginning of the CG discharges. We labeled the progressing
sequence of these sources and the time of their occurrence in Figures 5.4,
5.25, 5.42, and 5.65. The initial paths formed by the VHF sources for
the four studied flashes were: (1) path length of 4.8 km at 28 off
vertical between a height of 9.9 and 6.5 km, (2) path length of 12 km at
55 off vertical between a height of 9.8 and 4.1 km, (3) path length of
7.8 km at 22 off vertical between a height of 11 and 4.9 km, and (4)
path length of 7.5 km at 26 off vertical between a height of 9.9 and
4.0 km. The PB sources initially formed a cylinder of about 500 meters.
During the period of time that these cylinders were formed there was no
correlated electric field change indicating no. significant charge trans
fer. The timing sequence of the beginning of the VHF sources is random
in the first two flashes but appears to follow an ascending then

292
descending sequence in the remaining two PB's. The location of some
of the sequential VHF sources were not caused by the propagation of
the previous sources, since the time and distance yields a velocity
greater than the speed of light. For three of the four CG flashes the
initial electric field change occurs within a few hundred microseconds
of the final PB pulse, the tail end of which may be due to the recorder
response. Proctor (1976) claims that over 90% of the stepped leader
radiation began with a sharp burst of noise of higher amplitude. In
addition, Proctor (1976) reports that sometime the VHF noise began
suddenly before the start of the electric field records. These
characteristics observed by Proctor appear to be consistent, with our
definition of preliminary breakdown.
From a study of the VHF sources during the PB, we determined that
the path of the series of pulses riding a slowly varying envelope is
generally about 4 km. This path is probably caused by a potential wave
that propagates throughout part of the initial PB path. In addition,
breakdown regions in different parts of the path are probably the con
tributors of the high frequency pulses superimposed on the envelope.
Most of the individual pulses during the entire PB are detected within
about 1 km perpendicular radius from the initial path. Some of the
pulses are located in small isolated regions. Pulses during the PB's
appear similar to the isolated SP's studied in Chapter V and discussed
In Section 7.1.7. That is, both are probably potential waves of about
4 km length with lLttie charge transfer.
7.1.2 Stepped Leader
We studied a total of 20 leader-return stroke sequences in the
four randomly selected CG flashes. From these 20 leaders, 12 were

:,ij 3
classified as stepped leaders, 1 as a stepped-dart leader, and 7 as
dart leaders. Even though we had a limited sample of 20, over 50% of
the return strokes were preceded by stepped leaders. The initial
stepped leader that followed the preliminary breakdown had slightly
different properties from the subsequent stepped leaders. Therefore
we chose to divide the stepped leader discussion in two subsections.
7.1.2.1 First Stepped Leader. At the end of the preliminary
breakdown the VHF radiation decreased to about twice the noise level,
corresponding to the lowest level of VHF radiation for any identified
process in either CG or IC flashes. This type of radiation was
characterized by high frequency pulses with less than 4 ysec width and
a pulse rate of one every 13 to 15 ysec (Figure 5.16). The stepped
leader VHF radiation has unique characteristics and has been used
throughout this thesis to identify the beginning of CG flashes. The
duration of the stepped leader VHF noise ranged between 2.9 and 7.9
msec. In contrast with the low amplitude, high frequency, stepped
leader pulses at 30 to 50 MHz shown in this thesis, Proctor (1976),
working at 253 MHz, and Brook and Kitagawa (1964), working at 420 and
850 MHz, observed strong radiation during the stepped leader. Work
reported by Malan (1958) showed an increase in the stepped leader
radiation between 3 KHz and 12 MHz. Therefore, it appears that the
stepped leader radiation increases are a function of frequency.
We studied the VHF noise sources during initial stepped leaders
and determined that about 70% of the sources followed a regular progres
sing downward sequence which extended the previous path formed by the PB
sources. The remaining 30% of the sources are detected in two other
regions as follows: (1) Sources detected in the horizontal direction
which widen the main PB-stepped leader path to about 1 or 1.5 km radius,

e.g., stepped leader branches, and (2) Active sources which still
radiate at higher altitudes in the neighborhood of the PB-stepped leader
junction while the leader propagates to ground.
The fact that the VHF pulses appear to be associated with the
stepped leader steps and that correlated electric field change is
detected up to about 1 msec prior to the stepped leader pulses suggests
the following sequence of events in the formation of a CG flash:
(1) The path of the PB sources becomes an ionized channel or arc;
(2) Current starts to flow through the channel providing correlated
electric, field change from the motion of the electric charges; and
(3) The steps of the stepped leader formation start and stepped leader
propagation continues from the cloud charge.
We found the VHF source locations during the PB-stepped leader
transition. A source which corresponds to the locations in the
transition between the PB and the stepped leader VHF noise is chosen
as the beginning of the stepped leader. The VHF sources are detected
throughout the leader path to near-ground. In addition to the poor
accuracy of our detection system for altitude locations near-ground,
we found two other limitations in trying to obtain stepped leader source
locations. First, stepped leader sources, most likely from leader
branches or leader path enhancement, are simultaneously active over a
large volume. Second, the VHF noise for sources near the ground usually
decreases prior to the return stroke. The stepped leader velocity that
we calculated from the beginning source of the stepped leader VHF
radiation to the last detectable stepped leader source ranged from 9.2
x 10J m/sec to about 4.3 x 1.0 m/sec. These initial stepped leader
velocities are about a factor of 10 larger than those reported from
optical measurements by Schonland and his co-workers and by Proctor (1976).

1.1.2.2 Subsequent Stepped Lenders.
Subsequent stepped leaders
had the following properties that distinguished them from first stepped
leaders:
(1) The VHP noise level had the same high frequency, uniform ampli
tude pulse characteristics but a magnitude twice as large as the initial
stepped leaders.
(2) All subsequent stepped leaders were preceded by active VHF radi
ation from the J-change which lasted for at least 7 msec with a pulse
about every 10 psec. This high repetition rate of VHF pulses appeared
to be a necessary condition before the initiation of subsequent stepped
leaders. There is a 5 to 1 ratio between the magnitude of the VHF
noise during the J-change and the subsequent stepped leader. This fea
ture in the VHF noise is used to identify subsequent stepped leaders.
Some of the J-changes that preceded subsequent stepped leaders were
formed in a concentrated region in a slanted path. If the previous
J-change was mainly horizontal, the stepped leader descended from a
concentrated VHF source region, usually near the center of the VHF source
region (SL2 and SL3, Section 5.2). If the previous J-change was mainly
vertical, the stepped leader propagated from the lower part of the
vertical region (SL2, Section 5.3; SLD, Section 5.1). Clear evidence
of the subsequent stepped leader following the vertical propagation
path of the J-changes is seen in Figures 5.18 and 5.48.
(3) Subsequent stepped leaders are difficult to identify in the
electric field record. Of 12 subsequent stepped .Leaders Identified in
the VHF record, only four could be identified^at any of ten electric
field stations. The beginning of the subsequent stepped leader
electric field record often does not show a change in the slope of the

previous J-change. However, we did not have any problem identifying
subsequent stepped leaders from a single channel VHF radiation.
(4) Subsequent stepped leaders are considerably longer and prop
agate at slower velocities than initial stepped leaders. This might be
due to the fact that all subsequent stepped .leaders that we studied had
a much larger horizontal component than the initial stepped leader. A
possible explanation of this feature is that negative charges still
remaining in the first stepped leader channel to ground will repel the
new stepped leader. Therefore, the subsequent stepped leaders had to
propagate around the old stepped leader to find a new path to ground.
The duration of subsequent stepped leaders ranged from 14.2 to 35.0 msec
5 6
and we obtained velocities between 1.6 x 10 and 1.1 x 10 msec, close
to the range reported by Schonland et al. (1938).
7.1.3 Dart Leader
The properties of the dart leader were quite different from the
previously discussed stepped leader properties. We studied seven dart
leaders which occurred in the four CG flashes. The magnitude of the
VHF noise sources during the dart leader exceeded the stepped leader
radiation by a factor of 20 to 1. The VHF noise during the dart leader
started with a large pulse, usually between 150 and 200 psec wide.
The remainder of the dart leader contains mostly high frequency pulses
of less than 20 psec width superimposed on a slow envelope with a pulse
width of about 500 psec. The total VHF radiation during dart leaders
lasted between 0.35 and 1.70 msec.
The VHF noise sources during the dart leader were either in the
neighborhood of the previous J-change (Section 5.3 prior to the fifth
and sixth return stroke) or connected the end of the preceding J-change

297
with the previous return stroke channel (Section 5.1 prior to the second
return stroke, and Section 5.3 prior to the third and fourth return
strokes). In the former case the dart leader expanded from the bottom
of the path formed by the J-change noise sources. However, in the
latter case the dart leader radiation path was mainly horizontal between
4 and 6 Ion. The wide pulse at the beginning of the leader with a mag
nitude of 20 times that of the stepped leader is probably caused by a
potential wave that propagated from the previous J-change. No dart
leader VHF sources were detected in the leader path to ground.
Brook and Kitagawa (1964) and Proctor (1976) also reported strong
radiation during dart leaders. They also concluded that the dart leader
radiating sources were located in the cloud and not along the leader
channel to ground. Proctor (1976) did so using the same technique we
use; Brook and Kitagawa (1964) used arguments based on the time difference
between the electric field and the high frequency radiation.
7.1.4 Return Strokes
The VHF radiation during return strokes lasted between 92 and 859
psec and was characterized by either one large pulse of duration 92 to
250 psec or a succession of pulses between 30 and 100 psec width. VHF
radiation was absent during the fourth return stroke in Section 5.3.
Otherwise, the maximum magnitude of the VHF radiation during return
strokes was about 25 times larger than the stepped leader.
The VHF sources during return strokes preceded by stepped leaders
were located in the neighborhood of the previous stepped leader channel
and throughout the PB or J-change that preceded the leader- Return
strokes VHF sources after stepped leaders were detected between a height
of 14.5 and 0.7 km. Similarly, VHF sources during return strokes

298
preceded by dart leaders were located in the neighborhood of the previous
J-change between a height of 12.6 and 6.5 km. It was not possible to
detect accurately return stroke velocities because only a few sources
were detected and they did not necessarily follow an upward progressing
sequence. On the basis of the fact that there was no VHF radiation in
one of the return strokes and that the VHF sources in the remaining of
the return strokes were located along the channel to ground (for those
return strokes preceded by stepped leaders) and in the J-change (for
return strokes preceded by dart leaders), it appears that the VHF
radiation during return strokes is generated by extensions of the pre
viously existing leader channel. The return stroke wide VHF pulse
represents a potential wave that propagates throughout the previous
channel toward the higher altitudes.
We presented in our analysis the location of the stepped leader-
return stroke source obtained by Krehbiel (private comm.) using the
technique of Krehbiel et al. (1979). We determined that the location
of Krehbiel's point charge center for the return strokes of the four
flashes were in fairly good agreement with the location of the PB-stepped
leader path (for initial SL), or J-change-stepped leader path (for
subsequent stepped leader). The point charge provided to use for the
return strokes of these flashes ranged between -25.7 and -2.9 Coul and
a height between 7.9 and 4.4 km.
In addition to finding the return stroke point: charge using multiple
station electric field measurements, we assumed the location of the
stepped leader-return stroke charge was the PJ3-SL junction and calculated
the charge using the technique described in Section 3.6. We obtained
results which were comparable to the ones determined by Krehbiel.

299
The point charges that we determined by using these techniques ranged
between -24.1 and -3.6 Coul for heights between 10.5 and 5.9 km.
7.1.5 Activity Following the First Return Stroke (FR)
During the FR interval we obtained the fastest pulse repetition
rate and largest amplitude in the CG and IC flashes. We chose to call
this process "FR" (following return) because the locations of the VHF
noise sources were directly related to the first stepped leader-return
stroke sequence. The pulse repetition rate during the FR was a pulse
every 3 or 4 p sec and the magnitude of these pulses were about 25 times
larger than that of the stepped leader. At the end of the FR we
measured return stroke-like pulses of a magnitude 40 to 50 times larger
than the stepped leader. For three of the four FR intervals, the VHF
noise started immediately after the return stroke, but for one of the
flashes (Section 5.1) there was a 2.4 msec quiet period between the
return stroke and the FR interval. The FR interval lasted between 4.3
and 8.8 msec and always ended with a wide pulse of the largest magnitude
in the CG, which because of its similarities to the return stroke pulse
we associated with the propagation of a potential wave.
The location of the VHF sources for three of the four FR's were in
the neighborhood of the previous PB-stepped leader-return stroke chan
nel. In the fourth case (Section 5.4), the VHF sources were located
right on the top of the previous PB-leader channel. The height of the
VHF sources ranges between 9.5 and .1.8 km. The HR phase of the CG flash
may be related to M-components (Malan and Schonland (1947), Kitagawa
et al. (1962), and Uman (1969)); that is, the increases in channel
luminosity following a return stroke. For two of the four FRs
intervals, the VHF sources propagated upwards in a regular progressing

30
sequence. We correlated the VHF noise with the electric field change
at the multiple stations. We determined that during the FR interval
either negative charges propagated downward from a region of higher
altitudes, or that positive charges (probably from the previous return
stroke) propagated upwards or both. We attempted to determine the
amount of charge transfer during the FR interval for one of the flashes
and found that for electric field ground stations whose distance is
greater than the charge height, a charge of A.5 2.1 Coul was trans
ferred. For close electric field measurements, no consistent charge
transfers could be found indicating that the charge distribution could
not be approximate as a point charge.
7.1.6 The J-Change Process
Throughout this thesis we have referred to the J-change or the J-
change process as the portion of the interstroke process, with continuous
active VHF radiation, that preceded dart leaders or subsequent stepped
leaders. This J-change process occupied 80, Al, 75, and 59% of the
total VHF radiation emitted by the four studied CG flashes (disregarding
the VHF radiation after the final return stroke). Other studied
characteristics of the interstroke period included the FR interval after
the first return stroke, solitary pulses, quiet periods, dart leaders,
and subsequent stepped leaders. The quiet periods are discussed in
this subsection as they relate to the J-change process.
To study one of the properties of the J-change process, let us
first make a comparison to the leader-return stroke sequence and the
PB-stepped leader sequence. A return stroke cannot occur without a
preceding leader, and an initial stepped leader cannot propagate unless
it had a preceding PB. Here we claim that dart leaders or subsequent

30.1
stepped leaders cannot propagate unless they are immediately preceded
by active VHF radiation from the J-change process. As we shall see in
this section, the physical reason for the J-change-leader sequence is
that the J-change makes available the charges which are lowered by the
dart or subsequent stepped leader.
Two of the studied flashes (Sections 5.1 and 5.3) had VHF radiation
emitted during J-changes which originated at a height near 14 km. The
path of these two flashes were more vertically inclined and we refer to
them as vertical flashes. The other two flashes only extended to a
height of about 12 km and we refer to them as horizontal flashes.
The VHF sources for the first J-change in the two vertical flashes
followed a regular progressing sequence from a height of 13.7 and 14.2
km, and propagated downwards in paths of 35 and 25 off vertical,
respectively. These two J-changes lasted 44.3 and 8.1 msec and the VHF
sources propagated at a velocity of 1.5 x 10^ m/sec and 5.0 x 10> m/sec,
respectively. We fitted a point charge model that lowered negative
charge along the regular progressing sequence of the path and found that
-2.4 and -1.8 Coul were lowered by these processes. From al.1 the J-
change in the four flashes, these two J-changes were the only ones that
exhibit a regular progressing sequence of the noise sources. It is
interesting to note that these J-changes were the first ones in these
two flashes and they were preceded by 16 and 16.5 msec quiet periods.
d
Quiet periods are those time intervals in the flash which have electric
field change buL no VHF radiation. We do not know If the quiet period
had any effect in the sequence of propagation ,of the noise sources, or
if it was a coincidence.

32
The initial J-change in the other two flashes formed a well defined
path. However, the noise sources occurred randomly throughout the path.
The path of the VHF noise sources during subsequent J-changes
extended to regions of high altitudes and occupied a larger volume in
space. Some of the paths of the noise sources during subsequent J-
changes were located in the same location or in the neighborhood of the
path of the previous J-change. Other subsequent J-changes developed
parallel to the path of the previous one. The fact that some previous
VHF sources remain active during subsequent J-changes (Figures 5.53 and
5.55) was previously observed by Proctor (1976). As the stroke number
increases, subsequent J-changes became less organized. In the last
J-change in the six and the eight stroke flashes the VHF sources did
not form an obvious path and were randomly located over a larger volume.
Our interpretation of the given facts about J-change processes is
as follows:
1) The J-change process makes available the negative charge needed
for subsequent strokes to ground.
2) As the number of strokes increases, this charge is being drained
from higher places in the cloud. Since there is less negative charge
available near the end of the flash, the J-changes associated with the
last strokes occupied a larger volume.
3) As it is clearly shown in this thesis in Figures 5.18, 5.48,
5.70, and 5.74, some of the subsequent stepped leaders propagated from
the lower and most concentrated region of the J-change. That is, the
negative charge made available by the J-changes is then lowered to
ground. In the remaining of the J-changes-leader paths, not shown in
the above figures, the dart leaders or the subsequent stepped leaders

303
VHF sources were detected in the neighborhood of some of the lower
regions of the J-change.
7.1.7 SP and K-Changes
Kitagawa et al. (1958) defined a K-change as a small, rapid field
change with accompanying pulses of luminosity. We refer to K-changes as
those small, rapid field changes with accompanying VHF radiation. In
addition, we refer to SP's (solitary pulses) as those isolated VHF
pulses with a magnitude 30 to 45 times larger than the stepped leader
and with no detectable electric field change. SP's were preceded and
followed by quiet periods and were detected during the J-change, after
the last return stroke in CG flashes, and in the junction phase of IC
discharges. The duration of the SP1s is about 1 msec and the VHF noise
is characterized by pulses 1 to 30 ysec wide superimposed in an envelope
with a pulse width between 100 and 180 ysec. Figures 5.13(a), 5.13(b),
and 5.13(c) show the VHF noise during three SP's that occurred in a quiet
period during the interstroke process. Figure 5.36 shows the VHF noise
for a K-change that occurred after the last return stroke of one of the
CG flashes.
The VHF noise sources for the SP's in the interstroke process
(Figures 5.14(a), 5.14(b), and 5.14(c)) propagated upwards 2 to 5 km
at a velocity between 1 and 4 x 10^ m/sec. A K-change initiated the J1
change in the flash discussed in Section 5.2. This K-change lasted 1.1
msec and propagated downwards about 4 km from a height of 10.6 km at a
velocity of 9.5 x 10^ m/sec. No other SP or K-changes were detected
during the J-process. Other rapid electric field changes during the

304
J-process were preceded and followed by continuous VHF radiation and we
chose to consider them as an integral part of the J-process.
Solitary pulses and K-changes were observed after the last return
stroke of the CG flashes. One SP after the last return stroke in Sec
tion 5.1 propagated upwards about 5 km, but most of the SP's and
K-changes in the other three CG flashes propagated downwards as shown
in Figure 5.76. The VHF noise sources in one of the K-changes shown in
Figure 5.37 followed a path similar to that suggested by Kitagawa arid
Kobayashi (1958). That is, a downward propagation path followed by an upward
moving path, except that the velocities of the downward path were much
larger than those suggested by Kitagawa.
7.1.8 Continuing Current
We studied only one. continuing current interval which occurred
after the last return stroke of the flash reported in Section 5.3. Next
we summarize our findings about this continuing current.
The continuing current interval lasted 223 msec in the VHF record.
On the basis of the VHF radiation and its source locations, we divided
the continuing current in two intervals: (a) continuous VHF radiation,
and (b) discrete VHF radiation. The continuous and the discrete VHF
radiation lasted 85 and 138 msec, respectively. The VHF noise during
the continuous portion of the continuing current interval has the same
characteristics as the J-change. The discrete portion has similar
characteristics to the VHF radiation at the end of two other CG flashes
and all other IC flashes. That is, isolated SP's with durations between
1 and 11.5 msec separated by about 10 msec.
During the initial 23 msec the VHF noise sources formed a 14 km
channel parallel to the previous J-changes (Figure 5.59). During the

305
remainder of the continuous radiation, the VHP sources widened the
channel. The SP's in the discrete part of the radiation path propagated
downward at speeds between 5 x 10^ and 4 x 10^ m/sec. The paths of
these SP's started from regions between 7 and 14 km and joined the main
CG channel that lowered negative charge to ground.
7.2 Intracloud Lightning
Three IC lightning flashes were studied in Sections 5.1.13, 5.5,
and 5.6. The beginning of the VHF radiation for the IC flashes has
been shown in Figures 5.14, 5.79, and 5.83. In addition, we showed the
VHF radiation at the beginning of the IC's in Figure 6.1(e), (f), and
(g). The intracloud discharge can be divided in three phases: initial,
very active, and junction phase, as done by previous investigators
(Kitagawa et al., 1960). Next we provide a discussion of these phases.
7.2.1 Initial Phase
Two of the three flashes started with a pulse about 25 times larger
than the stepped leader radiation and a pulse width ranging between 20
and 100 psec. The pulse repetition rate during this initial phase was
a pulse every 25 to 100 psec. This phase was not observed in the IC
flash described in Section 5.6.
Correlated electric field records during this phase showed an
increasing field change at close range and a decreasing change at
distances further away. During the initial phase of the 1C flashes,
the VHF sources formed the 1C channel. The 1C In Section 5.1.13 formed
a 10 km path 35 off vertical between a height of 6 and 15 km. The IC
in Section 5.5 formed a path 40 off vertical between the heights of
9.2 and 14.5 km. Our best estimate of the propagation of

506
the channel was performed by doing histograms of the number of sources
along the channel at different heights for selected time intervals.
The histograms for one of these flashes are shown in Figure 5.21.
Proctor (1976) also observed this type of behavior at the beginning of
a cloud flash. That is, the development of the path was composed of
small sections which did not join to form a sequential continuous
channel. Four of the five flashes studied by Proctor showed a near
horizontal path. Two of the three 1C flashes studied in this thesis
showed a path of 45 and 30 off vertical and the third flash had a
vertical path. On the basis of the electric field reversal with dis
tance and the fact that most of the sources propagated upward during the
initial phase as determined from the histograms, we claim that for the
IC flashes in Sections 5.1.13 and 5.5, negative charges propagated
upward during the initial phase of the discharge.
7.2.2 Very Active Phase
The very active phase was characterized by a faster pulse repeti
tion rate, a pulse every 5 or 10 psec superimposed on a lower frequency
envelope, up to 500 psec width. During the very active phase the VHF
source region becomes wider and additional electric field change occurs.
One of the IC, described in Section 5.6, started with the very
active phase. For the first 18.8 msec the VHF noise sources for this
discharge were nearly vertical between a height of 8.5 and 13.5 km
(Figure 5.84). However, by the end of the very active phase, the noise
sources had propagated downward to a height of 4.5 km and widened the
previous channel. Since most of the propagation of the noise sources
were downwards, we claim that the positive charges were lowered during
the IC discharge.

3 07
For the studied IC flashes, we attempted to determine the location
of the estimated point charge centers and the amount of charge lowered
or raised by the discharge. By studying the field reversal with dis
tance and using equation (3.10), we determined that the positive and
the negative charge centers for the. IC flash described in Section 5.5
were located at 13.5 and 9.5 km, respectively. These locations for the
charge centers are in agreement with the VHF source locations but are
higher than previous estimates of charge centers above mean sea level
during IC's. Malan (1956) studied photographs of discharges in intra
cloud and concluded that the negative charge region (lower region)
reaches an altitude of 9.8 km. Mackerras (1968) using photographs and
time to thunder estimated that high altitude IC flashes ranged between
4 and 12 km. Takagi (1961) using electric field measurements reported
altitudes of IC's between 7 and 11 km. We attempted to determine the
charge transferred during the IC discussed in Section 5.1.13 using a set
of 9 stations. No calibrated electric field measurements were available
in the other two IC's. Curve fitting for 6 of the 9 available stations
and using equation (3.10), we obtained a charge transfer of 10.5 2.9
Coul. Three of the four stations beyond the field reversal gave us
inconsistent results. Even though our result of charge transfer is
more consistent than those obtained using one or two electric field
readings, these results indicate that the IC discharge in Section 5.1.13
cannot be adequately represented by a two point charge model.
7.2.3 The Junction Phase
Similar to the end of all the CG flashes, the IC flashes ended with
a phase in which only solitary pulses or K-changes were detected.
These pulses lasted between 0.5 and 2.2 msec and the pulse rate decreases

'308
toward the end of the discharge, starting with a pulse about every 5
msec and ending with a pulse every 30 or 50 msec. The only correlated
electric field change, during this phase, was directly related to the
detected K-changes.
The V1 IF sources of these SP's or K-changes were located in the
neighborhood of the previous IC path. These pulses extended the previous
ends of the paths widening the volume of the discharge.

CHAPTER VIII
CONCLUDING COMMENTS AND SUGGESTIONS FOR FUTURE RESEARCH
Briefly, this chapter provides a review of the sequence of events
described in this work and some needed areas of related research.
(1) We recorded VHF radiation simultaneously from multiple stations on
analog tapes during thunderstorms. (2) We randomly selected seven
lightning flashes, four cloud-to-ground and three intraclouds for study.
(3) The analog tapes containing these flashes were digitized. (4) From
the difference in the time of arrival of the VHF radiation pulses, we
determined the three-dimensional space locations. (5) Then, we corre
lated the source locations with the characteristics of the VHF noise and
VLF electric field to determine some important properties of lightning
discharges. Even though our sample size was limited, we obtained quite
consistent results. Therefore, our findings can be used to improve the
understanding of lightning flashes in general.
With the proper VHF recorded data, an algorithm was developed and
applied successfully to obtain VHF source locations. Our results indi
cate that the VHF sources are directly related to the charge motion in
the cloud. We differentiated between the the various phases of lightning
flashes and determined their properties. Finally we showed a summary
of our findings for the different phases of lightning flashes, providing
a view of the initiation and development of lightning flashes inside
thunderclouds.
309

310
Some suggested areas for future research follow:
(1) The results presented in this thesis would be improved if a
5 MHz tape recording system were used. Since we were limited to a 1.5
MHz upper frequency response, we could not properly detect pulses with
a risetime faster than 1/1.5 MHz 0.23 ysec. The detection of faster
pulses should lead to additional and more accurate source locations.
(2) All the sequential VHF radiation from lightning flashes for a
whole thunderstorm or thunderstorms should be studied. The relation
ship of the VHF source volumes from flash to flash could provide
important information about thunderstorm electricity. The statistical
results for individual processes (e.g. J-changes) in a large number of
flashes could serve to verify those observations of the individual
processes presented in this thesis.
(3) Data on cloud winds and precipitation structure obtained from
Doppler radar should be correlated with VHF lightning locations in an
effort to improve our understanding of cloud charging mechanisms and
their relationship to lightning initiation.

APPENDIX A
DERIVATION OF SOURCE LOCATION FROM
DIFFERENCE OF TIME OF ARRIVAL MEASUREMENTS
Let r and r. be the distances from the desired space-location
ox r
P(X,Y,Z) to the central Q(0,0,0) and remote i's stations Q^CX^jY^.Z^)
for i = 1, 2, and 3 (Figure A.l). Since the relative elevation of the
stations is less than 2 m, and the remote stations are about 10 km from
the central station (negligible earth curvature), co-planar stations
are assumed. Then
represents the measured range difference, and
2 2 2 2 2
rQ = (PQ) = X + Y + Z
2 2 2 2 2
r. = (PQ.) = (X-X.) + (Y-Y.) + Z
l i l i
(A.l)
(A.2)
(A.3)
represent the square of the distances from the space-location to the
ground-based stations. From equation (A.l) we have
2 2 2
r, = r 2r u. + u.
I o OIL
(A.4)
Substituting equations (A.2) and (A.3) into (A.4), we get
X.2 + Y.2 2XX. 2YY. = -2u.r + u.2
11 1 1 1 O 1
(A.5)
311

3 I 2
Figure A.l. Three-dimensional hyperbolic system.

313
*
Let
2 2 2
d = X. + Y. (A. 6)
ill
and
vi-i'L2 i2) (A-7>
Equation (A.5) becomes
XX. + YY. u.r = V. (A.8)
The time difference between a signal arriving at the central
and a remote is given by
u. =
i
cT.
i
(A. 9)
Since is known from the measurement T^, equation (A.8) represents
three equations with three unknowns (X,Y,rQ) which can be solved for
the unknowns. With this solution Z is calculated as
(A.10)
By definition the locus of equation (A.8) represents a hyperbola.
The intersection of the three hyperbolas for the three time difference
(i = 1, 2, and 3) provides a unique source location. Therefore, this
method of finding the space-location is called the three dimensional
hyperbolic system. Another method of finding space-locations based on
a spherical triangulation system is described in Holmes (1951). For
the application to our research, the hyperbolic system is used because
it provides lower random errors over a wider range of space-locations.

314
Figure 3.1 indicates the relative location of six remote stations
(Wl, W2, W3, Ml, M2, and M3) and the central station. The position of
a calibration signal located on the top of the Kennedy Space Center
Vertical Assembly Building is shown as VAB CAL. Analog VIIF data are
recorded for the central and the six remote stations. Only the central
and three of the remote stations are digitized. The factors used in
the selection of the three remote stations are: (1) the stations with
maximum signal-to-noise ratio and (2) the stations whose locations
provide the maximum accuracy. In our research, the data processed for
the summer of 1976 are from the Wl, Ml, and W3 remote stations which
form a T configuration. The 181806 flash on 8th August 1977 was
analyzed using the Wl, Ml, and M3 locations. The remaining flashes
studied in this thesis were analyzed using the Ml, M2, and M3 stations.

APPENDIX B
ACCURACY OF THE LOCATION OF
LIGHTNING SOURCES USING THE HYPERBOLIC EQUATIONS
The errors in source location can be determined from the solution
of the hyperbolic equations ((A.7) and (A.8)) previously discussed.
Solving equation (A.8) for the source locations, X, Y, and r^ we obtain
V1
Y1
U1
X1
V1
U1
X1
Y1
V1
V2
Y2
U2
X2
V2
U2
X2
Y2
V2
V3
Y3
U3
V
X3
V3
U3
X3
Y3
V3
X1
Y1
U1
X1
Y1
U1
0
X1
Y1
U1
X2
Y2
U2
X2
Y2
U2
X2
Y2
u2
X3
Y3
u3
X3
Y3
U3
X3
Y3
u3
or
X
Y
(B.2)
Since the coordinates of the three remote stations (X^,Y^), (X^jY^) and
(X^,Y^) are known to a tenth of a meter, the primary error in X, Y, and
Z will be caused by uncertainties in the measurements of Uj, u^, and u^.
The partial derivatives OX/du., DY/Ou., and dr /Ou. can be calculated
l i o i
from equation (B.2).
have that
Since Z
Y from equation (A.10) we
315

dZ
1
Z
(B.3)
316
3r
o
o 3u.
i
i
The X, Y, and Z measurements are a function of the three time delays
represented in the u.'s (u. = cT. in equation (A.9)). The u.'s are indepen-
iii i.
dent with RMS error du.. We define the RMS source location errors as
i
dX
RMS
3
3x
2
r i
l
3u.
1 y
du.
=1
1 J
dY
RMS
3
v
3Y
2
' s
i
du.
i=l
du .
1/
dZ
3 '3Z ^
RMS
I
i1
3u.
du.
(B.4)
A computer program was developed to determine the error associated
with the channel locations. Two classes of errors must be considered:
(1) the quantization error, and (2) the calibration error.
The quantization error is due to the discrete sample interval used
in digitizing the data. This sample interval limits the measurement of
the difference in the time of arrival (DTOA) to 0.23 microseconds
(du_j, = du^ = du^) The raw-data analog tape input had a frequency
response between 400 Hz and 1.5 MHz, flat response in the medium range,
3 dJ5 down at the end points, and 20 dB/decade beyond the ends. In order
to accurately reproduce this spectrum with sampling, the tapes were
digitized at 4.352 MHz, that is, sample intervals of 0.23 microseconds.
Hence the original frequency response of the data determines the quanti
zation error.

317
The RMS quantization error was obtained by using du_. = cdT_. =
300. .23 = 68.93 meters in equation (B.4) and solving for dX ,
RMS
dYn.._, and dZ for any specified DTOA. The relative location of the
VHF source with respect to the ground-based station is an important
factor in the solution of equation (B.4). The X and Y error increases
as we get away from the VHF ground-based network. Since only discrete
measurements of time differences are available, we get only discrete
locations for X, Y, and Z. These locations are generally within 100
meters for X, and 500 meters for Y and Z for the VHF sources studied in
this thesis. The Z error measurement increases for VHF locations near
the ground and for Z larger than 10 km. Figure 3.1 shows the source
locations of every sample, corresponding to variations along
T^, T^, and T^. This graph illustrates the effect of the quantization
error in any of the three DTOA. Figure 3.2 shows a mapping of all the
55,171 three dimensional locations obtained within the range of the
graph axis for 50 iterations of T^, T^, and T^ every sampling interval
(.230 ysec). The remaining 69,829 locations of the possible 125,000
fell outside the boundaries of the graph. Figure B.2 also shows the
discrete pattern of the locations of the hyperbolic equations which is
obtained for the discrete sample intervals. Figure B.3 shows a mapping
of 49,581 three-dimensional locations obtained within the range of the
graph axis for 50 iterations of T^, T^, and T taken every 0.1 ysec.
Since the quantization error is smaller, the pattern in Figure B.3 is
less evident.
In addition to the uncertainties produced by the quantization
error, the calibration error must be considered. The calibration error
is determined by the uncertainties in the retransmission delay, the

Figure B.l. Two-dimensional views: (a) top view, EW-NS, (b) elevation view, EW-height, and
(c) elevation view, NS-height of the noise sources obtained when only one of the
tine delays (T^, T^, or T^) is varied in discrete sample intervals of 0.23 ysec.

NORTH
24
23
22
21
20
19
18
17
16
15
14
13
12-
II-
¡O
9
8
-2
-I 0 I
EAST
(a)
16
15
14-
13-
12-
II
10
9
I-
X
C2 8
J
X
7
3
2
2 3 4 -2 -I 0
EAST
(b)
16-
15
14
13
12
II
10
9
I-
x
E2 8
L
X
7
6
5
4-
3-
/ '
/ *
-4%
//
8
2
10 II 12 13
NORTH
(c)
14 15 16

EAST NORTH
(a) (b) (c)
Figure B.2. Two-dimensional views: (a) top view, EW-NS, (b) elevation view, EW-height, and (c)
elevation view, NS-height of all noise sources in 50 consecutive iterations of the
three time delays for a sample interval of 0.23 usee.
OZf

Figure B.3. Two-dimensional views: (a) top view, EW-NS, (b) elevation view, EW-height, and (c)
elevation view, NS-height for all the noise sources in 50 consecutive iterations of
the three time delays for a sample interval of 0.1 psec.

NORTH
12 ¡3 4 15 16 17 ¡8 B 20
NORTH
(c)

32 3
electronics, the tape recorder, and reproducer head configurations.
Since all the VHF signals were recorded at the central station, we had
to subtract the retransmission and other time delays between each one
of the remote and the central station. The retransmission and other
delays were determined using a calibration signal at a known location
(VAB CAL, in Figure 4.1). For each year ten readings of the calibration
signal recorded at all the stations were digitized at 8 MHz. Since the
location of the calibration signal is known, the average value of these
readings is used to determine the average retransmission delays. The
RMS error in the measurement of the DTOA for the calibration signal
varied between .19 and .62 ysec for the various remote stations. The
calibration error can now be determined by using equation (B.4) for the
uncertainties in the calibration of the remote stations. Once three of
the remote stations in Figure 4.1 are selected, the retransmission
delays for these are calculated. The average value of the retransmission
delay is fixed for all the calculations relating to any specific flash.
However since the error in X, Y, and Z is also a function of the location
of the VHF source relative to the location of the ground-based network,
the calibration error also varies with the selection of the remote
stations and the lightning locations.
The total error related to any calculation of channel location
(CJ ) is calculated from
tRMS
O
2
tRMS
2
qRMS
+ o
2
c RMS
( B. 5 )
The quantized error (o
while the calibration
QRMS^
error
is the random error in the measurement,
(a represents any additional time
cRMS

delay error. Next we present a solution for a ,w, o _w, and a w_ for
QRMS cRMS tRMS
the four main flashes studied in this thesis.
B.1. Error Analysis for the Locations of the 165959 Flash on 19th
July 1976
The remote stations selected to determine channel locations were
Wl, Ml, and W3 (Figure 4.1). The RMS uncertainties in the calibration
error for Wl, Ml, and W3 were .62, .25, and .41 microseconds. The flash
extended between -2 and 6 km EW, 9 and 16 km NS and up to 16 km in
altitude. Table B.l shows the quantization, calibration, and total
error for the three-dimensional channel locations over the entire range
of the flash.
B.2. Error Analysis for the Locations of the 181806 Flash on 8th
August 1977
The remote stations selected to determine channel locations were
Wl, Ml, and M3 (Figure 4.1). The RMS uncertainties in the calibration
error for Wl, Ml, and M3 were .56, .19, and .57 microseconds. The flash
extended between -3 and 9 km EW, 7 and 17 km NS and up to 15.5 km of
altitude. Table B.2 shows the quantized, calibration, and total error
for the three-dimensional VHF sources over the entire range of the flash.
B.3. Error Analysis for the 180710 and 182357 Flashes on 8th August 1977
The remote stations selected to determine channel locations were Ml,
M2, and M3. The RMS uncertainties in the calibration error for Ml, M2,
and M3 were .19, .38, and .57 microseconds. The 180710 flash developed
in the NE of the central station, 3 to 7 km EW, 8 to 15 km NS, and up to
10 km of altitude. The 182357 flash developed in the NW of the central
station, -8 to 1 km EW, 5 to 14 km NS, and up to 13 km of altitude.

Table B.l. Error Analysis for the 165959 Flash. The selected locations cover the entire volume of the
flash and they are listed in ascending order in z.
Source Locations
Quantization
RMS
Calibration
RMS
Total RMS Error
(Meters)
Error (Meters)
Error (Meters)
(Meters)
X
y
z
%
dyQ
dzQ
dx
c
dy
J c
dz
c
dxt
dY t
dzt
-307.1
11634.5
1870.9
19.3
260.1
548.9
29.3
419.4
1372.9
35.1
493.5
1478.6
-983.8
10519.8
2761.4
29.7
232.3
304.5
39.4
371.4
750.7
49.3
438.1
810.1
-731.5
10867.9
3377.2
26.1
254.6
274.4
36.9
408.5
676.3
45.2
481.3
729.8
3357.0
15518.8
3713.6
108.4
565.4
778.1
158.5
913.9
1576.7
192.0
1074.6
1758.2
-1332.5
11156.8
3888.6
37.2
264.0
268.0
50.7
423.7
640.8
62.9
499.2
694.5
1506.5
9634.2
5140.2
33.6
301.5
186.4
63.2
485.4
392.8
71.5
571.4
434.8
1126.6
10827.5
5401.8
25.5
327.7
215.3
53.7
528.1
470.8
59.5
621.5
517.7
1724.8
9376.4
5746.8
40.6
310.8
183.0
73.4
501.2
350.6
83.9
589.8
395.4
1468.5
9366.2
6317.3
35.4
313.7
176.9
68.8
506.6
330.2
77.4
595.9
374.6
300.0
11423.7
6739.2
17.0
354.7
213.4
45.0
572.4
447.6
48.1
673.4
495.9
2377.5
10241.3
6887.3
64.2
374.5
239.6
105.1
604.2
392.3
123.1
710.9
459.6
2072.1
10057.2
7577.8
56.2
372.4
228.9
97.2
601.8
336.1
112.3
707.7
431.8
2579.6
10345.1
7876.6
74.3
402.7
265.1
120.6
650.3
397.5
141.7
764.9
477.8
2745.3
10549.0
8653.0
83.3
429.9
293.7
134.3
694.5
420.8
158.0
816.8
513.2
-388.0
13914.4
9718.0
28. 7
506.1
303. 7
61.7
816.7
559.4
68.1
960.8
636.5
2794.5
11026.8
9895.7
90.4
473.8
337.0
147.3
765.6
470.3
172.8
900.4
578.6
3556/3
11882.5
10888.6
128.3
555.4
434.7
199.4
895.3
583.6
237.1
1053.6
727.7
2747.6
11346.4
11090.6
93.7
510.6
378.0
155.4
825.5
522.5
181.5
970.7
644.9
4307.1
12031.1
11178.0
166.8
599.2
513.4
250.8
964.3
668.3
301.2
1135.4
842.7
3013.8
12092.1
11384.7
107.2
555.6
416.8
173.6
896.5
574.2
204.1
1054.7
709.5
5342.8
13130.3
12431.3
236.7
727.2
694.3
348.3
1165.9
892.8
421.1
1374.1
1131.0
4522.8
13244.3
12549.4
188.9
693.8
604.9
285.4
1114.4
796.0
342.3
1312.7
999.8
6685.1
14 0 jl 3.6
13834.6
342.8
881.8
963.7
496.8
1408.3
1236.5
603.6
1161.6
1567.6
7038.8
15385.6
14319.8
381.3
995.0
1074.6
552.5
1585.3
1383.1
671.3
1871.7
1751.5
5749.6
14127.0
14535.1
278.1
845.7
847.0
413.0
1353.7
1109.3
497.9
1596.1
1395.7
6333.9
14774.4
14947.8
325.1
925.0
962.5
478.7
1477.4
1257.3
578.6
1743,1
1583.4
8061.2
14805.4
15752.0
474.8
1060.7
1315.5
685.6
1687.8
1712.3
834.0
1993.4
2159.3
7787.8
15594.7
15923.4
455.1
1093.4
1281.2
660.5
1739.4
1671.0
802.1
2054.5
2105.6
7474.5
16358.0
15343.6
429.2
1107.7
1215.8
623.4
1761.8
1577.7
756.9
2081.1
1991.8
Average error for
in this flash.
locations
150
558
535
227
900
813
L
354
1058
973
szc

Table B
.2. Error Analysis for the Locations in the 181806 Flash,
ascending order in z.
The locations are arranged in
Source Locations
(Meters)
-1172
-2176
-656
-1093
-593
-458
-710
-202
-372
260
-50
-257
819
1177
48
-1235
-905
1186
3959
4331
1522
4013
1313
5478
5547
2796
2671
6318
8841
8293
8937
9191
9231
9295
9372
8695
9096
11410
9320
9708
12050
12137
9704
10245
9527
10560
10426
10855
1103
10944
10654
11529
117 98
10055
12294
12710
633
1865
2966
3287
3646
4510
4915
5373
5789
6464
7033
7484
7763
7887
8237
8682
9379
9777
9953
10521
lu634
10659
12385
12658
13152
13355
13663
14864
Average e
tions in
rror
this
for loca-
flash.
Quant
Erro
dx.
50
57
56
58
60
64
65
69
70
97
83
83
133
160
94
88
89
162
561
657
195
570
191
923
932
329
341
1152
264
ization RMS
r (Meters)
dy,
Q
326
276
432
407
473
515
505
530
550
846
636
657
1058
1161
712
660
665
981
1678
1888
1107
1757
1069
2280
2321
1202
1530
2717
1033
dz.
3004
1887
747
648
657
526
461
355
357
662
309
312
650
702
302
285
271
439
1171
1392
526
1221
601
2069
2120
914
959
2719
938
Calibration RMS
Errors (Meters)
dx
106
105
133
127
143
156
153
170
171
236
204
204
311
360
231
200
210
370
1089
1271
438
1117
443
1805
1832
713
737
2281
547
dy.
710
593
936
881
1024
1112
1089
1136
1181
1841
1363
1411
2298
2523
1527
1416
1418
2106
3607
4061
2377
3779
2285
4895
4983
2563
3282
5830
2222
dz
7302
3649
1804
1565
1577
1244
1085
801
798
1473
594
591
1292
1334
467
509
391
455
1228
1566
537
1347
837
2989
3129
1463
1330
4326
1632
Total RMS Error
(Meters)
dx.
118
120
144
140
155
169
166
184
185
256
221
220
338
394
250
218
229
404
1225
1431
480
1254
482
2029
2056
785
812
2555
608
dyt
781
654
1031
971
1128
1226
1201
1253
1303
2026
1504
1557
2530
2778
1685
1562
1567
2323
3978
4479
2622
4167
2523
5400
5497
2831
3621
6432
2451
dz
7896
4108
1953
1694
1708
1351
1179
876
875
1615
670
669
1447
1507
556
584
476
633
1697
2095
752
1819
1031
3636
3780
1725
1640
5110
1882
326

327
Tables B.3 and B.4 show the quantized, calibration, and total error for
the three-dimensional VHF source locations over the entire range of
these flashes.

Table B.3. Error Analysis for the Locations in the 181807 Flash. The locations are arranged in
ascending order in z.
Source Locations
(Meters)
Quantization RMS
Error (Meters)
Calibration RMS
Errors (Meters)
Total RMS Error
(Meters)
X
y
z
dxQ
dyQ
dzQ
dx
c
dy
J c
dz
c
dKt
dyt
dz
t
5612
8301
705
101
97
3856
167
200
5387
196
223
6625
5569
8211
1055
98
97
2444
162
198
3455
189
221
4232
7027
14997
1587
225
264
5759
345
328
7888
412
421
9767
5458
8310
2308
92
100
1050
153
195
1537
179
219
1862
6761
14847
2411
208
257
3557
324
320
4924
385
411
6075
5969
9263
3555
103
113
885
173
198
1287
201
228
1563
5633
13719
4048
147
216
1544
240
275
2232
282
350
2714
5982
9486
4369
101
119
737
171
200
1093
199
233
1318
5950
12421
4715
133
178
1127
221
244
1633
258
302
1984
5364
9413
5190
90
123
549
152
203
852
177
237
1014
4038
8864
5226
77
118
393
120
203
661
143
235
769
5358
11929
5865
109
172
754
184
239
1146
214
295
1372
4254
10151
5956
83
139
469
134
216
766
158
257
898
3740
9418
6031
77
130
376
117
211
641
141
247
743
4967
10296
6047
90
141
526
151
216
833
176
258
986
5095
8528
6555
82
119
369
134
198
611
157
231
714
4551
10595
6653
37
150
481
143
223
781
168
269
917
4600
10781
7055
88
155
477
145
227
776
170
275
911
5752
11742
7698
107
178
599
184
246
937
213
303
1112
6333
10613
8590
105
161
515
185
231
817
213
282
966
5074
13639
9003
107
236
629
184
302
1012
213
383
1192
3631
10146
10469
85
165
344
121
238
598
148
290
690
Averace error for
loca-
tions in
this flash.
109
156
1247
178
232
1812
209
280
2201
328

Table B.4. Error Analysis for the Locations in the 182357 Flash. The locations are arranged in
ascending order in z.
Source Locations
Quantization RMS
Calibration
RMS
Total RMS Error
(Meters)
Error (Meters)
Errors (Meters)
(Meters)
X
y
z
%
dyQ
dzQ
dx
C
dyc
dz
c
dx
t
dyt
dz
t
-487
5915
2219
63
99
267
62
192
630
89
216
685
-3655
12638
3332
124
239
821
144
292
1753
191
378
1936
-3940
5458
4421
76
115
243
85
206
525
114
236
579
-2933
13562
4738
123
261
667
137
310
1387
184
406
1539
-3342
12171
5050
120
225
532
133
283
1127
179
362
1247
-2986
11851
5080
112
214
493
122
275
1044
166
348
1155
-5975
9194
5144
135
187
507
180
257
1067
225
318
1182
-4718
7742
5808
106
151
326
127
233
687
166
278
761
-935
10823
6672
90
178
330
86
249
673
124
307
750
-3831
11237
6964
126
212
408
141
275
849
189
348
942
-4560
8509
7199
116
166
323
136
244
667
179
295
741
-4415
11139
7414
136
218
422
159
281
870
210
356
967
-1256
11053
7701
97
189
328
91
257
660
134
320
737
-5393
9276
7862
139
189
387
172
261
785
221
322
876
-2819
12412
8432
125
237
409
130
296
824
181
380
920
-7855
9353
8880
197
221
560
279
288
1097
342
363
1232
-551
7582
9210
136
165
342
169
247
668
217
297
750
-2262
12857
9546
124
249
410
124
308
807
176
397
906
-137
12522
9764
99
226
379
91
289
719
135
367
813
-3225
13322
10309
146
275
451
155
333
884
213
432
993
-9196
10455
11336
261
271
701
376
336
1332
458
432
1505
582
14293
12192
105
288
467
98
354
850
144
457
970
Average error for loca
tions in this flash.
125
208
444
145
276
905
193
346
1008
329

APPENDIX C
COMPUTER ALGORITHM TO DETERMINE VHF SOURCE LOCATIONS
FROM THE DIFFERENCE IN THE TIME OF ARRIVAL OF VHF RADIATION DATA
In this appendix we give the Fortran computer program code used
to determine the three dimensional source locations based on the
measured difference in the time of arrival of VHF radiation. The input
of the program is a digital tape with four VHF series digitized at
4.352 MHz. There are two types of outputs: (1) a printout of all the
three dimensional source locations and their relative time of occur
rence, and (2) a digital tape where the same printout information is
stored for future access. This appendix also contains on page 355 an
example of a computer printout of the output. This output consists of
the source location for successive 376 Usee cross-correlated time
intervals and the relative time and location of each one of the
individual sources.
330

331
DEFINITION OF VARIABLES USED IN THE COMPUTER ALGORITHM DESCRIBED IN
THIS APPENDIX:
LCHAN
- Digital tape channel number (0, 1, 2, 3)
LREC
- Six bit byte of data read from seven track digital tape
LINT
- Value of the VHF radiation reconstructed from the bytes
X6, X7, X8, X9 Value of the VHF radiation for the central and the
three remote stations, respectively
X1ME, X2ME, X3ME, X4ME Average value of the VHF radiation in the
selected data window for the central and the
three remote stations
Till, TI21, TI31, TI41 Value of the VHF radiation for the channels
(without a mean value)
LHOUR,
LSEC, LMIN, LMIL Converting time code value on digital tape to
hour, minute, second, and millisecond
TIL2S,
TIL3S, TIL4S Normalization factor for VHF radiation of remote
stations versus central station
XI, X2, X3, X4 Subsections of the value of the VHF radiation for the
central and the three remote stations
AVEMO
- Moving average of the' VHF radiation in the central station
AVEM02
- Moving average of the VHF radiation for the remote station
AVE
- Average value of a section of the VHF data
LAG1, LAG2, LAG3 Amount of samples needed to maximize the cross
correlation function
DELTA1, DELTA2, DELTA3 Time corresponding to the cross-correlation
intervals
X, Y, Z Three-dimensional locations
MABLMA
- Sample value for local maximum for the central station
MX2GEN
- Estimation of the cross-correlation value for local maximum
SLPR2
- Slope to the right of local maximum
SLPL2
- Slope to the left of local maximum >.
NDSLRI
- Number of reversals on descending slopes to the right of
local maximum
NDSLLE
- Number of reversals on descending slopes to the left of
local maximum
NDSLLE

<
3 12
NGOD
- Degree of acceptance of
pattern recognition
DEL1UB
- Upper bound
station
of
the
lime
lag between
one remote
and
the
central
DEL1LB
- Lower bound
station
of
the
time
lag between
one remote
and
the
central

nono nnnn nonn ooo
133
2 1 JUNE 1979
C
C
C
c
c
c
c
c
c
c
c
c
* * *
*
THIS algorithm determines the three-dimensional locations
OF VHF NOISE SOURCES DURING A LIGHTNING FLASH- THE PRO
GRAM IS BASED CN DETERMINING THE DIFFERENCE IN THE TIMF
OF ARRI VAL (DTOA ) OF FOUR TIME SERIES VHF RADIATION DATA.
THE DTOA IS DETERMINED BY USING PATTERN RECOGNITION AND
THE CROSS-CORRELATION FUNCTION.
A
*
*
*
*
*
*
DI MENS ION LCHAN(167 0).LREC 2,16 70),X6(361 0) ,X7{86 I 0).
* X£(86l0) AVE( 128) ORDLMA( 128 ) MABL MA( 12 6) AVEMO I 2 04 0) ,
* AVEM02(2048),MX2GEN(128),MA0LM2(12B),NUMDER(128),
* NRROWE(128).NRR0W2(128)
DIMENS ION SLPR 128) ,SLPR2( 128) SL_PL( 128) SLPL2( 128) .
* NUMDEL( 128) NUMDL2 ( I 28 ) NGOOD ( 5 ) MGCJODt b ) DELTA 1 ( 128 ) ,
* DELTA2(l23).DELTA3(128),X(128),Y(128),Z(128),NDIFB0(5),
* MAOSCI(10)Ll(10),NDSLRI(10 ) ,NDSLLE(10).PENDRI(10),
* PENOLE( 10),X9(8610) ,NSTDEV( 10 ) ,MBSC K 128),TI ME(123),
* NIN(128),NUMDR2(l28),LINT(1670)
LOGICAL*! LCHAN
INTEGE R* 2 LR EC
COMMON KK,N,MP,NP.NNN(128),MMM(12Q),X1(2048),X2(2040)
10 FORMAT(75(75A1))
ZERO=0.
W R IT E ( 6,700)
70 0 FORMAT (IH I )
WR ITE( 6,722)
722 FORMAT(33X,32H5TURM ACTIVITY ON I 9 TII JULY 1 976.//21X,
* 6OHST ART TIME = 16 HOURS 59 MINUTES 59 SECONDS
* 008 MILLISECONDS, //20X, 6 1 HE INI 3H TIME = 17 HOURS
* 00 MINUTES 01 SECONDS 009 MILLISECONDS)
** SKIP THE CALIBRATION BLOCK **
READ( l 1,1 0) ( (LCHAN( I ) (LRE C(J,I),J=l,2)),I=1.100)
** SKIP A PRE-DETERMINED TIME CORRESPONDING TO THE NOISE **
** LEVEL BEFORE THE SIGNAL IS DETECTED. **
DO 12 LK-. 1,310
12 READ(11,10)
** PROCESS THE NEXT 500 BLOCKS OF DATA. A BLOCK HAS 410 **
** DATA POINTS OF EACH OF THE FOUR SERIES. **
DO 520 I 1 M = 1 ,25
DO 20 K=1,21
R E AD( 1 1, l0)( (LCHAN(I ), (LREC(J, I ) J = 1 ,2) ) 1=1 1670)
** CONVERT THE DATA ON THE TAPE FROM *
** POP-COMPUTER FORMAT TO IBM FORMAT. **
DO 18 1=1.1670
DC 16 J=1 ,2
16 LRECJ ,1) =(LREC(J,I )-64)/256
18 L I NT ( I )=L RFC (1,1) *G>4 + LREC(2,I)
IF(K.EC.1) GO TO 805
GO TO 802
C
C ** THE FOLLOWING INFORMATION IS NEEDED TO DETERMINE **
C ** THE ABSOLUTE UNIVERSAL TIME. **
805 LSAVE1=LI NT( 1641 )

noo r>nnr> non non
2 1 JUNE 1979
LS/WE2 =LC HAN (164 1 )
M SAVE 1 =LINT( 1 642 )
M SAVE2 =LC HAN( 1642)
802 DC 20 L = 1,410
** S EPAR A T If i G THE FOUR TIME SERIES **
X6( 4 1 0 *( K- 1 )+L)=LINT( 4 *L 3 )
X7(41 0 *{ K-l ) +L )=L I NT (4*L-2 )
X8(41 0*(K-l )+ L ) = L I NT(4 *L 1 )
20 X9(410*(K-1 )+L )-LINT(4*L)
** SUBTRACTING THE MEAN OF THE SERIES +*
X N 1 = 0 0
XN2=0. 0
X N 3= 0.0
XN4=0.0
TILIL = BIG(X6,861 0)
T IL2L = B IG ( X 7,8610)
TIL3L=BIG(X 8,8610)
TIL4L = O IG(X 9,8610)
DC 22 1=1,86 1 0
XN 1 = XN 1 + X 6 ( I )
X N 2= XN 2+ X 7 ( I )
X N3=XN 3 + X 8( I )
22 XN4=XN4+X9( T )
X l ME= XN1/8610 ,
X2ME=XN2/861 0 .
X 3 ME = XN3/861 0 .
X 4 ME = X N4/36 1 0 .
TI1L = TIL1L-X1 ME
T I 2L = T IL 2L-X2ME
T I 3L=T IL3L-X3.ME
T I 4L = T IL4L-X4ME
**r DC NOT PROCESS THE DATA IF THE SIGNAL IS WITHIN **
THE NOISE LE VEL( 100.) **
IF((TI 1L.LE.100.).0R.TI2L.LE.100.).OR.(TI3L.LE. I 00.)
* OR.(TI4L.LE.100.))GO TO 520
DO 26 J=1,8610
X 6(J)=X6( J)-X1ME
X 7(J) = X 7( J) X 2ME
X 8(J)=XO( J) X 3ME
26 X9(J)=X9(J)-X4ME
** CGMPUTE THE ACTUAL TIME OF DIGITIZATION **
LSEC=LSAVE1H4096*LSAVE2
LMIL = MSAVEl +4096*M5AVE2
LH CUR = LSEC/36 0 0
LM IN = L SEC/6 0L HOUR *60
LSECR=LSEC-LHOUR*3600-LMIN*60
C
DO 591 MN=I,l4
591 WRITE(6,586)
586 FORMAT( 1H 0)
WRITE(6.507) L HOUR,LMIN L SECR,LMIL
58 7 FORMAT ( 1 H 0,2 OX 1 8HD I GI T I ZAT I ON T I ME= 'l 4 1 X 5HHOURS 5X
* 14, IX,7HMIUTES,5X, 14,1 X,7HSECONDS,5X.I 4,1X,
* 12HMILLI SECONDS )
WRITE! £,588) LHGUR,LMI N.LSECR,LMIL
588 FORMAT(11X, 13HDIGITIZATION TIME=, I 4, lX,5HHOURS,15,
* IX.7HMIUTES,14,IX,7HSECNDS, I 4, lX, 11HMILI SECONDS)

nnri nono nn
135
2 1 JUNE 1979
** CONVERT TO THE ABSOLUTE TI ME **
LHCUR=16
MINU=59
LSECD=59
LMIL-LRIL + 1 000
LSEC^LSEC- 1
LSECOl-LSEC-13584
LMILD1=LMIL984
5ECO1=LSECDl
RMILD1 =LMILD t
SECD= SECD 1/32.
RM ILD 1 =RM ILD 1/32.
LSECD=SECD
R MILD =(SECDFLO A T(LSECD) )* 1 0 00 + RMILD1
M ILO=RM ILD
RMICRO = ( RMI LC-FLOAT (MILD) ) *100 0 .
M ICROT = RMICRO
MILST=8+MILD
IF( ( MILST.GE. 1000) .AND. (LSECD.GT.0 ) )GO TO 592
L SECL)= 59 tLSECD
IF(LSECD.GT.59) GO TO 592
GO TO 593
59 2 LSCCD=C
MINU-0
LHOUR= 17
M ILST=MILST-1000
593 DO 599 MN=1,6
599 WRITE!6*506)
WRITE(6.862) L hCUR.MINU.LSECD,M ILST,MICROT
862 FORMAT(l2X, UN I VERSAL TIME =* I 3, HOURS 13 'MI NUTES* ,
* 2X, 13.IX 'SECONDS' 14, lX, 'MIL I SECONDS' I 4, lX,
* MICROSECONDS' )
594 FORMAT{UNIVTRSAL TIME = .IJ,'HOURS' I 3, MI NUTES' .
* 2 X I 3 IX, 'SECONDS' 4. IX, 'MILL I SECOND S' I 4,1X,
* 'MICROSECONDS)
WRITE!0,594) LHOUR,MINU.LSECD,MILST,MICROT
** NORMALIZING THE FOUR TIME SERIES TO THE CENTRAL **
** STATION THRESHOLD LEVEL **
TIL12D-TIL1L TIL2L
IFTIL12D.EQ.O.O)GO TO 521
T IL23 = TILIL/TIL2L
DO 517 J = I .8610
5 17 X 7( J ) =TIL23tX7( J )
521 T IL13D = T IL1L-TIL3L
IF(TILI3D.EQ.0.OJGO TU 523
T IL3S=T IL IL/T IL3L
DO 519 J=1.36 1 0
519 X0(J)=TIL3S*X0(J)
523 T IL 1 4D=T IL t L-T l L4L
IFCTIL14D.E0.0i0)GQ TO 528
IIL4S=IIL1L/TIL4L
DC 526 J= 1,86 10
526 X9(J)=TIL4S+X5CJ)
** INITIALIZATION **
528 KK= 512
N-2040
M M = 1 6
T I ME 1=0.0
J J = I2e
J 1 -0

noon ono nono noon ooonoo ono ooo
'136
21 JUNE 1979
500
MKN=0
WRITE! e. 531 )
531
FORMAT (101,17X 5HDELAY,5X,24 UMAX I MUM CROSSCORRELATION,
* 5X, 13HTIME INTERVAL)
501
DO 501 K-l,2048
Xl(K)=X6(20484Jl-4 4Q4Jl-H<)
*4 CALCULATE ONE AVERAGE POINT PER SUBSET *
3
1
f
DO 1 J=1,JJ
XS=0 .0
DC 3 J K = 1 ,MM
XS = XSFX1( (J-1)4MM+JK)
AV E( J)=XS/FLGAT(MM)
C 44
c
CALCULATE MOVING AVERAGE UF THE SET 44
V
5
X I=0.0
DO 5 1=1,MM
X I =X I + X l ( I )
A VEMO( l ) = XI/FLOAT(MM)
KL=MM+1
9
l 1 3
c
DC 9 I= KL ,2047
X 1 = X14-X1{ IJ-Xl (I MM)
AVEMO( 1-15 ) = XI/FLOAT(MM)
F C RMAT<3r10.2)
CALL RMEAN(AVEMO,2032,0.0)
C 44
C 4=
C 4 4
C -4 4
C
CALCULATE THE STANDARD DEVIATION OF THE DATA IN THE SET 44
BY USING A FUNCTION SUBPROGRAM STDSET, THE THRESHOLD 44
LEVEL LY FUNCTION SUBPROGRAM DIV4SM, AND THE STANDARD 44
DEVIATION OF THE SUBSET BY FUNCTION SUBPROGRAM STDSUB. 44
CALL LCC.M AX ( M A ELM A, MM J J A V E S LPR SL PL NUMDER,
* NUMDEL NRRGWE )
C 44
C 44
C
97
r
LOCMAX IS THE SUBROUTINE THAT CALCULATES LOCAL MAXIMUM 44
IN THE DATA 44
F CRMAT(110,3F10.2,3I10)
v_
C 4 4
C 44
C
502
f
TEE DATA IS RE-FORMATTED TO BE ABLE TO PROCESS THE DATA 44
NEAR THE END CF THE SET 44
DO 502 K= 1,2048
X2(K)=X7(20484Jl4484J1+K)
C 4 4
MKN IS THE COUNTER FOR THE NUMBER OF STATIONS 44
c
17
MKN=MK N+ 1
L
C 4 4
C 4 4
r
GETTING THE AVERAGE AND THE MOVING AVERAGE FOR 44
THE RFMOTF STATIONS 44
1 3
1 l
C
DO 11 J=l,JJ
X S = 0.0
DO 13 1=1,MM
XS=XS+X2( (J-l ) 4M M + I )
A VE( J ) = XS/FLOAT ( MM )
X I =0.0
DO 15 1=1.MM
1 5
X [=XIFX?( I)
A VEM02 (1 ) =XI/FLOAT(MM)
DO 19 I=KL,2047

n ri n n n orino o onon noonOn noon
(37
2 1 JUNE 1979
19
c
X I = X I - X2 ( 1 )-X2( l MM )
AVEM2(I-15 ) = XI/FLUAT(MM)
CALL RMEAN(AVEM02,2032.0.0)
V
C *
C *
r
LAG IS THE SUBPROGRAM THAT CALCULATES THE TIME DELAY **
TO PEAK THE CROSSCORRELAT10N FUNCTION. **
L
52 9
L A GL = L AG( AVEMO,AVEM02 ,MKN)
IF(LAGL.LE.5)GO TO 585
IF(MKN.EQ.l) L AG 1 =L A GL
IF(MKN *E Q 2) L AG2 =LA GL
IFMKN.EQ.3) GO TO 529
GO TO 530
LAG3=LAGL
DELTA 1( l)=.22978*FLOAT(LAGl)
DELTA2(1 ) = 2 2 9 7 8*FLOAT(LAG2)
DELT A3( 1 )=.229784FLOAT(LAG3)
N l N ( l ) = 1
t.
C *
C *
c *
c #*
r
HYPERM IS THE SUBROUTINE THAT FINDS THE LOCATION **
BASED ON THE DTO A IN THIS CALL ONLY THE LOCATION **
THAT CCRR ESPGNOS TO THE CROSS-CORRELATION VALUES *
IS FOUND **
v.
580
WRITE(6,580)
FORMAT( 1H0,1 OX,l 1HX IN METERS, lOX, 1 1 MY IN METERS,
* I OX,1 1HZ IN METERS)
WRITE(6,581) X(i),Y(1),Z(1)
50 1
FORMAT ( 3F 20. 3 )
WRITE(6,724)
724
r~
F ORMA T(IOX,11HX IN METERS,1 OXI 1 HY IN METERS,
* 1 OX, 1 1HZ IN METERS)
v,
c **
c **
c
c
IF THE SIGNAL LEVEL IS LOW AND BAD CORRELATION RESULTS, **
THE DATA IS ELIMINATED* 4*
IF((Z( 1 ).LE.0. ) ,CR. ((ABS(X(1 )) ).GE.40000.).OR.
* ( (AOS(Y( 1 ))).GE.40000.).OR.(Z( 1).GE.16000. ))GO TO 585
IF((LAG1 .LE.5) .OR (LAG2.LE.5).OR.
* (LAG3.LE.5)) GO TO 585
V.
702
530
c
WRITE( 8.7 02) X(l ),Y( 1 ) ,Z(1 ),ZERO
FORMAT(4F20.3)
CALL L0CMA2(MA0LM2,MM,JJ.AVE,SLPR2,SLPL2.NUMDR2.NUMDL2,
* NRROW2)
C *
c **
c
r
THE PROPERTIES OF THE LARGEST PULSE WITHIN THE **
SUBSET IS STUDIED **
DO 73 K=1,MP
IF(K.GE.2) MDIFTE=NDIFTE
v_
C **
c *
c *
s~
MABLMA IS THE ABSCISSA OF THE LOCAL MAXIMUM IN THE + *
CENTRAL, MX2GEN IS THE ABSCISSA OF THE LOCAL MAX- **
IMUM FOR THE REMOTE STATIONS **
C
160
M X 2GE N(K) -MAELMA (NNN(K) )+L AGL
I FMX2CEN(K) .GT.(N+l5) ) GO TO 7 3
NCCUNT =0
DO 70 J = 1,NP
IF ( IAf3S( MX2GEN( K ) M ADL M2 (MMM(J) ) ) .LE.( 16) )GO TO 160
GO TO 70
NC GUNT = NC 0 UN T +1
MABSC I(NCOUNT)=MMM( J)
LI(NCOUNT)=MABLM2(MMM(J))

nnoo nno
38
2 1 JUNE 1979
C ** NO SLR I NOSLLE, PENOR PENOLE AND NSTDEV ARE THE FIVE **
C ** PUL5E PROPERTIES BEING USED FOR PATTERN RECOGNITION. **
C ** THEY CORRESPOND TO THE NUMBER OF DESCENDING PATTFRN TO **
C ** THE RIGHT AND TO THE LEFT OF THE PULSE. THE SLOPES TO **
C ** THE RIGHT AND TO THE LEFT OF THE LOCAL MAXIMUM, AND **
C ** THE NOFROWNESS OF THE PULSE. **
C
NDSLRI (NCCUNT )-NUMDR2(MMM(J) )
NDSLLE NCOUNT)=NUMDL2{MMM(J) )
PENOR I (NCOUNT)=5LPR2(MMM(J > )
PENOLE(NCOUNT)=SLPL2 (M M M{J) )
N SIDE V(NCOUNT)=NRROW2(MMM { J) )
70 CONTINUE
IF{NCOUNT.EQ.OIGC TO 73
DO 75 J-l.NCOUNT
L P ASS-0
JPASS= 0
NPASS= 0
IPASS=0
KPAS S=0
** MATCHING CHARACTERISTICS FOR THE FIVE GIVEN PROPERTIES **
IF(IAOS(NUMDER(NNN(K) )-NDSLRI(J) ) .LE. 1 ) JPAS3=JPASStl
I F( I ABS( NUMDEL ( NNN( K ) ) -NDSLLF ( J) ).LE.l) L P A SS = L PASS + 1
IF (AL1S ( SLPR( NNNI K ) ) ) .GE. ( 1 0. ) A NO ABS( PENDRI< J) ).GE.( 10.> )
* GO TO 79
IE(AOS(3LPR( NNN(K) )-PENDR I (J) ) .LE.2.5) NPASS=NPASS+1
IF(ACS(SLPL(NNN(K))PENOLE(J)).LE.7.5) lPASS=IPASS+1
GO TO 81
79 IF(AOS(SLPRINNN(K) )-PENDRI{J) ) .LE .7.5) NPAS S= NP AS 5 + I
IF(AOS(SLPL(NNN(K))-PENDLE(J)).LE.7.5) IPAS5=IPA3S+l
81 IF ( I AOS( NRRO'wE ( NNN ( K ) ) NSTDEV (J)).LE.(10)> KPAS5-KPASS+ I
NGOOD( NCOUNT)=LPASS+IPASSFKPASSFNPASS+ JPASS
75 CONTINUE
IF(NCOUNT.EQ.1)GO TO 180
NO IFT E-15
DO 420 MK=1,NCOUNT
NDIFDQ (MK ) = I ABSL1 ( MK) MX2GE! N ( K ) )
IF(NO I FOB(MK ) .LE .NDIFTE)GO TO 435
GO TO 420
435 NDIF TE =NDIFOB(MK)
LKNM=MK
420 CONTINUE
** ALL THE PATTERN RECOGNITION PROPERTIES ARE USED TO **
** DETERMINE IF A PROPER MATCH HAS OCCURE. **
IF((ND 1FTE.LE.4.AND.NGOOD(LKNM) .GE.1>.OR.(NDIFTE.LE.8.
* AND. NGOOD(LKNM) .C.E.2) .OR. ( N D I FT E L E 1 2 A ND NGCUO < LK NM )
+ GE.3) .OR.(NU IFTE.LE 16.AND.NGOOD(LKNM) .GE.4) )GO TO 430
180 N DIF T E =I A US(Ll ( 1 )-MX2GEN(K ) )
I E{NDIFTE.LE.4.AND.NGOOD( l ) .GE .I ) GO TO 4 00
I F (N J I FTE .L E 8 AND N GOOD ( 1).GE.2)GU TO 400
IE(NDIETE.LE.12.AND.NGOOD(1).GE.3)GO TO 400
I F(M!) IETF .LE I 6. AND. NGOOD ( 1 ) .GE .4 ) GU TU 400
CO TU 73
400 IF( IAOStL 1 ( 1 )LAGLMAOLMA NNN (K+T) ) J.LE.NDI FT E ) GO TO 73
MOSCI(K)=L1(1)
IF{(K.CE.2) .ANO.(NO IFTE.GE.MDIETE) .ANb.(MBSCI (K).
* EQ.MBSCI (K-l ) ) ) GO TO 73
GO TU 84
43 0 IF((IA8S(LI ( l )-LAGL-MAOLMA{NNN( K l ) ) ).GT.NDIFTE). AND.
* { LK NM.EQ.l)) GO TO 491
I F ( ( IA ES(Ll (2)-L AGL-MAOLMA(NNN(K+I ) ) ).GT.NDIE TE). AND.

norm nnon n nono oOnn
.139
21 JUNE 1979
* (LKNM.EQ.2)) GO TO 491
IF(( [A ES(L1 (3)-L AGL MAB LMA(NNN(K+l ) ) ) GT.NDIFTE).AND.
* (LKNM.EQ.3)) GO TO 491
GO TQ 73
49 1 MSCH K)-Ll(LKNM)
IF((K.GE.2) .AND.(NO IFTE.GE.MDIFTE) .AND.(MB3CI(K).EQ.
* MBSCI(K-l))) GO TO 73
e4 CONTINUE
IF (MOSCI ( K ) GT .( NFl 5) ) GO TO 73
IF(MKN2) 87.89.9l
** CELT A1 DELTA2. AND DELTA3 CONTAIN THE TIME DIFFERENCE
** FOR EVERY IDENTIFIED PULSE.
87 DELTA1 (K)=(MBSCI(K)MABLMA(NNN(K)))*.22978
GO TO 73
89 DELTA2(K) = (MDSCI (K)-MABLMA(NNN(K ) > )*.22978
GO TU 73
9 1 DELTA3(K)=(MOSC I (K)-MABLMA(NNN(K) ) )*.22978
73 CONTINUE
** CHECK FOR WHAT STATION SHOULD BE READ NEXT **
IF(MKN.EQ.3)GO TO 93
IF (MKN .CQ .2 ) GO T 95
DO 503 K= 1 ,2 04 8
503 X2(K)=X8(2048*J1-448*J1+K)
GO TD 17
95 DO 50 4 K~ 1,2 04 3
504 X2(K)=X9(20484J1448*J1+K)
GO TO 17
** A REASONABLENESS TEST IS USED TO ENSURE THE TIME **
** DIFFERENCE IS WITHIN PROPER BOUNDS. **
93 DELlUD-.2 2978*FLGAT(LAGl 1+2 5.0 *.22978
DELILB = .22978*FL0AT(LAG1 1-25.0*.22978
DEL2UB=.22978* FL OAT(LAG2)+25.0*.22973
DEL2LD =.22978*FLCAT(LAG2)25.0 *.22978
DEL3UB =.22978*FLGAT(LAG3)+25 0*.22978
DEL3L8=22978*FLOAT(LAG3)-25.0*.22978
N X =0
CO 4 52 IK = I MP
IF((DELTA 1 ( IK) .GE.DELILB.AND.
* DELTA1(IK).LE.DELlUB).AND.(DELTA2(IK).GF.0EL2L0.
* AND.DELTA2( IK ) .LC.DEL 2UB) .AND.(DELTA 3( IK) .GE.DEL3LB.
* ANDD FLT A3(IK).LE.DEL3U) ) GU TO 571
GO TQ 452
7 1 NX-NX + 1
N 1 N(NX) = I K
52 CONTINUE
** CALCULATE THF LOCATIONS FOR ALL THE PULSES MATCHED **
** FOR ALL THE STATIONS *
CALL HYPE RM( DELTA1 DEL T A2 DELT A3 X Y 7. N l N NX )
WR ITE ( £.5 35)
535 FORMAT ( 1H0, tOX1 1 HX IN METERS, 10X, l lHY IN METERS,
* l OX, L 1HZ IN METERS 5X.20HTIME IN MICROSECONDS )
WR ITE( 8,706 )
DO 1 72 LK = 1 NX
T1 ME(LK)=.22978*ELOAT(J 1*2 048-J1*44 8 ) +
* .22978*FL0AT(MAOLMA(NNN(NIN(LK))))
if. t
**

nnnn nnnn
340
21 JUNE 1979
IF({J1 .GE. I ) .AND.(TIMELK) .LE.T IMF 1 ) )GO TO 172
WRITE! 6.1 01) X(L K) ,Y(LK) ,Z(LK) TI ME(LK)
WR ITE!8,7 00) X(LK),Y(LK),Z(LK) ,TIME(LK)
172 CONTINUE
T I ME 1 = T I M E ( N X )
GO TO 815
585 IF(Jl.EQ.O) TIME 1=0.
815 T IME 1=TIMF 1 + 2.
** WRITE A ZERU TO INDICATE THAT THE T HREE IMENS I ONAL **
** LOCATIONS, FOP ALL THE MATCHED PULSES, HAVE OEEN READ. **
WRITE(8,705)ZERO,ZERO,ZERO,ZERO
J1=J1 + 1
IFJ1.LE.4) GO TO 500
WRITE!0,537)
537 FORMAT 1 l )
** BACKSPACE THE TAPE TO ENSURE THE DATA AT THE END OF **
** THE LAG INTERVAL IS NOT MISSED. **
BACKSPACE 11
520 CCNTINUE
REWIND 11
101 FORMAT(4F20.3)
109 FORMAT !3E10.3)
170 FORMAT(5110)
It 2 FORMAT (FI 0.2 )
164 FORMAT(2 I 10,F10.2, I 10)
10 7 FORMA T(I 5)
705 FORMAT(3F10.3,F2t.3)
706 FORMAT(8X,11HX IN METERS. OX, 11HY IN METERS,
* 8 X, 1 IHZ IN METERS, 3X, 2 OH TI ME IN MICROSECONDS)
STOP
C
C ** THIS IS THE END OF THE MAIN PROGRAM TO CALCULATE **
C ** LIGHTNING LOCATIONS FROM TIME SERIES MEASUREMENTS. **
C ** NEXT A DESCRIPTION OF ALL THE SUBROUTINES AND **
C ** SUBPROGRAMS U5ED IN THIS ALGORITHM IS GIVEN. **
END

nnnn
21 JUNE 1979
FUNCTION STDSET(Xl.N)
** FUNCTICN SUBROUTINE TO CALCULATE THE
** DEVIATION OF SET
D I MENS ION XI ( 1 }
T S UM S = 0 0
DO 536 1=1 N
536 T S UM 5= T3UMS+-X1 ( I )
AV SET = TSU MS/FLUAT(N)
T SUMS= 0*0
DO 530 1=1 ,N
SUM5 =( X1 ( I)-AVSET)**2
530 TSUMS=TSUVSFSUVS
S TDSE T = SQR T ( T SUMS/FLOAT ( N-l ) )
RETURN
END
ST ANOARD

nrsn
2 1 JUNE 19/9
SUBROUTINE RMEAN(DATA,NDAT A,XMEAN)
** THIS SUBROUTINE SUBTRACTS THE MEAN UF THE DATA **
DIMENS ION DA TA( 1 )
DOUBLE PRECISION DDATA,DSUM,ONDATA
DSUM-0.0
DNDATA-NOATA
DO 10 1=1,NDATA
DOATA = DATA{ I )
10 DSUM = DSUM 4-DDAT A
DSUM=D SUM/DNDATA
A VG=DSUM
DO 20 1 = 1 ,NDAT A
20 DATA(I)=DATA(I)-AVO*XMEAN
RETURN
END

nnn
2 1 JUNE 1979
VtJ
FUNCTION QIG(XiN)
** THIS SUBROUTINE FINDS THE LARGEST NUMBER IN THE SET
DIMENSION X ( 1 )
T = X ( 1 )
DO 570 I = 1 N
IF (T-X(I) )56 5,570,570
565 T=X( I )
570 CONTINUE
n I G= T
RETURN
END
**

non
344
21 JUNE 1979
FUNCTION SMALL( X N)
** THIS SUBROUTINE FINDS THE SMALLEST NUMBER IN THE SET
O I VENS ION X( 1 1
T=X( 1 >
DO 57S 1=1,N
IF(T-X(I))575,575,580
580 T=X( I )
575 CONTINUE
SMALL = T
RETURN
END
* *

non
21 JUNE 1979
34 5
FUNCTION DIV4SMX1.N)
** FUNCTICN SUBPROGRAM TO CALCULATE THRESHOLDt DIV4SM
DIMENSION XIDIM(4 ) ,XIOIV4(512) ,X1<20 48)
KK=512
DO 2 MK = I ,4
DO 4 I = 1 KK
4 X 1DIV4( I )=Xi ( (MK1 ) *KKF l )
2 X IDIM(MK) =UIG(X1DIV4512)
DIV4SM = SM ALL(X IDIM.4)
RETURN
END
* *

uuu^
146
2 1 JUNE 1979
FUNCTION STD SUB(XlLMiAVESFT MM)
** SUBPROGRAM TO CALCULATE THE STANDARD DEV. **
** OF THE SUBSET (STDSUB) **
I MENS ION X 1 LM ( l 6 )
T SUMS= 0.0
DO 14 1=1,MM
SUMS = ( XlL M( r 1 -AVESET ) **2
14 TSUMS=TSUMS+SUMS
S T DSUU = SQR T(T SUM S/FLOAT(MM1 ) )
RETURN
END

nnn nonn nnnn
147
21 JUNE 1979
FUNCT I ON LAG ( AVCMU AVE MO 2 MKN)
** SUOPROGPA w TC CALCULATE THE CROSSCORRFLATt ON **
** OF THE ENVELOPE **
DI MENS ION RHC(2 040) .PRO(2048).AVEMO<2048),AVEM02C 2048 )
RH0FTE=-1.0
** LK1 AND LK2 ARE THE DEG INNING AND THE END OF **
** THE CORRELATION LAG, *
LK 1= 1
LK2= 30 0
N K =203 2
IF{MKN.EQ3) GO TO 891
IF(MKN.EQ.l) L K 2=15 0
GG TO 892
891 L K 1 = 300
LK 2= 60 0
892 DO 37 K=LKi,LK2
X I 1=0. 0
X 12=0.0
NK1=NK-K+1
P R D= 0 0
00 35 1=1,NK1
PRC( I ) =AVEMO( I )*AVEM02( IFK-I )
XI 1= X I IF A VEMO ( I ) =¡=*2
X I 2=X12 FA VEM02( I+ K- 1 )**2
35 PRD=PRDFPRO(I)
SNORM = SQRT(XI t*XI2)
PHO(K)=PR0/S NORM
37 CONTINUE
49 FORMAT( 1 OF 1 0.3)
LK 1=LK1+4
** DETERMINING THE LARGEST CROSS-CGRRELAT I ON **
DC 41 K=LK1,LK2
IF(RHO(K).GT.RHOFTE)GO TO 53
GG TO 41
S3 LAG=K
RHOFTE=RHO(K)
41 CONTINUE
T I MEX=.22978FLOAT(LAG)
WR IT E( 6,3 89 ) LAG, RHOFTE, TIMEX
389 FORMAT (122,2F22.3)
RETURN
END

nnno
348
21 JUNE 1979
SUBROUTINE L OCM AX ( M ABL MA M M ,JJ .AVE.SLPR, SLPL.NUMDER,
* NUMOEL,NRROWE)
** SUBROUTINE TO CALCULATE THE LOCAL MAXIMUM OF CENTRAL **
** STATION **
O I ME NS ION MAELMA(128) .XILM( 16) ,SLPR( 128) SLPL( 123) ,
* NUMDER128),NUMDELf128).NRROWE(128),AVE(128)
COMMON KK,N,MP,NP,NNN( 1 28 5 ,MMM( 128) ,XI( 2 0 48) ,X2(2 04 8)
C
C ** THIS SUBROUTINE COMPUTES THE COORDINATES OF A LOCAL *
C ** MAXIMUM PER SUBSET- FUR A POINT TO BE A LOCAL MAXIMUM **
C ** ONE OF THESE THREE CONDITIONS MUST BE MET. A) ORDINATE *
C ** LARGER THAN 1/2 OF THE SMALLEST VALUE OF THE SECTION, **
C ** ) STANDARD DEVIATION OF SUQSET LARGER THAN STANDARD **
C *A DEVIATION OE SET, AND/OR C) ORDINATE LARGER THAN THE **
C ** AVERAGE PLUS TWO TIMES THE STD DEV. OF THE SUBSET. **
C
MP = 0
RT=2.0
DC 6 K=l,JJ
AVESET = AV E(K)
DO 8 J=1,MM
8 X1LM(J)=X1((K-L)*MMFJ)
XISM=BIG{X1LM.MM )
X1TEST=(DIV4SM(X1,N))/RT
X l PEQ=SMALL( X1LM ,MM)
X IDIFE = XlSM-X1PEQ
DO 22 J=l,MM
IF(X1LM(J).NE.X1£M)GG TO 22
MAELMA(K)= J +(K-l )*MM
GC TO 200
22 CONTINUE
200 N A BCIS-M ABL M A(K)
IF(NACIS.LE.5)GC TO 6
IF (NABOS .GE .2043 ) GO TO 6
IF(XISM.GE.X1 TEST)GO TO 24
IF(STD SUB(XILM.AVESE T,MM).GE.STDSE T(X1 ,N) ) GO TO 24
TEST=AVESET+RT *S TDSUBXILM,AVESET,MM)
IF(XISM.GE.TE5T)G0 TO 24
MRR= 0
MLL = 0
DO 202 MN1=1,5
IF(X1(NAB CIS+MNI 1) GE.X1 (NABCIS+MN1 ) ) MRR = MRR+1
IF(XI (NABCIS-MNl+1 ).GE.X1 (NABCIS-MN1 ) ) MLL=MLL+1
202 CONTINUE
IF((MRR+MLL) .GE.8 ) GO TO 24
IF(XIDIFE.GE.( 100 ).AND. (MRR + MLL).GE.7 )GO TO 24
GO TO 6
24 CALL PULSF(Xl,NABCIS.SLOPR.SLOPL,MR,ML,NARROW)
SL PR ( K ) = S LUP R
S L PL ( K ) = 5 L O P L
NUMBER(K)=MR
NUMDEL(K)=ML
NRROWE(K)=NARROW
IF(5LPL(K ) .LL 0 )GO TO o
i F(SLPR(K).GL.O. )GO TO 6
MP =MP+ 1
NNN(MP)=K
IF ( MP. E-Q. 1 ) GC TC 6
I F ( ( MABl M A ( NNN ( MP ) ) MAI3LMA ( NNN ( MP- 1 ) ) ) LE. 3 ) MP = MP-1
6 CONTINUE
121 FORMAT(2F10.2,5110)
RETURN
END

n ft n n
21 JUNE 1979
/(9
S UDRUU TINE PULSE(XI .NABCIS.SLOPR,SLOPE.MR.ML.NARROW)
** THIS PULSE SUBROUTINE DETERMINES THE CHARACTERISTICS **
** OF THE PULSE **
D I MENS IUN XI (2048 )
HIGHL=X1( NABCI S) X1 (NAQCIS-5)
H I GHR= X 1 (NAE3CIS) XI (NACIS+5)
SLGPR=-HIGHR/5.0
SLGPL=HIG HL/5.0
M = 0
DO JO MN=1,5
I F(X1( NA3CIS+MN-1).GE.XIINABCIS + MN) ) MR=MR+ 1
30 CONTINUE
ML =0
DO 3 2 MN- 1*5
IF (XI { NAO C I S MN +.1 ) G E X 1 ( N ADC I S -MN ) ) ML = ML +- l
32 CONTINUE
CALL NARRO(XINAECIS.NARROW)
RETURN
END

n o Ci o
21 JUNE 1979
')()
SUBROUTINE NARRO(XI,NABCIS.NARROW)
** THIS SUBROUTINE FINDS THE STANDARD DEVIATION OR **
** NARROWNESS OF THE PULSF. AROUND THE LOCAL MAXIMUM **
D I MENS ION XI (2048)
N A RR = 0
NARL-0
DO 04 VL= 1 5
IF(X I ( NAOCI S + ML- 1 ) .GE.XI (NABCI S+ML) ) GO TO 38
N ARR=ML
GO TO 06
33 NARR=NARR + 1
34 CONTINUE
36 DO 40 KJ=1t 5
IF(XI(NABCI5-KJ+l)GE.XI(NABCIS-KJ))G0 TO 42
NA RL = K J
GO TO 44
4 2 NARL= N ARL + 1
40 CONTINUE
44 TSUM5=G.O
DO 46 JK-l.NARR
D I F=(X1 (NABCIS) XI (NABCIS+KJ) )**2
46 TSUMS=TSUMS+DIF
DO 48 JK=1NARL
D IF=(X1 (NABCIS)-Xl (NABCIS-KJ > )**2
48 TSLMS=TSUMS+DIF
NARROW=SQRT(TSUMS/FLGAT(NARR+NARL+1))
RETURN
END

nnnon noon
21 JUNE 1979
SUEROUTI ME LGCMA2(MA0LM2.MM,JJ,AVE,SLPR2,5LPL2,NUMDR2,
* NUMDL2.NRROW2)
** THIS SUBROUTINE COMPUTES THE LOCAL MAXIMUM FOR *
** THE REMOTE STATIONS **
DI MENS ION MABLM2(12 8),X2LM(16) .SLPR2(128) SLPL2( 128),
* NUMDR2C123),NUMDL2(128),NRROW2(123), AVE(128)
COMMON KK,N,MP,NP,NNN(128),MMM(128).X1(2048),X2(2048)
** THIS SUBROUTINE IS SIMILAR TO THE CENTRAL STATION LOCAL *
** MAXIMUM. DOING THIS ANALYSIS SEPARATELY WE CAN ESTABLISH **
** STRICTER TOLERANCES FOR PULSE SELECTION IN THIS STATIUN. **
NP-0
R T = 2 0
MT = l.75
DO 50 K=l.JJ
M ABLM2 (K ) =0
A VE SET = AV E(K )
DO 52 J=1,MM
52 X2LM( J)=X2( (K1 )*HM + J)
X2SM=0IG(X2LM,MM)
IX?5M=X2SM
X 1 TE5T=(DIV4SM(X2,N) )/RT
X2PEQ=SMALL(X2LM.MM)
X2DIFE-X2 SM X2PEQ
DO 56 J = 1,MM
IX2LM=X2LM(J )
IF(IX2LM.ME. IX2SM)GO TO 56
MABLM2(K)=J+(K-1)*MM
GO TO 300
56 CONTINUE
300 MABC IS=MABLM2(K)
I F (MAOC IS .LE .5 ) GC TO 50
IF(MAOCIS.GE.2043)GO TO 50
IF{X2SM.GE.XI TEST)GO TO 60
IF(STD SUB(X2LM,AVESETMM)GE.STD SET( X2* N) )GO TO 60
TEST-AVESET+MT*STDSUB(X2LM,AVESET,MM)
IFX2SM.GE.TESTIGO TO 60
MR F = 0
MLL = 0
DO 302 MN1=1,5
I F ( X2 ( MAO CIS MN 1 + 1 ) GE X2 { MABC I S-MN 1 ) ) MLL = MLL- 1
IF(X2(MAQCIS+MN1-1).GE.X2(MABCISEMN1)> MRR=MRR41
302 CONTINUE
IF((MRR + MLL) .GE.8 )GO TO 60
IF(X2DIFF.GE.I 00.AND.( MRR+MLL) .GE.7 ) GO TO 60
GO TO 50
60 CALL PULS E(X2,MA0CIS,S L0PR2SLO PL 2,MR2 ML2,NARRW2)
S L PR 2 ( K) = SLOPR2
SLPL2(K)= SLOPE 2
NUMDR2(K)=MR2
NUMDL2(K)=ML2
NRRJW2(K)=NARRW2
IF(SLPL2(K).LE.0.)GO TO 50
IF(SLPR2(K).GE.0.)GO TO 50
NP=NP+1
MMM(NP)=K
IF(NP.EQ.l) GO TO 50
I F ( ( MA EL M2 ( MMM ( NP ) ) MADLM2 (MMM ( NP 1 ) ) ) ,LF 3 1NP=NP-1
50 CONTINUE
125 FORMAT(2F10.2,5l10)
RETURN
END

nnno
2 1 JUNE 1979
SUBROUTINE HYPERM{DELTA 1 .DELTA? .DELTAJ ,X .Y.Z.Nl N, NX)
** THIS SUBROUTINE USES THE HYPERBOLIC EQUATIONS TO **
** DETERMINE THE THREE-DIMENSIONAL LOCATIONS. **
D I MENS ION DELTAl (128) ,DELTA2( 128) ,DELI A3( 128) ,M(9 ) .
* V(3) X{ 1 28) Y( 128).Z( 123) ,N1N( 128)
RE AL M
DO 62 K=1 .NX
M(7) = < DELTA 1 (NIN(K) )-33.55)* <-3 00.)
M ( 8 ) = ( DELTA2 (N1N(K) )-29.520 )*(-30 0. )
M( S)=(DEL TA3(N1N(K) ) 113.43)*(300)
V( 1)=( 10 3 12.28** 2 M( 7)**2)/2.0
V(2)=(8222.076**2M(8)**2)/2.0
V( 3)-( 8089,20**2 M(9 ) * 2 )/2.0
** THE NEXT PARAMETERS ARE THE COORDINATES OF THE **
** REMOTE STATIONS IN METERS. **
M( 1 )=36 7 7.05
M ( 2) = 816 0.79
M ( 3)=7432.93
M{ 4)=9 634 .44
M( 5)=- 1002.0 1
M(6)=3191 .68
CALL SIMQ(M.V,3.0)
ZSQ=V( 3)* *2(V( 1 ) * 2 +V(2)**2)
X(K)=V (l )
Y(K)=V(2)
IF(ZSQ>63,64,64
64 Z1= 3 Q R T(ZSQ)
Z ( K)=Z l
GO TO 62
68 ZSQ=ZSQ
Z(K)= SOR T(ZSQ )
02 CONTINUE
RETURN
END

n n nnn orn non non non oonono
21 J UN E 1979
153
SUBROUTINE SIMQCA,0,N,KS)
** THIS SUBROUTINE SOLVES SIMULTANEOUS EQUATIONS BY **
4* USING GAUSSIAN ELIMINATION. 44
DIMENS ION All ) E ( 1 )
44 FORWARD SOLUTION 44
T CL 0 0
KS = 0
J J=-N
DO 65 J=1 ,N
J Y = JF 1
J J = JJ + N+l
BIGA= 0
l T = J J J
DO 30 I=J,N
44 SEARCH FOR MAXIMUM COEFFICIENT IN COLUMN 44
I j = I r + i
IFIABSIBIGA)-ABS(A(IJ))) 20,30,30
20 0 IGA = A( I J )
IMAX =I
30 CONTINUE
44 TEST FOR PIVOT LESS THAN TOLERANCE (SINGULAR MATRIX)
IF(ABS(DIGA)-TOL) 35,35,40
35 KS-1
RETURN
44 INTERCHANGE ROWS IF NECESSARY 44
40 I I= J+N4(J-2)
I T = I M A X J
DO GO K=J,N
I I = I I + N
12=11+ IT
SAVE = A( I I )
A( I I )=A( I 2)
A ( 12 ) = SAV E
44 DIVIDE EQUATION BY LEADING COEFFICIENT 44
50 A{ II ) = A( l I)/BIGA
S AVE= B( IMAX )
( I MAX )=U(J)
13 ( J) = SAVE /!3 IGA
+4 ELIMINATE NEXT VARIABLE 4*
1 F ( J N ) 5 5,7 0,55
55 S=N*(J-l>
DO 65 IX= J Y,N
I XJ=IQS + IX
I T = J I X
DO 60 JX=JY,N
I X JX=N4( JX-1 ) FIX
J JX= I X JXF I T
60 A ( IXJX ) = A( I X JX ) 1 A( IXJ ) A( J JX ) )
05 B ( IX) =B( I X) ( 0 ( J ) *A ( IX.J > )
* 4

on
21 JUNE 1979
** BACK SOLUTION **
70 NY-N-1
IT=N*N
DO 80 J=1 N Y
i a=ir-j
I = N J
IC=N
DO 80 K=1 iJ
U( IU)=B(IB)-A< I A )*Ul IC)
I A = I A N
80 IC=IC-1
RETURN
END

2 1 JUNE 19 79
STORM ACTIVITY UN 1QTH JULY 1976
START TIME
= I 6
HOURS 59
MIN 5 9
SEC
008
MIL
FINISH TIME
= 1 7
HOURS 00
MIN 01
5 I. C
00 9
M IL
DIGITIZATION T
l ME
= 3 HOURS
4 6 MIN
25
SEC
5 9 MIL
UNIVERSAL TIME = 16
HOURS 59 MIN
59 SEC
l 0
MIL
343 MICROSEC
IN METERS
Y IN METERS
Z
IN METERS
370.292
11573.102
6925.770
IN METERS
Y IN METERS
Z
IN METERS
TIME IN MICRO SEC
337. 332
11503.008
6830.449
2.068
222.583
1 154 2.4 92
75 12. 641
0.961
328.820
11510.613
66 7 0,266
10.302
370.759
1 16 10.777
80 16.242
22 .289
294.204
10929.129
5781.023
28.033
828.517
13032.410
9006.430
36.07 5
332.326
1 1 93 4.977
7672.242
40.441
268.830
12133.840
7899.730
53.998
170.478
11o50.094
7151.047
57 .675
502.776
1 1264.688
572 3. 504
63.419
358.633
10492.359
596 7.738
76.057
229.142
10562. 19 5
053 7.320
08 .00 6
-56.677
14875.063
11791.336
98. 116
487. 560
l1295.305
5602.904
100.07 3
644.544
10253.074
5 1 13.4 77
103.401
488.974
10967 .37 9
5344.094
109.146
58 8.8 18
12416.773
0445.395
1 14.660
2 7.4 58
12505.129
8631.641
124.081
147.415
12125.922
804 2. 1 1 3
l29.026
231.690
12206.934
7644.430
l34.881
-46.448
11944.910
7964.465
1 42.693
249.756
1 3016.94 l
8542.205
1 47.289
-20 7. 222
1 1C4 9.02 7
5787. 840
159.238
241.063
1 1808.273
7346.617
173.254
424.066
12 489.72 3
8332.617
181.986
205.637
1 1657.006
7006.504
187.500
1341.814
1 2474.340
8217.180
213.006
444.904
10839.1l7
59 7 1.152
2 30 .0 1 0
356.226
11513.992
749 1.148
2 36.6 73
17.986
10783.199
5903.059
2^1 039
307.271
12050.375
01 54. 040
246.784
46 6.636
12313.009
7962.027
259.422
120.853
1 1752.56 3
6788.270
275 .506
302.356
11622.184
7127.852
279.872
223.504
1 184 3.57 4
7223.500
286536
216.027
11504.516
6817.984
292.280
370,720
10712.215
58 0 1.590
298.484
1 9 5. 02 1
11964.461
769 1.543
3 06.986
289.562
11774.191
8 3 1 5. 9 30
3 12. 73 0
195.683
12277.715
7300.680
3 16.40 T
423.099
12027.262
8012.141
3 24 .21 9
G 74.4 08
il266.602
4300.104
327.896
1 124. 6 74
14503.461
12378.633
347.198

APPENDIX D
COMPUTER ALGORITHM TO DISPLAY A
THREE-DIMENSIONAL DRAWING OF VHF NOISE SOUNDS
This appendix contains the computer algorithm we wrote to display
the VHF noise sources in three-dimensions. The input of the algorithm
is the three-dimensional sources stored in digital tape which are pro
duced by the algorithm given in Appendix C. The output of the algorithm
is an isometric view of either the cross-correlated (94 or 376 ysec
intervals) or the individual VHF noise sources. Examples of the output
of this program are shown several times in Chapter V.
356

21 JUNE 1079
C ****************************************** ************>{:
C *
C THIS PROGRAM PLOTS THE THREE-DIMENSIONAL LOCATIONS OF THE *
C VHF NUISE SOURCES. THE INPUT IS A 9-TRACK 1600 3PI TAPE *
C WITH VHF SOURCE LOCATIONS. THE OUTPUT IS AN ISOMETRIC VIFW *
C OF THE COORDINATES OF THE NUISE SOURCES. *
C *
C *********************************************************** ***
C
C
REAL MUX, MUY, MUZ
DI MENS ION XM( loo).YM( 100) ,ZM( 100) ,T1ME{ l2d) ,A( 1S) ,B(15) ,
* C(15) iD( 15), E( 15) ,F( 15),XPM( 100) ,ZPM( 100),YP M( 100),
* XXM( 1 00) ,YXMI 1 00) ,XYM( 100) ,YY MI 1 00 ) ,XMP lOO).YMP(lOO),
* ZMP( l 00 ) YPPMI 100) XPEM 100) YPOI 100) X=>T( 1 00) YPT( 100) ,
* X XT ( 1 00 ) ,YXT( 100) YYT ( 100 ) ,XYT (100) XXB I 100) XYB I 100 ) ,
* YYBI 1 00) ,X YB( 100) YPPBI 1 00) YPPTI 100)
40 RE ADI 1 3, 1 0 ) { ( A( I ) I = 1,8 ) ( B( I ) 1= 1 1 5) ( C I I ) I = l l 5) )
10 FORMAT(33 X,0A4,//21X,L4 A4 ,A3,//20X, 15A4 )
PI=3.141593
KRS=1 0
N = 0
M= 1
NM=0
NN = 8
XSHIFT = l .0
Y S H I F T =2 .0
RX = 2.0
RY=2.0
RZ=2.0
DE GX= 0.0
D E GY = 3 3.0
C
C ** ANGX AND ANGY ARE THE PLANAR PRUJECTIUN ANGLES. **
C
ANGX =D EGX*PI/180.0
ANGY = DEGY*P 1/180.0
DO 29 II M = 1 NN
C
C ** READING TAPE HEADINGS **
C
READ!13, 12) I (A( l ) 1 = 1,5),LHOUR. (OI I) 1 = 1,2) ,LMIN, (CII),
* 1 = 1 2 ), L SEC.R I D ( I ) 1=1 ,2 ) ,LMIL ,( El I ) I = l ,2 ) )
12 FORMAT C11X,4A4,A2, I 4, IX *A4,A 1, 15, IX,A4.A3,
* 14, 1 X ,A4 A3 I 4,1 X ,2 A4 A3 )
READ! 13, 14)( (A{ I ), I= 1,4),LHOUR, (Oil) ,1 = 1,2) ,LMIN ICC I ) .
* 1=1,2) ,LSEC, I DI I), 1 = 1 ,2) .MILST,I El t), 1=l .3 ) ,MICRT, (FI I) ,
* 1=1,3))
14 FORMAT 14 A 4, I3.A4.At, 13,A4,A3.2X,£ 3, 1X.A4.A3,
* I 4,1X,2A4,A3, I 4 i X ,3A4)
DU 2 8 J= 1 5
RE AD (1 3 l 6) I I A ( I ), I = 1,3 ) ( t ( I ) I = l 3 ) I C I 1 ) I = 1,3 ) )
16 FORMAT( 10X.2A4,A3, l OX,2A4, A 3,10X.2A4 ,A3 )
C
C ** READING THE CROSS-CORRELATED LOCATION **
C
READ! 13, 18) X1,Y 1,Z1,ZERO
18 FORMAT(4F20.3>
IF(Xl.EQ.0.0> GO TO 28
IF I IZl .LE.O. ) .OR(Xl .GE.4 000. ) .UR.I V l,GE .400 0 0. ) )
* GO TO 28
N M = NM + 1
XM(NM) =X1/I0 00.0
YMINM)=Y1/I000.0
ZM I NM) = Z1 /I 0 00.0

non nnn
158
21 JUNE 1979
WRITE(6, 10) XM(NM), YM(MM ) .ZM{NM )
RE AD{ 13.2 0) ( (A( I). I=1,3) (0( I) .1 = 1,3 ) (C( I).1 = 1,3),
* (0(1),1 = 1*5))
20 FORMAT(8X,2A4,A3.8X,2A4,A3,8X,2A4,A33X,5A4)
DO 22 1=1,128
** READING ALL THE LOCATIONS **
R E AO( 13, 42) X1,Y l ,Z1,TIME( I )
M X =X 1
IF(MX.EQ.O) GO TO 28
IF(Z1 .LE.O .0 ) GO TO 22
N = N+ 1
22 CONTINUE
GO TO 28
69 READ( 13,42) ZERO ZERO,ZERO,ZERO
28 CONTINUE
29 CONTINUE
42 FORMAT(3E18.3.E26.3)
W R IT E ( 6,5 0 )
50 FORMAT(/////)
NF = 0
DC 3 I=1,NM
NF =NF + l
XMP(NF ) = XM{ I )
Y M P ( NF ) =Y M ( I )
ZMPNF)=ZM( I )
WRITE!6,18) XMP(NF),YMP(NF),ZMP(NF)
3 CONTINUE
WRITE(6,50)
NL=NF
** DETERMINATION OF THE SCALES **
SX=SMALL(XMP,NF)
SY = SMALL( YMP,NF )
SZ=SMALL(ZMP,NF )
BX=0 I G (XMP, NF )
BY=BIG BZ=BIG(ZMP,NF)
IF(SX-O.O) 4,6,5
4 SX=A INT{ SX-1.0)
GO TO 6
5 SX=AINT(SX)
6 IF(SY-0.0) 7,9,8
7 SY=AINT(SY-1.0)
GO TO 9
8 SY=AINT(SY)
9 SZ-AINT1SZ-1 .0)
IF(OX-O.O) 11,15,13
11 0X=AINT(OX)
GO TO 15
13 UX=A INT( D X+ 1.0)
15 I F {11Y-0.0 ) 17,21,19
17 U Y = A I M I ( U Y )
GU TO 21
19 BY =AINT(DY + 1 .0 )
21 B Z =A INK fl Z+l .0)
IF(KRS.EQ.l) SZ = 0.0
XU S=BX SX
YB S=BY-SY
ZBS=BZ-SZ
W RITE( 6,26) DX, SX,BY,SY,UZ,SZ
26 FORMAT(10X,6(El 0.3,5X) )
DO 23 1=1,ML

nnnn non oooo co
559
2 1 JUNE 1979
** SETTING THE VALUES INSIDE THE SCALES **
XMP( I ) =XMP( I )-3X
YMP( I)=YMP(I) -SY
23 2MP( I } -ZMP( I )-SZ
DO 45 1=1,NL
45 WRITE(6*18) XMP( I ) ,YMP( I ) ,ZMP( I)
WRITE!£,50)
PX1=0.0
** PROJECT I UN OF THE SCALE ON THE BASE EARTHS AXES. SETTING **
** UP THE CUTER PERIMETER. **
PX 2= XB S*C 03!ANGX)
PX3=YBS*CS C ANGY)
PX4=PX2+PX3
PY 1 = 0.0
PY2=XOS*5IN(ANGX)
P Y 3= YO S* SIN!ANGY >
PY 4=PY 2+P Y3
PY5=Z0S
PY6=PY5+PY2
PY7=PY5+PY4
PYfl=PY 3+PY5
X l=PX3
Y 1=PY3
X2=PX2
Y2-PY2
** SETTING UP THE GOULD PLOTTER **
CALL PLOTS!15.0,20.0,01*XSHIFT,YSHIFT)
CALL L INE WT(2)
** DRAWING THE THREE-DIMENSIONAL DOX AND DOING ALL *+
** THE PROJECTIONS. **
CALL PLOT(PXl*PY1,3)
CALL PLOT(PX1,PY5,2>
CALL PLOT !PX2,PY6,2 )
CALL PLOT(PX2 ,PY2 ,2)
CALL PLOT(PX1*PY1,2}
CALL PLOT(PX2.PY2,3)
CALL PLOT(PX4,PY4,2
CALL PLOT(PX4,PY7*2)
CALL PLOT(PX2,PY6,2)
CALL PLOT(PXI,PY5,3)
CALL PLOT(PX3,PYa,2)
CALL PLOT(PX4,PY7,2)
CALL PLOT(0.0.0.0,3)
C ALL L INEWT(0 )
SPACE= 0.25
L=Y03/SPACE
L =L/2
DO 25 1= l *L
CALL WHLREXW, YW ,XF YF )
XW=XW-FSPACE*CQS( ANGY >
Y W = Y W + SPACE 5 IN(ANGY)
CALL PLOT(XW,YW,2)
XW = XW+ SPACE*CQS(ANGY)
YW=YW + SPACE* SIN!ANGY)
2 5 CALL PLOT (XW YW 3 )
CALL WHERE!XW,YW ,XF ,YF)
X 5 5= X W
YSS=YW

;(>
2 1 JUNE 1979
L = ZB5/SP ACE
L = L/2
DO 27 1= l ,L
CALL WHERE(XW,YW ,XE,YF)
Y W = Y W + SPACE
CALL PLOT(XW,YW,2)
YW=YW4-SPACE
27 CALL PLOT(XW,YW,3)
CALL PLOT (XSSiYSS>3)
L = Xf3S/5PACE
L=L/2
DO 31 1=1,L
CALL WHERE(XW Y W *XF YF)
XW=XW+SPACE*CS(ANGX)
Y W = Y W+- SPACE* SIN(ANGX}
CALL PLOT(XW,YW,2)
X W =X W -f SP A CE *COS( ANGX )
Y W=Y W+SPACE*SIN(ANGX)
31 CALL PLOT(XW,YW,3)
CALL PLOT (O.0,O.0,3 I
SKIP=3.O
LP = ZBS/SK IP
DO 43 J=1,LP
CALL L INE W T( 2)
CALL PLOT(O.O,SKIP,-3}
CALL PLOT(PX1,PY1 ,3 )
CALL PLOT(PX2.PY2,2)
CALL PLOT (PX4,PY4,2 )
CALL LINTWT(O)
DO 44 1= l ,L
CALL WHEPEIXW,YW ,XF,YF)
X W = X W SPACE*COS(ANGX)
YW = YV-SPACERS INI ANGX)
CALL PLOT(XW,YW ,2)
X W = X WSPA CE *C S (ANGX)
Y W=YW SPA CE SIN(ANGX)
44 CALL PLOT(XW,YW,3)
LL = YDS/SP ACE
LL=LL/2
DO 43 1 = 1 ,LL
CALL WHERE(XW,YW,XF ,YF)
XW=XW-SPACE*COS(ANGY )
YW=YW-SPACE*SIN(ANGY)
CALL PLOT(XW,YW,2)
XW=XW-SPACE*COS(ANGY)
YW=YW-SPACE*SIN(ANGY)
43 CALL PLOT (XW,YW,3 )
CALL PLOT (0, 0,0,0,3)
POS=FLOAT(LP)*SKIP
CALL PLOT(0.0,POS,-3)
CALL L INF WT(-2)
ZE = ZDS/2.0
CALL SYMOOL(-0.25,70.0. 15, ALT I TUDE (KM) ,90.0, 13,0. 15, 1 )
NT ICK = Z0 S +1
DO 38 I = l ,N T IC K
XN--0.1
YN = FLOAT( I- 1 )
VAL=SZ+YN
CALL N UM 8 E R (XN.YN.O.1 ,VAL,0.0,-1 ,0.1 ,1 )
CALL SYMBOL ( 0.0 YN 0.1 15, 0. 0, l 0. 1 ,'l )
30 CONTINUE
XOX= X8S*COS(ANGX)/2.OTO.4*SI N( ANGX)
XOY=XBS*S IN ( ANGX )/2 .0-0.4*C0S( ANGX)
CALL SYMBOL(XOX,XBY,0.15,"EAST (KM),DEGX,9,0.15,l)
NT ICK= XBStI

361
21 JUNE! 1979
DO 39 1 = 1 ,NT ICK
X N=FLO AT( I-l )*COS(ANGX)+0.2*SIN(ANGX )
Y N = FL O AT ( 1-1 )*5IN(ANGX)-0.2*COS(ANGX)
VAL=SX +FL0AT( I 1 )
CALL NUMQER(XN,YN,0.1 ,VAL DE GX,-l ,0.1.1 )
XN = FLOAT( I-l HCOS( ANGX)
YN=f-LOAT( I-l ) *SI N( ANGX )
THETA = 9 0.0+-DEGX
CALL SYMBOL{XN,YN,0.1,15,THETA,-l,0.1,1)
39 CONTINUE
CALL PLOT(0.0,0.0,3)
CALL PLOT YX=YB£*COS( ANGY ) /?. 0+ 0.4 S I N ( A NG Y )
YEY=Y8S*3 IN( ANGY )/2.0-0.4*CUS( ANGY)
CALL SYMBOL!YBX,YGY,0.15,NORTH (KM) ,DEGY. 10,0 .I 5, l)
NTI CK= YD S +1
DC 4 1 1-1 NT t CK
XN=FLOAT( l -1 )*COS{ANGY) +0.2 *51N(ANGY)
Y N = FL 0 AT ( I-l ) S 1N ( ANGY ) 0 2 £CU S ( A NGY )
Y AL~SY fFLAT ( I-t )
CALL NUMBER! XN.YN.O.i ,VAL,DEGY,-l ,0.1,1 )
XN=FLOAT!I-l)*COS(ANGY)
YN=FLOAT ( I-l ) S I N ( AN GY }
THETA=90.O+DEGY
CALL SYMBOL(XN,YN,0.1, I 5,THETA,-l ,0.1, 1 )
41 CONTINUE
CALL PLOT(0.0,0.0,3)
CALL PLOT (X2,Y23)
CALL TRNSFM!XMP,YMP,ZMP,ML,XXM,YXM.XYM,YYM,XPM,YPM,
YPPM,ANGX,ANGY)
DS-(Y2Yl)/{X2-X1)
WR ITE( 6,50)
N 1 =0
N2 = 0
DO 35 1 = 1 ,NL
D5S=YPM( I )/XPM ( I )
XINT=(DS*X1Yl)/(DS-DSS)
IF(XINT.LT.XPM(I)) GO TO 36
N 1 =N1 + 1
XPDN1 )= X P M( I)
YPH(Ml ) = YPM( I >
Y Y E(N1 )=YYM( I)
X YB(N1 ) = X YM{ I )+XBS
X X E ( N 1 ) = XXM( I )
Y X 0{Nl )=YXM( I )
YPPB(N l )=YPPM( I )
GO TU 35
36 N2=N2+ 1
XPT(N2 ) = XPM( I )
YPT(N2)=YPM(I)+ZSS
YYT( N2 ) YYM( I ) + ZBS
X Y T(N2 ) = XYM( I )
X X T(N2 )=X XM( I )
Y X T(N2) = Y X M( I ) FZOG
YPPT(N2)=YPPM(l)
3 5 C CN rI NUL
DO 33 1=1,Ml
WRITE( 6,4 7) XPIH I ) YPE3 ( D.YYOl I ) XYO ( I ) X X13 ( I ) YXO! I )
3 3 CONTINUE
W n IT E (6,50)
DO 37 1=1, N2
WR ITF ( 6,4 7) XPT( I ) YPT! I ) YYT ( I ) X Y T ( I ) X X T ( I ) YX T ( I )
37 CONTINUE
WRIT r. (6,50)
DO 46 1=1,NL

n n n n n nn
21 J UN E 1979
4 6 WR ITC( 6,4 7 ) XXM ( I) YXM ( I ),XYM( I),YYM(I ) ,XPM{I) YPM(I)
* YPPM(I)
** GETTING THE SCALES LUWER POUND *
47 FORMAT(7F15.7)
XPE(N1f1)=0.0
XPD(Ml+2)=1.0
YPPBIN t + 1 ) = 0.0
YPPU( N l -2 )= 1 .0
XP T(N2 + 1 ) =0.0
XPT Y P PT(N 2+1 )=0.0
YPPT(N 2 + 2 )=1.0
XPE ( N1 + 1 )=0.0
X P Q(Nl+2) =1.0
YPQ( N 1 M ) =0. 0
YPE(Nl*2)=1.0
XP T(N2 + 1 )=0.0
XPTN2 +2)=1 .0
YPT(N2+1)=0.0
YPT CALL LINEWT(-2)
PROJECTING THE SOURCE LOCATIONS EITHER ON THE TUP *
** PLANE(Nl) OR ON THE BOTTOM PLANEIN2). **
C ALL LIME(XPB YPPUN1,1.-1.2,0.1)
CALL L INE(XPT,YPPT,N2, 1 ,-l .2,0 1 )
CALL LINE WTI-1 )
CALL L INE(XPC.YPB,N1 t, 1 10,0.1)
CALL LINE(XPT,YPT,N2,1 .- l 10.0.1 )
CALL L INF WT( 1 )
DU 24 1=1,Nl
CALL PLOT(XPBII),YPD(1).3)
CALL PLOTIXPBI I) ,YPPB( I ) ,2)
24 CONTINUE
DO 32 1=1,N2
CALL PLOT (XPT( I ) ,YPT( I ) ,3)
CALL PLOT (XPT ( I ) ,YPPTI I ) ,2 )
32 CONTINUE
DO 30 1=1 N1
CALL PLOT(XX(I),YXO(I),3)
CALL PLOT(XPB( I ) ,YPO( l) ,2)
CALL PLOT (XYI3 ( 1 ) YYB( I ) 2)
30 CONTINUE
DO 34 1=1,N2
CALL PLOT(XXT(I),YXT(I),3)
CALL PLOT(XPT( I ) YPT< I) ,2 )
CALL PLOT(XYT(I),YYT(I),2)
34 CONTINUE
CALL PLOT(0.0.0.0,999)
STOP

OnO
21 JUNE 1979
63
SUBROUTINE TRNSFMfX ,Y,Z.NtXX.YX.XY,YY,XP,YP,YPP,AX.AY )
** THIS SUBROUTINE IS USED FOP. COORDINATE TRANSFORMATION.
D I WENS ION X( 100) Y{ 100) Z ( 1 00) XX (, 100) YX ( 1 00 ) ,XY ( 100 )
* Y Y(100 ) iXP(100 ) > YP( 100),YPP( 100)
DC 1 I =1 N
XX ( I )-X( I )*C05(AX)
YX(I)=X(I)*SIN(AX)
X Y( 1 ) = V ( I ) *CCS( A Y )
YY(I)=Y( I ) S IN { A Y )
XP (I) = XX( I )+XY( [ )
YP< I ) = Y Y ( I ) + YX { I )
YPP( I >=YP ( I ) +Z( I )
1 CONTINUE
RETURN
END
**

APPENDIX E
FREQUENCY DOMAIN APPROACH TO
DETERMINE DIFFERENCE IN THE TIME OF ARRIVAL
There are several techniques to measure time delays in either the
frequency or the time domain. Chapter IV describes the theoretical
basics of our time domain technique. This technique is implemented
using the algorithm in Appendix C. For the work in this thesis we did
not select a frequency domain technique for reasons discussed in this
appendix. We investigated some of the frequency domain techniques
using Fast Fourier Transforms (FFT). The two most effective frequency
domain techniques consist of measuring time delays by determining either
the properties of the magnitude of the phase of the transfer function
between the input and the output (can be interpreted as central and
remote stations). However, for the data under study neither of these
techniques was appropriate because every pulse within a selected
interval in the time series had a different time delay with respect to
each consecutive pulse. To yield good results in a frequency domain
we had to isolate the frequency content of identifiable VHF pulses
which normally have a pulse width between one and five microseconds.
After some preliminary test results we decided that the use of any
frequency domain algorithm to systematically determine time delays
required more computations and made it more difficult to understand the
results than the use of any time domain technique. We will briefly
summarize those frequency domain techniques that we investigated. Both
364

¡65
of these techniques make use of the two point measurement problem (see
Figure E.i).
Let x and y represent the discrete time series at the central
n n
(x ) and either of the three remote stations (y ).
n y n
Figure E.l. The two point measurement problem.
y = x h 4- r
a n n n
(E.l)
where is the convolution operator, h^ is the transmission path, and
r is random noise. The transmission path in this case does not
n
represent,a physical transmission path but a conceptual one which is
introduced with the purpose of illustrating a number of digital tech
niques. Now we can proceed to determine the time difference between
identifiable pulses in x and y Once this time has been determined,
n il
the procedure is repeated for the remaining two remote stations.

366
E.1. Measurement of Time Delay by Determining the Peak of the Impulse
Function
This method has been explored by Roth (1970), and consists of
finding the time pulse response of the transfer function between and
y based on
*
G = S S
xy x y
(E.2)
G
xx
*
S S
X X
(E.3)
S = HS + R
y X II
(E.4)
~k
G = (HS + R ) (S ) = HS S + R S
xy x nx xx nx
(E.5)
where S is the Fourier Transform of x S is the Fourier Transform of
x n y
y G is the cross-spectrum density between x and y G is the
xy n 'n xx
auto-spectrum of x the upper index is the complex conjugate operator,
and equations (E.2) through (E.5) represent the two point measuring
problem illustrated in Figure E.l. Assuming that the system is linear
and averaging the cross and auto-spectrum obtained from different
ensembles in the same series, we can express the impulse transfer func
tion as
h
n
F_1(Gxy(w)/Gxx())
(E.6)
where F is the inverse Fourier transform operator.
The averaging process eliminates the contributions of NS^, and it
improves the estimate of h Therefore h should be an impulse function
n n .
at n = a or h ^ = 6(n-a). Several investigators, Roth (1970), Enochson
(1973), French (1971), Dummermuth (1967) have implemented this procedure

167
obtaining satisfactory results. Also looking at the number of computa
tions involved, there are fewer computations in this technique than in
other frequency techniques such as the phase measurement which will be
described in the next section.
E.2. Measurement of Time Delay by Measuring the Phase of the Frequency
Response Function
We can estimate the time difference by measuring the phase of the
frequency response function. Since and y^ can be approximated by a
linear system, we have
00
y l Vn-k R=-
where h^ is the impulse response between and y Using the two point
measuring problem, we get
n
= x
, + r
-A n
(E.8)
Y (f) = exp (-j 2irf A)X (f) + R(f) (E.9)
averaging different ensembles, dividing, and calculating the phase, we
obtain
Y(f)/X(f) = H (f) = Phase (2tt A) (E.10)
xy
Therefore the time delay A is determined as
A = 2irf A/2fir (E.ll)
The question still remains as to what frequency to use in the compu
tation of (E.ll). This can be solved by using the frequency that

'68
maximizes the coherence
tion is defined as
function between x and y .
n n
The coherence func-
2
Y = IG I /G G where 0 < y < 1
xy xy1 xx yy xy
(E.12)
Either by determining the time lag at which the peak of the impulse
function occurs or by determining the time delay of the phase in the
frequency response, we are limited to the data sample size. In the
impulse function, a time delay is determined between two selected inter
vals in x^ and y whereas in the phase frequency response, we can
select different intervals of y to maximize the coherence function. In
n
either case we need to determine the proper sample size to use to obtain
correct results. If a sample size in the neighborhood of 5 ysec width
is used, then we have to ensure that at least one entire pulse is within
the selected interval for all the stations. On the other hand, if a
sample size of several hundred microseconds is used, then we only get one
cross-correlated location.

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174
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BIOGRAPHICAL SKETCH
Pedro Luis Rustan, Jr., was born in Guantanamo, Cuba, in 1947. He
graduated first in his class from the Guantanamo High School in 1964.
He received the degree of Bachelor of Science in Electrical Engineering
in December 1969, and the degree of Master of Science in Electrical
Engineering in December 1970, both from the Illinois Institute of
Technology. In 1971 he became a United States citizen and entered
active service with the United States Air Force. From 1971 to 1976 he
worked in the areas of electromagnetic radiation, and guidance and
control. In June 1976, he was selected to attend the University of
Florida and work toward a degree of Doctor of Philosophy. He is presently
a captain in the Air Force, working as an instructor at the Air Force
Institute of Technology.
He is a member of Tau Beta Pi, Eta Kappa Nu, the Institute of
Electrical and Electronics Engineers and the American Geophysical Union.
He is married to the former Alexandra Cary, from Lake Bluff, Illinois,
and has a son, Peter Cary.
376

I certify that I have read this study and that in my opinion it
conforms to acceptable standards of scholarly presentation and is fully
adequate, in scope and quality, as a dissertation for the degree of
Doctor of Philosophy.
' ? / /
rns~u
Martin A. Uman, Chairman
Professor of
Electrical Engineering
I certify that I have read this study and that in my opinion it
conforms to acceptable standards of scholarly presentation and is fully
adequate, in scope and quality, as a dissertation for the degree of
Doctor of Philosophy.
Am
Donald G. Childers, Co-Chairman
Professor of
Electrical Engineering
I certify that I have read this study and that in my opinion it
conforms to acceptable standards of scholarly presentation and is fully
adequate, in scope and quality, as a dissertation for the degree of
Doctor of Philosophy.
Thomas E. Bullock
Professor of
Electrical Engineering
{
r.
I certify that I have read this study and that in my opinion it
conforms to acceptable standards of scholarly presentation''and is fully
adequate, in scope and quality, as a dissertation for-'the'-degree of
Doctor of Philosophy. ^ C-"
y'C
Michael E. Warden
Assistant Professor of
Electrical Engineering
1 certify that I have read this study and that in my opinion it
conforms to acceptable standards of scholarly presentation and is fully
adequate, in scope and quality, as a dissertation for the degree of
Doctor of Philosophy.
Jarnos T. McClave
Associate Professor of Statistics

This dissertation was submitted to the Graduate Faculty of the
College of Engineering and to the Graduate Council, and was accepted as
partial fulfillment of the requirements for the degree of Doctor of
Philosophy.
December 1979
Dean, Graduate School

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L = ZB5/SP ACE
L = L/2
DO 27 1= l ,L
CALL WHERE(XW,YW ,XE,YF)
Y W = Y W + SPACE
CALL PLOT(XW,YW,2)
YW=YW4-SPACE
27 CALL PLOT(XW,YW,3)
CALL PLOT (XSSiYSS>3)
L = Xf3S/5PACE
L=L/2
DO 31 1=1,L
CALL WHERE(XW Y W *XF YF)
XW=XW+SPACE*CS(ANGX)
Y W = Y W+- SPACE* SIN(ANGX}
CALL PLOT(XW,YW,2)
X W =X W -f SP A CE *COS( ANGX )
Y W=Y W+SPACE*SIN(ANGX)
31 CALL PLOT(XW,YW,3)
CALL PLOT (O.0,O.0,3 I
SKIP=3.O
LP = ZBS/SK IP
DO 43 J=1,LP
CALL L INE W T( 2)
CALL PLOT(O.O,SKIP,-3}
CALL PLOT(PX1,PY1 ,3 )
CALL PLOT(PX2.PY2,2)
CALL PLOT (PX4,PY4,2 )
CALL LINTWT(O)
DO 44 1= l ,L
CALL WHEPEIXW,YW ,XF,YF)
X W = X W SPACE*COS(ANGX)
YW = YV-SPACERS INI ANGX)
CALL PLOT(XW,YW ,2)
X W = X WSPA CE *C S (ANGX)
Y W=YW SPA CE SIN(ANGX)
44 CALL PLOT(XW,YW,3)
LL = YDS/SP ACE
LL=LL/2
DO 43 1 = 1 ,LL
CALL WHERE(XW,YW,XF ,YF)
XW=XW-SPACE*COS(ANGY )
YW=YW-SPACE*SIN(ANGY)
CALL PLOT(XW,YW,2)
XW=XW-SPACE*COS(ANGY)
YW=YW-SPACE*SIN(ANGY)
43 CALL PLOT (XW,YW,3 )
CALL PLOT (0, 0,0,0,3)
POS=FLOAT(LP)*SKIP
CALL PLOT(0.0,POS,-3)
CALL L INF WT(-2)
ZE = ZDS/2.0
CALL SYMOOL(-0.25,70.0. 15, ALT I TUDE (KM) ,90.0, 13,0. 15, 1 )
NT ICK = Z0 S +1
DO 38 I = l ,N T IC K
XN--0.1
YN = FLOAT( I- 1 )
VAL=SZ+YN
CALL N UM 8 E R (XN.YN.O.1 ,VAL,0.0,-1 ,0.1 ,1 )
CALL SYMBOL ( 0.0 YN 0.1 15, 0. 0, l 0. 1 ,'l )
30 CONTINUE
XOX= X8S*COS(ANGX)/2.OTO.4*SI N( ANGX)
XOY=XBS*S IN ( ANGX )/2 .0-0.4*C0S( ANGX)
CALL SYMBOL(XOX,XBY,0.15,"EAST (KM),DEGX,9,0.15,l)
NT ICK= XBStI


DART LEADER
-H
100
200
300 400 500
TIME IN MICROSECONDS
600
700
800
900
Figure 5.54. Logarithmic-amplitude VHF radiation during the dart leader that
preceded the fourth return stroke.
202


304
J-process were preceded and followed by continuous VHF radiation and we
chose to consider them as an integral part of the J-process.
Solitary pulses and K-changes were observed after the last return
stroke of the CG flashes. One SP after the last return stroke in Sec
tion 5.1 propagated upwards about 5 km, but most of the SP's and
K-changes in the other three CG flashes propagated downwards as shown
in Figure 5.76. The VHF noise sources in one of the K-changes shown in
Figure 5.37 followed a path similar to that suggested by Kitagawa arid
Kobayashi (1958). That is, a downward propagation path followed by an upward
moving path, except that the velocities of the downward path were much
larger than those suggested by Kitagawa.
7.1.8 Continuing Current
We studied only one. continuing current interval which occurred
after the last return stroke of the flash reported in Section 5.3. Next
we summarize our findings about this continuing current.
The continuing current interval lasted 223 msec in the VHF record.
On the basis of the VHF radiation and its source locations, we divided
the continuing current in two intervals: (a) continuous VHF radiation,
and (b) discrete VHF radiation. The continuous and the discrete VHF
radiation lasted 85 and 138 msec, respectively. The VHF noise during
the continuous portion of the continuing current interval has the same
characteristics as the J-change. The discrete portion has similar
characteristics to the VHF radiation at the end of two other CG flashes
and all other IC flashes. That is, isolated SP's with durations between
1 and 11.5 msec separated by about 10 msec.
During the initial 23 msec the VHF noise sources formed a 14 km
channel parallel to the previous J-changes (Figure 5.59). During the


10
either positive descending streamers, negative ascending streamers, or a
combination of both of these processes. The work in intracloud discharges
presented in this thesis will provide the VHF noise source locations in
three-dimensional space and in time. These findings should provide
additional information to help understand the mechanisms of the intra
cloud discharge.
2.2 Description of Electromagnetic Radiation Emitted by Intracloud
and Cloud-to-Ground Flashes
The most recent comprehensive study of the electromagnetic radia
tion produced by lightning discharges is given by Pierce (1977).
Briefly, this section presents a review of the radiation fields due to
the intracloud and cloud-to-ground flashes over the frequency range
from 1 KHz to 1 GHz.
One means of learning about discharge processes associated with
cloud-to-ground and intracloud lightning discharges is by measuring
the resultant electromagnetic radiation. Numerous investigators
(e.g., Malan, 1958; Brook and Kitagawa, 1964; Takagi and Takeuti, 1963;
Pierce, 1960; Kimpara, 1965; Uman, 1969; Proctor, 1971; Takagi, 1975;
Krider et al., 1977, 1979; Taylor, 1978; LeVine and Krider, 1977;
Serhan et al., 1979) have studied the electromagnetic radiation of
lightning in various frequency ranges with the purpose of deriving some
conclusions about the lightning discharge.
The electric field due to a small straight vertical conducting
element above a conducting plane can be calculated exactly at any distance.
These results are found in Uman and McLain (1970), and McLain and Uman
(1971).


NORTH (km)
Figure 5.44. Two-dimensional views: (a) NS-EW, (b) EW-height, and (c) NS-height of all the sources
(triangles) and the cross-correlated source locations (squares) during the PB and the first
stepped leader. The five circles represent the location of the cross-correlated noise
sources during the first return stroke. The circle Q1 is the two-dimensional projection of
Q1 in Figure 5.43.


150
away to the NE and SW sides, respectively, in Figure 5.32. The next
three VHF pulses (C, D, and E) were also located in the outer region.
We continued this analysis throughout the entire J2 process to determine
whether the VHF noise sources were grouped along any specific pattern
when the third stepped leader developed. The main result of this
analysis was that as the J2 process progressed the VHF sources formed
along the outside of a cylinder, but near the end of the process the J2
sources filled most of the internal regions of this cylinder. The third
stepped leader developed from Q (4.9, 11.2, 6.8) in Figure 5.32, which
is located inside the cylinder.
5.2.9 Third stepped leader
Figure 5.33(a) and Figure 5.33(b) show the cross-correlated and all
the individual noise sources, respectively, during the third stepped
leader. Figure 5.34 shows two-dimensional projections of the cross-
correlated (squares), and all the detectable sources (triangles). Both
first and third stepped leaders propagated downwards about 4 km and
horizontally about 3.5 km in the first 5.5 msec. The channel of the
respective VHF sources remained at least 1 km apart. The third stepped
leader lasted 15.5 msec and propagated from a region inside the J2
process source volume. The VHF source for the stepped leader propagated
off the Atlantic coast in the north-northeast direction about 10 km,
descending from 6.8 km to a height of 0.7 1cm. The stepped leader veloc
ity ranged between 7.6 x 10* m/sec and 1.1 x 10^ m/sec.
It is significant to note that the three stepped leaders propagated
from a common volume that can be approximated as a sphere with a 1 km
radius. It appears that the location of the charge volume is not the
principal factor determining whether subsequent return strokes will be


The five return stroke cross-correlated noise sources, 94 ysec
intervals, are shown as circles in Figure 5.26. The noise sources during
the return stroke occurred in ascending order between a height of 0.8
and 4.5 km at a velocity of 1.2 x 10^ m/sec. This return stroke veloc
ity, calculated by determining the cross-correlated VHF noise source
locations at the beginning and at the end of the return stroke and
dividing by the duration of the VHF record, can have large errors. These
errors are caused by two main factors: (1) In a 94 ysec interval the return
stroke upward propagating wave will extend several kilometers and a cross
correlation location might not be a true representation of the source.
(2) It appears that the return stroke VHF radiation is only obtained by
extensions of the previously ionized stepped leader channels, and there
fore return stroke source locations may not be a true representation of
the actual extent of the return stroke channel.
Krehbiel (private com), using the method of Krehbiel et al. (1979),
calculated that -21.1 Coul were lowered by the first return stroke from
a charge center located at Q1 (6.2, 11.1, 4.4). Figures 5.24 and 5.26
show the location of the return stroke charge source. Assuming s source
location at point B (this is the source location for the transition
between P3 and stepped leader in the VHF noise) and using the technique
described in Section 3.6, we calculated that -13.4 Coul were lowered by
the leader-return stroke process. The difference between our assumed
charge calculation source location at B (5.1, 11.7, 6.1) and Krehbiel's
calculated first return stroke charge is significant. However, Krehbiel
(private com) has indicated large uncertainty in the determination of
the locations of Ql.


90
stepped leader. In the IC flash, however, the VHF noise level remains
large and it has additional low frequency pulses. These features can
be seen in Figure 7.1. The observation that the two types of flashes
can be identified early supports the work of Kitagawa and Brook (1960),
who studied the characteristics of the electric field during CG and IC
flashes, and claimed that from the initial electric field pulse rate the
two types of discharges could be uniquely identified. Proctor (1976)
and Hewitt (1962) working at 253 MHz and 600 MHz, respectively, claim
that they could not differentiate between CG and IC flashes from their
noise records. From observing the electric field record, we know that
the presence of a stepped leader-return stroke sequence differentiates
CG flashes from IC flashes, but the return strokes do not occur in our
records until about 5 to 12 msec. The characteristics of the VHF radia
tion reported here are evident at the beginning of the discharge, that
is, during the formation of the VHF sources for the PB-stepped leader
process. Next we look at the characteristics of the different phases of
the CG and the IC flashes.
7.1 Cloud-to-Ground Lightning
The VHF noise, the VHF source locations, and the correlated electric
field records of eight basically different processes were studied in
this thesis. These eight processes are: (1) preliminary breakdown
(PB) (2) stepped leader (SL), (3) dart leader (DL), (4) return stroke
(RS), (5) activity following the first return stroke (FR), (6) J-change
processes, (7) solitary pulses (SP) and K-changes, and (8) continuing
current.


286
6.4 Characteristics of VHF Radiation
The VHF radiation pulse model presented in this chapter provides
fairly consistent results for the three selected processes in four
different flashes. The basic conclusion of this analysis is that the
properties of the sources underlying the physical process are very
common from flash to flash. Even though the process is not determinis
tic, we can predict that any future value of the output will fall between
any specified limits. In addition, the consistency of the results
allows us to characterize the VHF radiation for the different phases of
the lightning discharge, without need of other measurements, e.g.,
electric field from a study of the variations of the poles and the
zeros for the different phases of lightning flashes we can determine
properties of the pulse shape emanated by the VHF source.


27
every 2 msec.. In practical applications reasonable locations are only
obtained every 5 or 10 msec. In addition, using only amplitude thresholds
the LDAR system can match the wrong pulses and pass the redundancy
test. Let us illustrate this problem with an example. Assume that
there are two active VHF regions emitting radiation of the same magnitude,
and these regions are located at any height and are a few kilometers on
the opposite side of the central station. Pulses, received from the A
and B regions in an interval of a few tens of microseconds, will be
tested simultaneously in the Biomation. The pulse from A will be larger
in the station closer to A, whereas the pulse from B will be larger in the
station closer to B. Regardless of redundancy, there will be a consistent
matching of pulses from A and B and meaningless results will be obtained.
The work described in this dissertation used some of the components
of the LDAR system. These components were the sensors and the telemetry
for the four stations. Instead of the Biomations, we recorded the
4-station (3 remotes and 1 central) VHF data on analog tape. The VHF
noise from the analog tape was later digitized and processed to recon
struct the lightning VHF sources. By using a computer implemented algo
rithm to process the data and display the output, our technique can pro
vide source locations every 5 or 10 ysec. For any given flash we determine
about 500 locations for every location of the original LDAR system. This
abundant information permits us to study the lightning channels inside
a thundercloud, not visible to any type of photography. Our computerized
data processing provides tens of thousands of locations per flash after
two hours of computer processing, thus far surpassing the by-hand
technique used by Proctor (1976), which can determine about 1000 locations


69 !


Figure 5.10. Cross-correlated VHF noise sources, 376 ysec
intervals, during the first J-change. Parts A
and B represent the beginning and the end of the
J-change region, respectively. The arrows indi
cate the direction of propagation of groups of
sources which occurred in bursts. During the
dart leader following the J-change, a 4 km near
horizontal channel joint B with C (shown as
circles), a region near the previous leader
channel. Also shown as a continuous line in the
neighborhood of Q1 is the upper part of the pre
liminary breakdown which preceded the first
return stroke. Both first and second stroke
charge volumes are shown.


Figure 5.70(A).
Three-dimensional view of the cross-
correlated noise sources during the J3
process that preceded the fifth stepped
leader. The labels M and N represent
the beginning and the end of J3 while P
indicates a region in the neighborhood
of the fourth stepped leader that radiates
again or continues to radiate.
Figure 5.70(B). Three-dimensional view of the cross-
correlated noise sources during the fifth
stepped leader. The sources N and R
indicate the region at the end of J3 and
the last detectable cross-correlated
location, respectively.


147
of the previous stepped leader channel. Figure 5.30 shows the three
return stroke sources (circles).
Assuming point A in Figure 5.29 and Figure 5.30 as the point charge
for the second leader-return stroke and using the technique described in
Section 3.6, we determined that -11.5 Coul were lowered by the leader-
return stroke process. A charge value and location for the second or the
third return stroke using the technique of Krehbiel et al. (1979) was
not available for comparison of our results because the electric field
records at some of the stations were saturated.
5.2.8 Second J-Change (J2)
Figure 5.32 shows the VHF noise sources, 94 ysec intervals, during
the second J-change. The J2 VHF noise lasted 31.2 msec of which the
first 12.4 msec are shown in Figure 5.31 along with the VHF of the
previous stepped leader and return stroke. The J2 noise sources extended
about 5.3 km in a path 45 off-vertical. The location of the J2 process
was nearly coincident with the previous J1 process, but the J2 process
extended an additional 2 km in a northerly direction and was located
about .6 km higher than Jl. In addition, the J2 noise sources were more
spread out than Jl.
We studied the progressing sequence of the VHF noise pulses and
their source locations during the J2 interval with the purpose of improv
ing our understanding of the properties of this process. The first six
VHF pulses are labeled alphabetically A to E in Figure 5.31. The source
locations, 94 ysec intervals, for each of these pulses are also labeled
in a regular progressing sequence. The process started with pulse A
which generated locations Al to A5, followed by pulse B that generated
locations B1 to B7. The first two pulses, A and B, were located furthest


the F region extended between a height of 5.6 and 12.8 km while the
sources in the G region extended between a height of 5.2 and 9.9 km.
The J4 noise sources did not follow a regular progressing sequence.
We studied the VHF radiation at the central and the remote stations
whenever there was a shift in source locations between the F and G
regions. The purpose of this study was to determine whether there was
propagation between these regions or whether sources were active simul
taneously. Figure 5.72 shows the VHF radiation at the central (a) and
one of the remote stations during a transition from F to G. We have
displayed the graph such that pulse 1 which corresponded to the F region
is lined up in both stations. Some of the subsequent pulses (e.g., 2
through 7) shown in Figure 5.72 were located in the neighborhood of G
and the DTOA in these pulses is less than 2 ysec. When we account for
the absolute difference in the time of occurrence of 1 and 2 in stations,
it was clear that a source in F producing pulse 1 cannot propagate to
G to produce pulse 2 at a speed less :than the speed of light. There
fore, the F and G regions are independent. Even though an argument
could not be invoked for the source regions of the third and fourth
stepped leaders previously described, it provides an example of a pro
cess in which two different return strokes could occur almost simultane
ously.
I
A dart leader characteristic was evident from the VLF and VHF |
record after the J4 process. As shown in this thesis, the dart leader
does not radiate in its path to ground along the previous return stroke
channel. The noise sources just prior to the 'dart leader, the dart
leader, and the return strokes were located in the G region. Figure
5.71 shows six cross-correlated noise sources during the dart leader


Figure 2.1. Radiation field of a small current element.


50
b) Navigation (Aircraft, Missile, Vessel). Time delays are widely
used in the field of aircraft and missile navigation to deter
mine a location update (Holmes and Reedy, 1951). The LORAN
worldwide system presently used for civilian and military air
craft navigation update is based on the measurement of time
delay between signals at known positions to determine the air
craft position (Pitman, 1962).
c.) Seismic signal processing for oil and gas (Wood and Treitel,
1975). Time differences between reflected seismic signals map
structural deformation and provide the locations of oil and
natural gas layers.
d) Ground response to earthquake conditions (Enochson, 1973).
The time difference at two separate ground locations is used
to determine the transit time of particle velocity waves
through soil when activated with earthquake loading conditions.
e) Digital signal processing. Measurement of time delays between
a stimulus and a response to a system or between two time series
has wide applications in the field of communication (Roth, 1971).
f) Determination of lightning channels. Oetzel and Pierce (1969)
proposed the determination of lightning channels by measuring
the time delays between four stations. A similar technique
was independently implemented in South Africa in 1968 and
described by Proctor (1971). In the USA a real-time system was
developed by Lennon (1975) .
4.2 Data Characteristics
In order to find a systematic technique for measuring the difference
in the time of arrival between four data channels, it is necessary to study


OnO
21 JUNE 1979
63
SUBROUTINE TRNSFMfX ,Y,Z.NtXX.YX.XY,YY,XP,YP,YPP,AX.AY )
** THIS SUBROUTINE IS USED FOP. COORDINATE TRANSFORMATION.
D I WENS ION X( 100) Y{ 100) Z ( 1 00) XX (, 100) YX ( 1 00 ) ,XY ( 100 )
* Y Y(100 ) iXP(100 ) > YP( 100),YPP( 100)
DC 1 I =1 N
XX ( I )-X( I )*C05(AX)
YX(I)=X(I)*SIN(AX)
X Y( 1 ) = V ( I ) *CCS( A Y )
YY(I)=Y( I ) S IN { A Y )
XP (I) = XX( I )+XY( [ )
YP< I ) = Y Y ( I ) + YX { I )
YPP( I >=YP ( I ) +Z( I )
1 CONTINUE
RETURN
END
**


Figure 5.62. Sequence of photographs during the 182356 flash. The Julian date (220) and the time is shown
in each photo. Sequences a, b, c, d, f, and h show the six different stepped leader-return
stroke channels to ground. This photo is a courtesy of Douglas Jordan of the University of
Florida.


Page
4.2 Data Characteristics ....... 50
4.3 Technique for Determining Delays Based on the
Data Characteristics 55
4.4 Algorithm Flow Chart 62
4.5 Display of Three-Dimensional Locations and
Their Time of Occurrence 68
VANALYSIS OF RESULTS 72
5.1 The 165959 Flash 73
5.2 The 180710 Flash 123
5.3 The 181806 Flash 166
5.4 The 182356 Flash 220
5.5 The 180644 Flash 264
5.6 The 181416 Flash 27 3
VIDATA MODEL 281
6.1 Noise Level 284
6.2 Stepped Leader 284
6.3 J-Change 285
6.4 Characteristics of VHF Radiation 286
VIICHARACTERISTICS OF THE VHF RADIATION DURING THE
DIFFERENT PHASES OF LIGHTNING 287
7.1 Cloud-to-Ground Lightning 290
7.2 Intracloud Lightning 305
VIIICONCLUDING COMMENTS AND SUGGESTIONS FOR FUTURE
RESEARCH 309
APPENDIX
A DERIVATION OF SOURCE LOCATION FROM DIFFERENCE
OF TIME OF ARRIVAL MEASUREMENTS 311
B ACCURACY OF THE LOCATION OF LIGHTNING SOURCES
USING THE HYPERBOLIC EQUATIONS 315
xv


506
the channel was performed by doing histograms of the number of sources
along the channel at different heights for selected time intervals.
The histograms for one of these flashes are shown in Figure 5.21.
Proctor (1976) also observed this type of behavior at the beginning of
a cloud flash. That is, the development of the path was composed of
small sections which did not join to form a sequential continuous
channel. Four of the five flashes studied by Proctor showed a near
horizontal path. Two of the three 1C flashes studied in this thesis
showed a path of 45 and 30 off vertical and the third flash had a
vertical path. On the basis of the electric field reversal with dis
tance and the fact that most of the sources propagated upward during the
initial phase as determined from the histograms, we claim that for the
IC flashes in Sections 5.1.13 and 5.5, negative charges propagated
upward during the initial phase of the discharge.
7.2.2 Very Active Phase
The very active phase was characterized by a faster pulse repeti
tion rate, a pulse every 5 or 10 psec superimposed on a lower frequency
envelope, up to 500 psec width. During the very active phase the VHF
source region becomes wider and additional electric field change occurs.
One of the IC, described in Section 5.6, started with the very
active phase. For the first 18.8 msec the VHF noise sources for this
discharge were nearly vertical between a height of 8.5 and 13.5 km
(Figure 5.84). However, by the end of the very active phase, the noise
sources had propagated downward to a height of 4.5 km and widened the
previous channel. Since most of the propagation of the noise sources
were downwards, we claim that the positive charges were lowered during
the IC discharge.


CHAPTER I
INTRODUCTION
The main purpose of this research is to determine VHF lightning
source locations in three dimensions and to relate these results to
other simultaneously recorded data, notably the dc to 1.5 MHz wideband
electric field, in order to obtain a better understanding of the physics
of the lightning discharge. The VHF radiation data were recorded during
the summers of 1976 and 1977 at the Kennedy Space Center (KSC) using
the KSC Lightning Detection and Ranging (LDAR) system. The VHF locations
were determined from the difference in the time of arrival of the VHF
radiation pulses at four LDAR ground stations. This study was part
of the Thunderstorm Research International Project (TRIP). TRIP brought
together a group of outstanding scientists in atmospheric electricity
from the USA and foreign countries with the purpose of performing
coordinated measurements during thunderstorms. The work reported in
this thesis represents an important new dimension in lightning research.
For the first time the use of a fully computerized algorithm has made
it possible to understand in more detail the different phases of a
lightning flash. We now have a much fuller understanding of the electrical
activity inside a thundercloud and we are better able to describe the
generation and propagation of the different phases of both cloud and
ground lightning flashes. It is to be hoped that the new techniques
developed as a part of this study will facilitate future research in the
field of atmospheric electricity.
1


284
(2) Parameter estimation. Initial estimates of the coefficients of
the original series (d=0) or for the first difference (d=l) were chosen
to ensure convergence of the individual parameters to fit the previously
identified model. Next we discuss the results of the data models for
the three physical processes.
6.1 Noise Level
For reference purposes we identified the best model for the back
ground noise level of the four flashes. These models were chosen from
testing AR, MA, ARMA, and ARIMA for d=0 and d=l. The results obtained
are as follows: (1) Flash 165959, MA, order 3, d=l, = 0.108, 02 =
-0.431, 03 = -0.086; (2) Flash 180710, AR, order 3, d=0, (p1 = -0.1011,
2 = 0.5315, = -0.1797 ; (3) Flash 181806, AR, order 4, <|> = -0.1332,
= -0.5598, = 0.1687; (4) Flash 182356, AR, order 3,
d=0, 4)x = 0.0137, (p2 = 0.0237, cp3 = 0.0243.
The 165959 flash produced a better model for the first difference
MA of the 3rd order, however, the original 165959 series (d=0) for the
noise level also fits an AR 3rd order level. The standard deviation of
the above parameters is less than 10%. The fact that this process can
be represented as an AR of order 3 or 4 indicates that the VHF radiation
dies out quickly as a function.of the p r e v iou s.. v.a 1.ues oi the output.
6.2 Stepped Leader
We determined the best model for the initial stepped leader for
each of the four CG flashes. These models were chosen from testing AR,
MA, ARMA, and ARIMA for d=0 and d=l. The results obtained are as
follows: (1) Flash 165959, AR, order 5, d=0, (f>3 = -1.084, 4>3 = -0.4453, 4 = 0.2141, (j) = -0.1105; (2) Flash 180710, AR, order 3,


2ft
links (around 7.4 GHz). The signals from the other three remote stations
used 5 Miz bandwidth cables. At the central station a Biomation 1010
was assigned to each of the VHF signals. Biomation 1010 s were used to
digitize 2048 consecutive samples with a sample every 50 nanoseconds.
The output from the Biomation is transferred to the preprocessor. The
preprocessor has several functions. First, it performs a reasonableness
check by determining the largest signal in all the stations and by checking
if the DTOA of the largest signal is within the limitations of the
physical geometry. In addition, for this test to succeed, the central
station largest peak has to occur first. If these conditions are met,
the preprocessor is used to measure the DTOA between the largest signal
in the central and each one of the remote stations. Using the hyperbolic
system equations described by Holmes et al. (1951), Appendix A, two sets
of three-dimensional locations are calculated. If the values of the two
sets of stations do not agree within a few hundred meters, the data are
rejected. Otherwise the data are stored in digital tape and displayed in
a Plan Position Indicator (PPI) and a Range Height Indicator (RHI) CRT
screen. Since this process takes less than 100 msec, the output locations
are represented in near "real-time." Two milliseconds after the first
sample, the Biomation 1010's are ready to receive a new set of data and
repeat the same process.
This technique can provide very accurate fixes whenever only one
large VHF pulse is detected in all the stations. Since the data bandwidth
is 5 MHz and the sampling frequency is 20 MHz, this is a highly accurate
system. The system accuracy is within tens of meters for X and Y, and
150 meters for Z. For a study of lightning channels, however, this
processing is not adequate because a maximum of one location is determined


78
electric field records indicate that there is a small electric field
pulse of 2 ysec width at about the time of the initial VHF radiation,
but a clear correlation between VHF and electric field does not exist
until the final .8 msec of the preliminary breakdown which corresponds
to, a steady electric field change.
Figure 5.2 shows simultaneous records of VHF radiation during 117
ysec of the preliminary breakdown that preceded the initial stepped
leader. During the preliminary breakdown the log amplitude of the
envelope-detected VHF noise is characterized by large pulses having a
duration of 40 to 150 ysec. Superimposed on these slow pulses are
pulses of 1 to 5 ysec width. Pulses 1, 2, 3, and 4 of
Figure 5.2 illustrate the difference in the time of arrival of typical
pulses at the four stations. The "r" value shown in the figure repre
sents an approximate distance between the VHF source and the individual
ground-based stations. The computer algorithm when applied to the data
in Figure 5.2, generated source locations for pulses 1 through 4 and for
10 additional pulses.
Figure 5.3(a) shows all the 150 source locations identified during
the preliminary breakdown which occurred between locations A and B.
It is worth noting that most of the sources are concentrated within a
cylinder of 500 meter radius and many are inside the volume, source
of the first return stroke charge (Figure 5.3(b)). Figure 5.3(b) shows
the cross-correlated noise sources, 94 ysec intervals, associated with
the preliminary breakdown. The cross-correlated locations are weighted
toward the location of the larger pulses in the 94 ysec interval because
it is these that play the dominant role in maximizing the cross
correlation function.
The cross-correlated noise sources started near


127
5.2.1 Preliminary Breakdown (PB)
The VHF radiation started 10.0 msec prior to the first return
stroke. The first 2.1 msec of the 10.0 msec was associated with the
preliminary breakdown. The VHF noise characteristics of the PB are
shown in Figure 5.23 along with the VHF noise during the stepped leader,
first return stroke, and some of the activity after the return stroke.
Correlation with the electric field record was only possible to within
750 psec. At a distance of 3 km there was detectable field change
9.0 0.75 msec prior to the first return stroke, that is, about half
way through the preliminary breakdown. Thus the electric field change
started about 1.0 msec after the initial preliminary breakdown pulse
shown at 2.0 msec in Figure 5.23.
The first cross-correlated noise source was located at A (4.6,
10.8, 7.1) in Figure 5.24(a) and corresponded to the highest detectable
cross-correlated source of the preliminary breakdown-stepped leader
process. The noise sources,during the preliminary breakdown as found by
the computer did not occur in a regularly progressing sequence. Attempts
to determine a preliminary breakdown velocity did not produce consistent
results. At the end of the preliminary breakdown the noise sources were
at B (5.1, 11.7, 6.1). The cross-correlated noise sources during the PB
extended between 4.2 and 5.3 km EW, 9.8 and 13.0 km NS, and between 4.9
and 7.1 in altitude.
In addition to determining the cross-correlated and all the indi
vidual source locations (Figure 5.24(b)) using the computer algorithm
described in Chapter IV, we determined the individual source locations
manually during the first 600 psec of the preliminary breakdown. This
task was performed to show the progressing sequence of the initial




16 A
between a height of 6 and 7 km. The first and third stepped leaders
propagated over water and had large horizontal components. The second
stepped leader had a large horizontal component during the first 18.2
msec, then was propagated vertically making a ground contact near the
coast. The three stepped leader velocities were: 0.8 x 10"* to
1.7 x 10^* m/sec, 2.4 to 5.3 x 10"* m/sec, and 7.6 x 10"* to 1.1 x 10^
m/sec, respectively. The charge lowered by each one of the three
leader-return stroke processes was calculated by using a point charge
model: -13.4, -11.5, and -9.3 Coulombs, respectively, were lowered by
these processes. (4) The VHF sources corresponding to the VHF radiation
in the first 8.8 msec after the first return stroke were located in the
upper part of the previous stepped leader-return stroke process. By
correlating with the electric field we determined that either positive
charges were raised or negative charges were lowered from higher regions
in the cloud. (5) The second and third stepped leaders were preceded
by J-change processes that lasted 28.4 and 31.2 msec, respectively.
During these processes the bulk of the VHF noise sources were located
in overlapping cloud regions between the heights of 6 and 9 km. The
first J-change started with a K-change that propagated for about 6 km
lowering 0.85 Coulombs. The progressing sequence of the VHF locations
during the second J-change formed along the surface of a cylinder and
as the process continued the sources filled the inside of the cylinder.
(6) Two types of VHF radiation, continuous and discrete, occurred on
sequence after the third return stroke. The V1IF sources during the
87.1 msec of continuous VHF activity were loqated in the neighborhood
of the previous J-change. The discrete activity consisted of 5 solitary
pulses. The second, third, and last pulse had identifiable rapid


2 1 JUNE 19 79
STORM ACTIVITY UN 1QTH JULY 1976
START TIME
= I 6
HOURS 59
MIN 5 9
SEC
008
MIL
FINISH TIME
= 1 7
HOURS 00
MIN 01
5 I. C
00 9
M IL
DIGITIZATION T
l ME
= 3 HOURS
4 6 MIN
25
SEC
5 9 MIL
UNIVERSAL TIME = 16
HOURS 59 MIN
59 SEC
l 0
MIL
343 MICROSEC
IN METERS
Y IN METERS
Z
IN METERS
370.292
11573.102
6925.770
IN METERS
Y IN METERS
Z
IN METERS
TIME IN MICRO SEC
337. 332
11503.008
6830.449
2.068
222.583
1 154 2.4 92
75 12. 641
0.961
328.820
11510.613
66 7 0,266
10.302
370.759
1 16 10.777
80 16.242
22 .289
294.204
10929.129
5781.023
28.033
828.517
13032.410
9006.430
36.07 5
332.326
1 1 93 4.977
7672.242
40.441
268.830
12133.840
7899.730
53.998
170.478
11o50.094
7151.047
57 .675
502.776
1 1264.688
572 3. 504
63.419
358.633
10492.359
596 7.738
76.057
229.142
10562. 19 5
053 7.320
08 .00 6
-56.677
14875.063
11791.336
98. 116
487. 560
l1295.305
5602.904
100.07 3
644.544
10253.074
5 1 13.4 77
103.401
488.974
10967 .37 9
5344.094
109.146
58 8.8 18
12416.773
0445.395
1 14.660
2 7.4 58
12505.129
8631.641
124.081
147.415
12125.922
804 2. 1 1 3
l29.026
231.690
12206.934
7644.430
l34.881
-46.448
11944.910
7964.465
1 42.693
249.756
1 3016.94 l
8542.205
1 47.289
-20 7. 222
1 1C4 9.02 7
5787. 840
159.238
241.063
1 1808.273
7346.617
173.254
424.066
12 489.72 3
8332.617
181.986
205.637
1 1657.006
7006.504
187.500
1341.814
1 2474.340
8217.180
213.006
444.904
10839.1l7
59 7 1.152
2 30 .0 1 0
356.226
11513.992
749 1.148
2 36.6 73
17.986
10783.199
5903.059
2^1 039
307.271
12050.375
01 54. 040
246.784
46 6.636
12313.009
7962.027
259.422
120.853
1 1752.56 3
6788.270
275 .506
302.356
11622.184
7127.852
279.872
223.504
1 184 3.57 4
7223.500
286536
216.027
11504.516
6817.984
292.280
370,720
10712.215
58 0 1.590
298.484
1 9 5. 02 1
11964.461
769 1.543
3 06.986
289.562
11774.191
8 3 1 5. 9 30
3 12. 73 0
195.683
12277.715
7300.680
3 16.40 T
423.099
12027.262
8012.141
3 24 .21 9
G 74.4 08
il266.602
4300.104
327.896
1 124. 6 74
14503.461
12378.633
347.198


ALTITUDE (km)
(c)


87
A two-dimensional view with all the detected preliminary breakdown
and stepped leader sources is shown in Figure 5.6. Figure 5.6(a) shows
the plan view while Figures 5.6(b) and 5.6(c) show the elevation views
of all the located stepped leader sources. In both graphs, Figures
5.3 and 5.6, the 150-meter weather tower struck by the flash is shown.
The weather tower is located at (-1.1,9.5). Figure 5.6 also shows the
cross-correlated locations represented with circles. It is worth noting
that these cross-correlated locations form a narrow channel during the
preliminary breakdown, but this channel is widened at a later stage
during the stepped leader process.
The velocity during the first 700 microseconds of the stepped
leader ranged between 1.3 and 3.8 x 10^ m/sec and during the next 1.8
msec showed a nearly linear increase from about 1.5 x 10 m/sec at about
5 km altitude to about 7.0 x 10^ m/sec at 2.2 km. Although there was
strong VHF radiation during the last 0.4 msec of the stepped leader, no
sources were located during this time. It is probable that the pulses
on the four channels could not be correlated because too many VHF
sources, leader steps, were simultaneously active over a large volume.
Figure 5.7 shows three sequences of histograms of all the source
locations from the beginning of the preliminary breakdown to the last
detectable source in the stepped leader. The time sequences t^, t^,
and t^ in Figure 5.7 correspond to 1.5 msec intervals from the beginning
of the preliminary breakdown to the end of the detected VHF sources
from the stepped leader. Figure 5.7(a) is a distance histogram
referenced to the weather tower, as the time'progresses the radiation
sources approach the 150 meter weather tower. Figure 5.7(b) and Figure
5.7(c) show polar histograms of all the radiation sources with reference


32
the three remote stations in one of the Y configurations (Ml, M2, and
M3, Figure 3.2) were retransmitted to the central station using 10 MHz
bandwidth microwave links. Signals from the other three stations (Wl, W2,
and W3, Figure 3.2) forming the second Y were retransmitted to the central
station using 5 MHz bandwidth A-2A cables. All seven VHF radiation
signals were recorded at 120 ips on a 14 channel analog recorder operating
in a direct mode with a frequency response from 400 Hz to 1.5 MHz.
Timing information in IRIG B format (accuracy to fractions of milli
seconds) was recorded on one of the remaining tape recorder channels.
A minimum,, of four _recei.,yi.n,gi._st,ations i^ne^d^_..t-o_abt,a4n,^he_J\/HI^ radia
tion used for the determination of thTOe^dimensional-J.aca.tions.^Ololmes
and Reedy, 1951). Appendix A contains a derivation of the three-
dimensional locations obtained from the measurement of the difference of
the time of arrival between the remotes and the central station. The
baseline between the remotes and the central station in Figure 3.2 is
approximately 10 km. The 10 km choice was made by KSC personnel to
obtain accuracy in the order of 100 meters using a real time system for
source locations within the KSC geographical area. Figure 3.2 also
shows the location of the Vertical Assembly Building calibration signal
(VAB CAL) used to obtain the calibration error in the measurement of
source locations. An error analysis for the three-dimensional locations
is shown in Appendix B. During this research there were some variations
in the selection of the three remote stations for different flashes.
Appendix B also shows the selected remote stations for the different
flashes analyzed in this thesis.


EAST (km)
ALTITUDE (km)
CD CD n) 'CO CD O
O o O
non
T91


EAST (km) EAST (km)
ALTITUDE (km)
,o->r\j(Jj.fcicna>'sicocDO
ALTITUDE (km)
6ZZ


Figure 5.24(a).
Three-dimensional view of the cross-correlated noise sources during the first
PB-stepped leader process. Point A is the location of the first cross-correlated
source during the PB. Point B is a similar source at the beginning of the
stepped leader. The sphere Q1 represents the source charge for the first return
stroke provided by Krehbiel (private com) using the techniques of Krehbiel et al.,
(1979).
Figure 5.24(b).
Similar three-dimensional view for all the individual detected sources.


179
5.44. The average velocity of propagation during the final msec of the
PB was 9.2 x lO' m/sec.
5.3.2 First Stepped Leader
The first stepped leader immediately followed the preliminary
breakdown and lasted 5.9 msec. The VHF noise during the stepped leader
was characterized by high-frequency low-amplitude radiation. As we shall
show from an examination of all the flashes in this thesis, these high
frequency pulses are typical of stepped leaders and hence we can with
confidence associated them with the stepped leader process. The VHF
noise sources could be correlated during the first 3.5 msec of the
leader. During the last 2.4 msec the pulse rate becomes faster than a
pulse every 2 ysec and the pulses could not be correlated because too
many VHF sources were simultaneously active over a large volume. In
addition, the magnitude of the VHF stepped leader pulses decreased.
The stepped leader followed a near-vertical path from the PB to the
tower. Figure 5.43 shows the VHF noise sources during the PB and the
stepped leader. Figure 5.43(a) shows the 416 detected individual
sources. Figure 5.43(b) shows the cross-correlated sources (94 ysec
intervals) and the location of the tower struck by the flash. The
stepped leader cross-correlated sources were detected between a height
of 6.7 and 2.7 km. Point B shows the source location around the
transition point between the two different characteristics of the VHF
noise representing the PB and the SL. Figure 5.44 shows the two-
dimensional projections of all the PB and stepped leader sources. The
cross-correlated values, 376 ysec intervals, are shown as a square of
larger size than the actual source locations which are shown as tri
angles. The circles in Figure 5.44 correspond to the return stroke


Ill
Figure 5.17 shows a histogram of the interval between VHF pulses. If
we associate the high frequency VHF pulses with leader steps, the aver
age time interval between leader steps was 8.2 ysec (Figure 5.17) with
a standard deviation of 3.5 ysec. If there was a typical value of 50
ysec between leader steps, about 5 branches were simultaneously active.
The location of the VHF noise sources during the stepped leader
extended the path of the previous J-change as shown in Figure 5.18.
The VHF sources propagated from an altitude of about 8 km, the end of
J2, to a height of 3.3 km below which no radiation sources were located.
The bottom of the stepped leader nearly coincides with the previous
channel. The stepped leader velocity determined from the cross-correlated
source locations was about 4.5 x 10^ m/sec. After the last stepped
leader location and for 1.1 msec, the electric field showed a more
rapid variation of slope than previously and the VHF radiation indicated
the long-duration pulse characteristic of dart leader, return strokes,
and SPTs. The noise sources were located around an altitude of 3.5 km,
that is, near the bottom of the stepped leader channel. In view of the
above it is reasonable to assume that the stepped leader contacted the
previous stroke channel and at that point became a dart leader, making
the whole leader process a stepped-dart leader.
5.1.11 Third Return Stroke
The third return stroke lasted about 130 ysec in the VHF record.
The beginning of the return stroke VHF record shows a wide 80 ysec pulse
which seems to be an indication of the propagation of a potential wave.
All the four cross-correlated noise sources detected during the third
return stroke were located near the top of the stepped-dart leader
channel, which coincided with the end of J2.


DART '
>
RETURN
* LEADER
STROKE
-J
1 1 ¡
>[<
I
|
|
>j
I
1
IOO 200 300
j
400
1
500
600
700
1
800
1
900
TIME
IN
MICROSECONDS
Figure 5.56. Logarithmic-amplitude
VHF
radiation during
the
dart leader and
the
fifth return stroke.


noon ono nono noon ooonoo ono ooo
'136
21 JUNE 1979
500
MKN=0
WRITE! e. 531 )
531
FORMAT (101,17X 5HDELAY,5X,24 UMAX I MUM CROSSCORRELATION,
* 5X, 13HTIME INTERVAL)
501
DO 501 K-l,2048
Xl(K)=X6(20484Jl-4 4Q4Jl-H<)
*4 CALCULATE ONE AVERAGE POINT PER SUBSET *
3
1
f
DO 1 J=1,JJ
XS=0 .0
DC 3 J K = 1 ,MM
XS = XSFX1( (J-1)4MM+JK)
AV E( J)=XS/FLGAT(MM)
C 44
c
CALCULATE MOVING AVERAGE UF THE SET 44
V
5
X I=0.0
DO 5 1=1,MM
X I =X I + X l ( I )
A VEMO( l ) = XI/FLOAT(MM)
KL=MM+1
9
l 1 3
c
DC 9 I= KL ,2047
X 1 = X14-X1{ IJ-Xl (I MM)
AVEMO( 1-15 ) = XI/FLOAT(MM)
F C RMAT<3r10.2)
CALL RMEAN(AVEMO,2032,0.0)
C 44
C 4=
C 4 4
C -4 4
C
CALCULATE THE STANDARD DEVIATION OF THE DATA IN THE SET 44
BY USING A FUNCTION SUBPROGRAM STDSET, THE THRESHOLD 44
LEVEL LY FUNCTION SUBPROGRAM DIV4SM, AND THE STANDARD 44
DEVIATION OF THE SUBSET BY FUNCTION SUBPROGRAM STDSUB. 44
CALL LCC.M AX ( M A ELM A, MM J J A V E S LPR SL PL NUMDER,
* NUMDEL NRRGWE )
C 44
C 44
C
97
r
LOCMAX IS THE SUBROUTINE THAT CALCULATES LOCAL MAXIMUM 44
IN THE DATA 44
F CRMAT(110,3F10.2,3I10)
v_
C 4 4
C 44
C
502
f
TEE DATA IS RE-FORMATTED TO BE ABLE TO PROCESS THE DATA 44
NEAR THE END CF THE SET 44
DO 502 K= 1,2048
X2(K)=X7(20484Jl4484J1+K)
C 4 4
MKN IS THE COUNTER FOR THE NUMBER OF STATIONS 44
c
17
MKN=MK N+ 1
L
C 4 4
C 4 4
r
GETTING THE AVERAGE AND THE MOVING AVERAGE FOR 44
THE RFMOTF STATIONS 44
1 3
1 l
C
DO 11 J=l,JJ
X S = 0.0
DO 13 1=1,MM
XS=XS+X2( (J-l ) 4M M + I )
A VE( J ) = XS/FLOAT ( MM )
X I =0.0
DO 15 1=1.MM
1 5
X [=XIFX?( I)
A VEM02 (1 ) =XI/FLOAT(MM)
DO 19 I=KL,2047


Table 5.1. Time-Table for the VHF Activity in the 165959 Flash.
Start
Time
(msec)
Event
Duration
(msec)
Average Velocity
m/sec
Coordinates (km)
UPPER
LOWER
X
y
Z
X
y
Z
0.0
Preliminary Breakdown (PB
2.2
1.0 x 106
0.3
11.6
7.1
.2
10.8
5.1
2.2
Stepped Leader (SL)
2.7
1.3 to 7.0 x 106
0.2
10.8
5.1
-1.3
9.7
2.2
4.9
First Return Stroke (Rl)
0.25
5.15
Quiet Period
2.4
7.55
Follow Return Stroke (FR)
4.27
0.5
12.2
7.0
1.1
10.2
1.3
11.82
Quiet Period
15.5
27.37
VHF Portion of J1
43.27
1.5 x 105
0.0
16.0
13.7
-0.2
12.3
7.9
70.59 .
Dart Leader (DL)
.35
1.8 to 2.6 x 106
-0.1
12.0
7.8
0.3
11.2
6.6
70.94
Second Return Stroke (R2)
.26
71.20
1st Quiet Period of J2
11.52
82.72
SP No. 1 (SP1)
.775
1 to 4 x 107
83.50
2nd Quiet Period of J2
3.2
86.7
SP No. 2 (SP2)
.95
1 to 4 x 107
87.65
3rd Quiet Period of J2
7.78
95.43
SP No. 3 (SP3)
.57
1 to 4 x 107


CHAPTER TI
GENERAL REVIEW OF LIGHTNING AND PREVIOUS LIGHTNING VHP TOA RESEARCH
2.1 Description of Cloud-to-Ground and Intracloud Lightning
This section contains an introduction to the basic terminology of
the physics of lightning. Lightning is a transient, high current
electric discharge whose path length is measured in kilometers. A
lightning discharge starts when the electric field in some region of
the cloud exceeds the breakdown strength of air, that is, equal to or
6
less than 3 x 10 V/m, depending on pressure, temperature, and the
presence of precipitation. The most common source of lightning and the
only one considered in this thesis is the thundercloud. A typical Florida
thundercloud has a top between 9 and 15 km above sea level (Jacobson and
Krider, 1976).
The lightning produced by the thundercloud can take place within
a cloud (intracloud), between cloud and earth, between clouds, or
between the cloud and the surrounding air. Our study includes the
intracloud and the cloud-to-earth lightning usually called cloud-to-
ground or ground discharge. A complete discharge is called a flash.
Either discharge, the intracloud or the cloud-to-ground flash, typically
lasts 0.5 seconds.
Regardless of the type of flash being studied, one of the most im
portant factors in thunderclouds is the location and size of the charge
regions. The simplest and most accepted model of a thundercloud was
given by Wilson (1916). He assumed that the center of electric charges
6


'68
maximizes the coherence
tion is defined as
function between x and y .
n n
The coherence func-
2
Y = IG I /G G where 0 < y < 1
xy xy1 xx yy xy
(E.12)
Either by determining the time lag at which the peak of the impulse
function occurs or by determining the time delay of the phase in the
frequency response, we are limited to the data sample size. In the
impulse function, a time delay is determined between two selected inter
vals in x^ and y whereas in the phase frequency response, we can
select different intervals of y to maximize the coherence function. In
n
either case we need to determine the proper sample size to use to obtain
correct results. If a sample size in the neighborhood of 5 ysec width
is used, then we have to ensure that at least one entire pulse is within
the selected interval for all the stations. On the other hand, if a
sample size of several hundred microseconds is used, then we only get one
cross-correlated location.


nnno
2 1 JUNE 1979
SUBROUTINE HYPERM{DELTA 1 .DELTA? .DELTAJ ,X .Y.Z.Nl N, NX)
** THIS SUBROUTINE USES THE HYPERBOLIC EQUATIONS TO **
** DETERMINE THE THREE-DIMENSIONAL LOCATIONS. **
D I MENS ION DELTAl (128) ,DELTA2( 128) ,DELI A3( 128) ,M(9 ) .
* V(3) X{ 1 28) Y( 128).Z( 123) ,N1N( 128)
RE AL M
DO 62 K=1 .NX
M(7) = < DELTA 1 (NIN(K) )-33.55)* <-3 00.)
M ( 8 ) = ( DELTA2 (N1N(K) )-29.520 )*(-30 0. )
M( S)=(DEL TA3(N1N(K) ) 113.43)*(300)
V( 1)=( 10 3 12.28** 2 M( 7)**2)/2.0
V(2)=(8222.076**2M(8)**2)/2.0
V( 3)-( 8089,20**2 M(9 ) * 2 )/2.0
** THE NEXT PARAMETERS ARE THE COORDINATES OF THE **
** REMOTE STATIONS IN METERS. **
M( 1 )=36 7 7.05
M ( 2) = 816 0.79
M ( 3)=7432.93
M{ 4)=9 634 .44
M( 5)=- 1002.0 1
M(6)=3191 .68
CALL SIMQ(M.V,3.0)
ZSQ=V( 3)* *2(V( 1 ) * 2 +V(2)**2)
X(K)=V (l )
Y(K)=V(2)
IF(ZSQ>63,64,64
64 Z1= 3 Q R T(ZSQ)
Z ( K)=Z l
GO TO 62
68 ZSQ=ZSQ
Z(K)= SOR T(ZSQ )
02 CONTINUE
RETURN
END


Figure 5.22. Simultaneous records of the logarithm of the amplitude of the VHF radiation observed
at 9 km, and the electric field 3 km away, during the 180710 flash. The following
events in the flash are shown: Rl, R2, and R3 correspond to the three return strokes
SL1, SL2, and SL3 are the three stepped leaders; J1 and J2 are the J-change processes
PB is the preliminary breakdown; FR is the activity after the first return stroke; K
is the K-change pulse that initiated the J1 process; CAFS and DAFS are the continuous
, and discrete activity after the return stroke; last SP corresponds to the last soli
tary pulse during the DAFS process.


nnno
348
21 JUNE 1979
SUBROUTINE L OCM AX ( M ABL MA M M ,JJ .AVE.SLPR, SLPL.NUMDER,
* NUMOEL,NRROWE)
** SUBROUTINE TO CALCULATE THE LOCAL MAXIMUM OF CENTRAL **
** STATION **
O I ME NS ION MAELMA(128) .XILM( 16) ,SLPR( 128) SLPL( 123) ,
* NUMDER128),NUMDELf128).NRROWE(128),AVE(128)
COMMON KK,N,MP,NP,NNN( 1 28 5 ,MMM( 128) ,XI( 2 0 48) ,X2(2 04 8)
C
C ** THIS SUBROUTINE COMPUTES THE COORDINATES OF A LOCAL *
C ** MAXIMUM PER SUBSET- FUR A POINT TO BE A LOCAL MAXIMUM **
C ** ONE OF THESE THREE CONDITIONS MUST BE MET. A) ORDINATE *
C ** LARGER THAN 1/2 OF THE SMALLEST VALUE OF THE SECTION, **
C ** ) STANDARD DEVIATION OF SUQSET LARGER THAN STANDARD **
C *A DEVIATION OE SET, AND/OR C) ORDINATE LARGER THAN THE **
C ** AVERAGE PLUS TWO TIMES THE STD DEV. OF THE SUBSET. **
C
MP = 0
RT=2.0
DC 6 K=l,JJ
AVESET = AV E(K)
DO 8 J=1,MM
8 X1LM(J)=X1((K-L)*MMFJ)
XISM=BIG{X1LM.MM )
X1TEST=(DIV4SM(X1,N))/RT
X l PEQ=SMALL( X1LM ,MM)
X IDIFE = XlSM-X1PEQ
DO 22 J=l,MM
IF(X1LM(J).NE.X1£M)GG TO 22
MAELMA(K)= J +(K-l )*MM
GC TO 200
22 CONTINUE
200 N A BCIS-M ABL M A(K)
IF(NACIS.LE.5)GC TO 6
IF (NABOS .GE .2043 ) GO TO 6
IF(XISM.GE.X1 TEST)GO TO 24
IF(STD SUB(XILM.AVESE T,MM).GE.STDSE T(X1 ,N) ) GO TO 24
TEST=AVESET+RT *S TDSUBXILM,AVESET,MM)
IF(XISM.GE.TE5T)G0 TO 24
MRR= 0
MLL = 0
DO 202 MN1=1,5
IF(X1(NAB CIS+MNI 1) GE.X1 (NABCIS+MN1 ) ) MRR = MRR+1
IF(XI (NABCIS-MNl+1 ).GE.X1 (NABCIS-MN1 ) ) MLL=MLL+1
202 CONTINUE
IF((MRR+MLL) .GE.8 ) GO TO 24
IF(XIDIFE.GE.( 100 ).AND. (MRR + MLL).GE.7 )GO TO 24
GO TO 6
24 CALL PULSF(Xl,NABCIS.SLOPR.SLOPL,MR,ML,NARROW)
SL PR ( K ) = S LUP R
S L PL ( K ) = 5 L O P L
NUMBER(K)=MR
NUMDEL(K)=ML
NRROWE(K)=NARROW
IF(5LPL(K ) .LL 0 )GO TO o
i F(SLPR(K).GL.O. )GO TO 6
MP =MP+ 1
NNN(MP)=K
IF ( MP. E-Q. 1 ) GC TC 6
I F ( ( MABl M A ( NNN ( MP ) ) MAI3LMA ( NNN ( MP- 1 ) ) ) LE. 3 ) MP = MP-1
6 CONTINUE
121 FORMAT(2F10.2,5110)
RETURN
END


EGLIN AFB
ADTC/ADUA (MATH LAB)
ANALOG TAPE KSC
DIGITAL
400Hz 1.5 MHz
TAPES
I
ft
SLOW DOWN BY 4
K
SLOW- DOWN
SLOW- DOWN
N
DIGITIZE AT
8.5 KHz
4 CHANNELS
DIRECT-RECORDING
V^]
BY 16 FM MODE
V'H
BY 8 FM MODE
^
TIME COR.
PDP-15
SLOW-DOWN RATE-4 X 16 X 8 = 512
REAL TIME SAMPLE RATE1 8.5 KHz X 512 = 4.352 MHz
2F = 3MHz (MEET NYQUIST RATE)
MAX
(SAMPLE EVERY .229 MICROSECONDS)
3.10.
Slow-down and digitization
technique used at Eglin AFB.
Figure


39
the number of pulses and their magnitude decreases. Oetzel and Pierce
(1969) claimed that the maximum signal-to-noise ratio is obtained
between 20 and 100 MHz. Probably the lower part of the VHF range,
around 30 MHz, is the ideal center frequency to study lightning
radiation channels.
3.2.1.2 Bandwidth. The receiver bandwidth is an important fac
tor in determining the pulse characteristics. It is desirable to use
wideband receivers, since if narrow bandwidths are used, the detected
radiation pulses will appear almost identical making cross-correlation
difficult. The minimum pulse width detected in a telemetry system is
inversely proportional to the receiver bandwidth and the minimum rise
time is the reciprocal of the bandwidth. Therefore, a VHF receiver with
a narrow bandwidth of 1 KHz will only detect pulses equal or greater
than 1 msec. Studies performed by Oetzel and Pierce (1969), Pierce
(1977), and Proctor (1976) have shown that the maximum number of VHF
lightning radiation pulses ranged between 10,000 and 500,000 pulses per
second. That is a maximum pulse repetition rate of a pulse every 20
ysec. In order to measure time difference between the individual
pulses, resolution of about one microsecond is needed, which requires
a bandwidth of 1 MHz. However to determine lightning source locations
to an accuracy of hundreds of meters, time differences must be measured to
a fraction of a microsecond (Appendix B). With the exception of Lewis (1960),
who used a bandwidth of 41 KHz with center frequency in the VLF range,
all the recent researchers who have measured the difference in the time
of arrival on radiation from lightning have used a wideband system and
a center frequency in the VHF range (e.g., Proctor (1971), bandwidth
5 MHz with center frequency at 253 MHz; Taylor (1973), bandwidth 60 MHz


51
the properties of the multiple channel VHF radiation and the properties
of the time-series data.
4.2.1 Properties of the Multiple Channel VHF Radiation
Some of the important properties of multiple channel VHF radiation
are as follows:
1. The VHF radiation received at the three remote stations was
retransmitted to the fourth station (central). Since VHF radiation was
also recorded at the central station, any radiation pulse, from anywhere
in space, identified at the central station will arrive before the
arrival of the same pulse retransmitted from the remote stations.
Figure 4.1 shows an example of the four channel VHF radiation. The
signal from the central station (A) arrives before the signal from the
three remote stations (B, C, and D).
2. Since the radiation field is inversely proportional to the
distance from the space source location to the ground receiving stations,
there are differences in the magnitude of the radiation at each of the
stations. For ease of comparison the four channels are normalized with
respect to the central station. The amplitude normalization has no
effect in the shape of the pulses and provides a more effective compari
son between the four stations' data.
3. From equation (2.1) we know that the radiation field is propor
tional to the sine square of the angle between the center line of the
radiating element and the line to the ground station. Therefore, some
high amplitude pulses in a ground station with an angle near 90 might
fall within the noise level in another station 20 km away with an angle
near 180. This will be the case for a near-vertical radiating source
located immediately above a ground based station. In this case 0 = 180


1.1.2.2 Subsequent Stepped Lenders.
Subsequent stepped leaders
had the following properties that distinguished them from first stepped
leaders:
(1) The VHP noise level had the same high frequency, uniform ampli
tude pulse characteristics but a magnitude twice as large as the initial
stepped leaders.
(2) All subsequent stepped leaders were preceded by active VHF radi
ation from the J-change which lasted for at least 7 msec with a pulse
about every 10 psec. This high repetition rate of VHF pulses appeared
to be a necessary condition before the initiation of subsequent stepped
leaders. There is a 5 to 1 ratio between the magnitude of the VHF
noise during the J-change and the subsequent stepped leader. This fea
ture in the VHF noise is used to identify subsequent stepped leaders.
Some of the J-changes that preceded subsequent stepped leaders were
formed in a concentrated region in a slanted path. If the previous
J-change was mainly horizontal, the stepped leader descended from a
concentrated VHF source region, usually near the center of the VHF source
region (SL2 and SL3, Section 5.2). If the previous J-change was mainly
vertical, the stepped leader propagated from the lower part of the
vertical region (SL2, Section 5.3; SLD, Section 5.1). Clear evidence
of the subsequent stepped leader following the vertical propagation
path of the J-changes is seen in Figures 5.18 and 5.48.
(3) Subsequent stepped leaders are difficult to identify in the
electric field record. Of 12 subsequent stepped .Leaders Identified in
the VHF record, only four could be identified^at any of ten electric
field stations. The beginning of the subsequent stepped leader
electric field record often does not show a change in the slope of the


EAST NORTH
(a) (b) (c)
Figure B.2. Two-dimensional views: (a) top view, EW-NS, (b) elevation view, EW-height, and (c)
elevation view, NS-height of all noise sources in 50 consecutive iterations of the
three time delays for a sample interval of 0.23 usee.
OZf


Livingston, J. M. and E. P. Krider, "Electric fields produced by Florida
thunderstorms," J. Geophys. Res., 83, 385-401, 1978.
MacClement and R. C. Murty, "VHF direction finder studies of lightning,"
J. Appl. Meteorol., 17, 786-795, 1978.
Mackerras, D., "A comparison of discharge processes in cloud and ground
lightning flashes," J. Geophys. Res., 73, 1175-1183, 1968.
Malan, D. J., "Les dcharges dans 1'air et la charge enfrieure positive
d'un nauge orageux," Ann. Geophys., 8, 385-401, 1952.
Malan, D. J., "Visible electrical discharges inside thunderclouds,"
Geofis. pura Appl., 34, 221-236, 1956.
Malan, D. J., "Les dcharges orageuses intermittentes t continues de
la colonne de charge negative," Ann. Geophys., 10, 271-281, 1954.
Malan, D. J., "Radiation from lightning discharges and its relation to
the discharge process," in L. G. Smith (ed.), Recent Advances in Atmo
spheric Electricity, 557-563, Pergamon Press, New York, 1958.
Malan, D. J., Physics of Lightning, The English Universities Press,
London, 1963.
Malan, D. J. and B. F. Schonland, "Progressive lightning, pt. 7, directly
correlated photographic and electrical studies of lightning from nine
thunderstorms," Proc. Roy. Soc., A191, 485-503, 1947.
Malan, D. J. and B. F. Schonland, "The electrical processes in the
intervals between the strokes of a lightning discharge," Proc. Roy. Soc.
London, A206, 145-163, 1951.
McLain, D. K. and M. A. Uman, "Exact expression and moment approximation
for the electric field intensity of the lightning return stroke,"
J. Geophys. Res., 76, 2101-2105- 1971.
Murty, R. C. and W. D. MacClement, "VHF direction finder for lightning
location," J. Appl. Meteorol., 12, 1401-1405, 1973.
Nakano, M., "Lightning channel determined by thunder," Proc. Res. Inst.
Atmos. Nagoya Univ., 20, 1-7, 1973.
Nakano, M. "Characteristics of lightning channel in thunderclouds deter
mined by thunder," J. Meteorol. Soc. Japan, 54, 441-447, 1976.
Nishino, M., A. Iwai and M. Kashiwagi, "Location of the sources of atmo
spherics in and around Japan," Proc. Res. Inst. Atmos. Nagoya Univ.,
20, 9-18, 1973.
Oetzel, G. N. and E. T. Pierce, "Radio emissions from close lightning,"
in S. C. Coroniti and J. Hughes (eds.), Planetary Electrodynamics,
Vol. 1, 543-569, Gordon and Breach, New York, 1969.


26 3
in the northern region and the second stepped leader discended from
that region. About 80% of the J2 noise sources were concentrated in
the southern region which initiated the fourth stepped leader. The
remaining 20% of the J2 sources were located in the northern region
and initiated the third stepped leader. Most of the J3 noise sources
were located in the northern region and the fifth stepped leader
descended from that region. The J4 noise sources were spread in both
regions and the dart leader appeared to descend from the southern
region. The J5 noise sources were located in both regions and the
sixth stepped leader descended from the southern region. Finally the
J6 noise sources were spread everywhere and from the dart leader sources
it appears to be located in the northern region. All the subsequent
J-changes extended higher in altitudes and were less organized. (6) A
discrete VHF activity interval was observed for 168 msec after the last
return stroke. The pulse repetition rate continuously decreased during
this interval. The last solitary pulse in the flash was 21.6 msec from
the previous pulse. The noise sources during this SP propagated down
wards 50 off vertical in a 5 km path.


Figure 5.18.
Cross-correlated VHF noise sources, 94 ysec
intervals, during the 2.2 msec of the stepped
portion of the stepped-dart leader that preceded
the third return stroke. A corresponds to the
location at the end of the J2 process as shown
in Figure 5.15. Q3 is the charge center for the
third return stroke from Uman et al., (1978).


charge was located eastward to the previous J-changes and extended from
a height of 15 to 2.8 km. (11) We located 18,877 noise sources during
this flash, an average of a VHF source location every 22.1 psec.
However, there were some quiet periods with no detectable VHF radiation
and periods in which the pulse rate was less than a pulse every 22 psec
During active VHF radiation we detected a pulse every 9 psec. The
flash extended from 7 to 17 km in the north direction, -3 to 7 km in
the east direction, and up to a height of 16 km. The space volume
, 3
covered by this flash exceeded 450 km .


Table B.l. Error Analysis for the 165959 Flash. The selected locations cover the entire volume of the
flash and they are listed in ascending order in z.
Source Locations
Quantization
RMS
Calibration
RMS
Total RMS Error
(Meters)
Error (Meters)
Error (Meters)
(Meters)
X
y
z
%
dyQ
dzQ
dx
c
dy
J c
dz
c
dxt
dY t
dzt
-307.1
11634.5
1870.9
19.3
260.1
548.9
29.3
419.4
1372.9
35.1
493.5
1478.6
-983.8
10519.8
2761.4
29.7
232.3
304.5
39.4
371.4
750.7
49.3
438.1
810.1
-731.5
10867.9
3377.2
26.1
254.6
274.4
36.9
408.5
676.3
45.2
481.3
729.8
3357.0
15518.8
3713.6
108.4
565.4
778.1
158.5
913.9
1576.7
192.0
1074.6
1758.2
-1332.5
11156.8
3888.6
37.2
264.0
268.0
50.7
423.7
640.8
62.9
499.2
694.5
1506.5
9634.2
5140.2
33.6
301.5
186.4
63.2
485.4
392.8
71.5
571.4
434.8
1126.6
10827.5
5401.8
25.5
327.7
215.3
53.7
528.1
470.8
59.5
621.5
517.7
1724.8
9376.4
5746.8
40.6
310.8
183.0
73.4
501.2
350.6
83.9
589.8
395.4
1468.5
9366.2
6317.3
35.4
313.7
176.9
68.8
506.6
330.2
77.4
595.9
374.6
300.0
11423.7
6739.2
17.0
354.7
213.4
45.0
572.4
447.6
48.1
673.4
495.9
2377.5
10241.3
6887.3
64.2
374.5
239.6
105.1
604.2
392.3
123.1
710.9
459.6
2072.1
10057.2
7577.8
56.2
372.4
228.9
97.2
601.8
336.1
112.3
707.7
431.8
2579.6
10345.1
7876.6
74.3
402.7
265.1
120.6
650.3
397.5
141.7
764.9
477.8
2745.3
10549.0
8653.0
83.3
429.9
293.7
134.3
694.5
420.8
158.0
816.8
513.2
-388.0
13914.4
9718.0
28. 7
506.1
303. 7
61.7
816.7
559.4
68.1
960.8
636.5
2794.5
11026.8
9895.7
90.4
473.8
337.0
147.3
765.6
470.3
172.8
900.4
578.6
3556/3
11882.5
10888.6
128.3
555.4
434.7
199.4
895.3
583.6
237.1
1053.6
727.7
2747.6
11346.4
11090.6
93.7
510.6
378.0
155.4
825.5
522.5
181.5
970.7
644.9
4307.1
12031.1
11178.0
166.8
599.2
513.4
250.8
964.3
668.3
301.2
1135.4
842.7
3013.8
12092.1
11384.7
107.2
555.6
416.8
173.6
896.5
574.2
204.1
1054.7
709.5
5342.8
13130.3
12431.3
236.7
727.2
694.3
348.3
1165.9
892.8
421.1
1374.1
1131.0
4522.8
13244.3
12549.4
188.9
693.8
604.9
285.4
1114.4
796.0
342.3
1312.7
999.8
6685.1
14 0 jl 3.6
13834.6
342.8
881.8
963.7
496.8
1408.3
1236.5
603.6
1161.6
1567.6
7038.8
15385.6
14319.8
381.3
995.0
1074.6
552.5
1585.3
1383.1
671.3
1871.7
1751.5
5749.6
14127.0
14535.1
278.1
845.7
847.0
413.0
1353.7
1109.3
497.9
1596.1
1395.7
6333.9
14774.4
14947.8
325.1
925.0
962.5
478.7
1477.4
1257.3
578.6
1743,1
1583.4
8061.2
14805.4
15752.0
474.8
1060.7
1315.5
685.6
1687.8
1712.3
834.0
1993.4
2159.3
7787.8
15594.7
15923.4
455.1
1093.4
1281.2
660.5
1739.4
1671.0
802.1
2054.5
2105.6
7474.5
16358.0
15343.6
429.2
1107.7
1215.8
623.4
1761.8
1577.7
756.9
2081.1
1991.8
Average error for
in this flash.
locations
150
558
535
227
900
813
L
354
1058
973
szc


279
noise sources formed a near vertical channel between the heights of
8.5 and 13.5 km. About 90% of the cross-correlated noise sources were
located within a cylinder of 0.5 km radius and 5 km length. During the
first 18.8 msec the VHF noise sources did not follow a progressing
sequence either upwards or downwards. However, in the first 4.5 msec,
about 80% of the VHF sources were located in the bottom half of the
cylinder.
Figure 5.85 shows a two-dimensional view of all the cross-correlated
noise sources, 94 psec intervals, during the entire IC discharge. The
VHF sources spread radially with increasing height forming an inverted
cone about 9 km in height.


APPENDIX E
FREQUENCY DOMAIN APPROACH TO
DETERMINE DIFFERENCE IN THE TIME OF ARRIVAL
There are several techniques to measure time delays in either the
frequency or the time domain. Chapter IV describes the theoretical
basics of our time domain technique. This technique is implemented
using the algorithm in Appendix C. For the work in this thesis we did
not select a frequency domain technique for reasons discussed in this
appendix. We investigated some of the frequency domain techniques
using Fast Fourier Transforms (FFT). The two most effective frequency
domain techniques consist of measuring time delays by determining either
the properties of the magnitude of the phase of the transfer function
between the input and the output (can be interpreted as central and
remote stations). However, for the data under study neither of these
techniques was appropriate because every pulse within a selected
interval in the time series had a different time delay with respect to
each consecutive pulse. To yield good results in a frequency domain
we had to isolate the frequency content of identifiable VHF pulses
which normally have a pulse width between one and five microseconds.
After some preliminary test results we decided that the use of any
frequency domain algorithm to systematically determine time delays
required more computations and made it more difficult to understand the
results than the use of any time domain technique. We will briefly
summarize those frequency domain techniques that we investigated. Both
364


EAST(km)
Figure 5.25. Three-dimensional view of the VHF noise sources during the
first 600 ysec of the preliminary breakdown.


Figure 5.21. Histograms of the altitude of the source loca
tions during (a) the first 5.6 msec, and (b)
the next 11.2 msec of the intracloud discharge.


53


( 6
REPEAT THE PROCEDURE FOR
THE NEXT TIME INTERVAL
(c)


193
derivation of the quantization and calibration RMS error in the deter
mination of the three dimensional coordinates.
The noise sources during the J-change or PB2 started at a height
of about 14.2 km (point A, Figures 5.48 and 5.49) and propagated down
ward in a path 25 off-vertical to a height of 10.5 km (point B,
Figures 5.48 and 5.49). The velocity of propagation was 5.0 x 10"*
m/sec. Even though the VHF noise changed characteristics at point B,
the noise sources continued their downward propagation. Applying the
dipole model of equation (3.10) to the 8.1 msec Jl or PB2 for an electric
field station located 12 km from the tower, we find that 1.8 Coul were
transferred between A (1.8, 11.4, 14.2) and B (0.7, 9.2, 10.5). The Jl
or PB2 process apparently made available some of the negative charge
lowered by the new stepped leader. The stepped leader duration was
17.5 msec. The stepped leader propagated from point B to C in about
2.6 msec. At this time and for the next 8.7 msec two active regions
D and E (Figures 5.48 and 5.49) started emitting VHF radiation. The D
region is in the neighborhood of the Q2 charge center while the E region
appears to extend the leader path toward the lower altitudes. The VHF
radiation was only detected during the first 3.4 msec of the remaining
6.2 msec of the 17.5 msec stepped leader. In this time interval all
the VHF noise sources were located below a height of 6.5 km. From a
study of all the noise sources during the 3.4 msec (Figures 5.49(b) and
5.49(c)), it appears that the VHF radiation between the height of 5 and
1.5 km was emitted by two separate channels. We labeled these channels
as F and G in Figures 5.49(b) and 5.49(c). From the location of the
first return striking the 150-meter weather tower and from the locations
of other objects on the ground in Figure 5.39, we estimated the ground


Figure 5.48.
Three-dimensional view of the cross-correlated
VHF sources, 94 ysec intervals, during the J1
or PB2 and the second stepped leader. The labels
A, B, C, and E, F, G show different regions of
propagation of the VHF noise sources. Q2 is the
source charge for the second return stroke
obtained from electric field records.


138
a change of slope in the electric field record at the beginning of the
J1 process (K-change, Figure 5.22), and (2) The VHF noise sources were
located in a different region from the FR.
Figure 5.28 shows the cross-correlated VHF noise sources during
the J1 process. The K-change starting the J-process propagated from
point P in Figure 5.28, at a height of 10.6 km and descended into a
lower region between the heights of 5.7 and 7.5 km. The arrows in
Figure 5.28 show the initial sequence of the progressing of the K-change.
The K-change lasted 1.1 msec for an average velocity of 9.5 x 10 m/sec
and showed a descending path of the VHF noise sources from P to near the
center of the lower crowded region in Figure 5.28. By measuring the
electric field change and applying equation (3.10) between the end points
of the propagation path, we determined the K-change lowered .9 Coulombs.
During the remaining 27.3 msec of the J1 process the VHF noise sources
did not show any regular progressing sequence. The bulk of the VHF
sources during the Jl process are located about 2 km above the FR sources
as can be seen by comparing Figures 5.28 and 5.27.
5.2.6 Second Stepped Leader
The second stepped leader had a VHF duration of 29 msec and started
immediately after the end of the VHF associated with the first J-change
process. From an analysis of only the electric field record shown in
Figure 5.22 it is not clear whether the second stepped leader started at
the end of Jl or at the time of the faster changing slope prior to the
second return stroke. However, since stepped leaders have been shown in
this thesis to exhibit low amplitude and high frequency VHF radiation,
the comparison of the electric field with the VHF record in Figure 5.22
shows clearly the point of the beginning of the stepped leader process.


30
sequence. We correlated the VHF noise with the electric field change
at the multiple stations. We determined that during the FR interval
either negative charges propagated downward from a region of higher
altitudes, or that positive charges (probably from the previous return
stroke) propagated upwards or both. We attempted to determine the
amount of charge transfer during the FR interval for one of the flashes
and found that for electric field ground stations whose distance is
greater than the charge height, a charge of A.5 2.1 Coul was trans
ferred. For close electric field measurements, no consistent charge
transfers could be found indicating that the charge distribution could
not be approximate as a point charge.
7.1.6 The J-Change Process
Throughout this thesis we have referred to the J-change or the J-
change process as the portion of the interstroke process, with continuous
active VHF radiation, that preceded dart leaders or subsequent stepped
leaders. This J-change process occupied 80, Al, 75, and 59% of the
total VHF radiation emitted by the four studied CG flashes (disregarding
the VHF radiation after the final return stroke). Other studied
characteristics of the interstroke period included the FR interval after
the first return stroke, solitary pulses, quiet periods, dart leaders,
and subsequent stepped leaders. The quiet periods are discussed in
this subsection as they relate to the J-change process.
To study one of the properties of the J-change process, let us
first make a comparison to the leader-return stroke sequence and the
PB-stepped leader sequence. A return stroke cannot occur without a
preceding leader, and an initial stepped leader cannot propagate unless
it had a preceding PB. Here we claim that dart leaders or subsequent


REFERENCES
Baudry, M. and B. Dupeyrat, ''Speech pattern recognition," Proceedings
of the Second Joint International Conference on Pattern Recognition,
Copenhagen, 356-357, 1974.
Box, G. E. and G. M. Jenkins, Time Series Analysis: Forecasting and
Control, Holden-Day, San Francisco, 1976.
Brook, M. and N. Kitagawa, "Radiation from lightning discharges in the
frequency range 400 to 1000 Mc/s," J. Geophys. Res., 69, 2431-2434, 1964.
Brook, M., N. Kitagawa and E. J. Workman, "Quantitative study of strokes
and continuing currents in lightning discharges to ground," J. Geophys.,
Res., 67, 649-659, 1962.
Cianos, N., G. N. Oetzel and E. T. Pierce, "A technique for accurately
locating lightning at close ranges," J. Appl. Meteorol,, 11, 1120-1127,
1972.
Clegg, R. J. and E. M. Thomson, "Some properties of era radiation from
lightning," J. Geophys. Res., 84, 719-724, 1979.
Davenport, W. B. and W. L. Root, An Introduction to the Theory of Random
Signals and Noise, McGraw-Hill, New York, 1958.
Dennis, A. S. and E. T. Pierce, "The return stroke of the lightning flash
to- earth as a source of VHF atmospherics," Radio Sci., 68D, 777-794, 1964
Dummermuth, G. and H. Fluhler, "Some modern aspects in numerical spectrum
analysis of multichannel electroencephalographic data," Med. Biol. Engng.
5, 319-331, 1967.
Enochson, L., "The application of digital time series analysis to the
determination of time delays," U. S. Government Doc. Report #9024, 3199,
Nov. 1973.
Erich, R. W. and J. P. Foith, "Peak detection on picture rasters," IEEE
Trans, C-25, 725, 1976.
Fisher, R. J. and M. A. Uman, "Measured electric field risetimes for
first and subsequent lightning return strokes,"-J. Geophys. Res., 77,
399-405, 1972.
Fitzgerald, D. R., "Some theoretical aspects of the relation of surface
electric field observations to cloud charge distributions," J. Meteorol.,
14, 505-512, 1957.
369


32 3
electronics, the tape recorder, and reproducer head configurations.
Since all the VHF signals were recorded at the central station, we had
to subtract the retransmission and other time delays between each one
of the remote and the central station. The retransmission and other
delays were determined using a calibration signal at a known location
(VAB CAL, in Figure 4.1). For each year ten readings of the calibration
signal recorded at all the stations were digitized at 8 MHz. Since the
location of the calibration signal is known, the average value of these
readings is used to determine the average retransmission delays. The
RMS error in the measurement of the DTOA for the calibration signal
varied between .19 and .62 ysec for the various remote stations. The
calibration error can now be determined by using equation (B.4) for the
uncertainties in the calibration of the remote stations. Once three of
the remote stations in Figure 4.1 are selected, the retransmission
delays for these are calculated. The average value of the retransmission
delay is fixed for all the calculations relating to any specific flash.
However since the error in X, Y, and Z is also a function of the location
of the VHF source relative to the location of the ground-based network,
the calibration error also varies with the selection of the remote
stations and the lightning locations.
The total error related to any calculation of channel location
(CJ ) is calculated from
tRMS
O
2
tRMS
2
qRMS
+ o
2
c RMS
( B. 5 )
The quantized error (o
while the calibration
QRMS^
error
is the random error in the measurement,
(a represents any additional time
cRMS


48
during the correlated electric field change. Since the electric field
records from at least eight ground stations in the KSC area were provided
by Krehbiel (private comm.), we could verify our results by using differ
ent electric field stations. We found that as long as the horizontal dis
tance from the electric field station to the point charge source was
further than the height of the source, our charge calculation was within
20% for the E-field at each station. Throughout this work, we selected
an electric field station which gave results in the middle of the 20%
deviation. The fact that we obtained inconsistent results for a
horizontal distance less than the height is an indication that a point
charge is not a good approximation within this range. For all the
stepped leader-return stroke studied in this thesis, we have calculated
the value of its charge source using this technique and whenever available
we have compared this result with the values obtained by Krehbiel
(private comm.) using the technique described by Krehbiel et al., (1979).
As we shall see, our results compare well with those of Krehbiel for
charge magnitude and location.


0) > n
in
NORTH
12 13
-v 1
,7- y .v> *
HEIGHT
10
m
Q >
CT c/)
HEIGHT
10
^ o
O 3)
V ;,*:<. ** ,. ,., ,.
n" *T fc*Yi-Va-^i->'* * *<"
, ->y/i £ !/*
, V #v"V <'.' ?
\7, - V
h
TOi


5.1.4 Activity Following the First Return Stroke (FR)
For 2.4 msec after the first return stroke there was a quiet period.
No VHF sources were identified during this period. The VHF radiation
after the quiet period was significant, lasting 4.3 msec with a pulse
about every 4 fisec. This activity is shown by FR (following return
stroke) in Figure 5.1. The source locations of the FR period propagated
upward between 2 and 7 km in height. The lower sources were located in
the neighborhood of the eastern locations of the stepped leader sources
in Figure 5.3(a). However, most of the radiation originated at a height
between 4.5 and 5.8 km, that is, in the lower portion of the preliminary
breakdown and upper portion of the stepped leader. Figure 5.9 shows
the location of the cross-correlated VHF noise sources, 94 ysec inter
vals, during the FR interval. We have labeled A through Q the progressing
sequence of the sources. Figure 5.8 also shows the location of the
previous return stroke charge source. The FR activity terminated with
a large low frequency pulse similar to the characteristic return stroke
pulses. The electric field records indicate that either negative charge
was lowered or positive charge was raised or both during the 4.3 msec of
VHF activity. Taking into account the locations of the VHF noise it
appears that the FR activity raised positive charges.
5.1.5 First J-Change (Jl)
Even though the FR activity is in the interstroke process, its
properties seemed to be related to the previous return stroke. The Jl


7
within a thundercloud might be considered as point charges if the
dimension of the charge region was small compared to the ground distance
to the ground observation point. Under these assumptions the thunder
cloud charge was treated as an electric dipole with an upper part that
carried a positive charge and a lower part that carried a negative
charge. Electric field measurements performed by Malan (1963), and
balloon tests made by Simpson and Robinson (1941), and Gish and Wait
(1950) yielded an average value of 40 coulombs for each of the charge
regions. However, measurements of charge neutralization of the order of
40 coulombs or larger in single ground flashes made by Brook et al. (1962),
Uman et al. (1978), and Krehbiel et al. (1979) make us suspect that 40
coulombs is too low an estimate for cloud charge. In addition, Malan
(1952) estimated that about half of the cloud negative charge was
neutralized during the lightning flash. Since the external electric
field often used to compute the cloud's static charge is due to the net
of the thundercloud charge and the surrounding space charge, the actual
value of the thundercloud charge is larger than reported values. In our
study we used the difference in the electric field during the different
phases of a lightning flash to determine the charge being transferred or
destroyed in a thundercloud, so the actual value of static charge is not
important to our work.
A ground flash is composed of one or more separate strokes in the
same or separate channels. Each stroke lasts for milliseconds and the
time interval between strokes is roughly 50 msec.. A stroke is composed
of a downward propagating leader, which lowers cloud charge and cloud
potential toward ground level, followed by a return stroke, an earth-
potential wave, which propagates back up the leader channel, discharging


nnn nonn nnnn
147
21 JUNE 1979
FUNCT I ON LAG ( AVCMU AVE MO 2 MKN)
** SUOPROGPA w TC CALCULATE THE CROSSCORRFLATt ON **
** OF THE ENVELOPE **
DI MENS ION RHC(2 040) .PRO(2048).AVEMO<2048),AVEM02C 2048 )
RH0FTE=-1.0
** LK1 AND LK2 ARE THE DEG INNING AND THE END OF **
** THE CORRELATION LAG, *
LK 1= 1
LK2= 30 0
N K =203 2
IF{MKN.EQ3) GO TO 891
IF(MKN.EQ.l) L K 2=15 0
GG TO 892
891 L K 1 = 300
LK 2= 60 0
892 DO 37 K=LKi,LK2
X I 1=0. 0
X 12=0.0
NK1=NK-K+1
P R D= 0 0
00 35 1=1,NK1
PRC( I ) =AVEMO( I )*AVEM02( IFK-I )
XI 1= X I IF A VEMO ( I ) =¡=*2
X I 2=X12 FA VEM02( I+ K- 1 )**2
35 PRD=PRDFPRO(I)
SNORM = SQRT(XI t*XI2)
PHO(K)=PR0/S NORM
37 CONTINUE
49 FORMAT( 1 OF 1 0.3)
LK 1=LK1+4
** DETERMINING THE LARGEST CROSS-CGRRELAT I ON **
DC 41 K=LK1,LK2
IF(RHO(K).GT.RHOFTE)GO TO 53
GG TO 41
S3 LAG=K
RHOFTE=RHO(K)
41 CONTINUE
T I MEX=.22978FLOAT(LAG)
WR IT E( 6,3 89 ) LAG, RHOFTE, TIMEX
389 FORMAT (122,2F22.3)
RETURN
END


250
(squares) and four cross-correlated locations for the sixth return
stroke (circles).
Figure 5.73 shows the VHF noise during the last 5.8 msec of the
J4 process, the 1.7 msec dart leader, the 810 ysec return stroke, and
the first 8 msec of the quiet period following the return stroke. The
fact that there is a quiet period after the sixth return stroke is
interesting. It appears from our results that the dart leader lowered
the negative charge from one of the isolated regions, most likely the
G region. Therefore, we would have expected the charges in the remain
ing region to cause additional breakdown and not be affected by the
return stroke of the other region, as occurred in the third and fourth
return strokes.
5.4.13 The J5 Process, the Stepped Leader Preceding the Seventh Return
Stroke and the Seventh Return Stroke
Active VHF radiation for the next J process (J5) started after the
8.5 msec quiet period that followed the sixth return stroke. The J5
process lasted 55 msec and initiated a new stepped leader. Similar to
J4, the cross-correlated VHF noise sources were detected in the neighbor
hood of the F and G regions in an unorganized sequence. Figure 5.74(a)
shows the cross-correlated VHF sources during the J5 process. The cross-
correlated sources in the F region extended a horizontal distance of 4
km and between the heights of 5.4 and 10.6 km. Simultaneously, the
sources in the C region extended a horizontal distance of 7 km and
between the height of 5.3 and 12.8 km. Even though, the cross-correlated
noise sources did not follow any regular progressing sequence, most of
the sources detected near the beginning of the J5 process were located
at the higher altitudes and the sources located near the end of J5 were


--20C
-IOC
-oc
2-10 1
EAST (km)
(a)
EAST (km)
(b)


212
along the path during these 23 msec. For the remaining 193 msec of the
CC interval, VHF sources were located along the previous path for the
first 62 msec, and in a newly developed channel during the last 138 msec.
After the first 85 msec of the CC interval most of the VHF radiation was
concentrated in solitary pulses (SP's), similar to those previously de
scribed in this thesis during the study of the 165959 flash. The source
locations during the SP's developed in a downward propagating path which
merged with the CC channel between the heights of 4 and 10 km. The
longest of these SP's lasted 11.5 msec and propagated downward between
the heights of 11.8 and 2.8 km in a path 20 off vertical at a velocity
of 6.2 x 10^ m/sec. Figure 5.60 shows the cross-correlated noise
sources, 94 |isec intervals, during this SP. The arrows indicate the
regular progressing sequence during the SP. The VHF noise sources
during the 11.5 msec SP were located further west than the other SP's
and furthest away from the main CC channel. The VHF noise for this SP
is shown in Figure 5.40 and corresponds to the third SP from the end of
the CC interval. The SP's during the CC interval have opposite direc
tion and lower velocities than the SP's of the IC discharge in the
165959 flash. It appears that negative charges propagated in the SP's
during the CC interval. Probably SP's during the CC interval developed
new paths for negative charges to propagate down the channel.
5.3.17 Volume of the Flash
Figures 5.61(a), 5.61(b), and 5.61(c) show the two-dimensional
projections of the 18,887 noise sources located during the flash. The
average rate of a pulse .location is one every 22 psec. The pattern
evident in Figure 5.61 results from the quantization error for finding
locations with a discrete time interval of 229 nanoseconds as explained


and K-changes. The maximum energy of the radiation spectrum is at VLF.
The average source spectrum has a maximum at about 5 KHz and decreases
inversely proportional to frequency above 10 KHz. In the frequency
range from 300 KHz to 30 MHz the number of current elements increases
but the magnitude of the return stroke radiation pulse decreases. As
the frequency increases above 30 MHz the number of current elements
increases with a peak at 50 MHz, and then decreases (Oetzel and Pierce,
1969). Above 30 MHz the magnitude of the pulses decreases with increasing
frequency. At LF and VLF the length of the return stroke channel and the
K-change channel are of the order of magnitude of these wavelengths,
since the radiation half cycle time is the channel length divided by the
propagating velocity and this is the only radiation that exists. As
frequency increases into the HF and MF range, there are more current
elements with length comparable to the wavelength. We expect that most
current elements active during lightning discharges have lengths of the
order of tens of meters which will be detected with a center frequency
of tens of MHz.
Another important variable to consider in the study of atmospherics
is the effect of the propagation medium between the current elements and
the group receiving stations. Excellent reviews of the propagation
conditions of atmospherics can be found in Horner and Bradley (1964),
Oetzel and Pierce (1969), Harth (1974), and Pierce (1977). The charac
teristics are a function of the frequency of the emitting source, the
propagating distance, and the reflective properties of the earth and the
ionosphere. The ionosphere has complex reflection properties as a
function of frequency. According to Pierce (1977), the propagating
conditions of atmospherics can be separated into three groups. Below


210
5.3.16 Continuing Current
The six-stroke cloud-to-ground flash was followed by a 1.5 quiet
period and then a 216 msec continuing current. The reason we deter
mined that this period of time was a continuing current is as follows:
(1) The electric field variation in stations located 2 to 21 km away
from the discharge rose steadily during this time interval. Distant
intracloud discharges with significant vertical components should
exhibit a falling electric field as in the 165959 flash. (2) The
luminosity following the last return stroke was observed on TV and com
pared to that following a stroke with no steady field change. We
determined that the last return stroke channel had some luminosity for
195 msec, a time about 100 msec longer than the luminosity observed in
a similar flash without a following field change indicative of contin
uing current.
The VHF noise sources during the continuing current (CC) interval
developed in a 14 km channel 40 off vertical between height of 2.8 and
15 km. The western tip of the channel was located in the neighborhood
of the western part of J3, but the channel extended 4 km further toward
the northeast at the higher altitudes. Similar to the first few J-
changes, the noise sources were organized into a relatively well defined
channel. Figure 5.59 shows the cross-correlated noise sources, 94 ysec
intervals, during the first 23 msec of the CC interval. It appears
that negative charges propagated throughout the CC channel to the return
stroke channel. Since VHF radiation is not emitted by channels carrying
relatively steady currents, most of the VHF1source locations were
detected above a height of 4 km. The noise sources in Figure 5.59 did
not occur sequentially in a downward path but were located randomly


non nnn
158
21 JUNE 1979
WRITE(6, 10) XM(NM), YM(MM ) .ZM{NM )
RE AD{ 13.2 0) ( (A( I). I=1,3) (0( I) .1 = 1,3 ) (C( I).1 = 1,3),
* (0(1),1 = 1*5))
20 FORMAT(8X,2A4,A3.8X,2A4,A3,8X,2A4,A33X,5A4)
DO 22 1=1,128
** READING ALL THE LOCATIONS **
R E AO( 13, 42) X1,Y l ,Z1,TIME( I )
M X =X 1
IF(MX.EQ.O) GO TO 28
IF(Z1 .LE.O .0 ) GO TO 22
N = N+ 1
22 CONTINUE
GO TO 28
69 READ( 13,42) ZERO ZERO,ZERO,ZERO
28 CONTINUE
29 CONTINUE
42 FORMAT(3E18.3.E26.3)
W R IT E ( 6,5 0 )
50 FORMAT(/////)
NF = 0
DC 3 I=1,NM
NF =NF + l
XMP(NF ) = XM{ I )
Y M P ( NF ) =Y M ( I )
ZMPNF)=ZM( I )
WRITE!6,18) XMP(NF),YMP(NF),ZMP(NF)
3 CONTINUE
WRITE(6,50)
NL=NF
** DETERMINATION OF THE SCALES **
SX=SMALL(XMP,NF)
SY = SMALL( YMP,NF )
SZ=SMALL(ZMP,NF )
BX=0 I G (XMP, NF )
BY=BIG BZ=BIG(ZMP,NF)
IF(SX-O.O) 4,6,5
4 SX=A INT{ SX-1.0)
GO TO 6
5 SX=AINT(SX)
6 IF(SY-0.0) 7,9,8
7 SY=AINT(SY-1.0)
GO TO 9
8 SY=AINT(SY)
9 SZ-AINT1SZ-1 .0)
IF(OX-O.O) 11,15,13
11 0X=AINT(OX)
GO TO 15
13 UX=A INT( D X+ 1.0)
15 I F {11Y-0.0 ) 17,21,19
17 U Y = A I M I ( U Y )
GU TO 21
19 BY =AINT(DY + 1 .0 )
21 B Z =A INK fl Z+l .0)
IF(KRS.EQ.l) SZ = 0.0
XU S=BX SX
YB S=BY-SY
ZBS=BZ-SZ
W RITE( 6,26) DX, SX,BY,SY,UZ,SZ
26 FORMAT(10X,6(El 0.3,5X) )
DO 23 1=1,ML


327
Tables B.3 and B.4 show the quantized, calibration, and total error for
the three-dimensional VHF source locations over the entire range of
these flashes.


44
response from DC to 20 KHz and a direct recording channel with frequency
response from 300 Hz to 300 KHz. The electric field input to the
recorder had a response from 0.2 Hz to 1.5 MHz. In 1977 the recording
system was improved such that the analog data was recorded with a FM
frequency response from DC to 500 KHz, and a direct recording with a
frequency response from 400 Hz to 1.5 MHz.
The correlated waveforms from the NMIMT electric field stations
consisted of a network of nine stations spread out over the KSC area
(Krehbiel et al., 1974). The electric field sensed at eight remote
sites was retransmitted as amplitude modulation over a microwave telemetry
link to the central station (station nine). At the central station the
electric field from all the stations was recorded on analog tape. The
NIMIT electric field meter had a system decay of 10 sec and a frequency
response from 0.1 Hz to 5 KHz.
KSC IRIG B time code information was stored in all the analog tapes
containing electric field information. Time correlation between any of
the electric field stations and the four LDAR VHF radiation data was
accurate to one hundred microseconds.
3.5. Charge Locations Derived from Electric Field Stations
The electric field (E) detected at a horizontal distance d from a
charge Q at a height z from a perfectly conducting ground plane is given
by Uman, 1969, pp. 48-49.
E =
2 Q z
2 2
4tte (z + d )
o
3/2
(3.6)
where e is the permittivity of free space. The term d can be expressed


162
propagation ended the process. The regions F, G, X, Y, Z and H, I
correspond to the outer region of the previous Jl, J2, and CAFS volume.
Finally it is worth noting that the initial horizontal and downward
propagation velocity of 3.8 x 10^ m/sec (A to E) is comparable to the
upward propagation of 9.1 x 10^ m/sec (S to W).
5.2.12 Volume of the Flash
Figures 5.38(a), 5.38(b), and 5.38(c) show two-dimensional projec
tions of the 34,478 noise sources located during the flash. The average
rate of pulses is about one every 8 psec. The pattern evident in Figure
5.37 is explained in Appendix B. The flash occurred near the coast of
the Atlantic Ocean in the central part of the Cape Canaveral AFS, from
3 to 8 km EW, 7 to 17 km NS, and up to 12 km in height. With the excep
tion of the three stepped leaders most of the flash concentrated between
4 and 7 km EW, 9 to 12 km NS, and 4 to 8 km in height. The flash
1 3
extended throughout a volume of about 500 km during a time of 282 msec.
5.2.13 Concluding Remarks About the Flash
We now provide a summary of what we have learned about this flash.
(1) The flash lasted 282 msec and consisted of three return strokes each
preceded by a separate stepped leader to ground. (2) The flash started
with a PB that lasted 2.1 msec. During the first 600 msec of the PB
the VHF sources propagated upwards and horizontally and there was no
detectable correlated electric field change. During the last msec of
the PB the noise sources filled a path in an unorganized way f 1 km in
both the horizontal and vertical direction. (3) The three stepped
leaders lasted 7.9, 29.0, and 15.5 msec, respectively. All three
stepped leader paths to ground started within 2 km of each other and


23
often accompany a K-change. S pulses are those that do not fit the two
categories previously described. In addition, Proctor often refers to
R noise as the abrupt (starting noise) pulse which is characteristic of
most return strokes.
The P-type of pulse has been the subject of additional analysis.
In general, it was reported that the rate of electric field change was
directly related to the frequency of P pulses. That is, a sequence of
P pulses indicated fast E field change while their absence indicated a
reduction in the slope of the field change. P pulses seem to be emitted
from regions near the advancing tip. By determining a fix at the
leading and trailing edge of the pulse, propagation vectors have been
found. The sources appeared to form at very high velocities near the
speed of light. The directions of the vectors grouped in cones whose
axes appeared to lie in similar directions for any one storm. Proctor
speculated that the geomagnetic field might have some influence in the
direction of the sources.
The Q noise trains and K-changes were also studied further by
Proctor (1976). Of 26 Q noise trains reported in one flash, only eight
had detectable K-changes and six of these were associated with positive
streamers. Proctor attributed this difference to the low gain of the
field meters. Contrary to Proctor, the work reported in the present
finds that more than 50 percent of the Q noise trains did not show any field
meter change. Our equipment was sufficiently sensitive to detect a
2 volt/meter change. The Q noise that Proctor reported was weak and
only 5 out of 26 channel locations were studied. These Q noises were
emitted from regions below the lower extremity of the flash. K-changes


O 40 80 120 60 200 240 280 320 3G0 400 440 480 520 560 600 640 680 720 70 800 840 880 920 960
TIME IN MICROSECONDS
Figure 5.13. Logarithmic-amplitude VHF radiation during the three
solitary pulses (SP's) in the J2 process.


196
return stroke locations, 94 Msec intervals, are shown as circles in
Figure 5.49. The return stroke channel locations extended from 6.5 to
14.5 km of altitude. The return stroke channel propagated not only
throughout the previous leader but also in the previous J-change (J1)
or preliminary breakdown (PB2). This is a reasonable result since the
entire channel was apparently negative charged and the return stroke
neutralized part of this charge. Three of the seven return stroke
source locations were between 9 and 10 km. It was at about this loca
tion (point B, Figures 5.48 and 5.49) that the VHF noise changed
characteristics from J1 or PB2 to stepped leader. Taking point B
(0.7, 9.2, 10.5) as the point source of the second return stroke and
using the techniques described in Section 3.6, we calculated that -8.2
Coulombs were lowered by the second leader-return stroke sequence.
This number compares reasonably well with the -9.6 Coul shown in Table
5.6.
5.3.8 Second J-Change Process
Figure 5.51 shows the cross-correlated VHF noise sources, 376 ysec
intervals, during the second J-change (J2). The J2 process started
after a quiet period of ,5 msec, lasted 36.2 msec, and extended in a
path 32 off vertical between the heights of 5.8 and 12.7 km. Figure
5.51 also shows the Q3 location given in Table 5.6. The VHF noise
sources during the first millisecond were located at the bottom, the
middle, and the top of the J2 channel. These sources do not appear to
propagate upward in the channel, rather the noise sources are located
along isolated volumes along the path that joins these locations.
During the remaining 35 msec, 78% of the VHF noise sources are located
between the heights of 7.5 and 11.5 km. It is worth noting that even


to contact the ground first and produce the third return stroke.
5) After the third return stroke, most of the VHF sources were detected
below the A-B channel. About 3.9 msec prior to the fourth return
stroke, the lowest detectable source from the fourth stepped leader was
detected at a height of 3.7 km. It appears that the stepped leader
from the A-B region contacted ground 5.4 msec after the third return
stroke.
It is worth noting that the sources detected in the neighborhood
of C did not propagate from the B region, but there were two different
electrified regions. This claim is made from determining the source
location in the last pulse of the B region and the first pulse of the C
region, and calculating a velocity larger than the speed of light
between these sources. The sources that appeared between the A-B and
C-D regions in Figures 5.68 and 5.69 appeared in a random sequence
during the propagation of the third and fourth stepped leaders.
Table 5.6(a) does not show a charge location for the third return
stroke because it was not possible to determine the beginning of the
stepped leader by analyzing the electric field records. The Q4 charge
location for the fourth return stroke is in the region of the A-B path
that generated the fourth return stroke. Using the techniques described
in Section 3.6, we estimated that the third and fourth stepped leader-
return strokes lowered -14.4 and -3.6 Coni, respectively.
5.4.10 The J3 process and the Fifth Stepped Leader
The. J3 process lasted 21.1 msec and followed immediately after the
fourth return stroke. Figure 5.70(a) shows the location of the cross-
correlated VHF sources during the J3 process. Most of the activity was
concentrated in a region 1 1cm east and .6 km south of the source origin


175
EAST(km)


Figure B.3. Two-dimensional views: (a) top view, EW-NS, (b) elevation view, EW-height, and (c)
elevation view, NS-height for all the noise sources in 50 consecutive iterations of
the three time delays for a sample interval of 0.1 psec.


38
t z (f )
/
/
/\ /
>S(f )
A
/\A/2
2fo
-80MHz
K-2B-H
20 MHz
2f0
80 MHz
Figure 3.8. Frequency spectrum at the output of the envelope detector.
Figure 3.9. Frequency spectrum at the recorder.


ALTITUDE (km)
o
o
o
o
o


237
It appears from Figure 5.67 that these two regions merged together and
that the stepped leader had a large horizontal component in the NS
direction. The stepped leader velocity was about 2.6 x 105 m/sec.
5.4.7 Second Return Stroke
The second return stroke lasted 810 ysec in the VHF noise record.
Four cross-correlated noise sources are shown in Figure 5.67 (circles).
All these sources were located in the northern group between the heights
of 5 and 6.5 km. Using point P (-3.7, 11.7, 5.9) as the transition
point to stepped leader waveform, and the technique described in Section
3.6, we calculated that the second stepped leader-return stroke lowered
-8.2 Coul (Table 5.6(b)). This number is comparable to the -9.5 Coul
shown for Q2 in Table 5.6(a), however, our source location is about 3.7
km north and 1.7 km lower in altitude than Ql.
5.4.8 The J2 Change
The J2 change lasted 7.2 msec and started after the 5.7 msec quiet
period that followed the second return stroke. The noise sources during
the J2 change started 0.5 km West and 2.0 km South of Jl. During the
first 1.5 msec of the Jl. period the noise sources propagated upwards
between the heights of 5.2 and 8.0 km. This upward propagation appears
to be related to additional breakdown caused by extensions of the
previous return stroke channel. For the remaining 5.7 msec the VHF
noise sources extended between -6.0 and -4.5 km EW, 8.3 and 10.1 km NS,
and between the heights of 6.0 and 9.0 km.
5.4.9 Third andFourth Stepped Leaders and Return Strokes
We studied the electric field change measured at ten different
electric field stations but we could not clearly determine any slope


NOISE
LEVEL


i 9
Figure 5.2. Simultaneous records of the logarithm VHF radiation at
four different ground-based stations. Pulses 1, 2, 3, and
4 are identified as examples of pulses arriving at differ
ent times at different stations. The parameter "r" repre
sents the actual distance from the stations to the cloud
source.


Table 5.1 cont.
Start
Time
(msec)
Event
Duration
(msec)
Average Velocity
m/sec
Coordinates (km)
UPPER
LOWER
X
y
z
X
y
Z
96.00
4th Quiet Period of J2
52.45
148.45
VHF Portion of J2
47.0
2.0 x 105
3.6
16.2
13.1
0.1
11.8
8.5
195.45
Stepped Portion of SDL
2.2
4.5 x 106
0.4
12.2
8.0
-1.0
11.7
3.3
198.65
Dart Leader Portion of SDL
1.1
199.75
Third Return Stroke (R3)
.13
199.88
Quiet Period
29.82
229.70
SP No. 4 (SP4)
.625
230.32
Quiet Period
108.82
339.20
IC (Continuous Part)
501.00
7.5 x 105
6.0
13.6
14.0
1.7
9.5
5.9
889.5, 898.9, 910.7, 915.9,
and 937.3
msec Solitary Pulses after the
IC.


3 I 2
Figure A.l. Three-dimensional hyperbolic system.


Figure 5.31.
Log-amplitude VHF radiation during the second stepped leader, the second return
stroke, and the beginning of the J2 process. Cross-correlated source locations
for pulses A through E at the beginning of the J2 process are shown in Figure 5.32,
146


298
preceded by dart leaders were located in the neighborhood of the previous
J-change between a height of 12.6 and 6.5 km. It was not possible to
detect accurately return stroke velocities because only a few sources
were detected and they did not necessarily follow an upward progressing
sequence. On the basis of the fact that there was no VHF radiation in
one of the return strokes and that the VHF sources in the remaining of
the return strokes were located along the channel to ground (for those
return strokes preceded by stepped leaders) and in the J-change (for
return strokes preceded by dart leaders), it appears that the VHF
radiation during return strokes is generated by extensions of the pre
viously existing leader channel. The return stroke wide VHF pulse
represents a potential wave that propagates throughout the previous
channel toward the higher altitudes.
We presented in our analysis the location of the stepped leader-
return stroke source obtained by Krehbiel (private comm.) using the
technique of Krehbiel et al. (1979). We determined that the location
of Krehbiel's point charge center for the return strokes of the four
flashes were in fairly good agreement with the location of the PB-stepped
leader path (for initial SL), or J-change-stepped leader path (for
subsequent stepped leader). The point charge provided to use for the
return strokes of these flashes ranged between -25.7 and -2.9 Coul and
a height between 7.9 and 4.4 km.
In addition to finding the return stroke point: charge using multiple
station electric field measurements, we assumed the location of the
stepped leader-return stroke charge was the PJ3-SL junction and calculated
the charge using the technique described in Section 3.6. We obtained
results which were comparable to the ones determined by Krehbiel.


EAST (km)
D.OC-


Table B.3. Error Analysis for the Locations in the 181807 Flash. The locations are arranged in
ascending order in z.
Source Locations
(Meters)
Quantization RMS
Error (Meters)
Calibration RMS
Errors (Meters)
Total RMS Error
(Meters)
X
y
z
dxQ
dyQ
dzQ
dx
c
dy
J c
dz
c
dKt
dyt
dz
t
5612
8301
705
101
97
3856
167
200
5387
196
223
6625
5569
8211
1055
98
97
2444
162
198
3455
189
221
4232
7027
14997
1587
225
264
5759
345
328
7888
412
421
9767
5458
8310
2308
92
100
1050
153
195
1537
179
219
1862
6761
14847
2411
208
257
3557
324
320
4924
385
411
6075
5969
9263
3555
103
113
885
173
198
1287
201
228
1563
5633
13719
4048
147
216
1544
240
275
2232
282
350
2714
5982
9486
4369
101
119
737
171
200
1093
199
233
1318
5950
12421
4715
133
178
1127
221
244
1633
258
302
1984
5364
9413
5190
90
123
549
152
203
852
177
237
1014
4038
8864
5226
77
118
393
120
203
661
143
235
769
5358
11929
5865
109
172
754
184
239
1146
214
295
1372
4254
10151
5956
83
139
469
134
216
766
158
257
898
3740
9418
6031
77
130
376
117
211
641
141
247
743
4967
10296
6047
90
141
526
151
216
833
176
258
986
5095
8528
6555
82
119
369
134
198
611
157
231
714
4551
10595
6653
37
150
481
143
223
781
168
269
917
4600
10781
7055
88
155
477
145
227
776
170
275
911
5752
11742
7698
107
178
599
184
246
937
213
303
1112
6333
10613
8590
105
161
515
185
231
817
213
282
966
5074
13639
9003
107
236
629
184
302
1012
213
383
1192
3631
10146
10469
85
165
344
121
238
598
148
290
690
Averace error for
loca-
tions in
this flash.
109
156
1247
178
232
1812
209
280
2201
328


570
French, A. S. and A. V. Holden, "Frequency domain analysis of neurophysi
ological data," Computer Programs in Biomedicine, 1, 219-234, 1971.
Gish, 0. H. and G. R. Wait, "Thunderstorms and the earths general
electrification," J. Geophys. Res., 55, 473-484, 1950.
Gottman, J. and P. Gloor, "Automatic recognition and quantification of
interictal epileptic activity in the human scalp EEC," Electroenceph.
Clin. Neurophysiol., 41, 513-529, 1976.
Harth, W., "The propagation of atmospherics," in H. Dolezalek and
R. Reiter (eds.), Electrical Processes in Atmospheres, 663-682, Dr.
Dietrich Steinkopff Verlag, Darmstadt, 1974.
Hewitt, F. J., "The study of lightning streamers with 50cm. radar,"
Proc. Phys. Soc. London, Sec. B., 66, 895-897, 1953.
Hewitt, F. J., "Radar echoes from inter-stroke processes in lightning,"
Proc. Phys. Soc. London, Sect. B., 70, 961-979, 1957.
Hewitt, F. J., "Radar studies of noise in lightning, in monograph on
radio noise of terrestrial origin," edited by F. Horner, Elsevier Pub.
Co., Amsterdam, 72-84, 1962.
Holmes, C. R., M. Brook, P. Krehbiel and R. McCrory, "Reply," J. Geophys.
Res., 76, 7443, 1971.
Holmes, T. G. and P. H. Reedy, "Geometrical dilution of precision,"
Report 21, Patrick AFB, Fla., 1951.
Horner, F., "Radio Noise from thunderstorms," in J. A. Saxton (ed.),
Advances in Radio Research, vol. 2, 121-204, Academic Press, Inc.,
New York, 1964.
Horner, F. and P. Bradley, "The spectra of atmospherics from near lightning
discharges," J. Atm, and Terr. Phys., 26, 1155-1166, 1964.
Ishikawa, H., "Nature of lightning discharges as origin of atmospherics,"
Proc. Res, Inst. Atmos. Nogoya Univ., 8A, 1, 1960.
Jacobson, E. A. and E. P. Krider, "Electrostatic field changes produced
by Florida lightning," J. Atm. Sci., 33, 103-117, 1976.
Jerri, A., "The Shannon sampling theorem," Proc. IEEE, 65, Nov. 1977.
Jones, D. L., "Electromagnetic radiation from multiple return strokes of
lightning," J. Atmos. Ter. Phys., 32, 1077-1093, 1970.
Khastgir, S. R. and S. K. Saha, "On intra-cloud discharges and their
accompanying electric field changes," J. Atmos. Ter. Phys., 34, 775-786,
1972.
Kimpara, A., "Electromagnetic energy radiated from lightning," in
S. C. Goroniti (ed.), Problems of Atmospheric and Space Electricity,
352-365, American Elsevier Pub. Co., New York, 1965.


67
cross-correlation is calculated, either 94 or 376 ysec. The graph is
expanded in Figures 4.3(a), 4.3(b), and 4.3(c). Figure 4.3(a) shows the
algorithm initialization and the characterization of the central station.
Figure 4.3(b) shows a similar technique for the remote station and its
relationship with the central station to determine the time delays.
Finally, Figure 4.3(c) concludes the algorithm with a determination of
the three-dimensional locations. If additional data are desired, the
algorithm is repeated.
4.4.1 The Algorithm Limitations
The principal limitations in the development of this algorithm are
the time interval selected for the cross-correlation function and the
selected features for pattern recognition. Next we provide some argu
ments about these limiting factors.
The longest time delay between the central and a remote station is
determined for source locations near the ground and on the opposite side
of the line joining the central and the remote stations. For a 10 km
baseline between central and remote stations, the search for appropriate
time delays should include 33 ysec from the central station data.
From the test described in Section 4.2.2(3), we could have several
pulses which met any given tolerances for AS, DS, RR, RL, and NAR with
in the 33 ysec interval. This argument implies that pattern recogni
tion alone is not a sufficient factor for the determination of time
delays. Also from Section 4.2.2(3) we learned that we were 100%
successful matching the envelope of the time-series data. Therefore,
the use of the cross-correlation function is an essential part of the
algorithm. The cross-correlation time interval of 94 or 376 ysec was
chosen on the basis of the data properties and this is one of the


BEGINNING OF I.C.
1 1 1 1 1 1 1 1
00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00 9
TIME IN MILLISECONDS
Figure 5.83. Logarithmic-amplitude VHF radiation during the first 6.5 msec of
the intracloud discharge.


33
3.2 Telemetry System
Figure 3.3 shows the telemetry system used at each receiving sta
tion. The signal w^(t) is received by a 5 meter-high linear antenna
array that detects the electric field. The signal is passed through
a 30-50 MHz bandpass filter (30-50 MHz for 1976 data, 40-50 MHz for
1977 data), included in the VHF receiver. Then the logarithm of the
magnitude of the envelope signal is obtained using an envelope detec
tor .
Figure 3.3 is redrawn in Figure 3.4 to show the operation of the
receiving system. Here, f = 40 MHz, and the bandwidth, 2B, is equal
to 20 MHz. Figure 3.5(a) shows an approximation to the squared band
pass filter. The g^(f) filter has gain N^. Figure 3.5(b) shows the
corresponding time domain function, g^(t), of the wideband VHF receiver.
gx(t) = 2 NlB cos(2TTtfq) (3.1)
Equation (3.1) can be obtained from Figure 3.5(a) by doing the
inverse Fourier Transform of g^(t). The g^(t) term consists of a slow
varying waveform of the form sint/t which constitutes the envelope of
the waveform cos(27rtf ) which has been modulated. The output u.(t) can
o l
be written as
U(t) = w.(t) 2NXB cos(2?rfot) (3.2)
where is the convolution operator.
The spectra of atmospherics from nearby lightning discharges has
been studied by various investigators (e.g., Takagi and Takeuti, 1963).


Table 5.3. Events in the 181806 Flash.
Universal Time at the Start of the VHF
Radiation: 18
18 06
266.13,
8th August 1977
Start
Time
(msec)
Event
Duration
(msec)
Coordinates (km)
Velocity
m/sec
UPPER
LOWER
X
y
z
X
y
z
0
Preliminary Breakdown
1.9
-0.08
9.2
9.5
-.86
9.1
6.7
(*) 9.2 x 105
1.9
First Stepped Leader
5.9
-0.86
9.1
6.7
-.82
8.7
2.7
1.0 x 106
7.8
Return Stroke (Rl)
0.475
0.1
9.6
10.2
-1.5
9.7
2.9
8.2
Following 1st Return Stroke
8.86
-0.4
9.0
8.4
-1.5
8.8
5.1
1.2 x 107
17.0
Semi-Quiet Period
7.5
-0.3
9.1
9.5
-0.8
9.0
6.5
24.5
Quiet Period
16.5
41.0
First J-Change
8.1
1.8
11.4
14.2
0.7
9.2
10.5
5.0 x 105
49.1
New Stepped Leader
17.5
0.7
9.2
10.5
-2.4
8.9
2.8
6.7 x 105
66.6
Return Stroke (R2)
.859
1.8
11.1
14.5
-1.0
8.3
6.5
67.5
Quiet Period
.5
68.2
J-Change (J2)
36.2
1.9
10.08
12.7
-0.4
8.9
5.8
104.4
Dart Leader
.495
0.3
9.8
8.5
-0.6
9.7
7.5
104.9
Return Stroke (R3)
.092
0.8
11.8
12.6
-1.4
11.8
12.2
105.0
Quiet Period
1.1
l 70


0
" T ' "1 1 1
2 4 6 8
TIME IN
10 12
MILLISECONDS
f
14
16
18
Figure 5,23. Log-amplitude VHF radiat
cloud-to-ground flash.
ion at the beginning of
the 180710
1 28


I
. I 111
w in in u
; SI *. .) 0tS
MUS4 HI fl.lfl
SB fl tTg '
m am
Ml I j
i.
&' L i L
a i
SB
it.
ill 1
Ini
8 i C
£ I. I 8
r 11 *
& i j
n*jr
j ; III
* ir ii
I i I.Ji
|! Sf
II 1
j 11
i \ !! J
>i J I. 1*8
i J yi
3
, : inn II
I y '
\ n.i
i ;
i-H
fi
'll
*1

¡¡i1
/,* !n
¡I?]
1 ¡I
,1 f.
i
? t
j' .8
IIJ
I
I l> 1 .11
i i J l|r -
T
Ji
4§u
i g I
Ui
I?1
¡ n
ii
¡ I
I s
i
{ ¡ i 1
ill ;
|- i;l 1,
|jt
hill
j A
'|i
\
;( H
It v*.
MIT
i I
>ii !
1 ri! 1
:4 4* II
1 l. I
i
1(1 L I
11.
1 l
,! 11
' ri. t n
i i1
i i
in i
M !
i m;
; i
i
, .i
V
END OF
STEPPED
LEADER
>K-
4-
R2
H
0.10
0.20
0.30 0.40 0.50
TIME IN MILLISECONDS
0.60
0.70
0.80
Figure 5.50. Logarithmic-amplitude VHF radiation during the second return stroke.


O)


for that station and no VHF radiation is detected whereas significant
radiation is located at the other stations.
4. Since the analog tape direct recording follows a Butterworth
response with a 3 dB drop-off at 400 Hz and 1.5 MHz, only pulses with
an original period between 2.5 msec and 0.66 ysec could be properly
measured with this recorder bandwidth. The largest pulse width measured
was about 500 visee; therefore,the lowest recorder frequency did not
limit the characteristic of the data pulses. In addition, we studied
the characteristics of the VHF pulses obtained with a 5 MHz bandwidth
using the Biomation 1010 in the LDAR real-time system. We determined
that about 5% of the VHF pulses had a width between 0.2 and 0.6 ysec.
These pulses and any shorter ones were lost in our analysis.
4.2.2 Properties of the Multiple Time-Series Data
We displayed some selected data with a 10 dB signal-to-noise ratio,
from the four channels, with a resolution of 1 ysec per cm for the pur
pose of studying the characteristics of the pulses in the series. From
this display we manually determined the DTOA between identifiable pulses
Some of the important characteristics that we identified are listed
below:
1. With the exception of the stepped leader radiation discussed
in Chapters V and VI, the time-series data contained an envelope with
pulse widths between 5 and 500 ysec. In addition, there were higher fre
quency pulses of a pulse width usually less than 3 ysec superimposed on
the envelope.
2. To identify uniquely the same pulse on any two of the time-
series, two selection criteria were used. First, we matched the lower
frequency envelope on which the pulses were superimposed. Second, we


identified the corresponding pulses within the envelope. When we per
formed our manual matching of pulses, we attempted to determine a
minimum time interval, needed for a unique identification of the envelope.
After studying different sections of the data, we determined that the
minimum sample interval to uniquely characterize the envelope was about
100 ysec. In addition, we attempted to determine a time interval
required to uniquely identify the duration of the individual pulses
which are superimposed in a selected time interval of 100 ysec. Our
results indicated that a maximum interval of about 3 ysec was required.
3. An additional test that we performed was to pass the time-series
data through a low pass filter that eliminated all pulses wider than 10
ysec. When we attempted to match the individual pulses manually, we
were only 20% successful. On the other hand, when we smoothed the data,
getting rid of the high frequency pulses, we were 100% successful on
matching the envelope for a sample interval of about 100 ysec. In the
latter test, we have lost information on the individual high frequency
pulses.
4. To determine some additional characteristics of the time-series,
we measured the time delays of 185 consecutive individual pulses between
the central and each one of the remote stations in one flash and 50 pulses
in another flash. We learned that time delays for over 95% of the con
secutive pulses are within a 2.5 ysec interval.
4.3 Technique for Determining _Delays Based on the Data Characteristics
Our next step was to develop a computer algorithm to determine time
delays based on the data characteristics of our time-series. To meet
the data properties in Section 4.2.2, we chose to use cross-correlation


E FIELD (volts/meter) VHF RADIATION
997


!
RETURN STROKE
3
1 1 1 1 1 1 1 |
40 80 120 160 200 240 280 320
TIME IN MICROSECONDS
360
400
Figure 58. Logarithmic-amplitude VHF radiation during the first return
stroke.


range, Proctor, working in South Africa, had built and tested a five
station system to measure noise impulses in the VHP range. Proctor
has written only a Ph.D. thesis and a limited number of papers and
reports about his work in South Africa. Next we will present a summary
of Proctor's work (Proctor, 1971, 1974a, 1974b, 1974c, 1974d, and 1976)
and its relationship to the work presented in this thesis.
Proctor (1971) describes his telemetry system and gives some
preliminary results. The system consists of four 253 MHz crystal-
controlled receivers located at the ends of a cross (the remote stations),
and a fifth station (the central station) at the center of the cross.
The distance from the central to the remote stations ranged between 10.7
and 26.7 km. All stations consisted of a 10 MHz bandwidth VHF receiver
centered at 253 MHz and progression detection i.f. amplifiers to give
the receiver a logarithm response near 80 dB. This detection technique
is very similar to the band-pass filter and logarithm envelope detector
used in the telemetry of the work reported in this thesis. The remote
station spherics were retransmitted to the central station by frequency
modulated 10 GHz links with 5 MHz bandwidth. Therefore the overall
bandwidth was 5 MHz for the remote stations and 10 MHz for the central
station. All five signals together with 5-ysec timing markers were
displayed on cathode ray tubes (CRT's) and they were photographed by
35-mm rotating drum cameras. The film moved with a velocity of 8 m/sec.
CRT's were also used to display electric field change and time markers.
When the operator had decided that the storm was sufficiently close for
channel reconstruction (usually less than 20 km') a trigger signal
selected a threshold level to start the film. The maximum continuous
film time is 250 msec. Since most flashes last more than 250 msec


282
For a model to be valid it should fit the specific physical process
regardless of the selected flash. Therefore, we selected data from the
stepped leader, J-changes, and noise levels for all the flashes, deter
mined their respective models, and then compared the results. If con
sistent results were obtained, then we can claim that the physical pro
cess fits a specific data model.
For a data range larger than 500 microseconds all the analyzed
processes present some type of equilibrium because the larger pulses
determined in the VHF radiation have a width of the order of 240 micro
seconds. Each process studied has a constant mean for data records
larger than about 2.3 msec (about 10,000 samples) and can be treated as
stationary.
Four types of stochastic models are tested. The autoregressive
(AR), the moving average models (MA), the autoregressive-moving average
(ARMA), and the autoregressive-integrated-moving average models (ARIMA),
(Box and Jenkins, 1976). We will identify not only the type of model
that reproduces the data, but also the order and properties of such a
model. In the AR model a VHF radiation value of the output z^ is defined
as
z
t
>lZt-l + Vt-2 +
) z + a
P t~P t
(6.1)
where is a white noise representation of the VHF noise input and p is
the order of the AR model order. In the MA model is defined as
z
t
a
t
iat-i
2at-2
0 a,
q t-q
(6.2)
where q is the order of the moving average model. A more general data
model, the ARMA, includes both previous values of the output and (z^'s)
and the input (a 's):


EAST (km)
ALTITUDE (km)
,cno)'vjoo(DO-r\jw
9 Vi'


Figure 5.3(a).
All of the 422 VHF noise sources detected for both the preliminary breakdown
(A to B) and the stepped leader (below B) during the first 4.5 msec of the
4.9 msec before the first return stroke.
Cross-correlated VHF noise sources, 94 ysec intervals during the preliminary
breakdown (A to B) and during the stepped leader (below B). The sphere Q1
represents an estimate of the volume enclosing the charge source for the first
return stroke as derived from electric field records (Uman et al., 1978).
Figure 5.3(b).


Figure 7.1. VHF radiation during the beginning of the four
CG and three IC flashes studied in this thesis.
(A) 165959 CG flash, the arrow indicates the
first return stroke; (B) 1807.10 CG flash, the
first return stroke occurs off the drawing;
(C) 181806 CG flash, the first return stroke
occurs off the drawing; (D) 182356 CG flash, the
arrow .indicates the location of the first return
stroke; (E) 165959 IC flash; (F) 180644 IC flash;
(G) 181416 IC flash.


CHAPTER VII
CHARACTERISTICS OF THE VI1F RADIATION DURING
THE DIFFERENT PHASES OF LIGHTNING
This chapter provides a description of the properties of the indi
vidual phases of the cloud-to-ground and intracloud flashes studied in
Chapters V and VI. In this description we use the characteristics of
the 30-50 MHz VHF radiation, the location of the VHF noise sources, and
the correlated electric field measurements (0.1 Hz to 1.5 MHz). Although
our study and conclusions are based on a limited sample of four cloud-to-
ground and three intracloud flashes, we feel that the results presented
are sufficiently consistent that they may be considered valid.
Before we proceed to study the properties of each of the discharge
phases, we note that we can tell whether a CG or an IC lightning flash
will occur from the first 3 msec of the VHF noise. Figures 7.1(A),
7.1(B), 7.1(C), and 7.1(D) represent the beginning of the VHF radiation
in the four CG flashes studied in Sections 5.1 through 5.4, respectively,
whereas Figures 7.1(E), 7.1(F), and 7.1(G) represent the three IC flashes
studied in Sections 5.1.13, 5.5, and 5.6. The IC discharge that followed
140 msec after the 165959 flash discussed in Section 5.1 is shown
separately because its properties are similar to the other two IC
discharges. Both CG and IC radiation started with high frequency pulses
superimposed on the envelope of a slower varying signal. The CG VHF
noise after the first 2 or 3 msec changes to high frequency and uniform
low-magnitude pulses, which, in this thesis, are identified with the
287


Figure 5.33(a). Three-dimensional view of the cross-correlated noise sources during the third
stepped leader. Point A is the location of the first stepped leader cross-
correlated source.
Figure 5.33(b). Similar three-dimensional view for all the individual detected sources.


Figure 4.3. Block diagram of the LITMAT algorithm to obtain
the cross-correlated and all the noise sources
based on the calculation of time delays.


n ft n n
21 JUNE 1979
/(9
S UDRUU TINE PULSE(XI .NABCIS.SLOPR,SLOPE.MR.ML.NARROW)
** THIS PULSE SUBROUTINE DETERMINES THE CHARACTERISTICS **
** OF THE PULSE **
D I MENS IUN XI (2048 )
HIGHL=X1( NABCI S) X1 (NAQCIS-5)
H I GHR= X 1 (NAE3CIS) XI (NACIS+5)
SLGPR=-HIGHR/5.0
SLGPL=HIG HL/5.0
M = 0
DO JO MN=1,5
I F(X1( NA3CIS+MN-1).GE.XIINABCIS + MN) ) MR=MR+ 1
30 CONTINUE
ML =0
DO 3 2 MN- 1*5
IF (XI { NAO C I S MN +.1 ) G E X 1 ( N ADC I S -MN ) ) ML = ML +- l
32 CONTINUE
CALL NARRO(XINAECIS.NARROW)
RETURN
END


Figure 5.40. Simultaneous record of the logarithmic-amplitude VHF radiation observed at 10 km,
and the electric field 14 km away, during the 181806 flash. The following events
in the flash are shown: R1 to R6 represents the six return strokes; SL1 and SL2
are the two stepped leaders; J1 to J5 are the interstroke processes; FR is the
activity following the first return stroke; and CC is the continuous current
interval.


35
The general characteristics are shown in Figure 3.6(a). Figure 3.6(b)
shows an approximation of the frequency domain of the signal after the
VHF receiver.
The rectifier part of the envelope detector from u.(t) to
z^(t) is a log IF device designed by RHG Lab with center frequency at
40 MHz for the 1976 data and 45 MHz for the 1977 data. The IF device
has a 3 dB bandwidth which corresponds to the bandwidth of the VHF
receiver. The device risetime is better than .05 microseconds and its
dynamic range is about 80 dB. The input-output characteristic of the
log IF is given in Figure 3.7. The actual values are tabulated in
Table 3.1. It should be noted that the use of the log IF device is
quite convenient in this application because it permits an input range
4
from 30 microvolts (-80 dBm) to 300 millivolts (0 dBm), a factor of 10 ,
for an output range from .255 to 2.5 volts, a factor of 10.
Assuming that W (f) is constant over the frequency range of interest
(30 to 50 MHz), the u^(t) can be represented as a time dependent
modulation P(t) multiplied by a phase displacement, i.e.,
u.(t) = P(t)cos(w t + 0) (3.3)
i o
Therefore
z(t) = logjP(t)cos(wQt + 0)| = log|P(t)|
+ log|cos(w t + 0)| (3.4)
The second term will be filtered out by the envelope detector
because it is at a frequency higher than 50 MHz. The log|P(t)| will
be recovered at the output.


NORTH
12 ¡3 4 15 16 17 ¡8 B 20
NORTH
(c)


4 5
as
2 2 2
d = (x-xjL) + (y-y^)
(3.7)
where (x ,y.) is the ground coordinate at the electric field station,
t S
Therefore the electric field at any station can be expressed as
E.
i
2 Q z
4tt£ ((x-x.)^ + (y-y.)^ + z^)
o x 1
3/2
(3.8)
Assuming a one point charge model where the charge Q at (x,y,z) is
removed producing a field change E., four electric field measurements are
L- i
needed to determine the four unknowns Q, x, y, and z. Fitzgerald (1957)
obtained an analytical solution for this equation when the ground-based
electric field stations were located at the vertices of a parallelepiped.
Krehbiel et al. (1974) derived an analytical solution to equation (3.8)
without limiting conditions, assuming that a solution does exists. The
solutions obtained from a set of four stations using this technique were
1 to 3 km away from each other because the electric fields at each
station were slightly in error. However when several solutions of a
group of four stations were used, about 75% of the solutions fell in a
3
volume of 1 or 2 km This is a reasonable technique for finding the
charge center neutralized by return strokes whenever d z. When d
is comparable to z, the point charge model is not a reasonable approxi
mation to finding the value of Q and its location, and a solution
using this model usually does not exist.
Jacobson and Kridcr (1976) improved the analytical solution derived by
Krehbiel et al. (1974) using a nonlinear least square iteration technique
where all the electric field stations are considered. Iterations are


271
5.5.2 The Very Active Phase
The very active portion of the discharge is characterized by a
faster rate of change of the electric field than in the initial phase
as shown in Figure 5.78. In addition, the VHF noise pulse repetition
rate increased from a pulse every 20 to 50 psec to a pulse every 5 to
10 psec.
A study of the electric field variation with distance in Figure
5.78 suggests that an electric field station about 16 km away from the
flash will detect zero field change. Solving the two point charge
model in equation (3.10) for zero electric field change, we have
(5.1)
From a study of the VHF sources during the first 13 msec in Figure
5.80 and all the VHF sources in Figure 5.82, it is reasonable to select
the height of the charge centers at 9.5 and 13.5 km along the slanted
dipole. For these values of h^ and h^ we fitted equation (5.1) and
determined that the left and right side agreed within 10%. We also
selected other values of heights along the slanted dipole between the
heights of 9 and 14 km, but we could not obtain a better fit. There
fore, we conclude that a point charge model of this IC discharge will
have charge center at 9.5 and 13.5 km.
5.5.3 The Junction Phase
The junction or final phase of the intracloud discharge has
characteristics similar to the discrete activity after return strokes
(DAFS), (see, for example, Section 5.2.11.2) in the cloud-to-ground
flash and the final part of the IC in the 165959 flash (Section 5.1.13).


Figure 5.7. Three sequences of histograms, t]_, t2, and t^ (1.5 msec intervals) of all the
detected sources in the PB and stepped leader. Sequences (a), (b), and (c)
correspond to t^, t2, and t3, respectively. There are three histograms in each
sequence. The top row shows distance histograms referenced to the weather
tower. The middle row shows histograms of the elevation angle of the sources
referenced to the weather tower. The bottom row shows histograms of the azimuth
angle of the sources referenced to the weather tower.


20
18
16
14
!2
10
8
6
4
2
e 5.
Averc5ge-8.2yU.sec.
Std. Dev.; 3.5 /xsec.
Time (/xsec)
7. Histogram of the interval between VHF pulses during the stepped portion of the stepped
dart leader preceding the third return stroke.


Abstract of Dissertation Presented to the Graduate Council
of the University of Florida in Partial Fulfillment of the Requirements
for the Degree of Doctor of Philosophy
PROPERTIES OF LIGHTNING DERIVED FROM
TIME SERIES ANALYSIS OF VHF RADIATION DATA
By
Pedro L. Rustan, Jr.
December 1979
Chairman: Martin A. Uman
Co-Chairman: Donald G. Childers
Major Department: Electrical Engineering
The purpose of this research is to derive lightning properties by
correlating three-dimensional VHF source locations, characteristics of
the VHF (30 to 50 MHz) radiation, and electric field intensity (0.1 Hz
to 1.5 MHz). We study the discharge initiation, propagation, overall
geometry, and charge magnitude and location for the various phases of
both cloud-to-ground and intracloud lightning. We analyze in detail
four cloud-to-ground and three intracloud flashes, all selected
randomly. The experimental data were recorded during the summers of
1976 and 1977 at the Kennedy Space Center (KSC). The VHF radiation was
recorded using the multiple VHF stations of the KSC Lightning Detection
and Ranging (LDAR) system. We located the VHF noise sources from the
difference in the time of arrival (DTOA) between the pulses received at
the multiple VHF stations using a hyperbolic geometry. The electric
field data were recorded by the New Mexico Institute of Mines and
Technology (NMIMT) and the University of Florida. Leader-return strokes
vi


42
pulse risetime to 1/1.6 KHz = 625 ysec did not reduce the information
content. The significant aspect of this step was to reduce the band
width of the analog data to within 500 KHz, the maximum available band
width for FM modules. The remaining two slow down processes used FM
modules, first a factor of 16, then by a factor of 8. The FM modules
were used because they maintain the low frequency content of the data.
As part of the latter slow-down process, the four channels containing
the desired information were digitized simultaneously at a rate of 8.5
KHz. Since the total slow-down rate was 4 x 16 x 8 = 512, the real
time sample rate became 8.5 KHz x 512 = 4.352 MHz. This sample frequency
is well beyond the Nyquist rate of two times the maximum tape frequency.
Using this high sampling rate, digitized points can be linearly inter
polated with straight lines without significant loss of characteristics
(Jerri, 1977).
Time correlation is an important factor of the slowing down and
digitization process. The original IRIG B recorded in the tape is still
readable during the first factor of 4 slow-down. At this stage a
different IRIG A (ten times faster than IRIG B) is recorded on a
different channel and the initial desired processing time is converted
to the new IRIG A code. In the next slow-down (a factor of 16), the
previous IRIG A is still readable and a new IRIG A is introduced. The
desired starting time is converted from the previous IRIG A to the new
IRIG A. During the final slow-down process (a factor of 8), a time code
generator automatically reads the initial converted starting time, which
is typed in as part of the program, and starts 'digitizing when this time
is reached. Although the initial absolute time can only be read in
millisecond or a fraction thereof, from the original IRIG B timing


Page
B.l Error Analysis for the Locations of the 165959
Flash on 19th July 1976 324
B.2 Error Analysis for the Locations of the 181806
Flash on 8th August 1977 324
B.3 Error Analysis for the 180710 and 182357 Flashes
on 8th August 1977 324
C COMPUTER ALGORITHM TO DETERMINE VHF SOURCE LOCATIONS
FROM THE DIFFERENCE IN THE TIME OF ARRIVAL OF VHF
RADIATION DATA 330
D COMPUTER ALGORITHM TO DISPLAY A THREE-DIMENSIONAL
DRAWING OF VHF NOISE SOURCES 356
E FREQUENCY DOMAIN APPROACH TO DETERMINE DIFFERENCE
IN THE TIME OF ARRIVAL 364
E.l Measurement of Time Delay by Determining the
Peak of the Impulse Function 366
E.2 Measurement of Time Delay by Measuring the
Phase of the Frequency Response Function 367
REFERENCES 369
BIOGRAPHICAL SKETCH 376
v


Number of Source Locations
Number of Source Locations
ho-^cn cd oro.£> ao


previous J-change. However, we did not have any problem identifying
subsequent stepped leaders from a single channel VHF radiation.
(4) Subsequent stepped leaders are considerably longer and prop
agate at slower velocities than initial stepped leaders. This might be
due to the fact that all subsequent stepped .leaders that we studied had
a much larger horizontal component than the initial stepped leader. A
possible explanation of this feature is that negative charges still
remaining in the first stepped leader channel to ground will repel the
new stepped leader. Therefore, the subsequent stepped leaders had to
propagate around the old stepped leader to find a new path to ground.
The duration of subsequent stepped leaders ranged from 14.2 to 35.0 msec
5 6
and we obtained velocities between 1.6 x 10 and 1.1 x 10 msec, close
to the range reported by Schonland et al. (1938).
7.1.3 Dart Leader
The properties of the dart leader were quite different from the
previously discussed stepped leader properties. We studied seven dart
leaders which occurred in the four CG flashes. The magnitude of the
VHF noise sources during the dart leader exceeded the stepped leader
radiation by a factor of 20 to 1. The VHF noise during the dart leader
started with a large pulse, usually between 150 and 200 psec wide.
The remainder of the dart leader contains mostly high frequency pulses
of less than 20 psec width superimposed on a slow envelope with a pulse
width of about 500 psec. The total VHF radiation during dart leaders
lasted between 0.35 and 1.70 msec.
The VHF noise sources during the dart leader were either in the
neighborhood of the previous J-change (Section 5.3 prior to the fifth
and sixth return stroke) or connected the end of the preceding J-change


305
remainder of the continuous radiation, the VHP sources widened the
channel. The SP's in the discrete part of the radiation path propagated
downward at speeds between 5 x 10^ and 4 x 10^ m/sec. The paths of
these SP's started from regions between 7 and 14 km and joined the main
CG channel that lowered negative charge to ground.
7.2 Intracloud Lightning
Three IC lightning flashes were studied in Sections 5.1.13, 5.5,
and 5.6. The beginning of the VHF radiation for the IC flashes has
been shown in Figures 5.14, 5.79, and 5.83. In addition, we showed the
VHF radiation at the beginning of the IC's in Figure 6.1(e), (f), and
(g). The intracloud discharge can be divided in three phases: initial,
very active, and junction phase, as done by previous investigators
(Kitagawa et al., 1960). Next we provide a discussion of these phases.
7.2.1 Initial Phase
Two of the three flashes started with a pulse about 25 times larger
than the stepped leader radiation and a pulse width ranging between 20
and 100 psec. The pulse repetition rate during this initial phase was
a pulse every 25 to 100 psec. This phase was not observed in the IC
flash described in Section 5.6.
Correlated electric field records during this phase showed an
increasing field change at close range and a decreasing change at
distances further away. During the initial phase of the 1C flashes,
the VHF sources formed the 1C channel. The 1C In Section 5.1.13 formed
a 10 km path 35 off vertical between a height of 6 and 15 km. The IC
in Section 5.5 formed a path 40 off vertical between the heights of
9.2 and 14.5 km. Our best estimate of the propagation of


:'.o
3 x 10 m/sec. The manner in which the sources form appeared erratic.
During the initial stage they seem to be confined to a volume less than
3
1 km ; then the channel emerged. The emerging channel is accompanied
with a sharp change of electric field during the beginning of the
discharge. The propagating streamer during a cloud flash, according to
Proctor, emits radiation from near the tip of the advancing leader, in
contrast to the stepped leader which radiates from both extremities as
well as in the intervening channels. Four isolated regions were presented
in the horizontal projections of the source locations. It is reasonable
to assume that these sources would in some way be connected if all the
VHF noises were identified.
Proctor classifies two types of cloud flashes in accordance with the
pulse rate of the emitting cloud. The low pulse repetition frequency (prf)
flash emits about 2000 pulses/sec while the high prf flash emits about
30,000 pulses/sec.
Proctor (1974a) correlates VHF noise source locations with the
weather radar precipitation echoes. Some flashes were contained almost
entirely in the regions of heavy precipitation. Some of the streamers
terminated at the end of the precipitation echoes. Some other flashes
followed the path of highest reflectivity gradients. The radar corre
lation reported was performed using a constant altitude plan position
indicator (CARPI).
Proctor (1974b, 1974c, and 1974d) consist of three special reports
published by the Council for Scientific and Industrial Research (CSIR)
in Johannesburg, South Africa. These reports d'eal with the sources of
cloud-flash spherics, instantaneous spectra of spherics, and VHF radio
pictures of lightning. Next we give our views of the significant findings
in these reports which have not been discussed previously.


EAST (km)
ALTITUDE (km)
0*71


NORTH
24
23
22
21
20
19
18
17
16
15
14
13
12-
II-
¡O
9
8
-2
-I 0 I
EAST
(a)
16
15
14-
13-
12-
II
10
9
I-
X
C2 8
J
X
7
3
2
2 3 4 -2 -I 0
EAST
(b)
16-
15
14
13
12
II
10
9
I-
x
E2 8
L
X
7
6
5
4-
3-
/ '
/ *
-4%
//
8
2
10 II 12 13
NORTH
(c)
14 15 16


during consecutive return strokes either preceded or followed the electric
field waveforms by as much as a few hundred microseconds. In two
reported cases the VHF was absent during consecutive return strokes.
The locations of the beginning of the return stroke were usually found
near the top of the previous leader channel. The locations at the end
of the return stroke were usually found 1 or 2 km above the previous
return stroke sources. Very few locations were found near the previous
leader channel to ground. (3) Proctor reported that the largest amount
of VHF noise sources occurred during J-changes, but very little effort
was spent analyzing the process. He reported near-horizontal and near
vertical J-changes and that some VHF noise sources active during J-changes
occurred in sequence.
2.5 Review of Lennon's Work
Lennon (1976) described a VHF (30-50 MHz) DTOA Lightning Detection
and Ranging (LDAR) "real-time" system operated at the Kennedy Space
Center during the 1974-1975 period. Originally the system consisted
of four remote and one central stations. During 1977 the system was
extended to include six remote and one central station. Even though
only three remote and one central station are needed for DTOA measurements,
the additional stations provided redundancy. The remote stations were
located an average of 10 km from the central station forming two Y
configurations which share the central station. The system was designed
to sense the log of the envelope detected VHF radiation from atmospherics
in all the stations and retransmit the information from the remotes to
the central station. The signals from three of the remote stations were
retransmitted to the central station using 10 MHz bandwidth microwave


PROPERTIES OF LIGHTNING DERIVED FROM
TIME SERIES ANALYSIS OF VHF RADIATION DATA
By
PEDRO L. RUSTAN, JR.
A DISSERTATION PRESENTED TO THE GRADUATE COUNCIL OF
THE UNIVERSITY OF FLORIDA
IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE
DEGREE OF DOCTOR OF PHILOSOPHY
UNIVERSITY OF FLORIDA
1979


BEGINNING OF I.C.
1 !
00 1.00 2.00 3.00
| 1 1 1 1
9.00 5.00 6.00 7.00 3.00
9
TIME IN
MILLISECONDS
Figure 5.79. Logarithmic-amplitude
VHF radiation during the first 7.3 msec of
the IC discharge.
H9'<:


314
Figure 3.1 indicates the relative location of six remote stations
(Wl, W2, W3, Ml, M2, and M3) and the central station. The position of
a calibration signal located on the top of the Kennedy Space Center
Vertical Assembly Building is shown as VAB CAL. Analog VIIF data are
recorded for the central and the six remote stations. Only the central
and three of the remote stations are digitized. The factors used in
the selection of the three remote stations are: (1) the stations with
maximum signal-to-noise ratio and (2) the stations whose locations
provide the maximum accuracy. In our research, the data processed for
the summer of 1976 are from the Wl, Ml, and W3 remote stations which
form a T configuration. The 181806 flash on 8th August 1977 was
analyzed using the Wl, Ml, and M3 locations. The remaining flashes
studied in this thesis were analyzed using the Ml, M2, and M3 stations.


CHAPTER IV
COMPUTER ALGORITHM FOR LOCATION OF LIGHTNING CHANNELS
One important task of this research is the development of an
algorithm to measure time delays between every "identifiable" pulse
detected at the central and at the three remote stations. From the
measured time delays, the three-dimensional locations of the VHF
radiation sources are determined by using hyperbolic equations (Holmes
and Reedy, 1951). In this chapter, we review the available techniques
for determining time delays, and then we describe the technique chosen
for the present study.
4.1 General
Two types of computer processing are performed as part of this
thesis: First, we determine and display locations as calculated from
the measured time delays. Second, we determine a data model for the
VHF radiation time series data. The first task is described in this
chapter whereas the second task is studied in Chapter VI.
Since the Second World War the measurement of time delays has been
an important aspect of engineering work. Some important applications
of time delay measurements over the last 30 years include:
a) Radar technology based on the measurement of time delay between
a transmitted and a received pulse (Skolnik, 1962). Some of
the applications required estimating the distance to other
planets.
49


-20C
-10C
0C
5 -4 -3 "1
EAST (km)
(a)
-5 -4 -3 1
EAST (km)
(b)
2 36


NORTH (km)
13-
12-
11
10-
9t
8
-3
EAST (km) EAST (km) NORTH (km)
(a) (b) (c)
Two-dimensional views: (a) top view, EU-NS, (b) elevation view, EW-height, and (c) elevation
view, IiS-height of all the sources (triangles) and the cross-correlated source locations
(squares), 376 usee intervals, during the PB and first stepped leader. The circle Q1 is the
two-dimensional projection of Q1 in Figure 5.3.
cc
Figure 5.6.


contact about (-2.5, 8.4). This is 1.4 km west and .9 km south of the
150-meter weather tower struck by the first return stroke channel.
Channel F corresponds to a vertical extension of the location of the
stepped leader-second return stroke luminosity while the G channel
locations are in the neighborhood of the first stepped leader channel.
The average velocity for the stepped leader was 6.7 x 10^ m/sec.
From the VHF source locations and the sequence of photographs it
is clear that the second stepped leader developed in a separate channel
to ground as shown in the sequence of pictures in Figure 5.39. The four
succeeding strokes to ground traversed the second stepped leader-return
stroke channel. It is possible that the Jl or PB2 process is not
directly related to the first leader return stroke sequence. In that
case we have two separate flashes: a single stroke flash and a five
stroke flash with continuing current. However, the longer duration of
the preliminary breakdown of the second flash compared to the duration
of the PB's for the other flashes described in this thesis, and the fact
that the VHF noise sources at the beginning of the second flash were
located at much higher altitudes than other PB's sources in this thesis
tend to indicate that the second stepped leader had different character
istics from usual first stroke PB's. Further, the time between the
first two strokes was 58 msec, a typical interstroke time, indicating
that there probably was a connection between the two strokes.
5.3.7 Second Return Stroke
The second return stroke had a duration of 859 ysec in the VHF
record as shown in Figure 5.50. The return stroke radiation was
characterized by a succession of low frequency pulses between 10 and
100 psec wide with superimposed high frequency pulses. Seven average


Figure 5.19. Logarithmic-amplitude VHF radiation during the beginning of the intracloud discharge.


The cross-correlation function R (i) was normalized as
xy J
r (j) = R (j)/
xy J xy J
N-l _
c
r1
1
53
'T.
y x_2
l yn
- 1 r (j) 1
(4.5)
1! [
O
n=0
xy
To prevent any error due to ambiguous selection of r (j) when the
xy
function flattens out near maximum, four decimal digits are used for
comparison. For S/N greater or equal to 10 dB the optimum value of
r (j) ranged between 0.9300 and 0.9850. Once the four station time-
xy
series data are cross-correlated for a selected time interval of either
94 or 376 ysec, the procedure is continued for the next interval. For
the cross-correlation function to be applied the signal level must be
greater than the noise level. Before the beginning of the flash, the
noise threshold level is calculated and the data is not processed if
the S/N is equal to or less than 0 dB.
Once we have determined the cross-correlated time delays, we need
to calculate the time delays of the higher frequency pulses superimposed
on the envelope (see properties 4.2.2(1) and (2)). To achieve this task
we used pattern recognition techniques.
4.3.2 The Pattern Recognition Technique
Widrow (1974) has divided the field of pattern recognition into
two broad schools: the first group classifies the data by comparing
individual features with a pattern recognition list, the other group
attempts to fit the data to some type of template matching. Gottman
and Gloor (1976) working in electroencephalogram and Weinberg and
Cooper (1972) working in neurophysiology applied the first and second
pattern recognition techniques, respectively, obtaining successful
results. Additional pattern recognition applications include


Figure 5.67. Three-dimensional view of the noise sources during the second stepped leader.
Figure 5.67(a) shows all the individual noise sources. Figure 5.67(b) shows
the cross-correlated sources.


Kitagawa, N. and M. Brook, "A comparison of intracloud and cloud-to-
ground lightning discharges," J. Geophys. Res., 65, 1189-1201, 1960.
Kitagawa, N. M. Brook and E. J. Workman, "Continuing currents in cloud-
to-ground lightning discharges," J. Geophys. Res., 67, 637-647, 1962.
Kitagawa, N. and M. Kobayashi, "Distribution of negative charge in the
cloud taking part in a flash to ground," Papers Meteorol. Geophys.
(Tokyo), 9, 99-105, 1958.
Krehbiel, P. R., Private Communication, 1979.
Krehbiel, P. R., M. Brook and R. A. McCrory, "An analysis of the charge
structure of lightning discharges to ground," J. Geophys. Res., 84,
2432-2456, 1979.
Krehbiel, P. R., R. McCrory and M. Brook, "The determination of lightning
charge location from multi-station electrostatic field change measure
ments," Conf, on Cloud Phys., 21-24, Tucson, Arizona, Oct. 1974.
Krider, E. P., R. C. Noggle and M. A. Uman, "A gated, wideband magnetic
direction finder for lightning return strokes," J. Appl. Meteorol., 15,
301-306, 1976.
Krider, E. P., G. J. Radda and R. C. Noggle, "Regular radiation field
pulses produced by intracloud lightning discharges," J. Geophys. Res.,
80, 3801-3804, 1975.
Krider, E. P., C. D. Weidman and D. M. LeVine, "The temporal structure
of the HF and VHF radiation produced by intracloud lightning discharges,"
Submitted for publication in J. Geophys. Res,, Spring 1979.
Krider, E. P., C. D. Weidman and R. C. Noggle, "The electric fields pro
duced by lightning stepped leaders," J. Geophys. Res., 82, 951-960, 1977.
Lee, Y. W., Statistical Theory of Communication, Wiley and Sons, Pub.,
New York, 1960.
Lennon, C. L., "LDAR A new lightning detection and ranging system,"
Trans. Amer. Geophys. Union, 56, 991, 1975.
Lennon, C. L., "The performance of a real-time, time of arrival light
ning location system (LDAR)," EOS Trans., AGU, 57, it 12, 1976.
LeVine, D. M. and K. P. Krider, "The temporal structure of I IF and BIIF
radiations during Florida lightning return strokes," Geophys. Res. Lett.,
4, 13-16, 1977.
Lewis, E. A., R. B. Harvey and J. E. Rasmussen,."Hyperbolic direction
finding with sferics of transatlantic origin," J, Geophys. Res., 65,
1879-1905, 1960.


211
Figure 5.59. Three-dimensional view of the cross-correlated noise
sources during the first 23 msec of the CC interval.
The location of a spherical charge center for the sixth
return stroke and the first 23 msec of the CC interval
is shown as Q6-CC.


nnnn nnnn
340
21 JUNE 1979
IF({J1 .GE. I ) .AND.(TIMELK) .LE.T IMF 1 ) )GO TO 172
WRITE! 6.1 01) X(L K) ,Y(LK) ,Z(LK) TI ME(LK)
WR ITE!8,7 00) X(LK),Y(LK),Z(LK) ,TIME(LK)
172 CONTINUE
T I ME 1 = T I M E ( N X )
GO TO 815
585 IF(Jl.EQ.O) TIME 1=0.
815 T IME 1=TIMF 1 + 2.
** WRITE A ZERU TO INDICATE THAT THE T HREE IMENS I ONAL **
** LOCATIONS, FOP ALL THE MATCHED PULSES, HAVE OEEN READ. **
WRITE(8,705)ZERO,ZERO,ZERO,ZERO
J1=J1 + 1
IFJ1.LE.4) GO TO 500
WRITE!0,537)
537 FORMAT 1 l )
** BACKSPACE THE TAPE TO ENSURE THE DATA AT THE END OF **
** THE LAG INTERVAL IS NOT MISSED. **
BACKSPACE 11
520 CCNTINUE
REWIND 11
101 FORMAT(4F20.3)
109 FORMAT !3E10.3)
170 FORMAT(5110)
It 2 FORMAT (FI 0.2 )
164 FORMAT(2 I 10,F10.2, I 10)
10 7