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
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viii, 376 leaves : ill. ; 28 cm.
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English
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Rustan, Pedro Luis, 1947-
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Lightning   ( lcsh )
Electrical Engineering thesis Ph. D
Dissertations, Academic -- Electrical Engineering -- UF
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bibliography   ( marcgt )
non-fiction   ( marcgt )

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

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University of Florida
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oclc - 06572179
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Full Text












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





























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Z
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V) 17,
0 OD U) 0
rn co n C)
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-Li
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LJ
LLJ 0
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< < it LLI
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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


































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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.








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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






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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).














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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.





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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








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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














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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.









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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.