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Properties of lightning discharges from multiple-station wideband electric field measurements

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Properties of lightning discharges from multiple-station wideband electric field measurements
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Davis, Stephen M., 1968-
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vii, 228 leaves : ill. ; 29 cm.

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Subjects / Keywords:
Average speed ( jstor )
Electric fields ( jstor )
Electric pulses ( jstor )
Fine structure ( jstor )
Geometric mean ( jstor )
Lightning ( jstor )
Pulse amplitude ( jstor )
Speed ( jstor )
Statistical median ( jstor )
Waveforms ( jstor )
Dissertations, Academic -- Electrical and Computer Engineering -- UF ( lcsh )
Electric fields -- Measurement ( lcsh )
Electrical and Computer Engineering thesis, Ph.D ( lcsh )
Lightning -- Measurement ( lcsh )
Magnetic fields -- Measurement ( lcsh )
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bibliography ( marcgt )
non-fiction ( marcgt )

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Thesis:
Thesis (Ph.D.)--University of Florida, 1999.
Bibliography:
Includes bibliographical references (leaves 222-227).
General Note:
Typescript.
General Note:
Vita.
Statement of Responsibility:
by Stephen M. Davis.

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PROPERTIES OF LIGHTNING DISCHARGES FROM MULTIPLE-STATION
WIDEBAND ELECTRIC FIELD MEASUREMENTS














By

STEPHEN M. DAVIS


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

UNIVERSITY OF FLORIDA


1999














ACKNOWLEDGEMENTS

This dissertation represents the culmination of a long seven years of study. The final result would not have been possible without the support of my wife, Michelle. Her love and unwavering support made it possible to navigate the many obstacles and difficult times encountered during the past four years.

I would also like to thank my family, Morn, Dad, Carol, Cheryl, Steve, Walter and Jake, for their support throughout my entire academic career at the University of Florida. The support of my in-laws as well as my family at First Presbyterian Church was also instrumental in helping me during this project.

I would like to thank Dr. Ewen Thomson for his guidance and direction during the research and writing phases of this project. I am also indebted to Dr. Pedro Medelius and the crew at the Kennedy Space Center who were instrumental in the gathering of the data.

I thank Dr. Vladimir Rakov for countless discussions and advice, which contributed greatly to this work and my development as a researcher. Thanks also go to my fellow graduate students, Keith Kerle, David Crawford, and Jack Kavelieros, who functioned not only as sounding boards for ideas, but also offered numerous moments of levity, without which, these years would have been much harder to endure.














TABLE OF CONTENTS



ACKNOW LEDGEM ENTS .................................................................................. ii

ABSTRACT ......................................................................................................... vi

CHAPTERS

INTRODUCTION .................................................................................... . 1

2 EXPERIMENTAL SYSTEM AND DATA ANALYSIS ............................ 6

2.1 Introduction ................................................................................... . 6
2.2 System Overview .......................................................................... 6
2.3 Corrections for System Responses ................................................. 8
2.4 Timing ........................................................................................... 11
2.5 Locations ....................................................................................... 14
2.6 Average Speeds ............................................................................. 16
2.7 DE/dt Pulse Intervals ...................................................................... 19

3 LEADERS AND RETURN STROKE FINE STRUCTURE OF NEW
TERM INATIONS TO GROUND ............................................................. 21

3.1 Introduction .................................................................................... 21
3.2 Leaders Preceding Subsequent Strokes .......................................... 21
3.2.1 Results ................................................................................ 25
3.2.2 Discussion .......................................................................... 41
3.2.3 Conclusions ........................................................................ 50
3.3 Return Stroke Waveforms Separated By One Millisecond or Less.. 51
3.3.1 Results ................................................................................ 52
3.3.2 Discussion .......................................................................... 58
3.3.3 Conclusions ........................................................................ 65
3.4 Summary Conclusions .................................................................... 66

4 CHARACTERISTICS OF SUBSEQUENT LEADERS TO GROUND ..... 67

4.1 Introduction .................................................................................... 67
4.2 Leader Speed and dE/dt W aveshape .............................................. 67
4.2.1 Results ................................................................................ 71


iii














4.2.2 Discussion .......................................................................... 89
4.2.3 Conclusions ........................................................................ 106
4.3 Subsequent Leaders Showing and Increase in Speed ....................... 107
4.3.1 Results ................................................................................ 107
4.3.2 Discussion .......................................................................... 116
4.3.3 Conclusions ........................................................................ 118
4.4 Pulse Trains Present After Return Stroke Waveforms ..................... 119
4.4.1 Results ................................................................................ 119
4.4.2 Discussions ......................................................................... 121
4.4.3 Conclusions ........................................................................ 124
4.5 Leader Occurrences ........................................................................ 125
4.5.1 Results ................................................................................ 126
4.5.2 Discussion .......................................................................... 137
4.5.3 Conclusions ........................................................................ 140
4.6 Summ ary Conclusions .................................................................... 140

5 PULSE TRAIN COMPARISON AND POLARITY REVERSALS ........... 142

5.1 Introduction .................................................................................... 142
5.2 Pulse Trains in Intracloud Discharges ............................................. 142
5.2.1 Results ................................................................................ 144
5.2.2 Discussion .......................................................................... 153
5.2.3 Conclusions ........................................................................ 166
5.3 Pulse Train Comparison ................................................................. 166
5.3.1 Average Speeds .................................................................. 167
5.3.2 M edian pulse intervals ........................................................ 173
5.3.3 Step lengths ........................................................................ 190
5.3.4 Conclusions ........................................................................ 193
5.4 Polarities of Pulses in Intracloud Pulse Trains ................................ 196
5.4.1 Introduction ........................................................................ 196
5.4.2 Theory and M ethod ............................................................. 197
5.4.3 Results ................................................................................ 201
5.4.4 Discussion .......................................................................... 208
5.4.5 Conclusions ........................................................................ 216
5.5 Summary Conclusions .................................................................... 216

6 RECOMMENDATIONS FOR FUTURE RESEARCH ............... 218

6.1 Pulse Trains .................................................................................... 218
6.2 Observations of Other Field Waveforms ..................... 219
6.3 Summary Conclusions .................................................................... 221
















REFEREN CES ...................................................................................................... 222

BIOGRAPH ICAL SKETCH ................................................................................. 228









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

PROPERTIES OF LIGHTNING DISCHARGES FROM MULTIPLE-STATION

WIDEBAND ELECTRIC FIELD MEASUREMENTS By

Stephen M. Davis

August 1999

Chairman: Dr. Ewen Thomson
Major Department: Electrical and Computer Engineering

There has been no detailed analysis of wideband electric fields recorded at a sufficient number of sites, with adequate design constraints, such as baseline length and timing resolution, to give three-dimensional locations of lightning sources. We describe a system to locate and give times of occurrence of the sources of wideband dE/dt pulses. The major focus of this study was sequences of regularly occurring dE/dt pulses, or pulse trains. We identify pulse trains giving rise to three lightning processes: (1) leaders preceding new terminations to ground, (2) dart-stepped leaders along a previously formed channel propagating all the way to ground, and (3) intracloud discharge processes.

Leaders preceding new terminations were dart-stepped in nature prior to their transition to stepped leaders. Speeds over the dart-stepped portion of leaders were 1.0 12 x 106 m/s. Fine structure was present in the dE/dt waveform of both first strokes to ground and subsequent strokes in new channels to ground. The duration of the fine structure was shorter (37 ps median) for strokes in new terminations to ground than for first strokes in a flash (141 gs median). Sources of fine structure were related to the preceding stepped leader.









We provide the first interpretation of the complete electric field waveform of dartstepped leaders. Near ground, dart-stepped leaders exhibited pulses at regular intervals of several microseconds. Interpulse intervals were much smaller than several microseconds early in the leaders, at which time their speed was greater. Seven dart-stepped leaders decreased in speed towards ground, while two were found to increase, but only when joining an earlier section of the channel. For dart-stepped leaders we found an inverse relationship between average leader speed and interpulse interval.

We provide the first locations of the wideband sources from intracloud pulse trains. Speeds of these trains were similar to those during the dart-stepped portion of leaders preceding new terminations to ground and dart-stepped leaders near ground. A comparison of average speed, interpulse interval and step length is undertaken for the three types of pulse trains identified. Similarities include a constant or decreasing speed and a tendency for interpulse intervals to increase with time. Several important differences were found. Dart-stepped leader waveforms were comprised of pulses of irregular amplitude, making the interpulse interval dependent on the amplitude threshold used in pulse selection. Pulses from intracloud trains were more uniform in amplitude and interpulse intervals were nearly constant with respect to an amplitude threshold used to select pulses. Average step lengths of intracloud trains were several tens of meters, while those of dart-stepped leaders and leaders preceding new terminations were more difficult to determine. Average speeds near the beginning of dart-stepped leaders were higher than speeds near the beginning of intracloud pulse trains. Pulse polarities associated with intracloud pulse trains were dependent on channel orientation.














CHAPTER 1
INTRODUCTION

Thunder and lightning have fascinated mankind for hundreds of thousands of years. The first scientific study of lightning can be traced back to Benjamin Franklin in the last half of the eighteenth century. In 1752 Franklin performed his famous kite experiment proving his theory that lightning was electrical. Ever since, researchers have continued to conduct experiments to increase their understanding of this natural phenomenon. Photography and spectroscopy became available in the late nineteenth century allowing investigators to identify the individual components of a lightning discharge. The early part of the twentieth century saw the first electric field measurements used to study lightning. Wilson [1916, 1920] estimated charges involved in the lightning discharge from electric field measurements. More recently, in the past 25 years, improved measurement and analysis techniques have proved particularly valuable in the study of lightning. New high-speed computers have allowed the digitization, storage, and analysis of large amounts of data not previously available.

Lightning discharges are typically classified as one of two types. The first is termed cloud-to-ground discharges (CG) and produces the familiar, visible forked channel between the cloud and ground. The second is collectively termed cloud discharges. Lumped into cloud discharges are intracloud (within a cloud), cloud-to-cloud, and cloudto-air discharges. The earliest studies of lightning focused on cloud-to-ground discharges for two primary reasons, (1) because they were responsible for the most severe lightning









damage and (2) they were more easily photographed since they were visible below the cloud. However, more than half of all lightning takes place within the cloud. Historically, research on cloud discharges has lagged behind that of cloud-to-ground discharges for the two reasons stated above. With recent improvements in recording equipment and analysis techniques, the ability to study cloud discharges in greater detail has become possible, opening new avenues in lightning research.

Figure 1.1 shows the time sequence of the various processes that comprise a typical negative cloud-to-ground discharge. The discharge, also termed aflash, may be initiated by preliminary breakdown within the cloud, which in turn initiates the stepped leader. The stepped leader lowers negative charge to earth in a series of discrete steps, traveling at an average speed near 2 x 105 M/s. When the leader tip nears ground, the electric field at ground exceeds the breakdown value of air and one or more upward going positive streamers may be launched. When one of these streamers contacts the negative tip of the stepped leader, the attachment process, a connection to ground is established thereby initiating the first return stroke. The return stroke is a ground potential wave that propagates continuously up the previously ionized leader path at a fraction of the speed of light. The return stroke lowers to ground the negative charge deposited along the trunk of the leader channel and the branches.

After an interval on the order of tens of milliseconds, during which time the channel is dark, i.e. no current flows, additional charge may be available near the top of the channel and a continuos dart leader may propagate down the residual first stroke channel at a speed near 107 m/s. The dart leader initiates the second stroke, also termed a subsequent stroke. Leaders and return strokes after the first in a flash are termed subsequent. Some





















t=0









19 mS






40K-Processe


40 ins


Breakdown


1.00 ms


20 ms





Dart
Leader


60 in


Stepped
Leader 1.10 ms


1.15 ms


20.10 ms 20.15 ms 61 mas 62 ms


1.20 ms









20.20 ms Second Return Stroke 62.05 ma


Figure 1.1. Time sequence showing the typical components comprising
a negative cloud-to-ground discharge (Uman, 1987).



subsequent leaders are observed to follow the existing channel to ground, but appear stepped in optical records. These leaders are termed dart-stepped leaders and travel at speeds near 3 x 106 m/s.


Both CG discharges and cloud discharges are comprised of currents that can vary on a sub-microsecond scale. These current variations give rise to wideband electric and magnetic fields. In fact, the discharge physics of lightning processes that involve the largest currents have been based on wideband measurements. The electric field measurements of Weidnan and Krider [ 1980] indicated that electric and magnetic field









waveshapes associated with the peak return stroke current had a frequency content of 1 kHz to 4 MHz. A similar frequency range is observed for the peak electric field of stepped leaders (Krider et al., 1977), bipolar pulses associated with preliminary breakdown (Weidnan and Krider, 1979), narrow bipolar pulses (Le Vine, 1980) and regular pulse trains (Krider et al., 1975). While these and other studies have characterized electric field signatures from lightning, there are no reports in the literature of wideband electric fields recorded at sufficient number of sites with adequate design constraints, such as baseline length and timing resolution, to give three-dimensional locations of sources. At least four sites are required with baselines of the order of 10 km with timing resolution better than 100 ns (Proctor, 1971). We have developed a system to locate the sources of wideband dE/dt (derivative of the electric field) using five sites with appropriate baselines and a timing resolution of better than 50 ns. The system and methods for analyzing data are described in Chapter 2.

One particular type of electric field signature, that of a regular sequence or burst of microsecond-scale electric field pulses, is found in the wideband electric field records of both CG discharges and cloud discharges (Krider and Radda et al., 1975; Krider and Weidnan et al., 1977, Rakov et al., 1996). These sequences, also termed pulse trains, are comprised of more or less unipolar electric field pulses occurring at regular intervals of several microseconds. Previous studies have shown that the time between pulses are similar in pulse trains from both CG and cloud discharges, suggesting they may be the result of a common physical process. To better answer this question a study of other characteristics, such as average speed and step length, is needed. Until now, no sufficient measurements of pulse trains have been available in this regard.









This work provides the first source locations and electric field waveshapes, measured on a sub-microsecond scale, of electric field pulse trains from both CG and cloud discharges. We have identified three processes that produce pulse trains in the electric field. Two of these processes occur in CG discharges, the third in cloud discharges. Average speeds, pulse intervals, and step lengths of each are analyzed and compared. Chapter 3 investigates pulse trains that were associated with leaders preceding new terminations to ground. A new termination was defined to be a stroke after the first of the flash that occurred in a new channel to ground. Pulse trains produced by dart-stepped leaders are the focus of Chapter 4. Chapter 5 looks at characteristics of trains that occurred in cloud discharges and compares these with the results of the previous two chapters. Finally, Chapter 6 contains other observations from the current data set and suggestions for further study.

Rather than including a detailed literature review prior to presenting the current results, we have chosen to conduct a review in each chapter, as the topics are presented. Chapters 3, 4, and 5 are broken into sections; the structure of each follows that of most scientific journal publications. Each section begins with an introduction detailing the current state of research on that chapter's subject matter. The results of the current study follow the introduction. The third section is the discussion where the findings of the current study are analyzed and discussed in relation to pertinent information in the literature. Each section ends with a conclusion of the important findings of that section. A chapter summary is also included at the end of each chapter.














CHAPTER 2
EXPERIMENTAL SYSTEM AND DATA ANALYSIS


2.1 Introduction


In this chapter we describe the configuration of the recording system used in collecting data and the techniques developed for analyzing those data. In section 2.2 we present an overview of the system and describe the system components and recording method. In section 2.3 we describe a scheme of frequency and phase compensation to correct for differences in frequency responses of the individual sensing electronics and signal propagation links of each channel. Section 2.4 details the methodology used to derive source times and section 2.5 describes the method used in deriving source locations. The technique used to find average speeds is presented in section 2.6. Finally, a procedure to determine interpulse intervals is presented in section 2.7.


2.2 System Overview

The measurement system comprised five ground stations in a 15 km x 15 km network at Kennedy Space Center, FL. A map showing the station locations is shown in Figure 2.1. The derivative of the electric field (dE/dt) was detected at each station by sensing the displacement current intercepted by a flat plat antenna. Each antenna was placed near the center of a 3.5 m x 3.5 m ground plane elevated 0.5 m above ground. Gains from unity to 450 were achieved through the use of amplifiers and antenna plates as illustrated in Figure 2.2. Signals were sent via microwave or fiber optic links to the































Figure 2.1. Sensor station layout. Range rings are centered at the Shuttle Landing Facility.

Plate W inn" aydt

X3 U dx1O TO
Sw I Fl roptte ax | coax Transmitter


Figure 2.2. Block diagram for sensor electronics









central recording van. The signals were digitized at 20 MHz for 4096 samples (204.8 gs records) once a trigger was received. Consecutive trigger records were digitized with a 30 pls dead time between records until the 128 kS LeCroy memory was full. A maximum of 25 trigger records could be recorded per flash. The block diagram in Figure 2.3 illustrates the time sequence of a typical flash. Calibration signals were applied through a known resistance to the input of the dE/dt amplifier. Calibration signals consisted of a square wave, triangle wave, and an impulse. These signals were used to create digital filters to remove waveform distortions arising from finite frequency responses of radio transmitting and receiving equipment. The construction of these filters is now outlined.



2.3 Corrections for System Responses

Before processing data, we compensate for differences in the frequency response (magnitude and phase) between the sensing electronics and signal propagation links in each channel. To do this we first find the frequency response of each of the channels. We then design suitable filters that correct for differences between channels. The frequency response for each channel is determined from four distinct calibration signals; positive impulses, negative impulses, the rising edge of the fast square wave (differentiated with respect to time to give a positive impulse), and the falling edge of the fast square wave (differentiated with respect to time to give a negative impulse). Since each of these approximates an impulse, the Fourier transform is the system frequency response, and the mean and standard deviation for the amplitude and phase spectra can be found from the four responses. To minimize noise effects, we choose 1.6 ps windows around each impulse and average 10 signals for each channel. For accurate alignment of




















End Of
Flash



Record # 25 204.8 lis


Figure 2.3. Block diagram illustrating recording configuration of the system.


Start Of
Flash


30 pgs

474


Record # 1 204.8 Igs


Record # 2 204.8 gs









these impulses we zero padded the frequency domain spectra (Oppenheim and Schafer, 1989). The zero frequency (DC) value is obtained from the amplitude of the average square wave signals. From above DC to 1.25 MHz the spectrum is the mean of the two square wave spectra, and the remaining spectral components, to the Nyquist frequency of 10 MHz (corresponding to our digitization rate of 20 Ms/s), comprise the mean of all four calibration spectral components. Since 1.6 As windows are chosen for the calibration signals, 128 times smaller than the 204.8 pAs data record, there are 2032 undefined spectral components. These points are interpolated using a cubic spline fit for both the amplitude and the phase spectra. The spectra that we find using this procedure are reasonably smooth and physically consistent with the expected frequency responses. The two amplitude frequency spectra shown in Figure 2.4 are those chosen for normalization. The narrower response in Figure 2.4, curve a, is used whenever waveshapes are compared with channel 1 since channel 1 has a significantly narrower bandwidth than the other channels (6 dB down at 2 MHz compared with 4 MHz) as a consequence of the 32 pAs analog pretrigger delay at its input. Channels 2 through 5 are normalized to the broader response in Figure 2.4, curve b.

Consider a channel with impulse response I(t) in the time domain and frequency response, that is, the Fourier transform of I(t), given by A(f)e4(f) where A(f) is the amplitude spectrum and (f) is the phase spectrum. We normalize this channel by defining a compensating filter as N(f)/{A(f) e'4(0} where N(f) is the amplitude spectrum in either curve a or b of Figure 2.4. That is, if a particular dE/dt waveshape is given by g(t), then the normalized waveshape is found as the inverse Fourier transform













0.8


0.6

* b
0.4
a'

0.2 "


0 2 4 6 8 10 Frequency in MHz

Figure 2.4. Idealized frequency responses for curve a, channel 1, and curve b, channels 2 through 5. The idealized phase response is zero for all frequencies.



n) = F-'N( f)G ). (2.1)
n~t)= . (f)e'#(f) ,


where G(f) is the Fourier transform of g(t). Curves a and b in Figure 2.5 are the impulse responses corresponding to the normalized amplitude spectra in Figure 2.4, curves a and b, respectively, and a zero-phase spectrum.



2.4 Timing

The pulse times ti and timing errors 8ti are determined from three time parameters on each pulse: (1) the rising-edge half peak, (2) peak, and (3) falling-edge half peak. We denote these as t,, tp,, and tfi, respectively. For channels 2 through 5, t is defined as the mean value of these three time parameters where all measurements are made on















0
5-
4)






.- I n I I
#0 0.2 0.4 0.6 0.3 r

Time in microseconds

Figure 2.5. Impulse responses for the frequency responses shown in Figure 2.4.



waveshapes that have been filtered with the wideband filter shown in Figure 2.4, curve b. That is,


ti = i=2-5 (2.2)
3

For channel 1 we use the narrower filter shown in Figure 2.4, curve a, on all signals to obtain (different) values of these three time parameters, t,., t,., and t&. The mean times are found only for channel 1, ti., and the channel from 2 through 5 that is most closely correlated to channel 1, t,. The value t, is then defined as the adjusted time tc+tln-tm, where t, is given by Equation 2.2 with i = c.

We find the timing errors 8ti, from the variations between waveshapes recorded at different stations, as evident from the relative scatter in either t,, tpi, and tfi or tn, t4,m, and tfm, as follows. Consider the rising-edge half peak for channels 2 through 5. First, we find the mean deflection of each t,, from its time tag, t-










5
y(tn -t,)
= 4 (2.3)
4

Then, we determine the difference between each deflection and the mean kt, = t,, -(0i - ti) (2.4)

Figure 2.6 illustrates this procedure. This figure shows t.,, tpj, and t5 for a pulse recorded on the ih channel, the time, appropriately shifted, corresponding to t, and the deflection 8tn. Noting that 8t2 is a measure of the variance, we define the total variance for the ith pulse as

V = ti2 +&ti2 + tf2 (2.5) and the timing error as

ti= - (2.6) where t. and tf. (corresponding to the peak and falling edge half peak, respectively) are defined in a similar manner to t. (equation 2.3), 8tpi and 8tfi are defined in a similar manner to Stri (equation 2.4), and v, the number of degrees of freedom, is 2 since equation (2.2) is assumed in all the above calculations.

The error for channel 1, &1, is found in a similar fashion with the exceptions that t,, to., and ti are replaced by t., tp, and tfm, respectively, and equation (2.3) becomes
5
2 (tl. - t)
t,.,- i=1 5(2.7)
5

This tends to overestimate the errors in 8t, since we obtain t1 with reference only to the channel that has the closest waveshape to channel 1.






14




1 A











70
a' I I '- a






a t I I . I a


t + t t r i t "= I; I





Time


Figure 2.6. Sample dE/dt waveshape showing how timing parameters t,, tp,, tfi, and 5tj are defined. The value t- is given by equation 2.2 and t . is
given in equation 2.3.



2.5 Locations

Consider a radiation source at location (xy,z) that turns on at absolute time t. The start of the dE/dt pulse from this source arrives at the ith station (at location (X-, Y1, 0) at time t + Rj/c where


R =I(x-X,)2 +&Y1)2 +Z2(


(2.8)









and is recorded at the central station after a further delay di corresponding to the cumulative propagation time along the corresponding combination of coax cable, microwave, and fiber-optic links. For channel 1 we also subtract its 32 p.s pretrigger delay from the actual propagation delay between the SLF sensor and the recording site. The digitization window begins at absolute time T, corresponding to the trigger time of the window. Thus the pulse appears on the ih channel after a further interval t where t, =t+-�di -T (2.9)
C

Equation 2.9 gives the relationship among the measured quantities t- (the pulse times of the five channels), di (the calibration delays), T (the absolute time tag), and the parameters that need to be determined: the location (x, y, z) and the time of occurrence, t. Any four measurements give a unique solution for x, y, z, and t. Overdetermined equation sets such as this can be dealt with by (1) minimizing the squares of residuals based on equation 2.9 [e.g. Peters and Crosson, 1972], or (2) choosing the set of minimally determined equations (such as four equations of the form of equation 2.9) that gives the smallest spatial errors [e.g. Hofmanm-Wellenhof et al., 1993]. In a variation of method (2), Proctor [1971] explains how different equation sets may be appropriate for the different coordinates. While method (1) is computationally easier since only one minimization is required to find all four variables, it is unreliable for locations close to ground. Instead, we extend Proctor's ideas to find the weighted mean values of x, y, z and t independently using all five possible combinations of four-station data. We call this the "weighted hyperbola" technique and a detailed description of the method can be found in Thomson et al. [1994].









2.6 Average Speeds


We describe here a method for determining average speeds in three dimensions. Given a series of n locations that lie along an apparent linear channel, we wish to find the average speed along the three-dimensional track. We first divided the channel into linear segments in each of x, y, and z using a "chi-by-eye" technique. In most cases one segment was defined within a record (204.8 ps). Locations were obtained over, at most, 150 ps of data in each record owing to differences in the time of arrival of sources at different stations. The average speed and its associated error were found using a reduced chi-squared value as a guide for goodness of fit. The technique is as follows: For a particular section of the channel we wish to find the best function var(t) = a + b t (2.10) to fit the data. Following the method of Bevington [1969] we define



2= 1 (2.11) z = z-l( var - a - b ) (2.11) 'a

where ai is the error in the variable (x, y, or z) at the i point. Minimizing X2 and solving for a and b yields


1 _Z vartv a=- - L _ 1'. , ,*a, A , a, o ui

b= I[ 17,f var, t ,var, (2.12) A , � (-2 at2j (2.122 i 0 i 0t
2
A= 2"Y I'i _ (Y 1

The error in either a or b is obtained from









2 0.~2( I ' 2
8, var,


The errors in a and b become A;l.2 I,2 (2.14) 21 2
a-b -" 2


The test of whether the calculated speed and associated error are reasonable is provided by the reduced X2 value with an expected value of unity

2 (2.15) where v represents the number of degrees of freedom. Since we want the threedimensional average speed we can use the principle of linearity to combine the three components to obtain


2: -2 (var, - a - b t,)2
2 1 i (2.16) Xred i-2

The three dimensional speed over the segment is given by S= b +b,2+bP (2.17) The error in the slope is found from Cdop = (.2_ +(_.0.,Y +(-z .,,.2 (2.18) The reduced X2 value over the segment is given by



2 2 2
2 Z2 + go+ 3 (2.19)
Xrd,egnMen - 3






18

The error in the speed was defined as the product of the reduced chi-squared and the error in the slope (Hager and Wang, 1996) S 6 2 (2.20) As an example, a computation of the average speed over a segment of channel is illustrated in Figure 2.7.


0 0.1 0.2
Time in Microseconds


_ I I
0 0.1 0.2 0
Time in Microseconds


I I 9-~



0 0.1 0.2 0
Time in Microseconds


Figure 2.7. Segment of channel used in finding average speed



Using a "chi-by-eye" method we consider the locations in Figure 2.7 to resemble a roughly linear channel section. The calculation of average speed over this segment supports our assumption and was found to be 3.6 x 106 m/s with X2r"d = 0.4 and an error in the slope of 0.3 x 106 m/s. This leads to an error in the average speed of 5 %. In some


7


N
6


I ~T ~ ~ -









instances, the "chi-by-eye" technique suggested more than one linear channel segment. If errors obtained over these smaller segments were less than those for the entire segment, the channel segment was partitioned in this way. One problem with subdividing the channel into many small segments was an increase in the error in the slope when fewer points were used. Channel segments were therefore subdivided only where obvious kinks were observed and a sufficient number of locations were available.


2.7 Interpulse Intervals

We now outline a method for determining the time between individual dE/dt pulses in trains. Amplitudes of pulses in trains of the current study were often not uniform and the determination of whether a dE/dt pulse should be counted became somewhat subjective based upon one's criteria for the inclusion or exclusion of an apparent dE/dt pulse. No definition exists in the literature for resolving this problem so we propose an amplitude threshold be used in counting dE/dt pulses for the determination of interpulse intervals. For a given train of pulses we determined the largest pulse in the sequence and chose 50 % of this value as the highest threshold. Successively lower thresholds were selected, in 5 % increments, until the noise floor was reached. The noise level was defined as being four standard deviations above the mean as determined from a quiet portion of a record. For each record, we found the median time between dE/dt pulses (rising edge) as a function of threshold. This will be referred to as the median interpulse interval. In order to directly compare average speed and median interpulse interval, we limit the determination of intervals to the extreme pulses whose sources were located in each record, i.e., the median interpulse interval is calculated from the first to last located pulse within a record. An example of the determination of median interpulse interval is shown in Fig 2.8. A curve of the median interpulse interval vs. threshold is shown in Fig 2.9. If









there were fewer than five pulses at a given threshold, no median interpulse interval was found.


30%
8%


Time In Microseconds Figure 2.8. A section of data illustrating the use of different thresholds in
calculating median interpulse interval.






10










0 I I I
0 10 20 30 40 50
Threshold (percentage of maximum pulse amplitude) Figure 2.9. Median interpulse interval as a function of threshold for the sequence in Figure 2.8.


0I I I I I I I I I
0 20 40 60 80 100 120 140 160 180 200














CHAPTER 3
LEADERS AND RETURN STROKE FINE STRUCTURE OF NEW TERMINATIONS TO GROUND


3.1 Introduction

We investigate leaders and fine structure of new terminations to ground. In section 3.2 we present data from subsequent strokes to ground creating new terminations. We relate the preceding leader characteristic to the following return stroke fine structure. In section 3.3 we present several return strokes separated by one millisecond or less. We investigate possible mechanisms that may produce the observed return stroke waveforms. Section 3.4 contains a summary of the chapter's findings.



3.2 Leaders Preceding Subsequent Strokes

First strokes in negative cloud to ground lightning discharges are preceded by stepped leaders. The stepped leader propagates to ground in a series of discrete steps, each tens of meters in length with pause times of tens of microseconds between individual steps [Schonland, 1956]. The duration of the stepped leader is typically 20-40 ms [Pierce, 1955; Kitagawa and Brook, 1957, Beasley et al., 1982; Rakov et al., 1990c]. Stepped leaders prior to first strokes are usually heavily branched and have a downward speed of 0.8 - 8.0 x 10 m/s [Schonland, 1956]. After the leader reaches ground the leader channel is discharged by the first return stroke which propagates up the previously ionized leader path and out along the branches [Schonland et al., 1935]. The return stroke effectively









lowers to ground charge deposited on the stepped leader channel. After an interval of typically several tens of milliseconds a subsequent leader may propagate down the residual first stroke channel. If this leader appears to propagate continuously, it is termed a dart leader. Optical measurements give dart leader speeds in the range 2.9 - 24 x 106 m/s [Orville and Idone, 1982; Jordan et al., 1992] with a mean value near 1.0 x 107 m/s [McEachron, 1939; Brook and Kitagawa (Winn), 1965; Berger and Vogelsanger, 1967; Orville and Idone, 1982; Jordan et al., 1992]. Upon reaching the ground the dart leader initiates a subsequent return stroke that travels back up the dart leader channel. The dart leader and subsequent return stroke are not usually branched (Schonlandet al., 1935.)

Some subsequent leaders may follow an existing channel to ground but appear stepped in optical and electric field records. These leaders are termed dart-stepped leaders and have speeds intermediate between stepped leaders and dart leaders. Dart-stepped leader speeds measured optically by Orville and Idone [1982] were 0.76 - 17 x 106 m/s while those measured optically by Schonland [1956] were 5.0 - 17 x 105 m/s. Krider et al. [1977] found that regular microsecond-scale electric field pulses prior to subsequent strokes were associated with dart-stepped leaders. Median pulse intervals were 6.5 pts in Florida thunderstorms. Similar electric field pulse trains have been observed by Krider et al. [1975] in cloud discharges and more recently by Rakov et al. [1996] in both cloud and ground discharges.

Subsequent leaders in a discharge may branch from an existing channel to form a new path to ground via a stepped leader. Schonland et al. [1938b] and Schonland, [1956] observe this branching below the cloud base. Lightning discharges with spatially separate channels below cloud base are also quite common. Clifton and Hill [1980]









report 18 % of flashes with spatially separate channels, Brantley et al. [1975] 21 %, Winn et al. [1973] 32 %, Kitagawa et al. [1962] 49 % and Rakov and Uman [1990b] 50 %. A possible explanation for the observation of multiple channels below cloud base has been proposed by Thomson etal. [1984]. Thomson etal. [1984] suggest that multiple channels may be due to a subsequent leader following an old channel in the cloud and then branching before reaching cloud base. Rakov and Uman [1990c] found leaders preceding new terminations to ground to have a geometric mean duration of 15 ms. This value is intermediate between the geometric mean duration of stepped leaders (35 ms) and dart leaders (1.8 ms) found by Rakov and Uman [1990c]. They suggest a scenario such as that proposed by Thomson et al. [1984] to explain this intermediate duration of leaders preceding new terminations, which would have a higher speed (dart or dart-stepped) in the cloud and a slower speed (stepped) below cloud.

The large subsidiary peaks, also termed fine structure, in the electric field waveform following the return stroke peak in first strokes were first studied in detail by Weidnan and Krider [1978]. They attributed fine structure to the effects of branches as the return stroke discharged the leader channel. Proctor [1988], using a VHF time-of-arrival system, found sources of VHF radiation present during first strokes to be located alongside the channel formed by the stepped leader, consistent with the view of Weidman andKrider [1978]. Willett etal. [1995] recorded both electric field and the derivative of the electric field (dE/dt) from return strokes. Both first strokes and new terminations to ground exhibited fine structure after the return stroke peak. Subsequent strokes following the same channel as an earlier stroke were associated with a "quiet" dE/dt waveform after the return stroke peak. In one case, an "anomalous" waveform was recorded in which the









dE/dt waveform was initially noisy after the return stroke peak but became quiet 12 gs afterwards. Willett et al. [1995] proposed that fine structure in the dE/dt signature arose from new channels to ground while old channels produced a quiet dE/dt signature. They suggested that a critical test of this hypothesis might come from the "anomalous" type signature "if it could be shown that at the instant the return stroke passed from the new channel to an older channel that the corresponding dE/dt waveform became quiet".

In this section we present data from 16 cloud to ground lightning discharges creating at least one new termination to ground. In all cases the new termination was preceded by a dE/dt pulse train of at least 400 pis duration with average speeds of 1.0 x 106 m/s to 1.2 x 10 m/s, similar to those of dart-stepped leaders. However, pulse amplitudes near the end of trains fell below the trigger threshold of the system several milliseconds prior to the following return stroke. The average speed between the last recorded pulse in the train and the following return stroke was consistent with that characteristic of a stepped leader. Hence we conclude that the leader became stepped, forming the new path to ground. Fine structure was found in waveforms of both first strokes and strokes in new terminations, but its duration was shorter for new terminations (median value 37 pLs in 17 strokes) than in first strokes of a flash (median value 141 pIs in 17 strokes). For new terminations, locations of fine structure sources were consistent with having originated in the stepped leader channel. We conclude that the new terminations to ground were preceded by leaders which followed an old channel in a dart-stepped fashion and later adopted a new channel to ground, formed by a stepped leader, and that fine structure was a consequence of the stepped leader. The height at which the leader deviated from the old channel occurred from near ground to a height of 3.4 km.









3.2.1 Results In order to investigate dart-stepped leaders that did not appear to

propagate completely to ground, we chose ground flashes exhibiting a dE/dt pulse train that ended several milliseconds prior to a return stroke. Pulse trains were defined to be regular sequences of pulses lasting for at least 400 microseconds with interpulse intervals of 1-30 ps. In all flashes we consider, these trains arose from leaders to ground as opposed to intracloud (IC) K-changes which may also contain regular bursts of pulses [Krider et al., 1975; Rakov et al., 1996]. Since the location at ground of each return stroke origin was displaced from that of the previous stroke, it appears that a new termination to ground was formed. Both the first stroke in a flash and the stroke in the new termination exhibited fine structure in the dE/dt signature after the return stroke peak. We determined the duration of fine structure by choosing the channel with the largest signal (non-saturated) and defined the end of the fine structure to be when the signal had dropped below 10 % of the return stroke peak value for at least 12 4s.

We first summarize results for all 16 flashes analyzed and then give detailed results for three flashes. All data were recorded during the summer of 1992 at Kennedy Space Center. Table 1 summarizes features of the 16 flashes analyzed. Flash 2541810 produced two new terminations that were preceded by pulse trains, hence there are 17 strokes listed in the table. The first column contains the flash ID with the number of records triggered in parentheses. A maximum of 25 records could be recorded per flash and hence some later records were probably missed in the seven flashes that had 25 records. The second column indicates the order of the stroke following the pulse train analyzed, that is, in the new channel termination (counting each stroke from the first in the flash). Strokes producing new terminations were either the second, third or fourth in













Table 3.1. Summary of leaders preceding new terminations to ground.


Inter-Stroke Source Heights Train Speed x 100 Time interval Fine Structure Duration Flash ID Stroke Interval Max Min Duration Min Max to RS New term First (# triggers) Order (Ms) (km) (km) (ms) (m/s) (m/s) (ms) 64) (ILs) 2442517 (18) 2 170 7.3 0.7 3.2 1.6 12 2.7 31 131 2540472(18) 3 94 6.3 0.7 1.3 1.4 8.4 2.2 49 > 163 2420760 (18) 2 71 3.5 0.7 1.2 4.9 5.6 1.5 17,22 > 150 2540638 (25) 2 116 4.7 0.9 2.0 2.2 4.5 3.3 27 > 77 2541613 (25) 3 72 5.4 0.9 1.1 1.0 9.3 2.7 33 148 2420770 (24) 3 154 5.3 0.9 2.9 1.5 2.9 4.4 37 > 138 2442596(13) 2 119 5.6 0.9 3.4 1.1 4.3 11.8 37 > 131 2541403 (25) 2 131 2.6 0.9 1.4 1.5 2.5 4.2 33 > 83 2540631 (19) 3 165 5.1 1.1 1.5 2.2 4.8 5.0 71 > 165 2541713 (25) 3 182 5.1 1.4 1.9 1.4 4.9 3.5 34 > 191 2420739 (13) 2 190 2.9 1.6 0.9 1.8 2.9 11.0 37 97 2442546 (23) 2 68 2.8 2.0 0.4 2.1 8.8 6.0 49 > 97 2541810 (25) 3 92 3.4 2.3 0.9 1.6 2.7 9.0 44 > 203 2541810 (25) 2 77 3.2 2.8 0.8 2.2 3.1 18.0 61 > 203 2541295(25) 2 111 3.7 2.9 1.7 3.3 11 5.0 51 > 178 242066 (25) 2 174 5.4 3.3 1.6 2.0 3.6 21.0 109 > 110 2420744(20) 4 203 6.5 3.4 1.5 2.5 4.2 8.0 37 > 159 MEDIAN 2 119 5.1 1.1 1.5 5.0 37 > 141









the stroke sequence. The time between the preceding stroke and the stroke in the new termination is listed in column three. The fourth and fifth columns are the height range of sources associated with pulse trains. The sources always progressed downward. The sixth column gives the duration of the pulse train. These durations were between 400 Ps (the minimum we observed) and 3.2 ms. Columns 7 and 8 indicate the minimum and maximum observed speeds during each pulse train. An average speed was obtained for each record (204.8 jis) containing a pulse train as described in Chapter 2. Speeds ranged from 1.0 x 106 m/s to 12 x 106 m/s with speeds at the upper end, near 1.0 x 107 mIs, always occurring near the beginning of trains (see details in flash 2442517 below). In all 16 flashes there was a time gap between the end of the pulse train and the following return stroke since this was a major criterion for the flash selection. This time interval is shown in column nine. The average speed, found from the lowest pulse source height and this time interval, was between 0.8 - 5.8 x 105 m/s, in good agreement with stepped leader speeds measured optically by Schonland [1956]. Column ten lists the fine structure duration for the stroke in the new termination and column eleven the fine structure duration of the first stroke in that flash. In all flashes the duration of fine structure was shorter for strokes in new terminations than in the first stroke of that flash. Flash 2420760 produced two new terminations separated by 40 gs and we determined the fine structure duration for strokes in both channels. For 14 first strokes, fine structure was still present at the end of the record as indicated in Table 1. In most cases the criteria we used to determine the end of the fine structure agreed well with visual inspection of the dE/dt waveform, but the determination is still somewhat subjective and is discussed in detail in the case studies that follow.









Flash 2541403. Flash 2541403 occurred at 20:16:43 on day 254, 17 km SSW of the central recording station. Since we obtained 25 trigger records, we probably missed activity following our last triggered record. This flash was a simple one and illustrates well the dart-stepped portion of the leader prior to its creating a new termination to ground. Figure 3.1 shows dE/dt source locations. The flash began with two sources at t = 0 located at a height of 6.5 km represented by "0" in Figure 3.1. In all plots X is east, Y is north, and Z is vertically upward relative to the central station. The sources were associated with an electric field waveshape similar to the bipolar pulses described by Weidnan and Krider [1979] who suggest that the pulses may be associated with preliminary breakdown. At t = 29.0 ms nine sources occurred at 2.5 km in height and also are shown as "0" in Figure 3.1. The first return stroke of the flash occurred at t = 38.0 ms and its dE/dt waveform is shown in Figure 3.2 (top trace). The location of the return stroke is shown in Figure 3.1 as "0" and marked "1". For simplicity we have placed the locations of all return stroke peaks at ground level since calculated heights, of typically several hundred meters, were less than the errors in height. Two sources immediately prior to the first stroke were located several hundred meters high and are shown as "0". These sources were probably radiated from the stepped leader just above ground since errors were also on the order of several hundred meters. The dE/dt waveform of the first return stroke contained fine structure that persisted for at least 83 p.s, that is, until the end of the record. Locations for three sources during the fine structure of the first stroke are shown in Figure 3.1 as "X". Source locations increase in height with time from the return stroke peak. The corresponding pulses are labeled "FS" in Figure 3.2 and marked with arrows.

























-14 -12 -10
X (km)


-14
Y (km)


-8 -6


Figure 3.1. dE/dt source locations in flash 2541403. Sources preceding and including first stroke shown as "0". Locations of first stroke fine structure pulses "X". Pulse train locations preceding second stroke "+". Locations of fine structure pulses of second stroke "0". Strokes 3, 4, 5, and 6 were co-located with stroke 2 and are shown as "0".





































Time in microseconds


Figure 3.2. The derivative of the electric field of strokes 1, 2, and 5 in flash 2541403. Return stroke peaks are marked "RS" and located fine structure pulses as "FS". Time from the beginning of the flash is indicated on each trace.









At t = 164.2 ms we recorded a dE/dt pulse train having a duration of 1.4 ms, spanning 6 records. All of the dE/dt waveshapes recorded at one station during this time are shown in Figure 3.3 with a common scale factor. The earliest sources in the train were located at a height of 2.6 km, coincident with the earlier sources at t = 29.0 ms. Locations of sources during the train are represented by "+" in Figure 3.1. Source locations moved progressively lower with time, the last sources in the train (see Figure 3.3) being located near 0.9 km in height. The average speed over each record in the train varied from 1.5 � 0.4 x 106 m/s for the top trace in Figure 3.3 to 2.5 � 0.7 x 106 m/s for the fifth trace from the top. Note that the pulse amplitudes become smaller in the last record. The second return stroke occurred in a new termination at t = 169.5 ms, 4 ms after the last source in the pulse train. The dE/dt waveform of this stroke is shown in the second trace of Figure 3.2. This stroke was displaced 1.1 km horizontally from the first stroke and is shown as a "0" in Figure 3.1. Fine structure associated with this stroke persisted for 33 As after the return stroke peak compared with more than 83 pAs for the first stroke. Locations of pulses during the fine structure, shown as "[1" in Figure 3.1, extended from near ground to a height of 0.9 kin, approximately where the pulse train ended. Four more return strokes occurred at I = 186.0 ms, t = 204.3 ms, t = 220.0 ms, and t = 244.0 ms. All four strokes were co-located with the second stroke of the flash. The dE/dt waveshape of the fifth stroke in the flash (fourth down the channel formed by the second stroke) is shown in Figure 3.2, bottom trace. The dE/dt waveshapes of strokes 3, 4 and 6 were similar to the fifth.

Flash 2420739. Flash 2420739 occurred at 17:34:54 on day 242 and was located 14.5 kin ENE of the central recording site. This flash produced only 13 trigger records so that


















It r rr 1 1164.2 ms 1, L L . 1.-, J., _ IP 4, L 1JJ 1.1. Inslc
164.4 In

,Ij ,164.7ms

* ..
........ i 1 ..__ LL ,J JJ 164.9 M
r -T - " " I r r r r - I v " ,


-1 P , ,165.1 is
-4rTJ rI' r - r ! "1

" % 1 11- !1 - q---' "4 k.. ... . ... . : 165.4 mis
I I I I I I I I I I 20 40 60 80 100 120 140 160 180 200
Time in microseconds


Figure 3.3. Pulse train recorded at one station preceding the second stroke in flash 2541403. Time from the beginning of the flash is indicated at the right of each trace. All traces have the same vertical scale.









no records were missed as a result of the memory constraints of our system. Figure 3.4 shows dE/dt source locations for this flash. The first record, at I = 0, contained two pulses. These sources were located near 6.6 km in height and are shown as "0" in Figure 3.4. The next record, at t = 5.0 ms, contained two pulses whose sources were located near 6.2 km high, shown as "0" in Figure 3.4. The first return stroke followed at t = 63.9 ms. Its location is shown as an "0" and labeled "1" in Figure 3.4 and its dE/dt waveform is shown in the top trace of Figure 3.5. Fine structure after the first stroke lasted for 97 gs. Locations of several sources indicated as "FS" on the dE/dt trace in Figure 3.5 are shown as "X" in Figure 3.4.

At t = 236.6 ms a pulse train lasting at least 200 .ts was recorded. Pulse train sources were located 6.2 km high, near the sources preceding the first stroke at t = 5 ms, and are shown as "+" in Figure 3.4. At t = 242.2 ms another pulse train, ("+" in Figure 3.4), spanned three records, with a total duration of 900 p.s. These sources began at a height near 3 km and progressed to 1.9 km with speeds averaged over individual records ranging from 1.8 � 1.0 x 106 m/s to 2.9 � 0.6 x 106 m/s. Eleven milliseconds after the last sources in the pulse train, at t = 254.3 ms, the second stroke occurred. The location of the return stroke peak, (shown as a large 0 in Figure 3.4) was displaced 0.5 km from the first stroke in the flash and was therefore a new termination. The dE/dt waveform for the second stroke is shown in the bottom trace of Figure 3.5. Fine structure after the return stroke peak lasted for 37 ps, shorter than the 97 pgs duration for the first stroke fine structure. The locations of three pulses in the fine structure indicated on the bottom trace in Figure

3.5 are shown as "0" in Figure 3.4.





































X(kn)


S II
(b)


6 8
0 0
40

00

2+


0 1 2
I I I
2 4 6 10
Y (Iam)

Figure 3.4. Source locations during flash 2420739. Sources preceding and including the first stroke are shown as "0". Locations of first stroke fine structure "X". LDAR locations preceding first stroke shown as small "0". Pulse train locations preceding second stroke are shown as "+". Second stroke marked as large "0". Fine structure after the second stroke "E".






















I I I I I




SUrokel 2FF
t 63.9 ms I .r





t = 254.3 mis ,..t,"


I I I I I I I I I I
0 20 40 60 80 100 120 140 160 180 200
Time in microseconds



Figure 3.5. Derivative of the electric field of the two strokes in flash 2420739. Return stroke peaks are marked "RS" and located fine structure pulses as 'TS". Time from the beginning of the flash is indicated on each trace.









For this flash we had available locations obtained simultaneously by the Lightning Detection and Ranging (LDAR) system at Kennedy Space Center. The LDAR system is a time of arrival system utilizing 7 stations operating at 66 MHz [Poehler and Lennon, 1979]. The first LDAR locations for this flash occurred at t = 7 ms, or seven ms after our first trigger record. LDAR source locations, shown as small "0" in Figure 3.4, began near 6.6 km in height and progressed downward to a height of 1.8 kin, ending one millisecond prior to the first return stroke we record. The average speed of progression of LDAR sources was near 1.2 x 105 m/s, consistent with that of a stepped leader. None of the sources detected by LDAR triggered our system.

Flash 2442517. Flash 2442517 occurred at 18:26:47 on day 244 and was located 21.5 km WSW of the central recording site. This flash differed from the previous two by its development of two simultaneous branches during the dart-stepped leader phase. Figure 3.6 shows locations of dE/dt sources in this flash. The sources of two pulses in the first trigger record were located near 7.3 km in height. These are shown as "0" in Figure 3.6. At t = 52.9 ms the first return stroke occurred. The dE/dt waveform is shown in Figure 3.7, top trace, and its location is shown as an "0" in Figure 3.6 and labeled "1". Fine structure persisted for 131 ps after the return stroke peak. Sources located during this time are indicated on the trace in Figure 3.7 and mapped as "X" in Figure 3.6. Sources active during the fine structure were located up to a height of 4 In.

Starting at t = 217.0 ms (164 ms after the first stroke) a pulse train spanned 13 records and 3.2 milliseconds. Figure 3.8 shows several of these records. The top two traces are the first two records whose source locations ("+" in Figure 3.6) extended from near 7.3 km in height (near the earliest sources in the flash at t = 0 ms) to 6.3 km. The





6
B +
8; +


+




2
1 2
1 I I I I I I I
-26 -25 -24 -23 -22 -21 -20 -19 -18 -17 Y (km)

Figure 3.6. Source locations in flash 2442517. Sources preceding and including the first stroke are shown as "0". Locations of first stroke fine structure "X". Pulse train locations preceding the second stroke are shown as "+". Second stroke is designated as "V". Locations of pulses after second stroke fine structure shown as "0".


N


I I I I I I I


OH1 I I I I I i !

B
6






++
2



2 1
I I t I I I I I
8 9 10 11 12 13 14 15 X (km)


















_ud I FS' ' ''





Stdw 2 RS) FS
t= 222.9 im 1 .ltA .,0 20 40 60 80 100 120 140 160 180 200
Time in microseconds

Figure 3.7. Derivative of the electric field of the two strokes in flash 2442517. Return stroke peaks are marked "RS" and located fine structure pulses as "FS". Time from the beginning of the flash is indicated on each trace.









pulse sources formed a single channel, as shown in Figure 3.6. The average speeds during the first two records were 12 � 3.2 x 106 m/s and 5.7 � 4.1 x 106 m/s respectively. Sources during the next 1.5 ms (6 records) formed simultaneous branches A and B shown in Figure 3.6 at speeds of 2.8 � 0.2 x 106 m/s and 2.3 � 0.1 x 106 rn/s respectively. At this time branch B stopped while branch A extended from 4 km to 1 km in height during the next 1.2 ms at an average speed of 1.6 � 0.2 x 106 m/s. The last two dE/dt records in the pulse train, during the end of the development of branch A, are shown in the bottom two traces in Figure 3.8. Four hundred microseconds after these, an intracloud (IC) event occurred, comprising two sources located at a height of 7.6 kin, near the height of the earliest sources of the flash but displaced horizontally by 4 km. The second stroke in the flash occurred 2.5 ms after the IC event, or 2.7 ms after the last source in branch A, and formed a new termination to ground that was displaced 0.3 km from the first stroke. The dE/dt waveform for the second stroke is shown in Figure 3.7, bottom trace, and the location of the return stroke peak is shown as a "0" and labeled "2" in Figure 3.6. Fine structure in the dE/dt waveform of this stroke lasted for 31 gis, again shorter than the 130 jis of the first stroke, but we were unable to determine any locations during the fine structure. The burst of pulses occurring between 60 and 70 gs after the return stroke in Figure 3.7 was not considered to be part of the fine structure, based on the definition we used. Their source locations are shown in Figure 3.6 as "U", near 4 km in height.

The early portion of the pulse train merits further attention. In most flashes in this chapter first records in pulse trains were characterized by pulses occurring at 5-7 pts intervals as in Figure 3.3 but it was not clear that these first records represented the beginning of the pulse trains. However, in this flash we did record what appears to be the























A".&- -I J . .... 217.0 m


Tr-' r -- - 40- l..217.2 iK


.. .. tow -o- mJ0 %11 219.7 nis




0 20 40 60 80 100 120 140 160 180 200 Time in microseconds

Figure 3.8. Pulse train preceding the second stroke in flash 2442517.
The train spanned 13 records. The first two records are shown at the top,
the last two records at the bottom. Time from the beginning of the flash is
shown to the right of each trace. All traces have the same vertical scale.









beginning of the pulse train. In the first record (Figure 3.8, top trace) pulses occurred at irregular intervals, much shorter than the 5-7 gs interval in other trains presented. The average speed was 12 x 106 m/s, providing the upper limit we found for speeds of leaders preceding new terminations to ground.


3.2.2 Discussion

3.2.2.1 Pulse train characteristics

Dart-stepped leader phase. The flashes in this study radiated dE/dt pulse trains prior to new terminations to ground. While interpulse intervals for large pulses were typically several microseconds as in Figure 3.3, the beginning of some trains (see Figure 3.8) consisted of pulses spaced by as little as 1 pgs. Average speeds ranged from 1.0 x 106 m/s to 1.2 x 167 m/s. Pulse intervals and average speeds during trains are consistent with dart-stepped leader measurements. Krider et al. [1977] found that microsecond-scale electric field pulses 200 tis prior to subsequent strokes in Florida had a mean interval of 6.5 pts. From optical records Schonland [1956] found the time between steps to be 7.4 25 tis while Orville and Idone [1982] found intervals from 2 - 9 pts. Dart-stepped leader speeds from Schonland's study were in the range of 0.76 - 17 x 105 rn/s while the speeds from Orville and Idone's were 5.0 - 17 x 106 m/s. Our observations of pulse intervals and average speeds agree well with the above observations.

Unlike the pulse trains radiated by dart-stepped leaders, the pulse trains considered in this chapter did not continue up to the return stroke and therefore differ from those reported by Krider et al. [1977] that occurred in the 200 ps immediately preceding the return stroke. We record trains beginning at heights near 7 kin, lasting several









milliseconds, and progressing downward to heights near 1 km. This portion of leaders was dart-stepped like in nature, but was followed by a median time interval of 5 ms to the following return stroke during which time no pulses triggered our system.

Transition from dart-stepped to stepped leader. In 15 of the 17 strokes in Table 1, no records were triggered between the last sources in the pulse train and the following return stroke several milliseconds later. In the other two cases we recorded one and two dE/dt pulses respectively that did not appear to be associated with the propagating leader tip since their sources were in the cloud at a height of 7-9 km. In all cases the leader may have continued earthward without triggering our system if the pulse amplitudes were below our trigger threshold. Indeed this seems to have been the case since smaller amplitude pulses were always evident during the 30 pgs pre-trigger interval preceding the following return stroke. Assuming that the leader continued, we estimated its speed over the missing portion from the distance and time between the last source in the pulse train and the following return stroke. For the three flashes presented above this was 1.4 x 105 m/s, 2.6 x 105 m/s, and 2.1 x 105 m/s respectively for the average speed of the leader. For the strokes listed in Table 1 we find a range of speeds from 0.8 - 5.8 x 105 m/s over the gap from the lowest source in the train to the following return stroke. These speeds are consistent with stepped leader speeds of 0.8 - 8.0 x 105 m/s determined photographically by Schonland [1956]. The transition of a leader from dart-stepped to stepped has been documented by Schonland et al. [1938b] who photographed this transition and found a corresponding decrease in speed from 1.7 x 106 m/s to 3.8 x 10' m/s. We observe a similar decrease in speed from the end of the pulse train (about









106m/s) to the following gap that we interpret as a transition from dart-stepped to stepped leader.

The formation of a new termination to ground may produce more than one visible channel below the cloud base. Multiple channels below cloud base have been recorded by many investigators [Kitagawa et al., 1962; Krider, 1966; Barasch, 1970; Winn et al., 1973; Brantley et al., 1975; Clifton and Hill, 1980; Rakov and Uman, 1990b] with estimates of this occurrence in anywhere between 17% and 50% of flashes. Thomson et al. [1984] proposed that multiple channels below cloud base might be due to the leader following an old channel in the cloud and then branching before reaching cloud base. Rakov and Uman [1990c] found the geometric mean duration of leaders preceding new terminations to ground (15 ms) to be intermediate between those of stepped leaders (35 ms) and dart leaders (1.8 ms). Rakov and Uman suggested this intermediate value might arise from a leader that follows an old channel in part and adopts a new channel to ground, similar to the view of Thomson et al. [1984]. Schonland et al. [1938b] photographed branching from the old channel, forming new terminations, in the lower one-third of the visible channel but suggested that this branching could occur anywhere along the channel. Our results show this to be the case. In Table 1, column five lists the height of the last source in the pulse train prior to what we interpret as the transition to stepped leader. The values range from 0.7 km to 3.4 km, indicating that the transition may indeed occur at points inside the cloud as well as below. Cloud base is 1-2 km in Florida. Some heights near 0.7 km may in fact be lower or higher than this since our errors are several hundred meters in z at this height.









Records in the 16 flashes of this study were rarely triggered by pulses associated with the stepped leader preceding the first stroke to ground, but rather by the return stroke peak. Difficulty in detecting the stepped leader is well documented in the literature. Schonlandet al [1938b] photographed stepped leaders beginning as high speed, brightly luminous leaders that became slower, fainter and harder to record. Orville and Idone [1982] were unable to analyze three stepped leaders they recorded owing to the weak intensity of the steps. We see what appear to be stepped leader pulses in the tens of microseconds preceding both first strokes (see Figures 3.2 and 3.7) and new terminations to ground (Figure 3.7) but rarely trigger on them. The dE/dt pulses produced by stepped leaders appear to be smaller than those produced by dart-stepped leaders, that is, during pulse trains. The last pulses received in each train (bottom trace in each figure) have amplitudes 2-3 times smaller than those earlier in the train. This decrease in pulse amplitude at the end of the train occurred in 14 of the 17 strokes listed in Table 1.


3.2.2.2 Return stroke fine structure

Fine structure locations. Using a multiple-station VHF time-of-arrival system, Proctor [1988] found locations during "Q-noise" radiated during first strokes to ground to be located alongside the leader path to ground and near earlier stepped leader sources. Q-noise typically lasted 40 - 400 is and locations were obtained by timing the leading edges of pulses, changes in amplitudes, gaps in Q-trains, and the beginning and ends of trains. Q-noise from one flash lasted for 180 jis after the first stroke and was located to a height of 3.5 km. Q-noise was located in other flashes to heights of 4.5 km. Source locations increased irregularly in height with time during Q-noise. Average speeds of progression for sources active during Q-noise were 1.0 - 5.7 x 107 m/s. Proctor suggests









that VHF sources alongside the lightning channel may be associated with the tips of short branches, similar to the view of Weidman and Krider [1978] regarding sources of wideband electric fields during fine structure.

We could locate only a few sources of fine structure in each flash despite the many dE/dt pulses present. The location of fine structure, or any pulse for that matter, requires the alignment of common sources on at least 4 of the 5 traces. For pulses in the fine structure after return strokes this task was particularly difficult for two reasons: (1) the speed of the return stroke, up to 2 orders of magnitude higher than that of the dartstepped leader (that cause pulse trains), result in pulses in the fine structure to be out of alignment after several microseconds; and (2) multiple sources may be active simultaneously during the fine structure making it more difficult to distinguish common sources at different stations. To illustrate these difficulties, Figure 3.9 shows a portion of the fine structure from the first stroke of flash 24402517 (Figure 3.7, top trace) on an expanded time scale. A set of common pulses are discernable at each of the five stations and are marked "A" while at "B" pulses appear clearly at only 2 or 3 stations thus precluding us from finding a location. Nevertheless, we were able to obtain confident locations (with height errors of 500 m or less) for several fine structure pulses in each stroke in this study. For example, pulses marked "A" in Figure 3.9 were located with a height error of 255 m and had a X2 value of 0.19. For the first stroke in flash 24200739 (Figures 3.4 and 3.5), the sources active during the fine structure coincide with earlier stepped leader sources located by the LDAR system. During the first stroke of flash 24402517, we find locations of fine structure pulses to be alongside the channel that is later followed by the dart-stepped portion of the leader preceding the second stroke. We



































VI ~ SLF IR


UC9


USB

J EDL 52.94 52.96 52.98 53.0



Figure 3.9. Expanded time scale trace of dE/dt waveforms recorded at all five
stations during the first stroke in flash 2442517.









infer that the stepped leader preceding the first stroke produced the section of channel A, where these fine structure sources are located. In flash 25401403 (Figures 3.1 and 3.2), fine structure sources of the first stroke were located in the region consistent with the path the stepped leader probably took. Fine structure sources in first strokes were located to a height of 4 km. Higher source locations may have been missed since we were unable to obtain locations at the end of the fine structure in 14 strokes, owing to record length limitations on one or more channels. Fine structure locations obtained during flashes 25401403 (Figure 3.2) and 24200739 (Figure 3.5) for the new terminations were between ground and the last sources in the pulse train prior to the transition to stepped leader. These locations are consistent with those of the inferred stepped leader forming the new termination. An exception is flash 24402517 for which we were unable to locate any sources during the 31 pIs of fine structure immediately after the return stroke peak. Locations of sources occurring 60-70 pIs after the return stroke peak were located near 4 km high. These source locations are inconsistent with having been radiated from the region of the stepped leader occurring after the pulse train, presumably between ground and 1 km. It is interesting to note that the locations of the pulses 60-70 pis after the second stroke coincide with the extent that branch A had reached when branch B ceased propagating.

Origin and duration. Weidman and Krider [1978] suggested that fine structure in first stroke electric field waveforms is due to the effects of branches. Schonland and Collens [1934], Schonland et al. [1935], and Malan and Collens [1937] observed changes in luminosity and speed near points of intersection of the return stroke with large branches that may give rise to radiated fields. Weidman and Krider [1978] postulated that the









contribution of channel tortuosity to the fine structure is not as great as that of branches since the subsidiary peaks in subsequent strokes are quite weak and most subsequent strokes are not usually branched [Schonland et a., 1935].

Willett et aL [1995] found that all 34 electric field waveforms containing fine structure after the return stroke peak were associated with new channels to ground, including first strokes. Fine structure after return stroke peaks appeared "noisy" in dE/dt, similar to the waveforms we record (see Figure 3.2). Eighteen waveforms that were "quiet" in dE/dt after the peak were found to have been radiated from subsequent strokes in old channels. Bailey and Willett [1989] presented "anomalous" return stroke waveforms which were preceded by stepped leader pulses and appear as first stroke waveforms (noisy dE/dt) for the first few tens of microseconds, but resemble subsequent stroke waveforms thereafter (quiet dE/dt). They suggested this signature might be produced by a new channel to ground branching off an old channel within a few kilometers of ground, and postulated that new terminations to ground produce noisy dE/dt waveforms while later strokes in the same channel produce quiet dE/dt waveforms. They further hypothesized that a new fork to ground off an old channel offers a test as to some characteristic (possibly the presence of branches) that causes the noisy dE/dt structure. A new termination to ground would be expected to be initially noisy in dE/dt as the return stroke traverses the new channel segment, and later quiet upon reaching an older section of channel. We find sources of fine structure pulses in new terminations to be between ground and the last sources in pulse trains, consistent with having originated in a stepped leader channel. The maximum height of fine structure pulse locations in new terminations generally corresponds to the location of the last pulse in the preceding pulse train. These









observations support the hypothesis of Willett et al. (1995) that the dE/dt waveform becomes "quiet" after the return stroke has passed from the new channel segment (forged by a stepped leader) to the old channel.

The "anomalous" cases reported by Willett et al. [1995] and Bailey and Willett [1989] had fine structure durations of 10, 12, 20, and 6-17 As. Willett et al. [1995] assumed a return stroke speed of 1 x 108 m/s for the anomalous duration of 12 As to obtain a height of 1.2 km for the new branch off the old channel. However, for pulse trains ending at heights near 1 km (see Table 1), we find fine structure durations 2-3 times as long as the "anomalous" cases described by Willet et al. [1995] and Bailey and Willett [1989]. This suggests a lower average return stroke speed than 1 x 108 m/s over the lower 1-2 km of the channel. Idone and Orville [1982] observe return stroke speeds in the range of 2.9 24 x 107 m/s for the lowest 1-2 km of the channel in Florida. Their mean speed was 6.6 x 107 m/s for first strokes and 11 x 107 m/s for subsequent strokes. In flash 2442517 (Figure 3.7) we locate fine structure pulses 130 As after the first stroke to a height of near 4.1 km. This corresponds to an average return stroke speed of near 3 x 107 m/s, consistent with the lower values for first strokes obtained by Idone and Orville [1982].

Strokes occurring in new terminations in our study had a median fine structure duration of 37 As. The strokes whose last pulse train sources were located at 1 km or below had a median fine structure duration of 33 As, while strokes with trains ending at heights above 1 km had a median fine structure duration of 49 ps. This difference is to be expected since pulse trains ending at greater heights would produce longer fine structure owing to a longer stepped leader channel. In all flashes in this chapter the fine structure duration following new terminations (median value 37 As) was considerably









shorter than that from the first stroke in the flash (median value 141 jis). The median duration fine structure from first strokes we report, 141 gs, is very similar to the 137 gs found by Cooray and Perez [1994] for HF radiation at 3 MHz after first strokes in negative ground flashes. Longer duration fine structure associated with first strokes versus that of new terminations is consistent with the view of a stepped leader beginning at a greater height prior to a first stroke than a stepped leader preceding a new termination. In Florida, for example, first strokes typically begin at heights near 5 - 6 km [Krehbiel et al., 1979].



3.2.3 Conclusions

We have presented results of the properties of return stroke fine structure and leaders associated with new terminations to ground. We find evidence to support the hypotheses of Thomson et al. [1984] and Rakov and Uman [1990c] that multiple channels below cloud base are due to a leader following an old path in the cloud and later adopting a new path to ground forming a new termination. Strokes occurng in new terminations to ground, subsequent to the first stroke, are preceded by a leader that is dart-stepped in nature prior to a transition to a stepped leader. Leader speeds of 1.0 - 12 x 106 m/s are calculated during the dart-stepped portion of leaders. Leader speeds are estimated to be near 2 x 10' r/s after their transition from dart-stepped to stepped. The leader transition is found to occur at heights between ground and 3.4 km.

Fine structure is present in the dE/dt waveform of both first strokes to ground and subsequent strokes in new channels to ground. The duration of fine structure was found to be shorter (37 ps median) for strokes in a new termination to ground than for first









strokes of a flash (141 ps median). Sources of fine structure after strokes in new terminations were between ground and the transition of the leader from dart-stepped to stepped. This suggests that fine structure is the result of the preceding stepped leader and is therefore shorter in strokes occurring in new terminations to ground, compared to first strokes of a flash, owing to the shorter stepped leader path in the former. The stepped leader path length preceding new terminations had a median value of 1.1 km in this study.



3.3 Return Stroke Waveforms Separated by One Millisecond or Less

Electric field waveforms, indicative of two return stroke signatures separated by one millisecond or less, have been reported by Schonland et al. [1935], Guo and Krider [1982] and Rakov and Uman [1994]. Guo and Krider [1982] found that five of 246 flashes contained records with two return strokes separated by 46 - 110 pgs. Schonland et al. [1935] observed two different branches of a single stepped leader that produced two separate return strokes. They present streak-camera images showing two leader branches, apparently originating from a single trunk inside the cloud, that resulted in two return strokes separated by 73 pis. Rakov and Uman [1994] report nine cases where a double electric field waveform (two return stroke signatures) occurred with simultaneous double ground strokes, as determined from video records. These strokes were separated by 15 gs- 3.3 ms.

Guo and Krider [1982] note that multiple ground contacts by two branches of the same stepped leader are rare. They hypothesize that in order for the first branch to reach ground 50 - 100 pgs prior to the second, the tip of the leader along the second branch must









be within 5 - 40 m of ground. If not, it is assumed that the first stroke will travel up the first branch and out along the second branch, thus discharging it. Rakov and Uman [1994] point out that while the double field waveforms separated by up to 100 gs that they recorded were consistent with the view of Guo and Krider [1982], those separated by times greater than 165 tis were not. They proposed that double field waveforms were the product of two sequential strokes, each initiated by its own leader, rather than from the simultaneous branching of a single leader.

We studied five flashes, each containing two dE/dt signatures characteristic of return strokes, separated by up to one millisecond. In all cases the locations of the two strokes were distinct, indicating that they occurred in separate terminations to ground. The duration of fine structure associated with the secondary stroke was shorter, in each case, than that of the primary stroke, indicative of a shorter stepped leader channel prior to the secondary stroke (see discussion in Section 3.2). The temporal separation of strokes in two flashes was 40 pts and 50 pgs. In the remaining three flashes, strokes were separated by 250 - 1000 tts. In one of the latter, we find evidence that the strokes were preceded by two simultaneous branches of the same stepped leader.



3.3.1 Results

Table 3.2 summarizes data from five flashes with return strokes separated by one millisecond or less. All strokes produced first stroke type waveforms, i.e., the return stroke signatures were followed by fine structure, and occurred in different channels. Stroke orders are listed in column two of the table in accordance with their occurrence in the overall flash sequence. Strokes will also be referred to as primary or secondary when









discussing them together. In three of the five flashes the strokes were the first two of the flash, while in the remaining two flashes, the strokes were preceded by an earlier stroke at a nearby, but different location. The time between strokes is listed in column three. The duration of the fine structure following each stroke is listed in the fourth column of the table. In the first two flashes of the table, the two return stroke signatures occurred in the same record (204 g.s). Fine structure associated with the primary stroke of flash 2420744 was still present at the time of the secondary stroke. Notice that the difference



Table 3.2. Summary of five flashes with strokes separated by one millisecond or less.

Flash ID Stroke #'s A T FS Duration A D
(Ps) (tis) (kin)
2420760 2,3 40 28,22 0.9 2420744 2,3 50 50+,43 0.9 2540472 1,2 273 143,45 1.3 2420770 1,2 504 140+, 65 1.2 2540638 1,2 1000 200,48 1.4


in fine structure duration for the strokes in the last three flashes in Table 3.2 was a factor of 2 - 4, similar to the differences between first strokes and strokes in new terminations (see Table 3.1). The spatial separation between strokes is given in column 5 of the table. We now present two flashes in detail.

Flash 2420760. Flash 2420760 comprised 18 records in 740 ms. The final six records were at a location distant from the start of the flash and were considered to be from a









separate discharge. The first 12 records spanned 331 ms and contained six strokes to ground. The first stroke occurred at t = 50.9 ms with fine structure lasting at least 150 gs. At t = 121.2 ms we recorded the double field waveform, strokes 2 and 3, displayed in Figure 3.10. Fine structure after strokes 2 and 3 lasted for only 28 ps and 22 gs respectively, much shorter than that associated with the first stroke of the flash. Strokes 2 and 3 were preceded by a leader of the type described in Section 3.2. The leader began in a dart-stepped fashion at t = 119.7 ms, 70.3 ms after the first stroke. Sources progressed downward from 3.5 km to near 0.7 km at 4.9 - 5.6 x 106 m/s during the next 1.2 ms and exhibited two distinct branches below 1.8 km. There followed a 1.5 ms interval during which time we received no triggers, until the two strokes at t = 121.2 ms. Each stroke occurred in a new termination, as evidenced by the fine structure after each. Locations of dE/dt sources from flash 2420760 are shown in Figure 3.11. Sources preceding and including the first stroke of the flash are shown as "0". The second and third strokes were located at points "2" and "3" respectively. Leader sources prior to strokes 2 and 3 are marked as "+" and followed branches A and B before creating the two new terminations to ground. Locations of fine structure associated with the third stroke are shown as "XV and were near sources from the leader along branch A. Strokes four, five, and six were co-located with the second stroke of the flash and occurred at t = 156 ms, t = 241 ms, and t = 332 ms respectively. Little or no fine structure was associated with these strokes.

Flash 2420770. The first two strokes of this flash were separated by 504 gIs and 1.2 km. The dE/dt waveforms of the two strokes are depicted in Figure 3.12. The first stroke occurred at t = 48.0 ms and fine structure in the dE/dt waveform exceeded 140 gs. The






































Time in microseconds


Figure 3.10. dE/dt waveform of the double return stroke of flash 2420760.





1Jn











I I I I I I I I


Bt +
%X A
.............................................................. . O .... ....................................... ..............O
2 3 1
lII I I I I
11 12 13 14 15 16 17 18
X~km)













0 +
IlI I I I





04


1 3 2

0 1 2 3 4 5 6 7 8 Y (km)

Figure 3.11. dE/dt source locations during flash 2420760. Sources preceding and including the first stroke are shown as "0". Locations of second leader shown as "+". Second stroke represented by "box". Third stroke and fine structure locations shown as "X".





























Time in microseconds


Figure 3.12. dE/dt waveforms for the first two strokes of flash 2420770. The strokes occurred 504 microseconds apart and were located 1.2 km apart. The return stroke peaks are marked "RS". Time from the beginning of the flash is indicated on each trace.









second stroke waveform contained fine structure lasting 65 gis. Locations of the two return strokes, stepped leader sources, and several sources of fine structure after each stroke are shown in Figure 3.13. Stepped leader and return stroke sources are shown as "0". Actual stepped leader heights are probably only a several hundred meters above ground. Sources of fine structure after the first stroke are shown as "X" in Figure 3.13 and extend to near 2 km high. Locations are near those of the stepped leader prior to the first stroke. Fine structure after the second stroke was located to a height of 2 km and locations are marked as "0" in Figure 3.13. The third stroke in the flash occurred at t = 203 ms in a new termination to ground located 0.63 km from the second stroke. This location is labeled "3" in Figure 3.13 and marked with "0". The third stroke was preceded by a leader of the type described in Section 3.2. Beginning at t = 195.9 ms, and for 2.7 ms, we located sources that extended from 5.3 km to 0.8 km at 1.5 - 2.9 x 106 m/s, then the third stroke followed 4.5 ms after the last leader source we recorded. Fine structure after the third stroke persisted for 40 gs and was located to a height of 1.8 kin, near sources of the third leader. Leader sources are shown as "+" in Figure 3.13. Locations of fine structure following the third stroke are marked with "0". When sources from the leader preceding the third stroke are overlaid with those associated with the first two strokes, it appears that the leader branched near 3 km high, one branch going towards the location of the first stroke (1), the other towards the second (2), prior to creating a new termination to ground (3).

3.3.2 Discussion

Guo and Krider [1982] have suggested that double stroke waveforms, separated by 50

- 100 ps, may be the result of simultaneous branches of the same stepped leader












I I I I I I I


3 2 1 "1 12, 13 14 15 16 17 18 19 20 X(km)

8




6










4 4
2

0 ------------------ ---------------------.... . . . . . .1 3 2 ...... .........
I I I I I I I
-1 0 1 2 3 4 5 6 7 Y(km)
Figure 3.13. dF/dt source locations during flash 2420770. Sources preceding the first twostrokes are shown as "0". First stroke fine structure marked "X", second stroke fine structure "boxes". Third leader sources represented by "+". Fine structure after third stroke shown as "diamonds".









contacting ground at two points. For this scenario to occur, they argue that the secondary branch must be within 5 - 40 m of ground when the primary branch contacts ground. If this were not the case, the return stroke resulting from the primary branch would propagate up the channel established by the primary branch and out along the secondary branch, thus discharging it. Schonland et al, [1935] present streak-camera photographs that support this view. Two leader branches, apparently originating from a single trunk inside the cloud, produced two strokes separated by 73 Ps. The leaders emerged from the cloud 1.8 ms apart but due to differences in path lengths, arrived at ground 73 gs apart. The first two flashes in Table 3.2 contain strokes separated by 40 and 50 As. In each flash the strokes were distinctly located. Fine structure following strokes was 22 - 50 ps, much shorter than that of first strokes of flashes (median value 141 pjs from Section 3.2), indicating a new termination was formed near ground. Consider flash 2420760 with strokes separated by 40 gs. The leader preceding strokes two and three was of the type described in Section 3.2. The leader was dart-stepped from a height of 3.5 km to several hundred meters above ground. From a height of 2 km the leader followed two branches simultaneously, A and B. After reaching a height of several hundred meters above ground, the leader became stepped along each branch and forged two new paths to ground. The locations of the lowest dart-stepped leader sources and the short duration fine structure after each stroke indicates a short section of stepped leader channel preceded each stroke. We propose that the two branches, A and B, were formed prior to the third leader, most likely by the first leader of the flash. The second leader followed the two branches before deviating in the final few hundred meters of each branch, thus forming the double field new termination waveform of Figure 3.10. Thus the second and









third strokes were the result of two simultaneous branches of the same leader, consistent with the view of Guo and Krider [1982] and the photographic evidence of Schonland et al. [1935]. The two strokes of flash 2420744 were similar to those of 2420760, both were associated with a relatively short fine structure and occurred after the first stroke in the flash. We now discuss return stroke waveforms separated by more than 250 pts.

Using simultaneous video and electric field records, Rakov and Uman [1994] recorded double field waveforms coincident with two visible channels to ground branched between the top and bottom of the channel. Strokes were separated by 15 gs - 3.3 ms. In three flashes strokes were separated by 15, 22, and 100 gs and were consistent with the hypothesis of Guo and Krider [1982]. Two flashes, however, contained return strokes separated by 165 and 287 pgs, longer than the time assumed necessary for the first stroke to travel up to the branch point (observed below cloud base) and discharge the second branch. Rakov and Uman [1994] argue that these double field waveforms were unlikely the result of two return strokes initiated by two simultaneous branches of the same leader as suggested by Guo and Krider [1982]. Rakov and Uman [1994] also found three flashes that contained strokes separated by 442, 513, and 596 pts. Each of these was observed to produce two visible channels to ground and a double field waveform. No branch point was observed but may have been hidden within the cloud.

The first two strokes of flash 2420770 were separated by 504 pts. The strokes produced distinct locations at ground and were located 1.2 km apart. Locations of stepped leader sources prior to the strokes and fine structure after the strokes, are consistent with two separate channels below 2 km high (see Figure 3.13). It is not until source locations of the leader prior to the third stroke are overlaid with those of the first









two strokes that the complete picture of the flash is obtained. The leader prior to the third stroke followed what we assume to be the channel established by the first leader, branching near 3 km high. Several source locations extend out along branch A, near earlier stepped leader and fine structure sources from the first stroke to ground. The vast majority of leader sources, however, were located along branch B, coincident with earlier stepped leader and fine structure sources from the second stroke to ground. When all dE/dt source locations are considered, its appears that the first strokes shared a common channel in the cloud, above 3 km high.

Rakov and Uman [1994] suggested that strokes separated by 165 and 287 pgs were inconsistent with being initiated by two branches of the same stepped leader. Based on a maximum channel length of 2 km (below cloud) and a minimum return stroke speed of 2 X 107 m/s (Orville and Idone, 1982), they argue that the stroke along the more successful branch would reach the end of the less successful branch in a time not exceeding 100 p1s. Rakov and Uman [1994] hypothesize that the double ground events separated by 165 and 287 lis may be the result of two sequential return strokes of the same flash, each initiated by a different leader, rather than the simultaneous branching of a single leader. It is assumed that either: (1) the primary leader develops two branches, both are grounded and produce inseparable return stroke waveforms or (2) the second branch terminates close to, but above ground. In either case, the secondary leader can follow the secondary branch to ground or produce two inseparable return stroke signatures. Rakov and Uman [1994] argue against several physical situations, other than two consecutive leader-return stroke sequences, that may produce the observed double field waveform. We can also dismiss several of these in regard to the last three flashes in Table 3.2 by noting that in









each case, the two return stroke waveforms were indeed strokes to ground as verified by locations. Thus we can eliminate the following possibilities: (a) a random overlap of field signatures produced by strokes belonging to independent discharges, (b) the secondary waveform being an ionospheric or other reflection of the first waveform, and

(c) the secondary waveform being associated with an M-component. We now address the possibility of two separate, sequential leaders, as suggested by Rakov and Uman [1994], producing the return stroke signatures separated by 504 ps in flash 2420770.

Let us assume that the first two strokes of flash 2420770 were initiated by two separate leaders. The first stroke was initiated by a stepped leader that formed branch A (Figure 3.13). It is likely that this leader began near 6 km high, the earliest sources of the flash, and formed the channel to ground later followed by the subsequent leader. Fine structure associated with the first stroke was located near sources of the stepped leader along branch A, up to a height of 2 kin. Fine structure lasted for longer than 140 ps, consistent with the first strokes of flashes in section 3.2. If the second stroke were initiated by a separate leader, as suggested by Rakov and Uman [1994], the duration of the leader would be approximately 350 pgs (allowing for the current from the first stroke to cease). Although leaders with such a duration are rare, they have been reported. Rakov and Uman [1990a] found about 6 % of dart leaders had a duration between 200 500 pts. We report two subsequent leaders with durations between 130 - 200 ps in section 4.5. However, the waveform of the second stroke is inconsistent with the above scenario. Fine structure afiter the second stroke persisted for 65 pgs and was located to a height of 2 km. This suggests that the second stroke was preceded by a stepped leader, rather than a dart leader, and that fine structure was a result of the return stroke retracing









the stepped leader channel. Fine structure persisted for longer than the median value of 37 gs associated with new terminations in Section 3.2, but shorter than that of first strokes (median value 141 gis). The median lowest height of dart-stepped leader sources preceding new terminations in section 3.2 was 1.1 km, thus sources of fine structure located to a height of 2 km are consistent with a duration of 65 gs. It appears, therefore, that the second stroke was preceded by a stepped leader, from a height of at least 2 km that was not discharged prior to the second stroke. If the second leader was stepped over this portion, the average speed required to reach ground in 350 jis would be at least 6 x 106 m/s, an order of magnitude faster than typical stepped leader speeds. Therefore it appears unlikely that a second leader, separate from the first, could have produced the second stroke waveform.

We propose an alternative to the scenario described above, namely that the two strokes were the result of two simultaneous branches of the same stepped leader. We assume that the secondary branch (B) was concurrent with the primary (A) and continued to ground after the first stroke. In this scenario the leader tip along branch B would be approximately 100 m above ground when the first stroke occurred (this assumes a common stepped leader speed of 2 x 105 m/s). Prevailing assumptions in the literature suggest that the 504 pts interval between strokes should be sufficient for the first stroke to travel back up the primary branch (A), and out along the secondary branch (B), a total path length of near 6 km, thus neutralizing branch B. Assuming a return stroke speed of 2 x 107 m/s, the minimum observed by Orville and Idone [1982], the first stroke would reach the end of the second leader in approximately 300 ps, less than the observed 504 pts interval between the two strokes. Orville and Idone [1982], however, have noted a









decrease in return stroke speed between ground and cloud base of up to 25 % and Schonland et al. [1935] found a speed of 1 x 107 m/s for a return stroke along a very long horizontal branch (nearly 10 km). If a significant attenuation in speed occurs within the cloud, it may be possible to achieve the 504 gs needed to prevent the return stroke from reaching the end of the secondary branch. Another possibility may be that the first return stroke failed to neutralize any of the secondary branch. The duration (65 gs) and location of fine structure (to 2 km high) following the second stroke indicates that much of this branch may not have been neutralized by the first stroke. We found no locations of fine structure associated with the first stroke to be along the secondary branch, although only a small fraction of pulses could be located. Flashes 2540472 and 2540638 were similar to flash 2420770, the primary stroke in each case having a fine structure 3 - 4 times that of the secondary. Each of these is consistent with the secondary stroke discharging a relatively short stepped leader channel, similar to that of flash 2420770.



3.3.3 Conclusions

The first two flashes of Table 3.2, with strokes separated by 40 pts and 50 t s, were consistent with the theory of Guo and Krider [1982], the two strokes being the result of a single branched stepped leader. Fine structure associated with both the primary and secondary strokes was much shorter than that of first strokes in a flash, suggesting the strokes were preceded by relatively short stepped leaders. In one case we found the two strokes to be preceded by a leader that was dart-stepped along two branches, one towards each stroke location, prior to becoming stepped several hundred meters above ground.









The strokes therefore appear to be the result of two simultaneous branches of the same stepped leader.

Two strokes separated by 504 gs were found to share a common leader channel, branched below a height of 3 km. The waveforms and locations of the two strokes were inconsistent with having been initiated by two separate leaders. We found data to support the view that the two strokes may have been the result of two simultaneous branches of the same stepped leader.



3.4 Summary Conclusions

In this chapter we have investigated leaders preceding new terminations to ground and the fine structure associated with strokes in those flashes. Sources of fine structure appeared to be the result of the preceding stepped leader, suggesting that shorter stepped leader channels were associated with strokes having a shorter fine structure. We extended these findings to cases where two return strokes occurred less than one millisecond apart. Fine structure associated with the secondary stroke was shorter, in each of five cases, than that of the primary stroke. This suggests the secondary stroke was preceded by a shorter stepped leader channel than the primary, and that the two strokes were possibly the result of two branches of the same stepped leader.














CHAPTER 4
LEADER OCCURRENCES AND CHARACTERSTICS IN SUBSEQUENT STROKES TO GROUND

4,1 Introduction

In this chapter we investigate characteristics of leaders preceding subsequent strokes to ground. Unlike leaders preceding new terminations to ground in chapter 3, leaders follow old channels completely to ground. In section 4.2 we present data from seven subsequent leaders to ground that produce regularly occurring dE/dt pulses prior to the following return stroke. We give 3-D track speeds for these leaders and analyze changes in leader speed as a function of height. We present dE/dt waveforms of several leaders and investigate the relationship between interpulse interval and leader speed. Two leaders exhibiting an increase in speed towards ground and a corresponding decrease in interpulse interval are examined in section 4.3. Finally, in section 4.4, we note three cases in which pulses in the dE/dt waveform, indicative of a dart-stepped leader, continue through the time of the return stroke. Sources of these pulses are found to originate from locations higher along the channel to ground. The relationship between interstroke interval and leader waveform is explored in section 4.5. A summary of the major chapter findings is given in section 4.6.



4.2 Leader Speed and dE/dt Waveshape

Leaders preceding subsequent strokes to ground in a lightning discharge can be classified based upon their appearance in optical and electric field records. Leaders that









follow a previous channel and appear as continuous luminous sections of channel in optical records are termed dart leaders. Speeds of dart leaders near ground, determined optically, range from 1 - 24 x 106 m/s [Orville and Idone, 1982; Jordan et al., 1992] with a mean value near 10 x 106 m/s [McEachron, 1939; Winn, 1965; Orville and Idone, 1982]. Subsequent leaders that follow the channel of an earlier stroke, but exhibit steps in optical records after initially continuous propagation, are termed dart-stepped leaders. Dart-stepped leader speeds are intermediate to those of stepped leaders and dart leaders. Schonland [1956] found dart-stepped leader speeds of 0.5 - 1.7 x 106 m/s preceding six subsequent strokes to ground, while Orville andIdone [1982] found leader speeds of 0.76

- 17 x 106 m/s preceding four subsequent strokes. Time intervals between luminous steps of dart-stepped leaders were near 10 pgs in Schonland's [1956] study and between 2

- 9 t~s in that of Orville and Idone [ 1982].

Krider et al. [1977], Le Vine and Krider [1977], Weidman [1982], and Izumi and Willett [1991] have reported wideband electric field measurements of radiation from subsequent leaders. Krider et al. [1977] found that dart-stepped leaders contained regularly occurring pulses in the electric field waveform, 80 - 200 4~s prior to the following return stroke peak. Mean interpulse intervals were 6.5 ps in Florida thunderstorms, consistent with the time between luminous steps observed by Schonland [1956] and Orville and Idone [1982]. Izumi and Willett [1991] and Willett et al. [1995] have noted regularly occurring dE/dt pulses immediately (up to 20 pIs) prior to subsequent strokes.

Geometric mean duration of subsequent leaders, including both dart and dart-stepped, as determined from electric field measurements, are 0.6 - 1.9 ms (Malan and Schonland,









1951; Kitagawa, 1957; Workman et al., 1960; Krehbiel et al., 1979; Rakov and Uman, 1990c). However, these measurements were made on a millisecond time scale while individual pulses vary on a microsecond scale. No electric field measurements, recorded with sufficient bandwidth, to reveal microsecond scale variations, are available for the whole duration of subsequent leaders. If we assume a common dart-stepped leader speed of 3 x 106 m/s, source locations of dart-stepped leader pulses measured 200 Ps prior to return strokes by Krider et al. [1977] correspond to heights below 1 km. The optical measurements of dart-stepped leaders by Orville and Idone [1982] and Jordan et al. [1992] were confined to the lowest 2-km of the lightning channel, corresponding to heights below cloud base in Florida. Similarly, the measurements of Schonland [1956] were limited to the lowest 2 - 2.5 km of the lightning channel. Therefore there is a lack of electric field measurements on a microsecond scale for the full duration of subsequent leaders.

Several investigators have made measurements of the change in speed of subsequent leaders below cloud base with conflicting results. Schonland [1935] found little change in dart leader speed as a function of height and noted that the speed never increased towards ground. Optical measurements of dart leader speeds made by Mach and Rust [1997] are consistent with this view as they found "no significant" change in dart leader speed with height. Orville and Idone [1982], however, found 4 of 16 dart leaders to increase in speed towards ground, the first such findings. Additionally, Orville and Idone [1982] noted one dart-stepped leader that increased in speed towards ground and another that decreased in speed.









We investigate seven subsequent leaders to ground, each exhibiting regular pulses tens of microseconds prior to the return stroke peak, indicative of a dart-stepped leader. In each case the following return stroke peak is co-located with a previous stroke in the flash and lacks fine structure in the dE/dt waveform, indicating the leader followed an old channel completely to ground. Pulses in the derivative of the electric field are detected 0.6 - 2.0 milliseconds prior to these subsequent strokes. Several tens of microseconds, during which time no dE/dt pulses appear above the noise, precede the first dE/dt pulses in each leader record, suggesting we recorded leaders in full. The earliest leader sources spanned heights between 3.8 and 6.2 km, well above the cloud base in Florida. Each of the seven leaders exhibited a decrease in speed from its highest point to that near ground (lowest 1 kIn). Leader speeds, averaged over individual records, were between 1.4 x 106 m/s and 35 x 106 m/s, spanning the range of observed dart leader speeds in the literature as well as those of dart-stepped leaders. Speeds averaged 16 x 106 m/s during the first record of dart-stepped leaders and 3.6 x 106 m/s during the final record, corresponding to the lowest kilometer of the channel to ground. The median interpulse interval was dependent on the threshold used in pulse selection. We therefore defined a median interpulse interval as a function of threshold as described in Chapter 2. At a threshold of 20% of the maximum leader pulse, the median interpulse interval was larger, in each case, near the return stroke than it was at the start of the leader. Source locations progressed downward with time and were observed, in one case, to develop along two branches simultaneously, only one of which reached ground.









4.2.1 Results

We present results of seven leaders preceding subsequent strokes to ground. Each leader exhibited regular dE/dt pulses tens of microseconds prior to the following return stroke peak. Prior to the first dEdt pulses associated with each leader, there was a period of several tens of microseconds during which time no dE/dt pulses were above the noise threshold. Radiation from leaders was continuous (records were separated by 30 Ats owing to our system's recording configuration) up to the time of the return stroke.

Table 4.1 summarizes characteristics of seven subsequent leaders to ground. Column one contains the flash ID. Listed in column two are the records that the leader spanned, each 204.8 ts in duration. Columns three and four list the 3-dimensional track speed and its error observed in each record. In most instances a single average speed was determined per record as described in Chapter 2. In some cases we determined more than one speed in a given record. This was done when either (i) more than one branch was discernable (branches are labeled a and b) or (ii) a measurable change in speed occurred within a record (records are labeled fast or slow). Speeds ranged from a minimum of 1.4 x 106 m/s to a maximum of 35 x 106 m/s. Speeds during the final kilometer to ground are shown with an asterisk and were estimated in the manner of stepped leader speeds preceding new terminations in Chapter 3. The mean height of sources within a record is given in column 5. The duration of each leader is listed in column 6 and represents the time from the first dE/dt pulse to the return stroke peak. Durations were between 0.6 and 2.0 ms, similar to the geometric mean duration of subsequent leaders from several previous studies (Malan and Schonland, 1951; Kitagawa, 1957; Workman et al., 1960; Krehbiel et al., 1979; Rakov and Uman, 1990c]. The median interpulse interval at

















Table 4.1. Summary of seven subsequent leaders to ground.


Flash Record Speed/I 06 error Height Duration At (8%) At (20%) At (30%) ID # (mls) % (km) (ms) As Fs )S 2541679 19(fast) 35 11 4.2 0.83 0.8 1.1 1.7
19(slow) 24 9 3.4 0.8 1.1 1.7
20 3.3 14 2.1 0.8 1.4 2.8 21 3.3 14 1.4 1.8 3.7 4.0 22* 3.9 * 0.5 2.0 4.7 6.3 2420878 18 12 7 3 0.6 1.0 1.7 3.3
19 3.0 79 1.9 1.6 3.4 4.6 20* 5.4 * 0.7 2.1 3.8 3.6 2541487 14 12 9 3.7 0.69 0.8 1.1 1.5
15 5.4 28 1.5 0.7 1.2 1.8 16* 3.0 * 0.5 1.1 2.5 3.2 17* 3.0 * 0.5 1.6 2.9 3.6 2541810 19 16 10 4.3 1.2 1.2 2.2 4.8
20 6.7 11 1.9 0.8 1.9 2.5 21* 2.0 * 0.3 2.0 5.2 6.4 2541672 12(fast) 23 16 4.6 1.25 1.0 1.4 2.1
12(slow) 8 35 3.5 1.0 1.4 2.1
13 X X 2.8 0.7 1.1 2.2
14(b) 1.4 43 2.1 1.1 2.1 3.8 14(a) 2.2 14 2.7 1.1 2.1 3.8 15(b) 4.7 7 1.5 1.2 2.4 3.9 15(a) 1.9 61 2.2 1.2 2.4 3.9 16(b) 5.3 46 0.7 1.2 2.8 4.3 16(a) 1.9 18 1.9 1.2 2.8 4.3 17 (b)* 2.0 * 0.2 1.2 3.1 5.4 2540223 17 14 7 4.8 0.75 1.0 2.3 3.4
18 9.1 11 2.7 0.9 2.5 4.7 19 6.9 20 1.2 1.6 3.2 6.6 20* 6.2 * 0.5 1.9 3.3 3.3 2541062 9 14.0 18 5.5 1.4 1.1 1.5 3.1
10 7.8 9 3.7 0.9 1 1.8 11 6.0 23 2.2 1.0 1.5 2.4 12 2.9 34 1.5 1.2 2.9 5.3 13 3.0 37 0.7 2.5 5.4 8.1 14 1.4 99 0.4 3.6 5.5 7.7 15* 2.0 * 0.2 2.6 5.7 6.5
* - estimated speed (see text)









thresholds of 8 %, 20 %, and 30 % of the maximum leader pulse amplitude are given in columns 7 through 9 respectively. We now investigate three leaders in detail.

Flash 2541679. Flash 2541679 occurred at 20:28:15 on 10 September 1992, 11.7 km southwest of the central recording station. We recorded 25 records spanning 94 milliseconds, indicating we may have missed activity following our last record. Three return strokes were co-located during the flash. The locations of all dE/dt sources of the flash are shown in Figure 4.1. Source locations prior to the first return stroke are shown as "0". The earliest sources of the flash were located concurrently in regions A and B (Figure 4.1). Five milliseconds after the start of the flash, region A became inactive and sources were confined to the two branches, C and D, below region B. During the next 9 ms source locations progressed outward along branch C and down the main channel to ground, D, where the first return stroke was located at t = 14 ms. Sources prior to the first stroke propagated to ground with an average speed near 3 x 105 m/s, suggesting they were associated with the stepped leader. Two records, containing tens of pulses each, were recorded at t = 44 ms and t = 67 ms. Locations of these sources are shown as "X" in Figure 4.1, the earlier sources located near 4.5 km high and the latter near 5.6 km.

Beginning at t = 70.6 ms, radiation from the second leader to ground spanned four records and 0.83 ms. Locations of leader sources are shown as "+" in Figure 4.1 and progressed downward from a height near 4.8 ki, terminating at t = 71.4 ms in the second stroke, co-located with the first. Source locations associated with the second leader below 3 km high were coincident with those along the main channel to ground preceding the first stroke. The dE/dt waveform of the second leader is shown in Figure 4.2. The return stroke peak does not appear on the trace of this channel, owing to differences in

































-9 -8 -7 -6 -5 -4
X (kIn)


0 0'oA


4bo C


I
-11 -10


RS 1-3
I I- -


.......................... ...... 0I I


-9 -8 -7 -6 -5


X (km)

Figure 4.1. DE/dt source locations for flash 2541679. Source locations prior to and including the first stroke are shown as "0". Locations of sources from the second leader are shown as "+". Sources active between the first and second strokes are represented by "X".


IIII



x

4
)d9O
B P. A

0
0 0c





RS 1-3
. .... ........ .... ........ ... .... ..... .. ------------------------------------------------. --------------- .. ..... .... ..... ..--


-10


0 -....




























JJJAJIIJIIIJJJIkJAJIi [IU.JII ~iI1 [J1i~~i ikjJJiIiIim~auIJIihiJdiJ1i1iliiJ1 IA


70.6 ms Rec #19




70.8 ms Rec #20




71.0 ms Rec #21




71.2 ms Rec #22


Time in microseconds


Figure 4.2. dE/dt waveform of the leader preceding the second stroke of flash 2541679. Time from the beginning of the flash is indicated to the right of each trace. Return stroke occurred less than 30 microseconds after the end of record 22.









the time of its arrival at different stations, but was observed on others. The mean heights of pulse sources in each record are indicated in column 5 of Table 4.1 and the average speed in each record is listed in column 3. Source locations from the first record of the leader (record 19) descended from near 4.8 km high to 2 kin, at an average speed of 27 x 106 � 2.2 x 106 m/s. The average speed, determined over the next two records (20 and 21), was 3.3 x 106� 0.5 x 106 m/s as the leader descended from 2.3 km to 1 km. During the last record (record 22) the leader traversed the final kilometer to ground at an estimated speed of 3.9 x 106 m/s. We estimated the leader speed from the last source in record 21 to the return stroke by assuming a straight-line path between the two locations and dividing by the time between them. At heights below one kilometer, errors in source heights become comparable to the heights themselves, making a calculation of the 3dimensional track speed, as outlined in Chapter 2, susceptible to large errors. A profile of the leader development vs. time is depicted in Figure 4.3 where x, y, and z source locations are plotted individually vs. time. The four records of the leader are clearly distinguished by gaps between them resulting from our recording configuration. It appears that there was a kink in the leader track during the first record. This is most noticeable in the plot of the x-component of the speed. When the track was subdivided to reflect this we obtained speeds of 35 x 106 � 4.0 x 106 m/s over the first 16 is and 24 x 106 � 2.2 x 106 m/s over the next 45 ps.

A plot of median interpulse interval vs. threshold for the second leader is shown in Figure 4.4. At a threshold of 20 %, the median interpulse interval increased from 1.0 Ps during the first leader record to 4.7 gs during the last. In fact, at each threshold, intervals were larger for successively later portions of the leader record.













I I I


-5
break break
.5 5


o 4,
0-10

0 I I I I
70.6 70.8 71 71.2 71.4 70.5

Time from beginning of flash (ms) Time fror

-4


break



-68


71

n beginning of flash (ms)


-10

70.5 71

Time from beginning of flash (ms) Figure 4.3. Profile of leader development versus time in flash 2541679. ' 15

r.~
0

Ree #22


"�
, 10



~Rec #21





Rec #19
0 10 20 30 40 50

Threshold (percentage of largest pulse)
Figure 4.4. Median interpulse interval vs. threshold for the second leader
of flash 25401679


I j









At t = 94 ms the third stroke in the flash occurred and was co-located with the first two. The third stroke was not preceded by any dE/dt pulses above the noise level for 65 pts immediately prior to the return stroke peak. This record was the 25h of the flash and any later events that may have occurred were not recorded by our system.

Flash 2420878. Flash 2420878 occurred at 17:43:25 on 29 August 1992, 19.7 km WSW of the central recording station. The flash comprised 25 records, including four co-located return strokes, spanning 453 ms. Locations of dE/dt sources from this flash are shown in Figure 4.5. The earliest sources were located near 6 km high and are shown as "0". During the first 5 ms sources progressed downward to a height of 4 km. The horizontal spread of sources extended several hundred meters in both x and y. Since errors in individual locations were 40 - 60 m in each of x and y, we conclude that the spatial spread of sources was due to the presence of multiple branches, most likely associated with the stepped leader. Seventeen milliseconds later, at t = 22 ms, we recorded the first stroke of the flash, preceded by several small dE/dt pulses within the last 30 ps, indicative of a stepped leader.

Beginning at t = 74.9 ms radiation from the second leader to ground spanned three records and 0.6 ms. The dE/dt leader waveform is shown in Figure 4.6 and locations of individual pulse sources are indicated by "+" in Figure 4.5. The first pulse sources were located 3.8 km high, near the extent of the sources we detected 17 ms prior to the first return stroke. Leader source locations progressed downward with increasing time. The average speed during the first record of the leader (record 18), with source locations descending from 3.8 km to 2.4 km, was 12 x 106 � 0.84 x 106 m/s. Source locations from record 19 spanned the heights 2.0 - 1.4 km at an average speed of 3.0 x 106 � 2.4 x 106











8
0


6



--2 4 0



2 f I














0 . . . . . . . . . . . . . . . . . . . . . . . . . . ............................ ......................... o .......... .................. O
RS 1-3











I I III
-20 -18 -16 -14 -12












Y(m)
0
0

6 *A-- 0






Ark











Fiur 4.5. inldE/dft sure hw "" ocations of fls 407.sources pro

second leader are shown as "+". The second stroke occurred 54
milliseconds after first and in same channel. Stroke 3 followed the same
channel 26 milliseconds after stroke 2.


























3









I AI I I I
0 20 40 60 80 100 120 140
Time in microseconds

Figure 4.6. dE/dt waveform of the second leader of flash 2420878. flash is shown to the right of each trace.


74.9 ms Rec # 18




75.1 ms Rec# 19




75.3 ms Rec # 20





160 180 20


Time from the beginning of the









m/s. During the final record (record 20) the leader traversed the last kilometer to ground at an estimated average speed of 5.4 x 106 m/s. Note that the highest leader speed occurred during the first leader record, similar to the second leader in flash 2541679.

Figure 4.7 summarizes median interpulse interval vs. threshold for the three records of the second leader in flash 2420878. At a threshold of 20 % the median interval increased from 1.7 lts to 3.8 tis over the course of the leader. At all thresholds below 25 % the median interpulse interval was greater for successively later portions of the leader record, consistent with the observations of flash 2541679. However, unlike flash 2541679, this trend did not continue for all thresholds. At thresholds of 25 % to 35 %, the second record of the leader exhibited the greatest median interpulse interval. At a threshold of 40 % larger intervals were again associated with successively later leader records.

The third and fourth strokes of flash 2420878 occurred at t = 102 ms and t = 475 ms respectively and were co-located with the first two strokes of the flash. Waveforms of these two strokes are given in Figure 4.8. Small, irregular pulses preceded each of these strokes for 60 gis, the limit of our pretrigger delay. These small pulses appear similar to the "chaotic" leaders sometimes found in the electric field waveform prior to subsequent strokes [Weidman, 1977; Rakov and Uman, 1990b; Willett et al., 1995]. In order to compare these leaders with the second leader we used the same threshold values chosen for the second leader. Median interpulse interval vs. threshold is plotted in Figure 4.9 for the leaders prior to strokes three and four. At a threshold of 4.4 % (four standard deviations above the noise) the median interpulse interval was found to be 0.9 gs and 1.45 gs respectively for the leaders preceding strokes three and four. At a threshold of 20 % we found no dE/dt pulses to precede stroke three, and only two immediately prior to







82













15


0

lu
0










� ,-,Rec # 20

# 18



0oIf I II
0 10 20 30 40 50

Threshold (percentage of largest pulse)

Figure 4.7. Median interpulse interval vs. threshold for the leader
preceding the second stroke of flash 2420878.




















J~amA-LhddR -- - - - - - -- - -- -101.6 ms









475.1 mns





I I I .....I I ...I I I I I
0 20 40 60 80 100 120 140 160 180 200
Time in microseconds

Figure 4.8. dE/dt waveform of the third and fourth strokes of flash 2420878. Time from the
beginning of flash shown at right.







84














15



0

0



5
U














Rec # 21 L I .
0 10 20 30 40 so

Threshold (percentage of largest pulse)

Figure 4.9. Median interpulse interval vs. threshold for the leaders
prior to strokes 3 and 4 of flash 2420878.









stroke four. In fact, above a threshold of 10 %, there were no dE/dt pulses from either leader other than those mentioned immediately prior to the fourth stroke.

Flash 2541672. Flash 2541672 occurred at 20:27:56 on 10 September 1992, 17.9 km SSW of the central recording station. This flash differed from the first two of this section in that its second leader followed two simultaneous branches prior to reaching ground. Twenty-five records spanned 882 ms and three return strokes were co-located. Source locations for this flash are shown in Figure 4.10. The earliest sources, shown as "0" in Figure 4.10, were located at a height of 5.6 km and were followed 60 ms later by the first return stroke.

Beginning at t = 123.6 ms radiation from the second leader spanned 1.25 ms and six records. The entire dE/dt waveform of this leader is shown in Figure 4.11. The earliest sources were located at a height of 4.7 km. The channel followed by the leader during the first record (record 12) was divided into two segments. The average speed over the first portion (spanning 35 .s) was 23 x 106 �- 3.7 x 106 m/s, and decreased to 8.0 x 106 � 2.8 x 106 m/s during the second portion (37 ps). Sources progressed downward from a height of 4.7 km to 3.3 km. Beginning with record 14 of the leader, at t = 124.0 ins, leader sources developed simultaneously along branches A and B (Figure 4.10) during the next 600 ps (records 14 - 16). The profile of the leader development, x, y, and z vs. time, is depicted in Figure 4.12 where the two branches are readily discernable. The speed along branch A decreased from 2.2 x 106 � 0.3 x 106 m/s to 1.9 x 106 � 0.3 x 106 m/s during records 14 - 16 (124.0 - 124.6 ms). The speed along branch B increased from 1.4 x 106 � 0.6 x 106 m/s to 5.3 x 106 � 2.4 x 106 m/s during this same time interval.












A. I


4 +
A t



2 Y


0-...........................j
RS 1-3
I I III
-14 -12 -10 -8 -6
X(km)

10



8



6


49
4 + +~



2 A t I B

0 -.-.--------------------------------------------------------------- 4 .......................... ...................................................-----o

RS 1-3
I I II
-20 -18 -16 -14 -12 -10 X(km)

Figure 4.10. Locations of dE/dt sources of flash 2541672. Sources prior to and including first stroke shown as "O". Locations of sources from leader preceding second stroke represented by "+".
















123.6 ms Rec #12 123.8 ms Rec #13 124.0 ms Rec #14 124.2 ms Rec #15 124.4 ms Rec #16 124.6 ms Rec #17


time in microseconds


Figure 4.11. dE/dt waveform of the leader preceding the 2nd stroke of flash 25401672. Time from the beginning of flash is indicated to the right of each trace.




















I ! 5%


2I

0123 124 125 126 Time from beginning of flash (ms)


-15


-20


123 124 125 126 Time from beginning of flash (ms)


I I

-6


--8 B


I I
-123 124 125 126

Time from beginning of flash (ms)


Figure 4.12. Profile of leader development versus time in flash 25401672.


I

B



A

I I









Branch B followed the main channel to ground, covering the remaining several hundred meters at an estimated speed of 2.0 x 106 m/s.

The median interpulse interval vs. threshold curve of the second leader of flash 2541672 is shown in Figure 4.13. The first (record 12) and last (record 17) leader records are represented by traces with circles, record 12 being the lower trace. Unlike the previous two flashes in this section, we found the second record of the leader to exhibit the smallest median interpulse interval at all thresholds, though not much different from that of the first record. There was a tendency for successively later records to exhibit greater intervals at a given threshold, although several exceptions are readily seen in Figure 4.13.



4.2.2 Discussion

Leader speed vs. height. We first discuss the observed speed changes vs. height for the seven leaders in Table 4.1. Correlation between two-dimensional leader speed and height has been investigated by several researchers [Schonland, 1935; Orville and Idone, 1982; Mach and Rust, 1997] with conflicting results. Optical studies by Schonland [1935] revealed that dart-leader speeds often decreased towards ground and never increased. Mach and Rust [1997] found "no significant" change in dart-leader speed vs. height. Contrary to the results of Schonland [1935] and Mach and Rust [1997], Orville and Idone [1982], using high speed streaking photographic techniques, found 4 of 16 dart leaders to increase in speed towards ground. The increase in speed they observed was not more than a factor of two in any of the four leaders. Three of the leaders followed the same channel in one flash. Each of the three leaders first exhibited an apparent increase







90















15


rfl
0
o 0

#10
,' ec12 iI


Rec#17 *R 1
5 A
Rec~ ~ ~ ~e #1 -14'< ...


5 owrao,-:
" .*O- Rec#14





0 10 20 30 40 50

Threshold (percentage of largest pulse)


Figure 4.13. Median interpulse interval vs. threshold for the second
leader in flash 2541672. Threshold ranges from 4 standard deviations
above the noise level to 50 % of the largest dE/dt pulse in the leader.









in speed at their upper ends, near 2 km high, followed by a decrease, and a further increase near ground. The 2-dimensional height vs. speed profile (see Figure 4 of Orville and Idone, 1982) of each of the three leaders was similar. Since all three leaders followed the same path to ground it is possible that the observed profile could be explained by a constant leader speed with the hidden third dimension of the leader track accounting for the apparent speed change. In fact, Orville and Idone [1982] point out that the speed changes may have been real or "more likely apparent due to viewing of a 2-D photograph". Orville and Idone [1982] also note a speed change vs. height in four dart-stepped leaders. Three of these decreased in speed towards ground (17 - 0.76 x 106 m/s over 1.19 ms; 14 - 1.4 x 106 m/s over 0.46 ms; 5.3 - 1.9 x 106 m/s over 0.88 ms). One increased in speed towards ground (2.3 - 5.3 x 106 m/s during 0.11 ms).

We have plotted leader speed vs. height in Figure 4.14 for each of the seven leaders in Table 4.1. Each exhibited a decrease in speed from its highest point to ground, supporting the view of Schonland [1935]. In 6 of the 7 leaders the decrease was monotonic, within our errors in speed measurement. We found a mean speed of 16 x 106 m/s during the first record of leaders and a mean speed of 3.5 x 106 m/s during the final, a decrease of a factor of 4.5 on average. Recall that each speed in our study represents an average value measured over typically 80-150 pts (100 - 1000 m) in a record. In flashes 2541679 and 2420878 we subdivided the leader track during the first record and found the average speed to decrease by 30 % and 60 %, respectively. Therefore, the decrease in speed from the beginning of the leader to ground, a factor of 4.5 on average, should be regarded as a lower limit in our study. Changes in leader speed ranged from a decrease of a factor of 2.2 in flash 2420878 to 11.5 in flash 2541672. Orville and Idone [1982]




























, 1679
-~i87

-.N--1810
9 1672b ~--0-2o22
2 - --e1OS2


1 06






0
05 10 15 20 25 30 35 40

Speed (xI06 m/s)

Figure 4.14. Dart-stepped leader speed vs. height.









noted decreases in dart-stepped leader speeds by factors of 2.5, 10, and 22. These changes are similar to those we measure, although ours take place in the cloud (3 - 6 km high) while theirs are measured in the final 1 -2 km of the channel. Furthermore, the differences in leader speeds vs. height of the current study are real, and not apparent, since we have calculated speeds over 3-dimensional track lengths. While the increase in dart leader speeds observed by Orville and Idone [1982] may have been apparent, it is probable that the decrease in speeds they observed in dart-stepped leaders was real, a factor of 10 to 20 not likely to be explained by viewing a 2-D photograph. The one dartstepped leader they observe to increase in speed did so by a factor of two. We find no evidence of an increase in speed for the dart-stepped leaders in Table 4.1 and it is possible that the increase seen by Orville and done [1982] was the result of viewing a 2dimensional photograph.

The photographic studies of Schonland [1935], Orville and Idone [1982], Jordan et al. [1992] and Mach and Rust [1997], involved dart leader and dart-stepped leader speed measurements below cloud base (lowest 1 -2 km above ground). Each of the dartstepped leaders in Table 4.1 was observed to decrease in speed from heights of 3 - 6 km to ground. Rhodes et al. [1994] and Shao et al. [1995], using a VHF interferometer to locate radiation from dart leaders, note several leaders decreased in speed over even larger extents, 8 - 20 km. One leader of Shao et al. [1995] traveled at 8 - 10 x 106 MIS over 6 - 8 kin, and slowed down to 2 -3 x 106 m/s during the remaining portion of the channel to ground, 8 - 10 km. The leader developed horizontally in the cloud for 6 - 8 km before coming to ground, consistent with the behavior of dart leaders measured by Rhodes et al. [1994] and the findings of Krehbiel et al. [1979]. Krehbiel et al. [1979]




Full Text

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PROPERTIES OF LIGHTNING DISCHARGES FROM MULTIPLE-STATION WIDEBAND ELECTRIC FIELD MEASUREMENTS By STEPHEN M. DAVIS A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 1999

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ACKNOWLEDGEMENTS This dissertation represents the culmination of a long seven years of study. The final result would not have been possible without the support of my wife, Michelle. Her love and unwavering support made it possible to navigate the many obstacles and difficult times encountered during the past four years. I would also like to thank my family, Mom, Dad, Carol, Cheryl, Steve, Walter and Jake, for their support throughout my entire academic career at the University of Florida. The support of my in-laws as well as my family at First Presbyterian Church was also instrumental in helping me during this project. I would like to thank Dr. Ewen Thomson for his guidance and direction during the research and writing phases of this project. I am also indebted to Dr. Pedro Medelius and the crew at the Kennedy Space Center who were instrumental in the gathering of the data. I thank Dr. Vladimir Rakov for countless discussions and advice, which contributed greatly to this work and my development as a researcher. Thanks also go to my fellow graduate students, Keith Kerle, David Crawford, and Jack Kavelieros, who functioned not only as sounding boards for ideas, but also offered numerous moments of levity, without which, these years would have been much harder to endure. 11

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TABLE OF CONTENTS Page ACKNOWLEDGEMENTS ii ABSTRACT vi CHAPTERS 1 INTRODUCTION 1 2 EXPERIMENTAL SYSTEM AND DATA ANALYSIS 6 2.1 Introduction 6 2.2 System Overview 6 2.3 Corrections for System Responses 8 2.4 Timing 1 1 2.5 Locations 14 2.6 Average Speeds 16 2.7 DE/dt Pulse Intervals 19 3 LEADERS AND RETURN STROKE FINE STRUCTURE OF NEW TERMINATIONS TO GROUND 21 3.1 Introduction 21 3.2 Leaders Preceding Subsequent Strokes 21 3.2.1 Results 25 3.2.2 Discussion 41 3.2.3 Conclusions 50 3.3 Return Stroke Waveforms Separated By One Millisecond or Less.. 51 3.3.1 Results 52 3.3.2 Discussion 58 3.3.3 Conclusions 65 3.4 Summary Conclusions 66 4 CHARACTERISTICS OF SUBSEQUENT LEADERS TO GROUND 67 4.1 Introduction 67 4.2 Leader Speed and dE/dt Waveshape 67 4.2.1 Results 71 in

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4.2.2 Discussion 89 4.2.3 Conclusions 106 4.3 Subsequent Leaders Showing and Increase in Speed 107 4.3.1 Results 107 4.3.2 Discussion 116 4.3.3 Conclusions 118 4.4 Pulse Trains Present After Return Stroke Waveforms 119 4.4.1 Results 119 4.4.2 Discussions 121 4.4.3 Conclusions 124 4.5 Leader Occurrences 125 4.5.1 Results 126 4.5.2 Discussion 137 4.5.3 Conclusions 140 4.6 Summary Conclusions 140 5 PULSE TRAIN COMPARISON AND POLARITY REVERSALS 142 5.1 Introduction 142 5.2 Pulse Trains in Intracloud Discharges 142 5.2.1 Results 144 5.2.2 Discussion 153 5.2.3 Conclusions 166 5.3 Pulse Train Comparison 166 5.3.1 Average Speeds 167 5.3.2 Median pulse intervals 173 5.3.3 Step lengths 190 5.3.4 Conclusions 193 5.4 Polarities of Pulses in Intracloud Pulse Trains 196 5.4.1 Introduction 196 5.4.2 Theory and Method 197 5.4.3 Results 201 5.4.4 Discussion 208 5.4.5 Conclusions 216 5.5 Summary Conclusions 216 6 RECOMMENDATIONS FOR FUTURE RESEARCH 2 1 8 6.1 Pulse Trains 218 6.2 Observations of Other Field Waveforms 219 6.3 Summary Conclusions 221 iv

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REFERENCES 222 BIOGRAPHICAL SKETCH 228 v

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Abstract of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy PROPERTIES OF LIGHTNING DISCHARGES FROM MULTIPLE-STATION WIDEBAND ELECTRIC FIELD MEASUREMENTS By Stephen M. Davis August 1999 Chairman: Dr. Ewen Thomson Major Department: Electrical and Computer Engineering There has been no detailed analysis of wideband electric fields recorded at a sufficient number of sites, with adequate design constraints, such as baseline length and timing resolution, to give three-dimensional locations of lightning sources. We describe a system to locate and give times of occurrence of the sources of wideband dE/dt pulses. The major focus of this study was sequences of regularly occurring dE/dt pulses, or pulse trains. We identify pulse trains giving rise to three lightning processes: (1) leaders preceding new terminations to ground, (2) dart-stepped leaders along a previously formed channel propagating all the way to ground, and (3) intracloud discharge processes. Leaders preceding new terminations were dart-stepped in nature prior to their transition to stepped leaders. Speeds over the dart-stepped portion of leaders were 1.012 x 10 6 m/s. Fine structure was present in the dE/dt waveform of both first strokes to ground and subsequent strokes in new channels to ground. The duration of the fine structure was shorter (37 ps median) for strokes in new terminations to ground than for first strokes in a flash (141 ps median). Sources of fine structure were related to the preceding stepped leader. vi

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We provide the first interpretation of the complete electric field waveform of dartstepped leaders. Near ground, dart-stepped leaders exhibited pulses at regular intervals of several microseconds. Interpulse intervals were much smaller than several microseconds early in the leaders, at which time their speed was greater. Seven dart-stepped leaders decreased in speed towards ground, while two were found to increase, but only when joining an earlier section of the channel. For dart-stepped leaders we found an inverse relationship between average leader speed and interpulse interval. We provide the first locations of the wideband sources from intracloud pulse trains. Speeds of these trains were similar to those during the dart-stepped portion of leaders preceding new terminations to ground and dart-stepped leaders near ground. A comparison of average speed, interpulse interval and step length is undertaken for the three types of pulse trains identified. Similarities include a constant or decreasing speed and a tendency for interpulse intervals to increase with time. Several important differences were found. Dart-stepped leader waveforms were comprised of pulses of irregular amplitude, making the interpulse interval dependent on the amplitude threshold used in pulse selection. Pulses from intracloud trains were more uniform in amplitude and interpulse intervals were nearly constant with respect to an amplitude threshold used to select pulses. Average step lengths of intracloud trains were several tens of meters, while those of dart-stepped leaders and leaders preceding new terminations were more difficult to determine. Average speeds near the beginning of dart-stepped leaders were higher than speeds near the beginning of intracloud pulse trains. Pulse polarities associated with intracloud pulse trains were dependent on channel orientation. Vll

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CHAPTER 1 INTRODUCTION Thunder and lightning have fascinated mankind for hundreds of thousands of years. The first scientific study of lightning can be traced back to Benjamin Franklin in the last half of the eighteenth century. In 1752 Franklin performed his famous kite experiment proving his theory that lightning was electrical. Ever since, researchers have continued to conduct experiments to increase their understanding of this natural phenomenon. Photography and spectroscopy became available in the late nineteenth century allowing investigators to identify the individual components of a lightning discharge. The early part of the twentieth century saw the first electric field measurements used to study lightning. Wilson [1916, 1920] estimated charges involved in the lightning discharge from electric field measurements. More recently, in the past 25 years, improved measurement and analysis techniques have proved particularly valuable in the study of lightning. New high-speed computers have allowed the digitization, storage, and analysis of large amounts of data not previously available. Lightning discharges are typically classified as one of two types. The first is termed cloud-to-ground discharges (CG) and produces the familiar, visible forked channel between the cloud and ground. The second is collectively termed cloud discharges. Lumped into cloud discharges are intracloud (within a cloud), cloud-to-cloud, and cloudto-air discharges. The earliest studies of lightning focused on cloud-to-ground discharges for two primary reasons, (1) because they were responsible for the most severe lightning 1

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2 damage and (2) they were more easily photographed since they were visible below the cloud. However, more than half of all lightning takes place within the cloud. Historically, research on cloud discharges has lagged behind that of cloud-to-ground discharges for the two reasons stated above. With recent improvements in recording equipment and analysis techniques, the ability to study cloud discharges in greater detail has become possible, opening new avenues in lightning research. Figure 1.1 shows the time sequence of the various processes that comprise a typical negative cloud-to-ground discharge. The discharge, also termed a flash, may be initiated by preliminary breakdown within the cloud, which in turn initiates the stepped leader. The stepped leader lowers negative charge to earth in a series of discrete steps, traveling at an average speed near 2 x 10 5 m/s. When the leader tip nears ground, the electric field at ground exceeds the breakdown value of air and one or more upward going positive streamers may be launched. When one of these streamers contacts the negative tip of the stepped leader, the attachment process, a connection to ground is established thereby initiating the first return stroke. The return stroke is a ground potential wave that propagates continuously up the previously ionized leader path at a fraction of the speed of light. The return stroke lowers to ground the negative charge deposited along the trunk of the leader channel and the branches. After an interval on the order of tens of milliseconds, during which time the channel is dark, i.e. no current flows, additional charge may be available near the top of the channel and a continuos dart leader may propagate down the residual first stroke channel at a speed near 10 7 m/s. The dart leader initiates the second stroke, also termed a subsequent stroke. Leaders and return strokes after the first in a flash are termed subsequent. Some

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3 t = o Preliminary Stepped Breakdown Leader 1.00 ms 1.10 ms 1.15 ms 1.20 ms 19 ms 20 ms 20.10 ms 20.15 ms 20.20 ms 40 ms 60 ms 61 ms 62 ms 62.05 ms Figure 1.1. Time sequence showing the typical components comprising a negative cloud-to-ground discharge ( Uman , 1987). subsequent leaders are observed to follow the existing channel to ground, but appear stepped in optical records. These leaders are termed dart-stepped leaders and travel at speeds near 3 x 10 6 m/s. Both CG discharges and cloud discharges are comprised of currents that can vary on a sub-microsecond scale. These current variations give rise to wideband electric and magnetic fields. In fact, the discharge physics of lightning processes that involve the largest currents have been based on wideband measurements. The electric field measurements of Weidman and Krider [1980] indicated that electric and magnetic field

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4 waveshapes associated with the peak return stroke current had a frequency content of 1 kHz to 4 MHz. A similar frequency range is observed for the peak electric field of stepped leaders ( Krider et al., 1977), bipolar pulses associated with preliminary breakdown ( Weidman and Krider, 1979), narrow bipolar pulses (Le Vine, 1980) and regular pulse trains ( Krider et al., 1975). While these and other studies have characterized electric field signatures from lightning, there are no reports in the literature of wideband electric fields recorded at sufficient number of sites with adequate design constraints, such as baseline length and timing resolution, to give three-dimensional locations of sources. At least four sites are required with baselines of the order of 10 km with timing resolution better than 100 ns ( Proctor , 1971). We have developed a system to locate the sources of wideband dE/dt (derivative of the electric field) using five sites with appropriate baselines and a timing resolution of better than 50 ns. The system and methods for analyzing data are described in Chapter 2. One particular type of electric field signature, that of a regular sequence or burst of microsecond-scale electric field pulses, is found in the wideband electric field records of both CG discharges and cloud discharges ( Krider and Radda et al., 1975; Krider and Weidman et al., 1977, Rakov etal., 1996). These sequences, also termed pulse trains, are comprised of more or less unipolar electric field pulses occurring at regular intervals of several microseconds. Previous studies have shown that the time between pulses are similar in pulse trains from both CG and cloud discharges, suggesting they may be the result of a common physical process. To better answer this question a study of other characteristics, such as average speed and step length, is needed. Until now, no sufficient measurements of pulse trains have been available in this regard.

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5 This work provides the first source locations and electric field waveshapes, measured on a sub-microsecond scale, of electric field pulse trains from both CG and cloud discharges. We have identified three processes that produce pulse trains in the electric field. Two of these processes occur in CG discharges, the third in cloud discharges. Average speeds, pulse intervals, and step lengths of each are analyzed and compared. Chapter 3 investigates pulse trains that were associated with leaders preceding new terminations to ground. A new termination was defined to be a stroke after the first of the flash that occurred in a new channel to ground. Pulse trains produced by dart-stepped leaders are the focus of Chapter 4. Chapter 5 looks at characteristics of trains that occurred in cloud discharges and compares these with the results of the previous two chapters. Finally, Chapter 6 contains other observations from the current data set and suggestions for further study. Rather than including a detailed literature review prior to presenting the current results, we have chosen to conduct a review in each chapter, as the topics are presented. Chapters 3, 4, and 5 are broken into sections; the structure of each follows that of most scientific journal publications. Each section begins with an introduction detailing the current state of research on that chapterÂ’s subject matter. The results of the current study follow the introduction. The third section is the discussion where the findings of the current study are analyzed and discussed in relation to pertinent information in the literature. Each section ends with a conclusion of the important findings of that section. A chapter summary is also included at the end of each chapter.

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CHAPTER 2 EXPERIMENTAL SYSTEM AND DATA ANALYSIS 2.1 Introduction In this chapter we describe the configuration of the recording system used in collecting data and the techniques developed for analyzing those data. In section 2.2 we present an overview of the system and describe the system components and recording method. In section 2.3 we describe a scheme of frequency and phase compensation to correct for differences in frequency responses of the individual sensing electronics and signal propagation links of each channel. Section 2.4 details the methodology used to derive source times and section 2.5 describes the method used in deriving source locations. The technique used to find average speeds is presented in section 2.6. Finally, a procedure to determine interpulse intervals is presented in section 2.7. 2.2 System Overview The measurement system comprised five ground stations inal5kmx 15km network at Kennedy Space Center, FL. A map showing the station locations is shown in Figure 2.1. The derivative of the electric field (dE/dt) was detected at each station by sensing the displacement current intercepted by a flat plat antenna. Each antenna was placed near the center of a 3.5 m x 3.5 m ground plane elevated 0.5 m above ground. Gains from unity to 450 were achieved through the use of amplifiers and antenna plates as illustrated in Figure 2.2. Signals were sent via microwave or fiber optic links to the 6

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7 Figure 2.1. Sensor station layout. Range rings are centered at the Shuttle Landing Facility. Flat Plato Antennas XI X3 & € 5m coax & 1 — I Ibration Generator To FIberoptics Transmitter Figure 2.2. Block diagram for sensor electronics

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8 central recording van. The signals were digitized at 20 MHz for 4096 samples (204.8 ps records) once a trigger was received. Consecutive trigger records were digitized with a 30 ps dead time between records until the 128 kS LeCroy memory was full. A maximum of 25 trigger records could be recorded per flash. The block diagram in Figure 2.3 illustrates the time sequence of a typical flash. Calibration signals were applied through a known resistance to the input of the dE/dt amplifier. Calibration signals consisted of a square wave, triangle wave, and an impulse. These signals were used to create digital filters to remove waveform distortions arising from finite frequency responses of radio transmitting and receiving equipment. The construction of these filters is now outlined. 2.3 Corrections for System Responses Before processing data, we compensate for differences in the frequency response (magnitude and phase) between the sensing electronics and signal propagation links in each channel. To do this we first find the frequency response of each of the channels. We then design suitable filters that correct for differences between channels. The frequency response for each channel is determined from four distinct calibration signals; positive impulses, negative impulses, the rising edge of the fast square wave (differentiated with respect to time to give a positive impulse), and the falling edge of the fast square wave (differentiated with respect to time to give a negative impulse). Since each of these approximates an impulse, the Fourier transform is the system frequency response, and the mean and standard deviation for the amplitude and phase spectra can be found from the four responses. To minimize noise effects, we choose 1.6 ps windows around each impulse and average 10 signals for each channel. For accurate alignment of

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9 Start Of Flash 30 ns End Of Flash n Record # 1 Record # 2 Record # 25 204.8 fis • • 204.8 ns 204.8 ns 4 Figure 2.3. Block diagram illustrating recording configuration of the system.

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10 these impulses we zero padded the frequency domain spectra ( Oppenheim and Schafer, 1989). The zero frequency (DC) value is obtained from the amplitude of the average square wave signals. From above DC to 1.25 MHz the spectrum is the mean of the two square wave spectra, and the remaining spectral components, to the Nyquist frequency of 10 MHz (corresponding to our digitization rate of 20 Ms/s), comprise the mean of all four calibration spectral components. Since 1.6 p.s windows are chosen for the calibration signals, 128 times smaller than the 204.8 |is data record, there are 2032 undefined spectral components. These points are interpolated using a cubic spline fit for both the amplitude and the phase spectra. The spectra that we find using this procedure are reasonably smooth and physically consistent with the expected frequency responses. The two amplitude frequency spectra shown in Figure 2.4 are those chosen for normalization. The narrower response in Figure 2.4, curve a, is used whenever waveshapes are compared with channel 1 since channel 1 has a significantly narrower bandwidth than the other channels (6 dB down at 2 MHz compared with 4 MHz) as a consequence of the 32 |xs analog pretrigger delay at its input. Channels 2 through 5 are normalized to the broader response in Figure 2.4, curve h. Consider a channel with impulse response I(t) in the time domain and frequency response, that is, the Fourier transform of I(t), given by A(f)e'*^ where A(f) is the amplitude spectrum and
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11 Frequency in MHz Figure 2.4. Idealized frequency responses for curve a, channel 1, and curve b, channels 2 through 5. The idealized phase response is zero for all frequencies. ( 2 . 1 ) where G(f) is the Fourier transform of g(t). Curves a and b in Figure 2.5 are the impulse responses corresponding to the normalized amplitude spectra in Figure 2.4, curves a and b, respectively, and a zero-phase spectrum. 2.4 Timing The pulse times t, and timing errors Sti are determined from three time parameters on each pulse: (1) the rising-edge half peak, (2) peak, and (3) falling-edge half peak. We denote these as t„, t p i, and tg, respectively. For channels 2 through 5, ti is defined as the mean value of these three time parameters where all measurements are made on

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12 Figure 2.5. Impulse responses for the frequency responses shown in Figure 2.4. waveshapes that have been filtered with the wideband filter shown in Figure 2.4, curve b. That is, t ri + 1 , + 1 _n pi fi_ i = 2-5 (2.2) ' 3 For channel 1 we use the narrower filter shown in Figure 2.4, curve a, on all signals to obtain (different) values of these three time parameters, t™, t p i„, and tf m . The mean times are found only for channel 1, ti„, and the channel from 2 through 5 that is most closely correlated to channel 1, to,. The value ti is then defined as the adjusted time tc+ti„-tcn, where tc is given by Equation 2.2 with i = c. We find the timing errors Stj, from the variations between waveshapes recorded at different stations, as evident from the relative scatter in either tn, t p i, and tf, or t™, t p in, and tf m , as follows. Consider the rising-edge half peak for channels 2 through 5. First, we find the mean deflection of each tr* from its time tag, t,

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13 2X-0 (2-3) 4 Then, we determine the difference between each deflection and the mean ( 2 4 ) Figure 2.6 illustrates this procedure. This figure shows tn, tpi, and tf, for a pulse recorded on the i'*' channel, the time, appropriately shifted, corresponding to t n , and the deflection StriNoting that 6tn 2 is a measure of the variance, we define the total variance for the i th pulse as v i =a H 2 +st pi 2 +a/ ( 2 . 5 ) and the timing error as where tps and tf s (corresponding to the peak and falling edge half peak, respectively) are defined in a similar manner to t re (equation 2.3), 5tpi and 5tfi are defined in a similar manner to Stri (equation 2.4), and v, the number of degrees of freedom, is 2 since equation (2.2) is assumed in all the above calculations. The error for channel 1,
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14 Time Figure 2.6. Sample dE/dt waveshape showing how timing parameters tn, tpi, tfi, and 5tn are defined. The value t; is given by equation 2.2 and tr* is given in equation 2.3. 2,5 Locations Consider a radiation source at location (x,y,z) that turns on at absolute time t. The start of the dE/dt pulse from this source arrives at the i 1 * 1 station (at location (Xi, Yj, 0) at time t + Rj/c where y-rf+z 1 ( 2 . 8 )

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15 and is recorded at the central station after a further delay d; corresponding to the cumulative propagation time along the corresponding combination of coax cable, microwave, and fiber-optic links. For channel 1 we also subtract its 32 ps pretrigger delay from the actual propagation delay between the SLF sensor and the recording site. The digitization window begins at absolute time T, corresponding to the trigger time of the window. Thus the pulse appears on the i* channel after a further interval ti where f 7 1 (2.9) c Equation 2.9 gives the relationship among the measured quantities ti (the pulse times of the five channels), di (the calibration delays), T (the absolute time tag), and the parameters that need to be determined: the location (x, y, z) and the time of occurrence, t. Any four measurements give a unique solution for x, y, z, and t. Overdetermined equation sets such as this can be dealt with by (1) minimizing the squares of residuals based on equation 2.9 [e g. Peters and Crosson, 1972], or (2) choosing the set of minimally determined equations (such as four equations of the form of equation 2.9) that gives the smallest spatial errors [e g. Hofmann-Wellenhof et al., 1993], In a variation of method (2), Proctor [1971] explains how different equation sets may be appropriate for the different coordinates. While method (1) is computationally easier since only one minimization is required to find all four variables, it is unreliable for locations close to ground. Instead, we extend Proctor’s ideas to find the weighted mean values of x, y, z and t independently using all five possible combinations of four-station data. We call this the “weighted hyperbola” technique and a detailed description of the method can be found in Thomson et al. [1994].

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16 2.6 Average Speeds We describe here a method for determining average speeds in three dimensions. Given a series of n locations that lie along an apparent linear channel, we wish to find the average speed along the three-dimensional track. We first divided the channel into linear segments in each of x, y, and z using a “chi-by-eye” technique. In most cases one segment was defined within a record (204.8 ps). Locations were obtained over, at most, 150 ps of data in each record owing to differences in the time of arrival of sources at different stations. The average speed and its associated error were found using a reduced chi-squared value as a guide for goodness of fit. The technique is as follows: For a particular section of the channel we wish to find the best function var (t) = a + bt (2.10) to fit the data. Following the method of Bevington [1969] we define * 2 =Z“T ( va r,-a-Z>0 2 ( 211 ) , o-,. where a, is the error in the variable (x, y, or z) at the i 01 point. Minimizing % 2 and solving for a and b yields i i ’ i i cr 1 * °i i °i ( 2 . 12 ) i &i i G i i G i The error in either a or b is obtained from

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17 The errors in a and b become T ovar, ‘ A (CTj 2 2 _ J_ v^_i_ ° b ~ k.La -2 A i CTj ( 2 . 13 ) ( 2 . 14 ) The test of whether the calculated speed and associated error are reasonable is provided by the reduced x 2 value with an expected value of unity xh=— v ( 2 . 15 ) where v represents the number of degrees of freedom. Since we want the threedimensional average speed we can use the principle of linearity to combine the three components to obtain E~T( va r-a-b’t ,) 2 y* _ l gj i-2 The three dimensional speed over the segment is given by ( 2 . 16 ) ( 2 . 17 ) The error in the slope is found from ^ =y(y-°fcc ) 2 ( 2 . 18 ) The reduced % 2 value over the segment is given by X red , xl+xl+x] segment 3 ( 2 . 19 )

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18 The error in the speed was defined as the product of the reduced chi-squared and the error in the slope ( Hager and Wang, 1996) AS ~ £ slop€ ' Xnd.ugnunl (2.20) As an example, a computation of the average speed over a segment of channel is illustrated in Figure 2.7. Figure 2.7. Segment of channel used in finding average speed Using a “chi-by-eye” method we consider the locations in Figure 2.7 to resemble a roughly linear channel section. The calculation of average speed over this segment supports our assumption and was found to be 3.6 x 10 6 m/s with % 2 re d = 0.4 and an error in the slope of 0.3 x 10 6 m/s. This leads to an error in the average speed of 5 %. In some

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19 instances, the “chi-by-eye” technique suggested more than one linear channel segment. If errors obtained over these smaller segments were less than those for the entire segment, the channel segment was partitioned in this way. One problem with subdividing the channel into many small segments was an increase in the error in the slope when fewer points were used. Channel segments were therefore subdivided only where obvious kinks were observed and a sufficient number of locations were available. 2.1 Interpulse Intervals We now outline a method for determining the time between individual dE/dt pulses in trains. Amplitudes of pulses in trains of the current study were often not uniform and the determination of whether a dE/dt pulse should be counted became somewhat subjective based upon one’s criteria for the inclusion or exclusion of an apparent dE/dt pulse. No definition exists in the literature for resolving this problem so we propose an amplitude threshold be used in counting dE/dt pulses for the determination of interpulse intervals. For a given train of pulses we determined the largest pulse in the sequence and chose 50 % of this value as the highest threshold. Successively lower thresholds were selected, in 5 % increments, until the noise floor was reached. The noise level was defined as being four standard deviations above the mean as determined from a quiet portion of a record. For each record, we found the median time between dE/dt pulses (rising edge) as a function of threshold. This will be referred to as the median interpulse interval. In order to directly compare average speed and median interpulse interval, we limit the determination of intervals to the extreme pulses whose sources were located in each record, i.e., the median interpulse interval is calculated from the first to last located pulse within a record. An example of the determination of median interpulse interval is shown in Fig 2.8. A curve of the median interpulse interval vs. threshold is shown in Fig 2.9. If

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20 there were fewer than five pulses at a given threshold, no median interpulse interval was found. Time In Microseconds Figure 2.8. A section of data illustrating the use of different thresholds in calculating median interpulse interval. Threshold (percentage of maximum pulse amplitude) Figure 2.9. Median interpulse interval as a function of threshold for the sequence in Figure 2.8.

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CHAPTER 3 LEADERS AND RETURN STROKE FINE STRUCTURE OF NEW TERMINATIONS TO GROUND 3,1 Introduction We investigate leaders and fine structure of new terminations to ground. In section 3.2 we present data from subsequent strokes to ground creating new terminations. We relate the preceding leader characteristic to the following return stroke fine structure. In section 3.3 we present several return strokes separated by one millisecond or less. We investigate possible mechanisms that may produce the observed return stroke waveforms. Section 3.4 contains a summary of the chapterÂ’s findings. 3,2 Leaders Preceding Subsequent Strokes First strokes in negative cloud to ground lightning discharges are preceded by stepped leaders. The stepped leader propagates to ground in a series of discrete steps, each tens of meters in length with pause times of tens of microseconds between individual steps [i Schonland , 1956], The duration of the stepped leader is typically 20-40 ms [Pierce, 1955; Kitagawa and Brook, 1957, Beasley et al., 1982; Rakov et al., 1990c], Stepped leaders prior to first strokes are usually heavily branched and have a downward speed of 0.8 8.0 x 10 5 m/s [Schonland, 1956], After the leader reaches ground the leader channel is discharged by the first return stroke which propagates up the previously ionized leader path and out along the branches [Schonland et al., 1935], The return stroke effectively 21

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22 lowers to ground charge deposited on the stepped leader channel. After an interval of typically several tens of milliseconds a subsequent leader may propagate down the residual first stroke channel. If this leader appears to propagate continuously, it is termed a dart leader. Optical measurements give dart leader speeds in the range 2.9 24 x 10 6 m/s [Orville and Idone, 1982; Jordan et al., 1992] with a mean value near 1.0 x 10 7 m/s [McEachron, 1939; Brook and Kitagawa (Winn), 1965; Berger and Vogelsanger, 1967; Orville and Idone, 1982; Jordan et al., 1992], Upon reaching the ground the dart leader initiates a subsequent return stroke that travels back up the dart leader channel. The dart leader and subsequent return stroke are not usually branched ( Schonland et al., 1935.) Some subsequent leaders may follow an existing channel to ground but appear stepped in optical and electric field records. These leaders are termed dart-stepped leaders and have speeds intermediate between stepped leaders and dart leaders. Dart-stepped leader speeds measured optically by Orville and Idone [1982] were 0.76 17 x 10 6 m/s while those measured optically by Schonland [1956] were 5.0 17 x 10 5 m/s. Krider et al. [1977] found that regular microsecond-scale electric field pulses prior to subsequent strokes were associated with dart-stepped leaders. Median pulse intervals were 6.5 p.s in Florida thunderstorms. Similar electric field pulse trains have been observed by Krider et al. [1975] in cloud discharges and more recently by Rakov et al. [1996] in both cloud and ground discharges. Subsequent leaders in a discharge may branch from an existing channel to form a new path to ground via a stepped leader. Schonland et al. [1938b] and Schonland, [1956] observe this branching below the cloud base. Lightning discharges with spatially separate channels below cloud base are also quite common. Clifton and Hill [1980]

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23 report 18 % of flashes with spatially separate channels, Brantley et al. [1975] 21 %, Winn et al. [1973] 32 %, Kitagawa et al. [1962] 49 % and Rakov and Uman [1990b] 50 %. A possible explanation for the observation of multiple channels below cloud base has been proposed by Thomson et al. [1984]. Thomson et al. [1984] suggest that multiple channels may be due to a subsequent leader following an old channel in the cloud and then branching before reaching cloud base. Rakov and Uman [1990c] found leaders preceding new terminations to ground to have a geometric mean duration of 15 ms. This value is intermediate between the geometric mean duration of stepped leaders (35 ms) and dart leaders (1.8 ms) found by Rakov and Uman [1990c], They suggest a scenario such as that proposed by Thomson et al. [1984] to explain this intermediate duration of leaders preceding new terminations, which would have a higher speed (dart or dart-stepped) in the cloud and a slower speed (stepped) below cloud. The large subsidiary peaks, also termed fine structure, in the electric field waveform following the return stroke peak in first strokes were first studied in detail by Weidman and Krider [1978], They attributed fine structure to the effects of branches as the return stroke discharged the leader channel. Proctor [1988], using a VHF time-of-arrival system, found sources of VHF radiation present during first strokes to be located alongside the channel formed by the stepped leader, consistent with the view of Weidman and Krider [1978]. Willett et al. [1995] recorded both electric field and the derivative of the electric field (dE/dt) from return strokes. Both first strokes and new terminations to ground exhibited fine structure after the return stroke peak. Subsequent strokes following the same channel as an earlier stroke were associated with a “quiet” dE/dt waveform after the return stroke peak. In one case, an “anomalous” waveform was recorded in which the

PAGE 31

24 dE/dt waveform was initially noisy after the return stroke peak but became quiet 12 ps afterwards. Willett et al. [1995] proposed that fine structure in the dE/dt signature arose from new channels to ground while old channels produced a quiet dE/dt signature. They suggested that a critical test of this hypothesis might come from the “anomalous” type signature “if it could be shown that at the instant the return stroke passed from the new channel to an older channel that the corresponding dE/dt waveform became quiet”. In this section we present data from 16 cloud to ground lightning discharges creating at least one new termination to ground. In all cases the new termination was preceded by a dE/dt pulse train of at least 400 ps duration with average speeds of 1.0 x 10 6 m/s to 1.2 x 10 7 m/s, similar to those of dart-stepped leaders. However, pulse amplitudes near the end of trains fell below the trigger threshold of the system several milliseconds prior to the following return stroke. The average speed between the last recorded pulse in the train and the following return stroke was consistent with that characteristic of a stepped leader. Hence we conclude that the leader became stepped, forming the new path to ground. Fine structure was found in waveforms of both first strokes and strokes in new terminations, but its duration was shorter for new terminations (median value 37 ps in 17 strokes) than in first strokes of a flash (median value 141 ps in 17 strokes). For new terminations, locations of fine structure sources were consistent with having originated in the stepped leader channel. We conclude that the new terminations to ground were preceded by leaders which followed an old channel in a dart-stepped fashion and later adopted a new channel to ground, formed by a stepped leader, and that fine structure was a consequence of the stepped leader. The height at which the leader deviated from the old channel occurred from near ground to a height of 3.4 km.

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25 3.2,1 Results In order to investigate dart-stepped leaders that did not appear to propagate completely to ground, we chose ground flashes exhibiting a dE/dt pulse train that ended several milliseconds prior to a return stroke. Pulse trains were defined to be regular sequences of pulses lasting for at least 400 microseconds with interpulse intervals of 1-30 ps. In all flashes we consider, these trains arose from leaders to ground as opposed to intracloud (IC) K-changes which may also contain regular bursts of pulses [Krider et al, 1975; Rakov et al., 1996]. Since the location at ground of each return stroke origin was displaced from that of the previous stroke, it appears that a new termination to ground was formed. Both the first stroke in a flash and the stroke in the new termination exhibited fine structure in the dE/dt signature after the return stroke peak. We determined the duration of fine structure by choosing the channel with the largest signal (non-saturated) and defined the end of the fine structure to be when the signal had dropped below 10 % of the return stroke peak value for at least 12 ps. We first summarize results for all 16 flashes analyzed and then give detailed results for three flashes. All data were recorded during the summer of 1992 at Kennedy Space Center. Table 1 summarizes features of the 16 flashes analyzed. Flash 2541810 produced two new terminations that were preceded by pulse trains, hence there are 17 strokes listed in the table. The first column contains the flash ID with the number of records triggered in parentheses. A maximum of 25 records could be recorded per flash and hence some later records were probably missed in the seven flashes that had 25 records. The second column indicates the order of the stroke following the pulse train analyzed, that is, in the new channel termination (counting each stroke from the first in the flash). Strokes producing new terminations were either the second, third or fourth in

PAGE 33

T able 3.1. Summary of leaders preceding new terminations to ground. 26 2 3 Q £ 3 T5 2 55 CD ID C00 CO CO 00 CD o> o> o o hT“ in " *— T” v O) eg eg T“ ” x— T— A A A A A A A A A A A A A A A eg 0) • 4 -^ I rfflN>nsMOr-gNO)^r-r5s (0 a3 to a: s N m n n eg eg co eg 00 eg o in x CO 5 (/) (MgcoinnoicoiooqoioiwNT-^iDM oo in Tt a> eg ^ eg ^ tt eg oo eg co cb x o a> 0) CL CO c 5 co o)Noior;infggooT-(DNnoin ^N^r-VT-cg^T^CNi^cgcoNcg o co g= co (NICINOr-Oigco ^ * “ eg reg co* looirog-oioosttiin T-‘ T-' o' O O o' T-' T-' m « £ g> 'as X § 3 o (0 SNN0)0)0)0)OtOOOOOOOOt^ gcooneoang eg eg* eg eg co co* E cqcqiqe~Tj;cococq'»-;'^o)oq-g-egr^Teio co co -gin' m' in eg iri cn eg eg co co co m' co m a) 2 1 w | a) c 4 -» c Ss'-S'O’-t'XDfloroSSt^sp CD eg CO % n eg o oo n C'-COCOtm gs (D id egoooTg^eg-g-Tf . m gin in eg eg eg eg eg 8 CO o co co oi co o o m co in g iro) (o . .NSinoooorgio oegT-OT-oegi-T-T-o eg-g-Tj-^-Tj-eg'g-'g-Tr'g-eg gginmingginming egegegegegegegegegegeg

PAGE 34

27 the stroke sequence. The time between the preceding stroke and the stroke in the new termination is listed in column three. The fourth and fifth columns are the height range of sources associated with pulse trains. The sources always progressed downward. The sixth column gives the duration of the pulse train. These durations were between 400 ps (the minimum we observed) and 3.2 ms. Columns 7 and 8 indicate the minimum and maximum observed speeds during each pulse train. An average speed was obtained for each record (204.8 ps) containing a pulse train as described in Chapter 2. Speeds ranged from 1.0 x 10 6 m/s to 12 x 10 6 m/s with speeds at the upper end, near 1.0 x 10 7 m/s, always occurring near the beginning of trains (see details in flash 2442517 below). In all 16 flashes there was a time gap between the end of the pulse train and the following return stroke since this was a major criterion for the flash selection. This time interval is shown in column nine. The average speed, found from the lowest pulse source height and this time interval, was between 0.8 5.8 x 10 5 m/s, in good agreement with stepped leader speeds measured optically by Schonland [1956], Column ten lists the fine structure duration for the stroke in the new termination and column eleven the fine structure duration of the first stroke in that flash. In all flashes the duration of fine structure was shorter for strokes in new terminations than in the first stroke of that flash. Flash 2420760 produced two new terminations separated by 40 ps and we determined the fine structure duration for strokes in both channels. For 14 first strokes, fine structure was still present at the end of the record as indicated in Table 1. In most cases the criteria we used to determine the end of the fine structure agreed well with visual inspection of the dE/dt waveform, but the determination is still somewhat subjective and is discussed in detail in the case studies that follow.

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28 Flash 2541403 . Flash 2541403 occurred at 20:16:43 on day 254, 17 km SSW of the central recording station. Since we obtained 25 trigger records, we probably missed activity following our last triggered record. This flash was a simple one and illustrates well the dart-stepped portion of the leader prior to its creating a new termination to ground. Figure 3.1 shows dE/dt source locations. The flash began with two sources at t = 0 located at a height of 6.5 1cm represented by "0" in Figure 3.1. In all plots X is east, Y is north, and Z is vertically upward relative to the central station. The sources were associated with an electric field waveshape similar to the bipolar pulses described by Weidman and Krider [1979] who suggest that the pulses may be associated with preliminary breakdown. At t = 29.0 ms nine sources occurred at 2.5 km in height and also are shown as "O" in Figure 3.1. The first return stroke of the flash occurred at t = 38.0 ms and its dE/dt waveform is shown in Figure 3.2 (top trace). The location of the return stroke is shown in Figure 3.1 as "O" and marked “1”. For simplicity we have placed the locations of all return stroke peaks at ground level since calculated heights, of typically several hundred meters, were less than the errors in height. Two sources immediately prior to the first stroke were located several hundred meters high and are shown as “O”. These sources were probably radiated from the stepped leader just above ground since errors were also on the order of several hundred meters. The dE/dt waveform of the first return stroke contained fine structure that persisted for at least 83 M-s, that is, until the end of the record. Locations for three sources during the fine structure of the first stroke are shown in Figure 3.1 as “X”. Source locations increase in height with time from the return stroke peak. The corresponding pulses are labeled “FS” in Figure 3.2 and marked with arrows.

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29 -14 -12 -10 -8 -6 X (km) -18 -16 -14 -12 -10 Y (km) Figure 3.1. dE/dt source locations in flash 2541403. Sources preceding and including first stroke shown as “O”. Locations of first stroke fine structure pulses “X”. Pulse train locations preceding second stroke Locations of fine structure pulses of second stroke Strokes 3, 4, 5, and 6 were co-located with stroke 2 and are shown as “0”.

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30 t = 38.0 ms r Stroke 1 t = 38.0 ms RS RS _ Stroke 2 t= 169.5 ms "Vi NRS Stroke 5 t = 220.0 ms b+ 1 _L 20 40 60 80 100 120 Time in microseconds 140 160 180 200 Figure 3.2. The derivative of the electric field of strokes 1, 2, and 5 in flash 2541403. Return stroke peaks are marked “RS” and located fine structure pulses as “FS”. Time from the beginning of the flash is indicated on each trace.

PAGE 38

31 At t = 164.2 ms we recorded a dE/dt pulse train having a duration of 1.4 ms, spanning 6 records. All of the dE/dt waveshapes recorded at one station during this time are shown in Figure 3.3 with a common scale factor. The earliest sources in the train were located at a height of 2.6 km, coincident with the earlier sources at t = 29.0 ms. Locations of sources during the train are represented by "+" in Figure 3.1. Source locations moved progressively lower with time, the last sources in the train (see Figure 3.3) being located near 0.9 km in height. The average speed over each record in the train varied from 1.5 ± 0.4 x 10 6 m/s for the top trace in Figure 3.3 to 2.5 ± 0.7 x 10 6 m/s for the fifth trace from the top. Note that the pulse amplitudes become smaller in the last record. The second return stroke occurred in a new termination at / = 169.5 ms, 4 ms after the last source in the pulse train. The dE/dt waveform of this stroke is shown in the second trace of Figure 3.2. This stroke was displaced 1. 1 km horizontally from the first stroke and is shown as a “0” in Figure 3.1. Fine structure associated with this stroke persisted for 33 ps after the return stroke peak compared with more than 83 ps for the first stroke. Locations of pulses during the fine structure, shown as in Figure 3.1, extended from near ground to a height of 0.9 km, approximately where the pulse train ended. Four more return strokes occurred at f = 186.0 ms, / = 204.3 ms, / = 220.0 ms, and t = 244.0 ms. All four strokes were co-located with the second stroke of the flash. The dE/dt waveshape of the fifth stroke in the flash (fourth down the channel formed by the second stroke) is shown in Figure 3.2, bottom trace. The dE/dt waveshapes of strokes 3, 4 and 6 were similar to the fifth. Flash 2420739 . Flash 2420739 occurred at 17:34:54 on day 242 and was located 14.5 km ENE of the central recording site. This flash produced only 13 trigger records so that

PAGE 39

dE/dt 32 i i i 1 1 1 1 1 i n i I. L L 1. 1. 1.1 T T ~ r . ii.1 ' TJ J — y , — y-v If y-y ‘"’’ll — [ T — fTT TTrf r f [ — i w — Y — f — r — nr' r yT , p'' v, 'r' " V Plrmnn rr vl nn rr nr r TTTT 7 If 'r — V v 1 1 1 1 1 1 1 1 1 L_ 0 20 40 60 80 100 120 140 160 180 200 Time in microseconds 164.2 ms 164.4 ms 164.7 ms 164.9 ms 165.1 ms 165.4 ms Figure 3.3. Pulse train recorded at one station preceding the second stroke in flash 2541403. Time from the beginning of the flash is indicated at the right of each trace. All traces have the same vertical scale.

PAGE 40

33 no records were missed as a result of the memory constraints of our system. Figure 3.4 shows dE/dt source locations for this flash. The first record, at / = 0, contained two pulses. These sources were located near 6.6 km in height and are shown as “O” in Figure 3.4. The next record, at t = 5.0 ms, contained two pulses whose sources were located near 6.2 km high, shown as “O” in Figure 3.4. The first return stroke followed at t = 63.9 ms. Its location is shown as an “O” and labeled “1” in Figure 3.4 and its dE/dt waveform is shown in the top trace of Figure 3.5. Fine structure after the first stroke lasted for 97 (as. Locations of several sources indicated as "FS" on the dE/dt trace in Figure 3.5 are shown as “X” in Figure 3.4. At t = 236.6 ms a pulse train lasting at least 200 (is was recorded. Pulse train sources were located 6.2 km high, near the sources preceding the first stroke at / = 5 ms, and are shown as “+” in Figure 3.4. At t = 242.2 ms another pulse train, (“+” in Figure 3.4), spanned three records, with a total duration of 900 ps. These sources began at a height near 3 km and progressed to 1.9 km with speeds averaged over individual records ranging from 1.8 ± 1.0 x 10 6 m/s to 2.9 ± 0.6 x 10 6 m/s. Eleven milliseconds after the last sources in the pulse train, at t = 254.3 ms, the second stroke occurred. The location of the return stroke peak, (shown as a large 0 in Figure 3.4) was displaced 0.5 km from the first stroke in the flash and was therefore a new termination. The dE/dt waveform for the second stroke is shown in the bottom trace of Figure 3.5. Fine structure after the return stroke peak lasted for 37 ps, shorter than the 97 ps duration for the first stroke fine structure. The locations of three pulses in the fine structure indicated on the bottom trace in Figure 3.5 are shown as in Figure 3.4.

PAGE 41

34 12 14 16 18 20 X(M 2 4 6 8 10 Y (km) Figure 3.4. Source locations during flash 2420739. Sources preceding and including the first stroke are shown as “O”. Locations of first stroke fine structure “X”. LDAR locations preceding first stroke shown as small “0”. Pulse train locations preceding second stroke are shown as Second stroke marked as large “0”. Fine structure after the second stroke

PAGE 42

35 Figure 3.5. Derivative of the electric field of the two strokes in flash 2420739. Return stroke peaks are marked “RS” and located fine structure pulses as “FS”. Time from the beginning of the flash is indicated on each trace.

PAGE 43

36 For this flash we had available locations obtained simultaneously by the Lightning Detection and Ranging (LDAR) system at Kennedy Space Center. The LDAR system is a time of arrival system utilizing 7 stations operating at 66 MHz [Poehler and Lennon, 1979], The first LDAR locations for this flash occurred at t = 7 ms, or seven ms after our first trigger record. LDAR source locations, shown as small “0” in Figure 3.4, began near 6.6 km in height and progressed downward to a height of 1.8 km, ending one millisecond prior to the first return stroke we record. The average speed of progression of LDAR sources was near 1.2 x 10 5 m/s, consistent with that of a stepped leader. None of the sources detected by LDAR triggered our system. Flash 2442517 . Flash 2442517 occurred at 18:26:47 on day 244 and was located 21.5 km WSW of the central recording site. This flash differed from the previous two by its development of two simultaneous branches during the dart-stepped leader phase. Figure 3.6 shows locations of dE/dt sources in this flash. The sources of two pulses in the first trigger record were located near 7.3 km in height. These are shown as “O” in Figure 3.6. At / = 52.9 ms the first return stroke occurred. The dE/dt waveform is shown in Figure 3.7, top trace, and its location is shown as an “O” in Figure 3.6 and labeled “1”. Fine structure persisted for 131 tis after the return stroke peak. Sources located during this time are indicated on the trace in Figure 3.7 and mapped as “X” in Figure 3.6. Sources active during the fine structure were located up to a height of 4 km. Starting at / = 217.0 ms (164 ms after the first stroke) a pulse train spanned 13 records and 3.2 milliseconds. Figure 3.8 shows several of these records. The top two traces are the first two records whose source locations (“+” in Figure 3.6) extended from near 7.3 km in height (near the earliest sources in the flash at t = 0 ms) to 6.3 km. The

PAGE 44

37 Figure 3.6. Source locations in flash 2442517. Sources preceding and including the first stroke are shown as “O”. Locations of first stroke fine structure “X”. Pulse train locations preceding the second stroke are shown as Second stroke is designated as “0”. Locations of pulses after second stroke fine structure shown as

PAGE 45

38 Figure 3.7. Derivative of the electric field of the two strokes in flash 2442517. Return stroke peaks are marked “RS” and located fine structure pulses as “FS”. Time from the beginning of the flash is indicated on each trace.

PAGE 46

39 pulse sources formed a single channel, as shown in Figure 3.6. The average speeds during the first two records were 12 ± 3.2 x 10 6 m/s and 5.7 ±4.1 x 10 6 m/s respectively. Sources during the next 1.5 ms (6 records) formed simultaneous branches A and B shown in Figure 3.6 at speeds of 2.8 ± 0.2 x 10 6 m/s and 2.3 + 0.1 x 10 6 m/s respectively. At this time branch B stopped while branch A extended from 4 km to 1 km in height during the next 1.2 ms at an average speed of 1.6 + 0.2 x 10 6 m/s. The last two dE/dt records in the pulse train, during the end of the development of branch A, are shown in the bottom two traces in Figure 3.8. Four hundred microseconds after these, an intracloud (IC) event occurred, comprising two sources located at a height of 7.6 km, near the height of the earliest sources of the flash but displaced horizontally by 4 km. The second stroke in the flash occurred 2.5 ms after the IC event, or 2.7 ms after the last source in branch A, and formed a new termination to ground that was displaced 0.3 km from the first stroke. The dE/dt waveform for the second stroke is shown in Figure 3.7, bottom trace, and the location of the return stroke peak is shown as a “0” and labeled “2” in Figure 3.6. Fine structure in the dE/dt waveform of this stroke lasted for 3 1 (is, again shorter than the 130 (is of the first stroke, but we were unable to determine any locations during the fine structure. The burst of pulses occurring between 60 and 70 (is after the return stroke in Figure 3.7 was not considered to be part of the fine structure, based on the definition we used. Their source locations are shown in Figure 3.6 as near 4 km in height. The early portion of the pulse train merits further attention. In most flashes in this chapter first records in pulse trains were characterized by pulses occurring at 5-7 (is intervals as in Figure 3.3 but it was not clear that these first records represented the beginning of the pulse trains. However, in this flash we did record what appears to be the

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40 0 20 40 60 80 100 120 140 160 180 200 Time in microseconds 217.0 ms 217.2 ms 219.7 ms 220.0 ms Figure 3.8. Pulse train preceding the second stroke in flash 2442517. The train spanned 13 records. The first two records are shown at the top, the last two records at the bottom. Time from the beginning of the flash is shown to the right of each trace. All traces have the same vertical scale.

PAGE 48

41 beginning of the pulse train. In the first record (Figure 3.8, top trace) pulses occurred at irregular intervals, much shorter than the 5-7 ps interval in other trains presented. The average speed was 12 x 10 6 m/s, providing the upper limit we found for speeds of leaders preceding new terminations to ground. 3,2,2 Discussion 3.2.2, 1 Pulse train characteristics Dart-stepped leader phase . The flashes in this study radiated dE/dt pulse trains prior to new terminations to ground. While interpulse intervals for large pulses were typically several microseconds as in Figure 3.3, the beginning of some trains (see Figure 3.8) consisted of pulses spaced by as little as 1 ps. Average speeds ranged from 1.0 x 10 6 m/s to 1.2 x 10 7 m/s. Pulse intervals and average speeds during trains are consistent with dart-stepped leader measurements. Krider et al. [1977] found that microsecond-scale electric field pulses 200 ps prior to subsequent strokes in Florida had a mean interval of 6.5 ps. From optical records Schonland [1956] found the time between steps to be 7.4 25 ps while Orville and Idone [1982] found intervals from 2 9 ps. Dart-stepped leader speeds from SchonlandÂ’s study were in the range of 0.76 17 x 10 5 m/s while the speeds from Orville and IdoneÂ’s were 5.0 17 x 10 6 m/s. Our observations of pulse intervals and average speeds agree well with the above observations. Unlike the pulse trains radiated by dart-stepped leaders, the pulse trains considered in this chapter did not continue up to the return stroke and therefore differ from those reported by Krider et al. [1977] that occurred in the 200 ps immediately preceding the return stroke. We record trains beginning at heights near 7 km, lasting several

PAGE 49

42 milliseconds, and progressing downward to heights near 1 km. This portion of leaders was dart-stepped like in nature, but was followed by a median time interval of 5 ms to the following return stroke during which time no pulses triggered our system. Transition from dart-stepped to stepped leader . In 15 of the 17 strokes in Table 1, no records were triggered between the last sources in the pulse train and the following return stroke several milliseconds later. In the other two cases we recorded one and two dE/dt pulses respectively that did not appear to be associated with the propagating leader tip since their sources were in the cloud at a height of 7-9 km. In all cases the leader may have continued earthward without triggering our system if the pulse amplitudes were below our trigger threshold. Indeed this seems to have been the case since smaller amplitude pulses were always evident during the 30 ps pre-trigger interval preceding the following return stroke. Assuming that the leader continued, we estimated its speed over the missing portion from the distance and time between the last source in the pulse train and the following return stroke. For the three flashes presented above this was 1.4 x 10 5 m/s, 2.6 x 10 5 m/s, and 2.1 x 10 5 m/s respectively for the average speed of the leader. For the strokes listed in Table 1 we find a range of speeds from 0.8 5.8 x 10 5 m/s over the gap from the lowest source in the train to the following return stroke. These speeds are consistent with stepped leader speeds of 0.8 8.0 x 10 5 m/s determined photographically by Schonland [1956], The transition of a leader from dart-stepped to stepped has been documented by Schonland et al. [1938b] who photographed this transition and found a corresponding decrease in speed from 1.7 x 10 6 m/s to 3.8 x 10 5 m/s. We observe a similar decrease in speed from the end of the pulse train (about

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43 10 6 m/s) to the following gap that we interpret as a transition from dart-stepped to stepped leader. The formation of a new termination to ground may produce more than one visible channel below the cloud base. Multiple channels below cloud base have been recorded by many investigators [Kitagawa et al., 1962; Krider, 1966; Barasch, 1970; Winn et al., 1973; Brantley et al., 1975; Clifton and Hill, 1980; Rakov and Untan, 1990b] with estimates of this occurrence in anywhere between 17% and 50% of flashes. Thomson et al. [1984] proposed that multiple channels below cloud base might be due to the leader following an old channel in the cloud and then branching before reaching cloud base. Rakov and Uman [1990c] found the geometric mean duration of leaders preceding new terminations to ground (15 ms) to be intermediate between those of stepped leaders (35 ms) and dart leaders (1.8 ms). Rakov and Uman suggested this intermediate value might arise from a leader that follows an old channel in part and adopts a new channel to ground, similar to the view of Thomson et al. [1984], Schonland et al. [1938b] photographed branching from the old channel, forming new terminations, in the lower one-third of the visible channel but suggested that this branching could occur anywhere along the channel. Our results show this to be the case. In Table 1, column five lists the height of the last source in the pulse train prior to what we interpret as the transition to stepped leader. The values range from 0.7 km to 3.4 km, indicating that the transition may indeed occur at points inside the cloud as well as below. Cloud base is 1-2 km in Florida. Some heights near 0.7 km may in fact be lower or higher than this since our errors are several hundred meters in z at this height.

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44 Records in the 16 flashes of this study were rarely triggered by pulses associated with the stepped leader preceding the first stroke to ground, but rather by the return stroke peak. Difficulty in detecting the stepped leader is well documented in the literature. Schonland et al. [1938b] photographed stepped leaders beginning as high speed, brightly luminous leaders that became slower, fainter and harder to record. Orville and Idone [1982] were unable to analyze three stepped leaders they recorded owing to the weak intensity of the steps. We see what appear to be stepped leader pulses in the tens of microseconds preceding both first strokes (see Figures 3.2 and 3.7) and new terminations to ground (Figure 3.7) but rarely trigger on them. The dE/dt pulses produced by stepped leaders appear to be smaller than those produced by dart-stepped leaders, that is, during pulse trains. The last pulses received in each train (bottom trace in each figure) have amplitudes 2-3 times smaller than those earlier in the train. This decrease in pulse amplitude at the end of the train occurred in 14 of the 17 strokes listed in Table 1. 3, 2.2.2 Return stroke fine structure Fine structure locations . Using a multiple-station VHF time-of-arrival system, Proctor [1988] found locations during “Q-noise” radiated during first strokes to ground to be located alongside the leader path to ground and near earlier stepped leader sources. Q-noise typically lasted 40 400 ps and locations were obtained by timing the leading edges of pulses, changes in amplitudes, gaps in Q-trains, and the beginning and ends of trains. Q-noise from one flash lasted for 180 ps after the first stroke and was located to a height of 3.5 km. Q-noise was located in other flashes to heights of 4.5 km. Source locations increased irregularly in height with time during Q-noise. Average speeds of progression for sources active during Q-noise were 1.0-5.7xl0 7 m/s. Proctor suggests

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45 that VHF sources alongside the lightning channel may be associated with the tips of short branches, similar to the view of Weidman and Krider [1978] regarding sources of wideband electric fields during fine structure. We could locate only a few sources of fine structure in each flash despite the many dE/dt pulses present. The location of fine structure, or any pulse for that matter, requires the alignment of common sources on at least 4 of the 5 traces. For pulses in the fine structure after return strokes this task was particularly difficult for two reasons: (1) the speed of the return stroke, up to 2 orders of magnitude higher than that of the dartstepped leader (that cause pulse trains), result in pulses in the fine structure to be out of alignment after several microseconds; and (2) multiple sources may be active simultaneously during the fine structure making it more difficult to distinguish common sources at different stations. To illustrate these difficulties. Figure 3.9 shows a portion of the fine structure from the first stroke of flash 24402517 (Figure 3.7, top trace) on an expanded time scale. A set of common pulses are discemable at each of the five stations and are marked “A” while at “B” pulses appear clearly at only 2 or 3 stations thus precluding us from finding a location. Nevertheless, we were able to obtain confident locations (with height errors of 500 m or less) for several fine structure pulses in each stroke in this study. For example, pulses marked “A” in Figure 3.9 were located with a height error of 255 m and had a * 2 value of 0.19. For the first stroke in flash 24200739 (Figures 3.4 and 3.5), the sources active during the fine structure coincide with earlier stepped leader sources located by the LDAR system. During the first stroke of flash 24402517, we find locations of fine structure pulses to be alongside the channel that is later followed by the dart-stepped portion of the leader preceding the second stroke. We

PAGE 53

dE/dt 46 52.94 52.96 52.98 53.0 SLF IR UC9 USB EDL Figure 3.9. Expanded time scale trace of dE/dt waveforms recorded at all five stations during the first stroke in flash 2442517.

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47 infer that the stepped leader preceding the first stroke produced the section of channel A, where these fine structure sources are located. In flash 25401403 (Figures 3.1 and 3.2), fine structure sources of the first stroke were located in the region consistent with the path the stepped leader probably took. Fine structure sources in first strokes were located to a height of 4 km. Higher source locations may have been missed since we were unable to obtain locations at the end of the fine structure in 14 strokes, owing to record length limitations on one or more channels. Fine structure locations obtained during flashes 25401403 (Figure 3.2) and 24200739 (Figure 3.5) for the new terminations were between ground and the last sources in the pulse train prior to the transition to stepped leader. These locations are consistent with those of the inferred stepped leader forming the new termination. An exception is flash 24402517 for which we were unable to locate any sources during the 31 tis of fine structure immediately after the return stroke peak. Locations of sources occurring 60-70 tis after the return stroke peak were located near 4 km high. These source locations are inconsistent with having been radiated from the region of the stepped leader occurring after the pulse train, presumably between ground and 1 km. It is interesting to note that the locations of the pulses 60-70 tis after the second stroke coincide with the extent that branch A had reached when branch B ceased propagating. Origin and duration . Weidman and Krider [1978] suggested that fine structure in first stroke electric field waveforms is due to the effects of branches. Schonland and Collens [1934], Schonland et al. [1935], and Malan and Collens [1937] observed changes in luminosity and speed near points of intersection of the return stroke with large branches that may give rise to radiated fields. Weidman and Krider [1978] postulated that the

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48 contribution of channel tortuosity to the fine structure is not as great as that of branches since the subsidiary peaks in subsequent strokes are quite weak and most subsequent strokes are not usually branched [Schonland et al., 1935], Willett et al. [1995] found that all 34 electric field waveforms containing fine structure after the return stroke peak were associated with new channels to ground, including first strokes. Fine structure after return stroke peaks appeared “noisy” in dE/dt, similar to the waveforms we record (see Figure 3.2). Eighteen waveforms that were “quiet” in dE/dt after the peak were found to have been radiated from subsequent strokes in old channels. Bailey and Willett [1989] presented “anomalous” return stroke waveforms which were preceded by stepped leader pulses and appear as first stroke waveforms (noisy dE/dt) for the first few tens of microseconds, but resemble subsequent stroke waveforms thereafter (quiet dE/dt). They suggested this signature might be produced by a new channel to ground branching off an old channel within a few kilometers of ground, and postulated that new terminations to ground produce noisy dE/dt waveforms while later strokes in the same channel produce quiet dE/dt waveforms. They further hypothesized that a new fork to ground off an old channel offers a test as to some characteristic (possibly the presence of branches) that causes the noisy dE/dt structure. A new termination to ground would be expected to be initially noisy in dE/dt as the return stroke traverses the new channel segment, and later quiet upon reaching an older section of channel. We find sources of fine structure pulses in new terminations to be between ground and the last sources in pulse trains, consistent with having originated in a stepped leader channel. The maximum height of fine structure pulse locations in new terminations generally corresponds to the location of the last pulse in the preceding pulse train. These

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49 observations support the hypothesis of Willett et al. (1995) that the dE/dt waveform becomes “quiet” after the return stroke has passed from the new channel segment (forged by a stepped leader) to the old channel. The “anomalous” cases reported by Willett et al. [1995] and Bailey and Willett [1989] had fine structure durations of 10, 12, 20, and 6-17 ps. Willett et al. [1995] assumed a return stroke speed of 1 x 10 8 m/s for the anomalous duration of 12 ps to obtain a height of 1.2 km for the new branch off the old channel. However, for pulse trains ending at heights near 1 km (see Table 1), we find fine structure durations 2-3 times as long as the “anomalous” cases described by Willet et al. [1995] and Bailey and Willett [1989], This suggests a lower average return stroke speed than 1 x 10 8 m/s over the lower 1-2 km of the channel. Idone and Orville [1982] observe return stroke speeds in the range of 2.9 24 x 10 7 m/s for the lowest 1-2 km of the channel in Florida. Their mean speed was 6.6 x 10 m/s for first strokes and 11 x 10 m/s for subsequent strokes. In flash 2442517 (Figure 3.7) we locate fine structure pulses 130 ps after the first stroke to a height of near 4.1 km. This corresponds to an average return stroke speed of near 3 x 10 7 m/s, consistent with the lower values for first strokes obtained by Idone and Orville [1982], Strokes occurring in new terminations in our study had a median fine structure duration of 37 ps. The strokes whose last pulse train sources were located at 1 km or below had a median fine structure duration of 33 ps, while strokes with trains ending at heights above 1 km had a median fine structure duration of 49 ps. This difference is to be expected since pulse trains ending at greater heights would produce longer fine structure owing to a longer stepped leader channel. In all flashes in this chapter the fine structure duration following new terminations (median value 37 ps) was considerably

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50 shorter than that from the first stroke in the flash (median value 141 ps). The median duration fine structure from first strokes we report, 141 ps, is very similar to the 137 ps found by Cooray and Perez [1994] for HF radiation at 3 MHz after first strokes in negative ground flashes. Longer duration fine structure associated with first strokes versus that of new terminations is consistent with the view of a stepped leader beginning at a greater height prior to a first stroke than a stepped leader preceding a new termination. In Florida, for example, first strokes typically begin at heights near 5 6 km [Krehbiel et al., 1979], 3,2,3 Conclusions We have presented results of the properties of return stroke fine structure and leaders associated with new terminations to ground. We find evidence to support the hypotheses of Thomson et al. [1984] and Rakov and Uman [1990c] that multiple channels below cloud base are due to a leader following an old path in the cloud and later adopting a new path to ground forming a new termination. Strokes occurring in new terminations to ground, subsequent to the first stroke, are preceded by a leader that is dart-stepped in nature prior to a transition to a stepped leader. Leader speeds of 1.0 12 x 10 6 m/s are calculated during the dart-stepped portion of leaders. Leader speeds are estimated to be near 2 x 10 5 m/s after their transition from dart-stepped to stepped. The leader transition is found to occur at heights between ground and 3.4 km. Fine structure is present in the dE/dt waveform of both first strokes to ground and subsequent strokes in new channels to ground. The duration of fine structure was found to be shorter (37 ps median) for strokes in a new termination to ground than for first

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51 strokes of a flash (141 (is median). Sources of fine structure after strokes in new terminations were between ground and the transition of the leader from dart-stepped to stepped. This suggests that fine structure is the result of the preceding stepped leader and is therefore shorter in strokes occurring in new terminations to ground, compared to first strokes of a flash, owing to the shorter stepped leader path in the former. The stepped leader path length preceding new terminations had a median value of 1.1 km in this study. 3,3 Return Stroke Waveforms Separated by One Millisecond or Less Electric field waveforms, indicative of two return stroke signatures separated by one millisecond or less, have been reported by Schonland et al. [1935], Guo and Krider [1982] and Rakov and Uman [1994], Guo and Krider [1982] found that five of 246 flashes contained records with two return strokes separated by 46 110 ps. Schonland et al. [1935] observed two different branches of a single stepped leader that produced two separate return strokes. They present streak-camera images showing two leader branches, apparently originating from a single trunk inside the cloud, that resulted in two return strokes separated by 73 (is. Rakov and Uman [1994] report nine cases where a double electric field waveform (two return stroke signatures) occurred with simultaneous double ground strokes, as determined from video records. These strokes were separated by 15 ns -3.3 ms. Guo and Krider [1982] note that multiple ground contacts by two branches of the same stepped leader are rare. They hypothesize that in order for the first branch to reach ground 50 100 ps prior to the second, the tip of the leader along the second branch must

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52 be within 5 40 m of ground. If not, it is assumed that the first stroke will travel up the first branch and out along the second branch, thus discharging it. Rakov and Uman [1994] point out that while the double field waveforms separated by up to 100 ps that they recorded were consistent with the view of Guo and Krider [1982], those separated by times greater than 165 [is were not. They proposed that double field waveforms were the product of two sequential strokes, each initiated by its own leader, rather than from the simultaneous branching of a single leader. We studied five flashes, each containing two dE/dt signatures characteristic of return strokes, separated by up to one millisecond. In all cases the locations of the two strokes were distinct, indicating that they occurred in separate terminations to ground. The duration of fine structure associated with the secondary stroke was shorter, in each case, than that of the primary stroke, indicative of a shorter stepped leader channel prior to the secondary stroke (see discussion in Section 3.2). The temporal separation of strokes in two flashes was 40 ns and 50 ns. In the remaining three flashes, strokes were separated by 250 1000 ns. In one of the latter, we find evidence that the strokes were preceded by two simultaneous branches of the same stepped leader. 3.3,1 Results Table 3.2 summarizes data from five flashes with return strokes separated by one millisecond or less. All strokes produced first stroke type waveforms, i.e., the return stroke signatures were followed by fine structure, and occurred in different channels. Stroke orders are listed in column two of the table in accordance with their occurrence in the overall flash sequence. Strokes will also be referred to as primary or secondary when

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53 discussing them together. In three of the five flashes the strokes were the first two of the flash, while in the remaining two flashes, the strokes were preceded by an earlier stroke at a nearby, but different location. The time between strokes is listed in column three. The duration of the fine structure following each stroke is listed in the fourth column of the table. In the first two flashes of the table, the two return stroke signatures occurred in the same record (204 ps). Fine structure associated with the primary stroke of flash 2420744 was still present at the time of the secondary stroke. Notice that the difference Table 3.2. Summary of five flashes with strokes separated by one millisecond or less. Flash ID Stroke #Â’s AT (ps) FS Duration (Us) AD (km) 2420760 2,3 40 28, 22 0.9 2420744 2,3 50 50+,43 0.9 2540472 1,2 273 143,45 1.3 2420770 1,2 504 140+, 65 1.2 2540638 1,2 1000 200, 48 1.4 in fine structure duration for the strokes in the last three flashes in Table 3.2 was a factor of 2 4, similar to the differences between first strokes and strokes in new terminations (see Table 3.1). The spatial separation between strokes is given in column 5 of the table. We now present two flashes in detail. Flash 2420760 . Flash 2420760 comprised 18 records in 740 ms. The final six records were at a location distant from the start of the flash and were considered to be from a

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54 separate discharge. The first 12 records spanned 331 ms and contained six strokes to ground. The first stroke occurred at t = 50.9 ms with fine structure lasting at least 150 ps. At t = 121.2 ms we recorded the double field waveform, strokes 2 and 3, displayed in Figure 3.10. Fine structure after strokes 2 and 3 lasted for only 28 ps and 22 ps respectively, much shorter than that associated with the first stroke of the flash. Strokes 2 and 3 were preceded by a leader of the type described in Section 3.2. The leader began in a dart-stepped fashion at t = 119.7 ms, 70.3 ms after the first stroke. Sources progressed downward from 3.5 km to near 0.7 km at 4.9 5.6 x 10 6 m/s during the next 1.2 ms and exhibited two distinct branches below 1.8 km. There followed a 1.5 ms interval during which time we received no triggers, until the two strokes at t = 121.2 ms. Each stroke occurred in a new termination, as evidenced by the fine structure after each. Locations of dE/dt sources from flash 2420760 are shown in Figure 3.11. Sources preceding and including the first stroke of the flash are shown as “O”. The second and third strokes were located at points “2” and “3” respectively. Leader sources prior to strokes 2 and 3 are marked as “+” and followed branches A and B before creating the two new terminations to ground. Locations of fine structure associated with the third stroke are shown as “X” and were near sources from the leader along branch A. Strokes four, five, and six were co-located with the second stroke of the flash and occurred at t = 156 ms, t = 241 ms, and t = 332 ms respectively. Little or no fine structure was associated with these strokes. Flash 2420770 . The first two strokes of this flash were separated by 504 ps and 1.2 km. The dE/dt waveforms of the two strokes are depicted in Figure 3.12. The first stroke occurred at t = 48.0 ms and fine structure in the dE/dt waveform exceeded 140 ps. The

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55 o VO t" o (N 'f (N •C n cd 53 <41 o o o B I 3 a o T3 V J3 41 <41 O g <2
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z (km) Z (km) 56 Figure 3.1 1. dE/dt source locations during flash 2420760. Sources preceding and including the first stroke are shown as "O". Locations of second leader shown as "+". Second stroke represented by "box". Third stroke and fine structure locations shown as "X".

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RS #1 57 JP/3P

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58 second stroke waveform contained fine structure lasting 65 (is. Locations of the two return strokes, stepped leader sources, and several sources of fine structure after each stroke are shown in Figure 3.13. Stepped leader and return stroke sources are shown as “O”. Actual stepped leader heights are probably only a several hundred meters above ground. Sources of fine structure after the first stroke are shown as “X“ in Figure 3.13 and extend to near 2 km high. Locations are near those of the stepped leader prior to the first stroke. Fine structure after the second stroke was located to a height of 2 km and locations are marked as in Figure 3.13. The third stroke in the flash occurred at t = 203 ms in a new termination to ground located 0.63 km from the second stroke. This location is labeled “3” in Figure 3.13 and marked with “0”. The third stroke was preceded by a leader of the type described in Section 3.2. Beginning at t = 195.9 ms, and for 2.7 ms, we located sources that extended from 5.3 km to 0.8 km at 1.5 2.9 x 10 6 m/s, then the third stroke followed 4.5 ms after the last leader source we recorded. Fine structure after the third stroke persisted for 40 ps and was located to a height of 1.8 km, near sources of the third leader. Leader sources are shown as "+" in Figure 3.13. Locations of fine structure following the third stroke are marked with “0”. When sources from the leader preceding the third stroke are overlaid with those associated with the first two strokes, it appears that the leader branched near 3 km high, one branch going towards the location of the first stroke (1), the other towards the second (2), prior to creating a new termination to ground (3). 3.3,2 Discussion Guo and Krider [1982] have suggested that double stroke waveforms, separated by 50 100 ps, may be the result of simultaneous branches of the same stepped leader

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z (km) z (km) 59 12 . 13 14 15 16 17 18 19 20 X (km) Y (km) Figure 3.13. dE/dt source locations during flash 2420770. Sources preceding the first twostrokes are shown as "O". First stroke fine structure marked "X", second stroke fine structure "boxes". Third leader sources represented by "+". Fine structure after third stroke shown as "diamonds".

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60 contacting ground at two points. For this scenario to occur, they argue that the secondary branch must be within 5 40 m of ground when the primary branch contacts ground. If this were not the case, the return stroke resulting from the primary branch would propagate up the channel established by the primary branch and out along the secondary branch, thus discharging it. Schonland et al. [1935] present streak-camera photographs that support this view. Two leader branches, apparently originating from a single trunk inside the cloud, produced two strokes separated by 73 ps. The leaders emerged from the cloud 1.8 ms apart but due to differences in path lengths, arrived at ground 73 ps apart. The first two flashes in Table 3.2 contain strokes separated by 40 and 50 ps. In each flash the strokes were distinctly located. Fine structure following strokes was 22 50 ps, much shorter than that of first strokes of flashes (median value 141 ps from Section 3.2), indicating a new termination was formed near ground. Consider flash 2420760 with strokes separated by 40 ps. The leader preceding strokes two and three was of the type described in Section 3.2. The leader was dart-stepped from a height of 3.5 km to several hundred meters above ground. From a height of 2 km the leader followed two branches simultaneously, A and B. After reaching a height of several hundred meters above ground, the leader became stepped along each branch and forged two new paths to ground. The locations of the lowest dart-stepped leader sources and the short duration fine structure after each stroke indicates a short section of stepped leader channel preceded each stroke. We propose that the two branches, A and B, were formed prior to the third leader, most likely by the first leader of the flash. The second leader followed the two branches before deviating in the final few hundred meters of each branch, thus forming the double field new termination waveform of Figure 3.10. Thus the second and

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61 third strokes were the result of two simultaneous branches of the same leader, consistent with the view of Guo and Krider [1982] and the photographic evidence of Schonland et al. [1935]. The two strokes of flash 2420744 were similar to those of 2420760, both were associated with a relatively short fine structure and occurred after the first stroke in the flash. We now discuss return stroke waveforms separated by more than 250 ps. Using simultaneous video and electric field records, Rakov and Uman [1994] recorded double field waveforms coincident with two visible channels to ground branched between the top and bottom of the channel. Strokes were separated by 15 ps 3.3 ms. In three flashes strokes were separated by 15, 22, and 100 ps and were consistent with the hypothesis of Guo and Krider [1982], Two flashes, however, contained return strokes separated by 165 and 287 ps, longer than the time assumed necessary for the first stroke to travel up to the branch point (observed below cloud base) and discharge the second branch. Rakov and Uman [1994] argue that these double field waveforms were unlikely the result of two return strokes initiated by two simultaneous branches of the same leader as suggested by Guo and Krider [1982], Rakov and Uman [1994] also found three flashes that contained strokes separated by 442, 513, and 596 ps. Each of these was observed to produce two visible channels to ground and a double field waveform. No branch point was observed but may have been hidden within the cloud. The first two strokes of flash 2420770 were separated by 504 ps. The strokes produced distinct locations at ground and were located 1.2 km apart. Locations of stepped leader sources prior to the strokes and fine structure after the strokes, are consistent with two separate channels below 2 km high (see Figure 3.13). It is not until source locations of the leader prior to the third stroke are overlaid with those of the first

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62 two strokes that the complete picture of the flash is obtained. The leader prior to the third stroke followed what we assume to be the channel established by the first leader, branching near 3 km high. Several source locations extend out along branch A, near earlier stepped leader and fine structure sources from the first stroke to ground. The vast majority of leader sources, however, were located along branch B, coincident with earlier stepped leader and fine structure sources from the second stroke to ground. When all dE/dt source locations are considered, its appears that the first strokes shared a common channel in the cloud, above 3 km high. Rakov and Uman [1994] suggested that strokes separated by 165 and 287 ps were inconsistent with being initiated by two branches of the same stepped leader. Based on a maximum channel length of 2 km (below cloud) and a minimum return stroke speed of 2 x 10 7 m/s {Orville and Idone, 1982), they argue that the stroke along the more successful branch would reach the end of the less successful branch in a time not exceeding 100 ps. Rakov and Uman [1994] hypothesize that the double ground events separated by 165 and 287 ps may be the result of two sequential return strokes of the same flash, each initiated by a different leader, rather than the simultaneous branching of a single leader. It is assumed that either. (1) the primary leader develops two branches, both are grounded and produce inseparable return stroke waveforms or (2) the second branch terminates close to, but above ground. In either case, the secondary leader can follow the secondary branch to ground or produce two inseparable return stroke signatures. Rakov and Uman [1994] argue against several physical situations, other than two consecutive leader-return stroke sequences, that may produce the observed double field waveform. We can also dismiss several of these in regard to the last three flashes in Table 3.2 by noting that in

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63 each case, the two return stroke waveforms were indeed strokes to ground as verified by locations. Thus we can eliminate the following possibilities: (a) a random overlap of field signatures produced by strokes belonging to independent discharges, (b) the secondary waveform being an ionospheric or other reflection of the first waveform, and (c) the secondary waveform being associated with an M-component. We now address the possibility of two separate, sequential leaders, as suggested by Rakov and Uman [1994], producing the return stroke signatures separated by 504 (is in flash 2420770. Let us assume that the first two strokes of flash 2420770 were initiated by two separate leaders. The first stroke was initiated by a stepped leader that formed branch A (Figure 3.13). It is likely that this leader began near 6 km high, the earliest sources of the flash, and formed the channel to ground later followed by the subsequent leader. Fine structure associated with the first stroke was located near sources of the stepped leader along branch A, up to a height of 2 km. Fine structure lasted for longer than 140 (is, consistent with the first strokes of flashes in section 3.2. If the second stroke were initiated by a separate leader, as suggested by Rakov and Uman [1994], the duration of the leader would be approximately 350 (is (allowing for the current from the first stroke to cease). Although leaders with such a duration are rare, they have been reported. Rakov and Uman [1990a] found about 6 % of dart leaders had a duration between 200 500 |is. We report two subsequent leaders with durations between 130 200 (is in section 4.5. However, the waveform of the second stroke is inconsistent with the above scenario. Fine structure after the second stroke persisted for 65 (is and was located to a height of 2 km. This suggests that the second stroke was preceded by a stepped leader, rather than a dart leader, and that fine structure was a result of the return stroke retracing

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64 the stepped leader channel. Fine structure persisted for longer than the median value of 37 ps associated with new terminations in Section 3.2, but shorter than that of first strokes (median value 141 ps). The median lowest height of dart-stepped leader sources preceding new terminations in section 3.2 was 1.1 km, thus sources of fine structure located to a height of 2 km are consistent with a duration of 65 ps. It appears, therefore, that the second stroke was preceded by a stepped leader, from a height of at least 2 km that was not discharged prior to the second stroke. If the second leader was stepped over this portion, the average speed required to reach ground in 350 (is would be at least 6 x 10 6 m/s, an order of magnitude faster than typical stepped leader speeds. Therefore it appears unlikely that a second leader, separate from the first, could have produced the second stroke waveform. We propose an alternative to the scenario described above, namely that the two strokes were the result of two simultaneous branches of the same stepped leader. We assume that the secondary branch (B) was concurrent with the primary (A) and continued to ground after the first stroke. In this scenario the leader tip along branch B would be approximately 100 m above ground when the first stroke occurred (this assumes a common stepped leader speed of 2 x 10 5 m/s). Prevailing assumptions in the literature suggest that the 504 ps interval between strokes should be sufficient for the first stroke to travel back up the primary branch (A), and out along the secondary branch (B), a total path length of near 6 km, thus neutralizing branch B. Assuming a return stroke speed of 2 x 10 7 m/s, the minimum observed by Orville and Idone [1982], the first stroke would reach the end of the second leader in approximately 300 ps, less than the observed 504 ps interval between the two strokes. Orville and Idone [1982], however, have noted a

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65 decrease in return stroke speed between ground and cloud base of up to 25 % and Schonland et al. [1935] found a speed of 1 x 10 7 m/s for a return stroke along a very long horizontal branch (nearly 10 km). If a significant attenuation in speed occurs within the cloud, it may be possible to achieve the 504 ps needed to prevent the return stroke from reaching the end of the secondary branch. Another possibility may be that the first return stroke failed to neutralize any of the secondary branch. The duration (65 ps) and location of fine structure (to 2 km high) following the second stroke indicates that much of this branch may not have been neutralized by the first stroke. We found no locations of fine structure associated with the first stroke to be along the secondary branch, although only a small fraction of pulses could be located. Flashes 2540472 and 2540638 were similar to flash 2420770, the primary stroke in each case having a fine structure 3-4 times that of the secondary. Each of these is consistent with the secondary stroke discharging a relatively short stepped leader channel, similar to that of flash 2420770. 3,3,3 Conclusions The first two flashes of Table 3.2, with strokes separated by 40 ps and 50 ps, were consistent with the theory of Guo and Krider [1982], the two strokes being the result of a single branched stepped leader. Fine structure associated with both the primary and secondary strokes was much shorter than that of first strokes in a flash, suggesting the strokes were preceded by relatively short stepped leaders. In one case we found the two strokes to be preceded by a leader that was dart-stepped along two branches, one towards each stroke location, prior to becoming stepped several hundred meters above ground.

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66 The strokes therefore appear to be the result of two simultaneous branches of the same stepped leader. Two strokes separated by 504 ps were found to share a common leader channel, branched below a height of 3 km. The waveforms and locations of the two strokes were inconsistent with having been initiated by two separate leaders. We found data to support the view that the two strokes may have been the result of two simultaneous branches of the same stepped leader. 3,4 Summary Conclusions In this chapter we have investigated leaders preceding new terminations to ground and the fine structure associated with strokes in those flashes. Sources of fine structure appeared to be the result of the preceding stepped leader, suggesting that shorter stepped leader channels were associated with strokes having a shorter fine structure. We extended these findings to cases where two return strokes occurred less than one millisecond apart. Fine structure associated with the secondary stroke was shorter, in each of five cases, than that of the primary stroke. This suggests the secondary stroke was preceded by a shorter stepped leader channel than the primary, and that the two strokes were possibly the result of two branches of the same stepped leader.

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CHAPTER 4 LEADER OCCURRENCES AND CHARACTERSTICS IN SUBSEQUENT STROKES TO GROUND 4. 1 Introduction In this chapter we investigate characteristics of leaders preceding subsequent strokes to ground. Unlike leaders preceding new terminations to ground in chapter 3, leaders follow old channels completely to ground. In section 4.2 we present data from seven subsequent leaders to ground that produce regularly occurring dE/dt pulses prior to the following return stroke. We give 3-D track speeds for these leaders and analyze changes in leader speed as a function of height. We present dE/dt waveforms of several leaders and investigate the relationship between interpulse interval and leader speed. Two leaders exhibiting an increase in speed towards ground and a corresponding decrease in interpulse interval are examined in section 4.3. Finally, in section 4.4, we note three cases in which pulses in the dE/dt waveform, indicative of a dart-stepped leader, continue through the time of the return stroke. Sources of these pulses are found to originate from locations higher along the channel to ground. The relationship between interstroke interval and leader waveform is explored in section 4.5. A summary of the major chapter findings is given in section 4.6. 4,2 Leader Speed and dE/dt Waveshape Leaders preceding subsequent strokes to ground in a lightning discharge can be classified based upon their appearance in optical and electric field records. Leaders that 67

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68 follow a previous channel and appear as continuous luminous sections of channel in optical records are termed dart leaders. Speeds of dart leaders near ground, determined optically, range from 1 24 x 10 6 m/s [Orville andldone, 1982; Jordan et al., 1992] with a mean value near 10 x 10 6 m/s [McEachron, 1939; Winn, 1965; Orville and Idone, 1982], Subsequent leaders that follow the channel of an earlier stroke, but exhibit steps in optical records after initially continuous propagation, are termed dart-stepped leaders. Dart-stepped leader speeds are intermediate to those of stepped leaders and dart leaders. Schonland [1956] found dart-stepped leader speeds of 0.5 1.7 x 10 6 m/s preceding six subsequent strokes to ground, while Orville andldone [1982] found leader speeds of 0.76 17 x 10 6 m/s preceding four subsequent strokes. Time intervals between luminous steps of dart-stepped leaders were near 10 ps in Schonland.' s [1956] study and between 2 9 ps in that of Orville and Idone [1982], Krider et al. [1977], Le Vine and Krider [1977], Weidman [1982], and Izumi and Willett [1991] have reported wideband electric field measurements of radiation from subsequent leaders. Krider et al. [1977] found that dart-stepped leaders contained regularly occurring pulses in the electric field waveform, 80 200 ps prior to the following return stroke peak. Mean interpulse intervals were 6.5 ps in Florida thunderstorms, consistent with the time between luminous steps observed by Schonland [1956] and Orville and Idone [1982], Izumi and Willett [1991] and Willett et al. [1995] have noted regularly occurring dE/dt pulses immediately (up to 20 ps) prior to subsequent strokes. Geometric mean duration of subsequent leaders, including both dart and dart-stepped, as determined from electric field measurements, are 0.6 1.9 ms ( Malan and Schonland,

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69 1951; Kitagawa, 1957; Workman et al., 1960; Krehbiel et al., 1979; Rakov and Uman, 1990c). However, these measurements were made on a millisecond time scale while individual pulses vary on a microsecond scale. No electric field measurements, recorded with sufficient bandwidth, to reveal microsecond scale variations, are available for the whole duration of subsequent leaders. If we assume a common dart-stepped leader speed of 3 x 10 6 m/s, source locations of dart-stepped leader pulses measured 200 ps prior to return strokes by Krider et al. [1977] correspond to heights below 1 km. The optical measurements of dart-stepped leaders by Orville and Idone [1982] and Jordan et al. [1992] were confined to the lowest 2-km of the lightning channel, corresponding to heights below cloud base in Florida. Similarly, the measurements of Schonland [1956] were limited to the lowest 2 2.5 km of the lightning channel. Therefore there is a lack of electric field measurements on a microsecond scale for the full duration of subsequent leaders. Several investigators have made measurements of the change in speed of subsequent leaders below cloud base with conflicting results. Schonland [1935] found little change in dart leader speed as a function of height and noted that the speed never increased towards ground. Optical measurements of dart leader speeds made by Mach and Rust [1997] are consistent with this view as they found “no significant” change in dart leader speed with height. Orville and Idone [1982], however, found 4 of 16 dart leaders to increase in speed towards ground, the first such findings. Additionally, Orville and Idone [1982] noted one dart-stepped leader that increased in speed towards ground and another that decreased in speed.

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70 We investigate seven subsequent leaders to ground, each exhibiting regular pulses tens of microseconds prior to the return stroke peak, indicative of a dart-stepped leader. In each case the following return stroke peak is co-located with a previous stroke in the flash and lacks fine structure in the dE/dt waveform, indicating the leader followed an old channel completely to ground. Pulses in the derivative of the electric field are detected 0.6 2.0 milliseconds prior to these subsequent strokes. Several tens of microseconds, during which time no dE/dt pulses appear above the noise, precede the first dE/dt pulses in each leader record, suggesting we recorded leaders in full. The earliest leader sources spanned heights between 3.8 and 6.2 km, well above the cloud base in Florida. Each of the seven leaders exhibited a decrease in speed from its highest point to that near ground (lowest 1 km). Leader speeds, averaged over individual records, were between 1.4 x 10 6 m/s and 35 x 10 6 m/s, spanning the range of observed dart leader speeds in the literature as well as those of dart-stepped leaders. Speeds averaged 16 x 10 6 m/s during the first record of dart-stepped leaders and 3.6 x 10 6 m/s during the final record, corresponding to the lowest kilometer of the channel to ground. The median interpulse interval was dependent on the threshold used in pulse selection. We therefore defined a median interpulse interval as a function of threshold as described in Chapter 2. At a threshold of 20% of the maximum leader pulse, the median interpulse interval was larger, in each case, near the return stroke than it was at the start of the leader. Source locations progressed downward with time and were observed, in one case, to develop along two branches simultaneously, only one of which reached ground.

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71 4,2,1 Results We present results of seven leaders preceding subsequent strokes to ground. Each leader exhibited regular dE/dt pulses tens of microseconds prior to the following return stroke peak. Prior to the first dE/dt pulses associated with each leader, there was a period of several tens of microseconds during which time no dE/dt pulses were above the noise threshold. Radiation from leaders was continuous (records were separated by 30 ps owing to our systemÂ’s recording configuration) up to the time of the return stroke. Table 4.1 summarizes characteristics of seven subsequent leaders to ground. Column one contains the flash ID. Listed in column two are the records that the leader spanned, each 204.8 ps in duration. Columns three and four list the 3-dimensional track speed and its error observed in each record. In most instances a single average speed was determined per record as described in Chapter 2. In some cases we determined more than one speed in a given record. This was done when either (i) more than one branch was discemable (branches are labeled a and b ) or (ii) a measurable change in speed occurred within a record (records are labeled fast or slow). Speeds ranged from a minimum of 1.4 x 10 6 m/s to a maximum of 35 x 10 6 m/s. Speeds during the final kilometer to ground are shown with an asterisk and were estimated in the manner of stepped leader speeds preceding new terminations in Chapter 3. The mean height of sources within a record is given in column 5. The duration of each leader is listed in column 6 and represents the time from the first dE/dt pulse to the return stroke peak. Durations were between 0.6 and 2.0 ms, similar to the geometric mean duration of subsequent leaders from several previous studies ( Malan and Schonland, 1951; Kitagawa, 1957; Workman et al., 1960; Krehbiel et al., 1979; Rakov and Uman, 1990c], The median interpulse interval at

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72 Table 4.1. Summary of seven subsequent leaders to ground. Flash Record Speed/10 6 error Height Duration At (8%) At (20%) At (30%) ID # (m/s) % (km) (ms) ps ps ps 2541679 19 (fast) 35 11 4.2 0.83 0.8 1.1 1.7 1 9(slow) 24 9 3.4 0.8 1.1 1.7 20 3.3 14 2.1 0.8 1.4 2.8 21 3.3 14 1.4 1.8 3.7 4.0 22* 3.9 * 0.5 2.0 4.7 6.3 2420878 18 12 7 3 0.6 1.0 1.7 3.3 19 3.0 79 1.9 1.6 3.4 4.6 20* 5.4 * 0.7 2.1 3.8 3.6 2541487 14 12 9 3.7 0.69 0.8 1.1 1.5 15 5.4 28 1.5 0.7 1.2 1.8 16* 3.0 * 0.5 1.1 2.5 3.2 17* 3.0 * 0.5 1.6 2.9 3.6 2541810 19 16 10 4.3 1.2 1.2 2.2 4.8 20 6.7 11 1.9 0.8 1.9 2.5 21* 2.0 * 0.3 2.0 5.2 6.4 2541672 12(fast) 23 16 4.6 1.25 1.0 1.4 2.1 12(slow) 8 35 3.5 1.0 1.4 2.1 13 X X 2.8 0.7 1.1 2.2 14(b) 1.4 43 2.1 1.1 2.1 3.8 14(a) 2.2 14 2.7 1.1 2.1 3.8 15(b) 4.7 7 1.5 1.2 2.4 3.9 15(a) 1.9 61 2.2 1.2 2.4 3.9 16(b) 5.3 46 0.7 1.2 2.8 4.3 16(a) 1.9 18 1.9 1.2 2.8 4.3 17(b)* 2.0 * 0.2 1.2 3.1 5.4 2540223 17 14 7 4.8 0.75 1.0 2.3 3.4 18 9.1 11 2.7 0.9 2.5 4.7 19 6.9 20 1.2 1.6 3.2 6.6 « o eg 6.2 * 0.5 1.9 3.3 3.3 2541062 9 14.0 18 5.5 1.4 1.1 1.5 3.1 10 7.8 9 3.7 0.9 1 1.8 11 6.0 23 2.2 1.0 1.5 2.4 12 2.9 34 1.5 1.2 2.9 5.3 13 3.0 37 0.7 2.5 5.4 8.1 14 1.4 99 0.4 3.6 5.5 7.7 15* 2.0 * 0.2 2.6 5.7 6.5 * estimated speed (see text)

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73 thresholds of 8 %, 20 %, and 30 % of the maximum leader pulse amplitude are given in columns 7 through 9 respectively. We now investigate three leaders in detail. Flash 2541679 . Flash 2541679 occurred at 20:28:15 on 10 September 1992, 11.7 km southwest of the central recording station. We recorded 25 records spanning 94 milliseconds, indicating we may have missed activity following our last record. Three return strokes were co-located during the flash. The locations of all dE/dt sources of the flash are shown in Figure 4.1. Source locations prior to the first return stroke are shown as “O”. The earliest sources of the flash were located concurrently in regions A and B (Figure 4.1). Five milliseconds after the start of the flash, region A became inactive and sources were confined to the two branches, C and D, below region B. During the next 9 ms source locations progressed outward along branch C and down the main channel to ground, D, where the first return stroke was located at t = 14 ms. Sources prior to the first stroke propagated to ground with an average speed near 3 x 10 5 m/s, suggesting they were associated with the stepped leader. Two records, containing tens of pulses each, were recorded at t = 44 ms and t = 67 ms. Locations of these sources are shown as “X” in Figure 4. 1, the earlier sources located near 4.5 km high and the latter near 5.6 km. Beginning at t = 70.6 ms, radiation from the second leader to ground spanned four records and 0.83 ms. Locations of leader sources are shown as “+” in Figure 4.1 and progressed downward from a height near 4.8 km, terminating at t = 71.4 ms in the second stroke, co-located with the first. Source locations associated with the second leader below 3 km high were coincident with those along the main channel to ground preceding the first stroke. The dE/dt waveform of the second leader is shown in Figure 4.2. The return stroke peak does not appear on the trace of this channel, owing to differences in

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Z (km) Z (km) 74 Figure 4. 1 . DE/dt source locations for flash 2541679. Source locations prior to and including the first stroke are shown as "O". Locations of sources from the second leader are shown as Sources active between the first and second strokes are represented by "X".

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75 C /3 £ On _ o (N £ £ 6 £ C/3 £
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76 the time of its arrival at different stations, but was observed on others. The mean heights of pulse sources in each record are indicated in column 5 of Table 4.1 and the average speed in each record is listed in column 3. Source locations from the first record of the leader (record 19) descended from near 4.8 km high to 2 km, at an average speed of 27 x 10 6 ± 2.2 x 10 6 m/s. The average speed, determined over the next two records (20 and 21), was 3.3 x 10 6 ± 0.5 x 10 6 m/s as the leader descended from 2.3 km to 1 km. During the last record (record 22) the leader traversed the final kilometer to ground at an estimated speed of 3.9 x 10 6 m/s. We estimated the leader speed from the last source in record 21 to the return stroke by assuming a straight-line path between the two locations and dividing by the time between them. At heights below one kilometer, errors in source heights become comparable to the heights themselves, making a calculation of the 3dimensional track speed, as outlined in Chapter 2, susceptible to large errors. A profile of the leader development vs. time is depicted in Figure 4.3 where x, y, and z source locations are plotted individually vs. time. The four records of the leader are clearly distinguished by gaps between them resulting from our recording configuration. It appears that there was a kink in the leader track during the first record. This is most noticeable in the plot of the x-component of the speed. When the track was subdivided to reflect this we obtained speeds of 35 x 10 6 ± 4.0 x 10 6 m/s over the first 16 ps and 24 x 10 6 ± 2.2 x 10 6 m/s over the next 45 ps. A plot of median interpulse interval vs. threshold for the second leader is shown in Figure 4.4. At a threshold of 20 %, the median interpulse interval increased from 1.0 ps during the first leader record to 4.7 ps during the last. In fact, at each threshold, intervals were larger for successively later portions of the leader record.

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77 Time from beginning of flash (ms) Time from beginning of flash (ms) Time from beginning of flash (ms) Figure 4.3. Profile of leader development versus time in flash 2541679. Threshold (percentage of largest pulse) Figure 4.4. Median interpulse interval vs. threshold for the second leader of flash 25401679

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78 At t = 94 ms the third stroke in the flash occurred and was co-located with the first two. The third stroke was not preceded by any dE/dt pulses above the noise level for 65 Us immediately prior to the return stroke peak. This record was the 25 th of the flash and any later events that may have occurred were not recorded by our system. Flash 2420878 . Flash 2420878 occurred at 17:43:25 on 29 August 1992, 19.7 km WSW of the central recording station. The flash comprised 25 records, including four co-located return strokes, spanning 453 ms. Locations of dE/dt sources from this flash are shown in Figure 4.5. The earliest sources were located near 6 km high and are shown as “O”. During the first 5 ms sources progressed downward to a height of 4 km. The horizontal spread of sources extended several hundred meters in both x and y. Since errors in individual locations were 40 60 m in each of x and y, we conclude that the spatial spread of sources was due to the presence of multiple branches, most likely associated with the stepped leader. Seventeen milliseconds later, at t = 22 ms, we recorded the first stroke of the flash, preceded by several small dE/dt pulses within the last 30 ps, indicative of a stepped leader. Beginning at t = 74.9 ms radiation from the second leader to ground spanned three records and 0.6 ms. The dE/dt leader waveform is shown in Figure 4.6 and locations of individual pulse sources are indicated by “+” in Figure 4.5. The first pulse sources were located 3.8 km high, near the extent of the sources we detected 17 ms prior to the first return stroke. Leader source locations progressed downward with increasing time. The average speed during the first record of the leader (record 18), with source locations descending from 3.8 km to 2.4 km, was 12 x 10 6 ± 0.84 x 10 6 m/s. Source locations from record 19 spanned the heights 2.0 1.4 km at an average speed of 3.0 x 10 6 ± 2.4 x 10 6

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79 £ N -12 £ N Y (m) Figure 4.5. dE/dt source locations of flash 2420878. Sources prior to and including first stroke shown as "O". Locations of sources from second leader are shown as "+ M . The second stroke occurred 54 milliseconds after first and in same channel. Stroke 3 followed the same channel 26 milliseconds after stroke 2.

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80 TOP Figure 4.6. dE/dt waveform of the second leader of flash 2420878. Time from the beginning of the flash is shown to the right of each trace.

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81 m/s. During the final record (record 20) the leader traversed the last kilometer to ground at an estimated average speed of 5.4 x 10 6 m/s. Note that the highest leader speed occurred during the first leader record, similar to the second leader in flash 2541679. Figure 4.7 summarizes median interpulse interval vs. threshold for the three records of the second leader in flash 2420878. At a threshold of 20 % the median interval increased from 1.7 ps to 3.8 ps over the course of the leader. At all thresholds below 25 % the median interpulse interval was greater for successively later portions of the leader record, consistent with the observations of flash 2541679. However, unlike flash 2541679, this trend did not continue for all thresholds. At thresholds of 25 % to 35 %, the second record of the leader exhibited the greatest median interpulse interval. At a threshold of 40 % larger intervals were again associated with successively later leader records. The third and fourth strokes of flash 2420878 occurred at t = 102 ms and t = 475 ms respectively and were co-located with the first two strokes of the flash. Waveforms of these two strokes are given in Figure 4.8. Small, irregular pulses preceded each of these strokes for 60 ps, the limit of our pretrigger delay. These small pulses appear similar to the “chaotic” leaders sometimes found in the electric field waveform prior to subsequent strokes [Weidman, 1977; Rakov and Uman, 1990b; Willett et al., 1995], In order to compare these leaders with the second leader we used the same threshold values chosen for the second leader. Median interpulse interval vs. threshold is plotted in Figure 4.9 for the leaders prior to strokes three and four. At a threshold of 4.4 % (four standard deviations above the noise) the median interpulse interval was found to be 0.9 ps and 1.45 ps respectively for the leaders preceding strokes three and four. At a threshold of 20 % we found no dE/dt pulses to precede stroke three, and only two immediately prior to

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82 Figure 4.7. Median interpulse interval vs. threshold for the leader preceding the second stroke of flash 2420878.

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83 C/3 6 VO C/3 E r^ 1P/3P u -a c o o E H Figure 4.8. dE/dt waveform of the third and fourth strokes of flash 2420878. Time from the beginning of flash shown at right.

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84 Figure 4.9. Median interpulse interval vs. threshold for the leaders prior to strokes 3 and 4 of flash 2420878.

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85 stroke four. In fact, above a threshold of 10 %, there were no dE/dt pulses from either leader other than those mentioned immediately prior to the fourth stroke. Flash 2541672 . Flash 2541672 occurred at 20:27:56 on 10 September 1992, 17.9 km SSW of the central recording station. This flash differed from the first two of this section in that its second leader followed two simultaneous branches prior to reaching ground. Twenty-five records spanned 882 ms and three return strokes were co-located. Source locations for this flash are shown in Figure 4.10. The earliest sources, shown as “O” in Figure 4.10, were located at a height of 5.6 km and were followed 60 ms later by the first return stroke. Beginning at t = 123.6 ms radiation from the second leader spanned 1.25 ms and six records. The entire dE/dt waveform of this leader is shown in Figure 4.1 1. The earliest sources were located at a height of 4.7 km. The channel followed by the leader during the first record (record 12) was divided into two segments. The average speed over the first portion (spanning 35 ps) was 23 x 10 6 ± 3.7 x 10 6 m/s, and decreased to 8.0 x 10 6 + 2.8 x 10 6 m/s during the second portion (37 (is). Sources progressed downward from a height of 4.7 km to 3.3 km. Beginning with record 14 of the leader, at t = 124.0 ms, leader sources developed simultaneously along branches A and B (Figure 4.10) during the next 600 (is (records 14 — 16). The profile of the leader development, x, y, and z vs. time, is depicted in Figure 4.12 where the two branches are readily discernable. The speed along branch A decreased from 2.2 x 10 6 ± 0.3 x 10 6 m/s to 1.9 x 10 6 ± 0.3 x 10 6 m/s during records 14 — 16 (124.0 — 124.6 ms). The speed along branch B increased from 1.4 x 10 ± 0.6 x 10 6 m/s to 5.3 x 10 6 ± 2.4 x 10 6 m/s during this same time interval.

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ZO® 1 ) Z (km) 86 Figure 4. 1 0. Locations of dE/dt sources of flash 254 1 672. Sources prior to and including first stroke shown as H 0 M . Locations of sources from leader preceding second stroke represented by "+ H .

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87 Pi Pi M C4 Pi P i dl Vi CO Vi Vi Vi E E E E E E VO 00 O cs T VO r*-i rn MTf TITf cs
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88 I Time from beginning of flash (ms) Time from beginning of flash (ms) Time from beginning of flash (ms) Figure 4. 12. Profile of leader development versus time in flash 25401672.

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89 Branch B followed the main channel to ground, covering the remaining several hundred meters at an estimated speed of 2.0 x 10 6 m/s. The median interpulse interval vs. threshold curve of the second leader of flash 2541672 is shown in Figure 4.13. The first (record 12) and last (record 17) leader records are represented by traces with circles, record 12 being the lower trace. Unlike the previous two flashes in this section, we found the second record of the leader to exhibit the smallest median interpulse interval at all thresholds, though not much different from that of the first record. There was a tendency for successively later records to exhibit greater intervals at a given threshold, although several exceptions are readily seen in Figure 4.13. 4.2.2 Discussion Leader speed vs. height . We first discuss the observed speed changes vs. height for the seven leaders in Table 4.1. Correlation between two-dimensional leader speed and height has been investigated by several researchers [Schonland, 1935; Orville and Idone, 1982; Mach and Rust, 1997] with conflicting results. Optical studies by Schonland [1935] revealed that dart-leader speeds often decreased towards ground and never increased. Mach and Rust [1997] found "no significant" change in dart-leader speed vs. height. Contrary to the results of Schonland [1935] and Mach and Rust [1997], Orville and Idone [1982], using high speed streaking photographic techniques, found 4 of 16 dart leaders to increase in speed towards ground. The increase in speed they observed was not more than a factor of two in any of the four leaders. Three of the leaders followed the same channel in one flash. Each of the three leaders first exhibited an apparent increase

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90 Figure 4. 13. Median interpulse interval vs. threshold for the second leader in flash 2541672. Threshold ranges from 4 standard deviations above the noise level to 50 % of the largest dE/dt pulse in the leader.

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91 in speed at their upper ends, near 2 km high, followed by a decrease, and a further increase near ground. The 2-dimensional height vs. speed profile (see Figure 4 of Orville and Idone, 1982) of each of the three leaders was similar. Since all three leaders followed the same path to ground it is possible that the observed profile could be explained by a constant leader speed with the hidden third dimension of the leader track accounting for the apparent speed change. In fact, Orville and Idone [1982] point out that the speed changes may have been real or "more likely apparent due to viewing of a 2-D photograph". Orville and Idone [1982] also note a speed change vs. height in four dart-stepped leaders. Three of these decreased in speed towards ground (17 0.76 x 10 6 m/s over 1.19 ms; 14 1.4 x 10 6 m/s over 0.46 ms; 5.3 1.9 x 10 6 m/s over 0.88 ms). One increased in speed towards ground (2.3 5.3 x 10 6 m/s during 0. 1 1 ms). We have plotted leader speed vs. height in Figure 4.14 for each of the seven leaders in Table 4.1. Each exhibited a decrease in speed from its highest point to ground, supporting the view of Schonland [1935], In 6 of the 7 leaders the decrease was monotonic, within our errors in speed measurement. We found a mean speed of 16 x 10 6 m/s during the first record of leaders and a mean speed of 3.5 x 10 6 m/s during the final, a decrease of a factor of 4.5 on average. Recall that each speed in our study represents an average value measured over typically 80-150 ps (100 1000 m) in a record. In flashes 2541679 and 2420878 we subdivided the leader track during the first record and found the average speed to decrease by 30 % and 60 %, respectively. Therefore, the decrease in speed from the beginning of the leader to ground, a factor of 4.5 on average, should be regarded as a lower limit in our study. Changes in leader speed ranged from a decrease of a factor of 2.2 in flash 2420878 to 11.5 in flash 2541672. Orville and Idone [1982]

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92 D O) NON CM N 00 to r N n to (O N
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93 noted decreases in dart-stepped leader speeds by factors of 2.5, 10, and 22. These changes are similar to those we measure, although ours take place in the cloud (3 6 km high) while theirs are measured in the final 1 -2 km of the channel. Furthermore, the differences in leader speeds vs. height of the current study are real, and not apparent, since we have calculated speeds over 3-dimensional track lengths. While the increase in dart leader speeds observed by Orville and Idone [1982] may have been apparent, it is probable that the decrease in speeds they observed in dart-stepped leaders was real, a factor of 10 to 20 not likely to be explained by viewing a 2-D photograph. The one dartstepped leader they observe to increase in speed did so by a factor of two. We find no evidence of an increase in speed for the dart-stepped leaders in Table 4.1 and it is possible that the increase seen by Orville and Idone [1982] was the result of viewing a 2dimensional photograph. The photographic studies of Schonland [1935], Orville and Idone [1982], Jordan et al. [1992] and Mach and Rust [1997], involved dart leader and dart-stepped leader speed measurements below cloud base (lowest 1 -2 km above ground). Each of the dartstepped leaders in Table 4.1 was observed to decrease in speed from heights of 3 6 km to ground. Rhodes et al. [1994] and Shao et al. [1995], using a VHF interferometer to locate radiation from dart leaders, note several leaders decreased in speed over even larger extents, 8-20 km. One leader of Shao et al. [1995] traveled at 8 10 x 10 6 m/s over 6-8 km, and slowed down to 2 -3 x 10 6 m/s during the remaining portion of the channel to ground, 8-10 km. The leader developed horizontally in the cloud for 6 8 km before coming to ground, consistent with the behavior of dart leaders measured by Rhodes et al. [1994] and the findings of Krehbiel et al. [1979], Krehbiel et al. [1979]

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94 used a point charge model to determine charge source locations and found leaders developed horizontally in the cloud, originating at distances up to 8 km from the flash origin. The leaders in Table 4. 1 followed a predominately vertical path to ground and did not appear to originate from appreciable horizontal distances. In fact, the earliest dE/dt sources were often located near those prior to the first stroke in the flash (e.g. Figure 4.5). One reason for the differences between our measurements and those of Rhodes et al. [1994] and Shao et al. [1995] may be that our measurements were made at wideband frequencies (0-4 MHz) while theirs were made at VHF. Several studies have found differences in radiation from lightning processes at VHF and wideband frequencies. Le Vine and Krider [1977] found radiation at VHF from first strokes to ground did not peak until 10 30 ps after the start of the wideband return stroke electric field waveform. Similarly, dart leader radiation at VHF ceased about 100 ps prior to the return stroke according to Le Vine and Krider [1977] and Brook and Kitagawa [1964], Therefore, it is possible that a portion of subsequent leaders, such as those measured by Rhodes et al. [1994] and Shao et al. [1995] at VHF, may not produce appreciable radiation at wideband frequencies. dE/dt pulse train characteristics of subsequent leaders . In previous studies microsecond scale wideband electric field measurements for subsequent leaders have been recorded in the last 200 ps prior to subsequent return strokes. Krider et al. [1977] found about 10 % of all triggers were from subsequent strokes preceded by electric field pulses of uniform amplitude occurring at short, regular intervals (compared to stepped leader pulses) of 6 -7 ps. They suggested that these pulses were radiated by a dartstepped leader process similar to that observed photographically by Schonland [1935,

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95 1956], Each of the leaders in Table 4.1 exhibited pulses at regular intervals in the several tens of microseconds prior to the return stroke. However, dE/dt pulse intervals for these leaders were found to be dependent on the pulse amplitude used to determine pulse selection, i.e., dE/dt pulses were often not of uniform amplitude. Alternatively, the electric field pulses had varying rates of rise. No amplitude criteria for determining interpulse pulse intervals are mentioned by Krider et al. [1977], presumably because there was no ambiguity in identifying pulses. We suggest the use of a threshold, related to some characteristic of the electric field waveshape, to determine whether or not a particular pulse should be counted. We used thresholds based upon percentages of the maximum amplitude of the largest leader dE/dt pulse. We found significant differences in the median interpulse interval as a function of threshold as well as with time during the leader. We now discuss some of these observations. At a threshold of 20 % the median interpulse interval averaged 4. 1 (as during the final record (204 ps) of leaders in Table 4.1, slightly smaller than those observed by Krider et al. [1977] during the final 200 ps of dart-stepped leaders. At smaller thresholds intervals were often much shorter. As an example consider the last leader record (22) of flash 2541679 whose dE/dt waveform is shown in Figure 4.2 and median interpulse interval vs. threshold curve in Figure 4.4. At thresholds between 20 30 % the median interpulse interval was 4.7 6.3 ps, consistent with the findings of Krider et al. [1977], However, at the lowest threshold, 2 % (4 standard deviations above the noise level), the median interpulse interval was 0.9 ps, significantly smaller than the mean interval found by Krider et al. [1977], Figure 4.7 depicts median interpulse interval as a function of threshold for the second leader in flash 2420878. During the last leader record (20) the

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96 interpulse interval was 3.8 ps at a threshold of 20 %. In fact at thresholds between 15 35 % the median interpulse interval varied little, 3.6 4. 1 ps. At the lowest threshold the median interpulse interval decreased to 1.1 ps, again much smaller than that typically associated with dart-stepped leaders immediately prior to return strokes. In fact, at a threshold of 8 %, the median interpulse interval averaged 1.9 ps during the final record of the seven leaders in Table 4.1, half the value found at a threshold of 20 %, indicating the presence of smaller pulses in the dE/dt waveform. We discuss the origin of these smaller pulses later. We now investigate dE/dt pulse intervals from leader records more than 200 ps before return strokes. The measurements of the current study are the first to reveal the microsecond scale structure of wideband dE/dt from subsequent leaders 1 2 ms prior to the return stroke. While median interpulse interval, at a threshold of 20 %, during the final record of leaders averaged 4.1 ps, median intervals at a similar threshold from earlier leader records were significantly smaller. Consider again the second leader of flash 2541679 whose median interpulse interval vs. threshold curve is displayed in Figure 4.4 and dE/dt waveform in Figure 4.2. Successively later portions of the leader record were characterized by larger median intervals at all thresholds. At a threshold of 20 % the median interpulse interval increased from 1.1 ps during record 19, to 1.4 ps, 3.7 ps, and 4.7 ps for records 20 22 respectively. Similarly, at a threshold of 20 %, during the second leader of flash 2420878 (Figure 4.7), intervals increased from 1.7 ps, to 3.4 ps, to 3.8 ps for records 18, 19, and 20 respectively. In fact, the mean interpulse interval at 20 % for the leaders listed in Table 4. 1 was 1.6 ps during the first record of leaders, less than half the value found at the same threshold during final records. Recall that the greatest

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97 speeds during the leaders in Table 4.1 occurred during the first dE/dt record, suggesting that higher speeds may be associated with shorter interpulse intervals. We now investigate leader speed vs. median interpulse interval. Each of the leaders in Table 4.1 exhibited a decrease in speed and an accompanying increase in the median interpulse interval. Orville and Idone [1982] observed an increase in inter-step interval with decreasing speed in dart-stepped leaders. In flash 220:04 of their study, they observed a leader that emerged from the cloud dart-like, or continuous in appearance, at a speed of 14 x 10 6 m/s. Stepping began while the leader was still travelling at a speed of 1 1 x 10 6 m/s. At the onset of stepping the leader track appeared as "the superposition of the original continuous dart leader track and the just developing stepping mode". Further into the stepping process the time between steps became 2-3 |is and the continuous luminosity of the leader track, while still visible, was diminished. During the final 200 ps of the leader intervals increased from 5 to 9 ps, although not consistently, while the leader speed decreased to 1.4 x 10 6 m/s. Now consider Figure 4.15, a plot of average leader speed vs. median interpulse interval (20 % threshold). Each of the seven leaders showed a decrease in speed and an increase in median interpulse interval from start to end. In most cases the decrease in speed and increase in interval was monotonic. The average speed during the first record of leaders was 16 x 10 6 m/s with median intervals at a 20 % threshold of 1.6 ps. Speeds of the three leaders of Orville and Idone [1982] were between 14 17 x 10 6 m/s when emerging from the cloud, each leader appearing continuous in nature. The first leader steps appeared 2 3 ps apart, slightly larger than the 1.6 ps we see at the beginning of leaders. Resolution of individual steps through optical techniques appear to be limited to around 2 ps {Idone, V,

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98 o> r* o cm rv oo co tn co to oo cm o i00 r*CM »HIM! (s/ui 9 0ix) paads c/5 > .1 T3
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99 personal communication). Near ground the speeds of Orville and Idone [1982] decreased to 0.76 1.9 x 10 6 m/s with inter-step intervals increasing to 4 9 ps. The seven leaders of Table 4.1 had an average speed near ground of 3.5 x 10 6 m/s, slightly higher than that observed by Orville and Idone [1982], but consistent with dart-stepped leader speeds near ground measured optically by Schonland [1935, 1956], The median interpulse interval averaged 4.1 ps near ground, similar to the value obtained by Orville and Idone [1982] and consistent with other studies [Schonland, 1956; Krider et al. 1977], Figure 4.16 shows a scatter plot of leader speed vs. median interpulse interval for leader records in Table 4.1. There was an inverse relationship between leader speed and median pulse interval (at 20 %) for these leaders. Triangles correspond to records 14 16 of flash 2541672, i.e., where branches A and B occurred simultaneously. While two speeds were determined for each record, one along each branch, only a single value of interpulse interval was found. During record 16 of the leader we found a nearly equal number of pulses, at a 20 % threshold, attributable to each branch. There were a total of 93 pulses, of which 41 were attributable to branch A and 37 to branch B. Fifteen pulses could not be attributed to either branch, some owing to the lack of simultaneous data recorded at another station. The effect of two simultaneous branches on the median interpulse interval, in this case, was to effectively cut in half the expected number of pulses arising from the presence of either of the branches alone. Therefore the points marked as triangles may be considered to correspond to pulse intervals twice as large, 4 5 ps, moving them near the right most points on the graph. These points would then be consistent with other leader records exhibiting similar speeds.

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100 -O TO r CM o c rTO CD l— JO Tjc in 3 CM • 1 y 2 i a. a. f 1 £ a C/3 C/3 > o (N £ .1 Q oo 3 & £ [(s/ui 9 0 I X ) P»3ds] 3oq

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101 In summary, the leaders in Table 4.1 exhibited speeds and interpulse intervals (at a 20% threshold) near the return stroke, similar to values in the literature. Prior to the final 200 ps of leaders, we found speeds up to an order of magnitude faster and median intervals less than half their value near the return stroke. Orville and Idone [1982] observed three leaders with similar tendencies in addition to one showing the opposite tendencies, namely, an increase in speed and decrease in interpulse interval. We have observed two such leaders and discuss these in section 4.3. We now return to the issue of small amplitude dE/dt pulses in leader records. There are no reports in the literature of interpulse intervals from dart-stepped leaders shorter than 2 ps. At a threshold of 8 %, interpulse intervals averaged 1.0 ps during the first records of leaders and increased to 2.2 ps during final records. These values are less than half those obtained at a threshold of 20 % and are equal to or less than the minimum time between steps of dart-stepped leaders reported in the literature ( Orville and Idone, 1982). To investigate the origin of these smaller pulses, responsible for shorter median interpulse intervals at smaller thresholds, we examined the second leader of flash 2541679. The dE/dt trace of the last record is shown on an expanded time scale in Figure 4.17. The timing offsets between the four stations have been removed so that common pulses are aligned and a dotted line corresponding to a threshold of 10 % of the maximum leader pulse has been included on the trace from station 5. It was not possible to obtain a location for each dE/dt pulse since the times of occurrence of the pulses on at least four stations were required. Small pulses, present at one or two stations, were sometimes not discemable at others, thus precluding them from being located. However, we could determine the proximity of any pulse source to a location along the leader channel by

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dE/dt dE/dt dE/dt 40 42 44 46 48 50 52 54 56 58 Time in microseconds Figure 4. 17. dE/dt waveform of record 22 during the dart-stepped leader of flash 2541679. Stations 3-5 are shown for a) 0-60 ps, b) 60-120 ps, and c) 120180 ps.

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dE/dt dE/dt 103 Figure 4. 17— continued.

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dE/dt dE/dt 104 Figure 4.17--continued.

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105 comparing the relative alignment of pulses at two or more stations. Sources that developed along the channel, with relatively small spatial displacements between sources, maintained a similar timing offset on the traces from different stations. Pulses that occur on the trace of one station without a common pulse on another may lie off the channel. We have circled the pulses in Figure 4.17 that did not appear to have a common pulse on the dE/dt trace of at least one other station. We found 70 % (75 of 107) of the pulses on the trace of station five to have a corresponding pulse on that of at least one other station. This indicated that a majority of the dE/dt pulses above a threshold of 10 % were from sources along or near to the channel to ground. Notice the larger pulses in Figure 4.17 that were responsible for the 4. 1 p.s median interpulse interval found at a 20 % threshold. Both these large pulses and the smaller pulses appeared to originate from locations along or near to the channel to ground. A similar analysis during the first leader record of 2541679 indicated that 87 % (133 of 153) of the dE/dt pulses at a 10 % threshold likely originated from sources along or near to the channel to ground. Thus, a majority of the dE/dt pulses from this leader were associated with sources near to the channel to ground and the median interpulse interval was dependent on threshold. There are several possible reasons why we detect the smaller pulses in the dartstepped leader waveform prior to return strokes while Krider et al. [1977] may not. In our study these pulses were roughly 3 times smaller than the larger pulses occurring at 4 — 5 pis intervals near return strokes. The waveforms of Krider et al. [1977] appear smaller in amplitude since their events were more distant (tens of kilometers). Smaller electric field pulses may have been obscured for this reason. Also, our bandwidth is

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106 approximately twice theirs and we recorded dE/dt, rather than E, which may accentuate these smaller pulses. 4.2.3 Conclusions Subsequent leaders to ground exhibiting regular pulses near the return stroke peak, indicative of a dart-stepped leader, were found to progress at speeds from 1.4 x 10 6 m/s to 35 x 10 6 m/s. Each leader exhibited a decrease in speed between its highest point (3-6 km) and that nearest ground (last kilometer). Speeds decreased by a factor of 2.2 to 11.5, with a mean value of 4.5 in seven leaders. The median interpulse interval during final leader records averaged 4.1 ps at a threshold of 20 %. This interval is similar to that between the electric field pulses from dart-stepped leaders recorded by Krider et al. [1977], We present the first estimate of pulse intervals prior to the final 200 ns of leaders in subsequent strokes. The median interpulse interval generally increased with successively later portions of the leader record. During first leader records, median interpulse intervals had a mean value of 1.6 ps at a threshold of 20 %, a value less than half that during final records, 4. 1 ps. Speeds during first records of leaders had a mean value of 16 x 10 6 m/s. Speed decreased towards ground and leaders had a mean speed of 3.5 x 10 6 m/s during final records. In addition to a decrease in median interpulse interval over the course of leaders, intervals were found to vary with the threshold used in pulse selection. At a threshold of 20 %, median interpulse intervals during the first record of leaders averaged 1.6 ps, near the lower limit of dart-step intervals recorded optically by Orville and Idone [1982]. At a threshold of 8 %, interpulse intervals were less than 1 ps at the beginning of leaders and

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107 2.2 }j.s near the return stroke. Examination of the leader waveform suggests these smaller pulses were radiated from sources near to or along the channel to ground. These smaller pulses should therefore not be overlooked when determining pulse intervals and step lengths of leaders. 4,3 Subsequent Leaders Showing an Increase in Velocity In the previous section we presented a class of subsequent leaders, each exhibiting a decrease in speed towards ground. Two subsequent leaders that show a marked increase in speed during their descent are analyzed in this section. These two leaders were initially dart-stepped (large pulses several microseconds apart) and traveled at speeds near 3 x 10 6 m/s. After several hundred microseconds, the dE/dt waveform became similar to that seen during the first records of leaders in Table 4.1, i.e., there was a decrease in the median interpulse interval. The decrease in interval was accompanied by an increase in speed to greater than 10 x 10 6 m/s. In one of the two leaders, the transition apparently occurred near the region where the leader joined a section of channel which was newer (not as aged) than that prior to the transition. It is likely that this situation existed in the second leader as well. 4,3.1 Results Flash 2541487 . Source locations during flash 2541487 are shown in Figure 4.18. This flash occurred at 20:20:11 on 10 September 1992, 16 km SW of the central recording site. The flash consisted of 25 records comprising 4 strokes in 141 ms. The earliest sources were located 5.5 km high and are indicated as “O” in Figure 4.18.

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108 Figure 4.18. dE/dt source locations from flash 2541487.

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109 During the next 3 ms sources spanned 6 records and progressed downward to a height near 4.9 km. The first stroke followed at t = 28.6 ms. The second stroke occurred at t = 74.2 ms, co-located with the first. The second stroke was preceded by the leader whose dE/dt waveform is shown in Figure 4.19. Source locations are represented by “+” in Figure 4.18. The average leader speed decreased from 12 x 10 6 m/s, at its highest point, to 3.0 x 10 6 m/s immediately prior to the return stroke. Median interpulse intervals (20 %) increased from 1.1 ps to 2.9 ps. The third stroke of the flash occurred at t = 107.8 ms and was preceded by a leader lasting 1 . 1 ms. The dE/dt waveform of the third leader is shown in Figure 4.20. Notice that pulses appear somewhat regularly during the first four records of the leader but become less regular and more frequent, 180 ps prior to the return stroke. Sources from the beginning of the third leader (record 19) were located 6 km high, near the earliest sources in the flash, those preceding the first stroke. Source locations, shown as in Figure 4.18, progressed downward at 2.0 5.0 x 10 6 m/s during the first 0.7 ms of the leader, spanning four records, to a height of 3.6 km. After the end of record 22 the leader increased in speed to 20 x 10 6 m/s and went to ground, resulting in the third stroke, co-located with strokes one and two. The change in speed was accompanied by a change in the interpulse interval, which can be seen in record 23 (Figure 4.20). Several sources during the final 180 ps of the leader, were located in the lowest part of the channel to ground, coincident with those from the second leader, and also along a small branch, about 2 km high, that was active during the second leader. Note that the third leader was not coincident with the second leader above 3.6 km, that is, it rejoined an old channel during record 23. The fourth stroke in the flash occurred at t =

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110 IP/HP Figure 4. 19. dE/dt trace of the second leader of flash 2541487.

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Ill 1P/3P Figure 4.20. dE/dt trace of the third leader of flash 2541487.

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112 141 ms and was co-located with the first three in the flash. This was the 25 th and final record of the flash. Flash 2541323 . Unfortunately the beginning of flash 2541323, which occurred at 20:13:32 on day 254, was missed. Stroke orders were not available for this reason, but the leader waveform was of particular interest and was analyzed disregarding the lack of knowledge of all details of the flash development. The flash was located 23.8 km SSW of the central recording site. The first sources recorded in the flash were those from a subsequent leader. The leader was determined to be subsequent based on the lack of fine structure in the following return stroke waveform. The dE/dt waveform of the leader is shown in Figure 4.21. Notice the similarity of records 4 and 5 to record 23 of Figure 4.20. The first two records of the leader were characterized by pulses at regular intervals. Pulses in the final two records became less regular and more frequent, similar to the beginning of the leaders in section 4.2. Note in particular that the transition occurred within the second record and is remarkable. Source locations in the first two records progressed downward from 6.2 km high to near 5 km at an average speed of 3.0 x 10 6 m/s. Near the end of record 3 the leader increased in speed to 16 x 10 6 m/s and traveled to ground, resulting in a subsequent return stroke 400 (is later. The transition point is readily discernable in Figure 4.22 showing the profile of the leader development. Two sources were located near the end of the second record, after the transition, and form a “break point” in the leader profile. The median interpulse interval vs. threshold curve for the leader of flash 2541323 is shown in Figure 4.23. The median interval, at a 20 % threshold, for records two and three of the leader was 9.7 (is and 1 1.2 (is respectively. At the same threshold, intervals

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113 IP/HP Figure 4.21. dE/dt trace of a subsequent leader in flash 2541323. Time from beginning of flash not available.

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114 t Figure 4.22. Profile of subsequent leader development of flash 25401323.

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115 Threshold (percentage of largest pulse) Figure 4.23. Median interpulse interval vs. threshold for the subsequent leader of flash 2541323.

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116 decreased to 2.0 (is and 2.7 (is during records four and five respectively, that is, after the leader increased in speed from 3.0 x 10 6 m/s to 16 x 10 6 m/s. This leader was similar to the third of flash 2541487; both exhibited a marked increase in forward speed and a corresponding decrease in interpulse interval. These results are consistent with our findings in section 4.2, namely, that higher leader speeds were associated with shorter interpulse intervals. 4.3.2 Discussion In section 4.2 we presented a class of leaders that exhibited a decrease in speed as ground was approached. These findings were consistent with those of Schonland [1956], who found no subsequent leaders to increase in speed towards ground. Orville and Idone [1982] noted 4 of 16 dart-leaders increased in speed towards earth and one dart-stepped leader that did so. The increase in speed they observed was a factor of two in each case and may have resulted from a 2-dimensional recording of the leaders. The third leader in flash 2541487 of this section showed an increase in speed from 2.0 5.0 x 10 6 m/s to 20 x 10 6 m/s. This increase was much larger than that noted by Orville and Idone [1982] and was accompanied by a change in the overall dE/dt waveform near a height of 3.6 km (Figure 4.20). The first four records of the leader were characterized by median interpulse intervals, at the 20 % threshold, between 2.8 and 7.0 ps. During the final record, the average speed increased to 20 x 10 6 m/s while the median interpulse interval decreased to 1.1 ps. The decrease in the median interval and increase in speed are consistent with the observations in section 4.2, namely, leaders exhibiting higher speeds were associated with smaller median intervals than slower leaders. The subsequent

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117 leader of flash 2541323 increased in speed by a factor of 5. Here the change in the overall leader waveform occurred within a record and can be easily seen in the second trace from the top in Figure 4.21. Prior to the change in waveform the median interpulse interval was between 9.7 ps and 11.2 ps. After the transition the median interpulse interval was reduced to between 2.0 ps and 2.7 ps. These results are also consistent with our previous findings of leaders at higher speeds being associated with shorter median interpulse intervals. The two leaders in this section differed from those in section 4.2, each showing an increase in speed and decrease in interpulse interval with time. The reason for the increase in speed can be found by examination of flash 2541487. Consider again Figure 4. 18 showing dE/dt source locations of this flash. The first three milliseconds of the flash consisted of sources (shown as “O”) which progressed downward from 5.5 km to 4.9 km. No trigger records were received by our system during the next 25.6 ms, at which time the first stroke was recorded. It is likely that a stepped leader formed the channel to ground (see 2 nd and 3 rd leader locations) during this time with dE/dt pulse amplitudes below our triggering threshold. Sources associated with the second leader (shown as “+” in Figure 4.18), began at t = 73.5 ms and were located from near 4 km to ground. It appears that we recorded the entire leader (see Figure 4.19). Sources at the start of the third leader (shown as in Figure 4.18), at t = 106.9 ms, were located near 6 km high, above those of the second leader, and coincident with source locations prior to the first stroke. During the first 0.9 ms of the third leader, sources retraced locations that preceded the first stroke, but not the second, and extended downward to 3.6 km at an average speed of 3.0 x 10 6 m/s. At this point the leader increased in speed to 20 x 10 6

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118 m/s. Several source locations after the increase in speed were found to be in the channel followed by the second leader, between ground and 2 1cm high, indicating the third leader followed the main channel to ground. It appears that the third leader, at the end of record 22, joined the channel followed by the second leader. Upon reaching the region near the start of the second leader, active only 33 ms earlier, the third leader increased in speed by more than a factor of six. We argue that the section of channel traversed by the second leader had not decayed to the extent as that above it, and thus had a higher conductivity resulting in the observed increase in speed of the third leader. In making this argument we have assumed that no other sources were active in the channel above 4 km, during the time between sources prior to the first stroke and those at the start of the third leader. Figure 4.19 indicates that no sources associated with the second leader were missed and that it began near 4 km high. While it is possible that we could have failed to trigger on small pulses originating from heights of 4 6 km occurring between the first and second strokes, or second and third strokes, the observation that leader speed was much smaller in this section tends to corroborate our conclusion that the second leader did indeed begin at 4 km and not higher. The increase in speed of the subsequent leader of flash 2541323 (see Figure 4.21) may have resulted from a similar scenario, although proof is lacking since locations of sources prior to this leader were not available. 4,3,3 Conclusions Two subsequent leaders were found to increase in speed by a factor of 5 10 during their descent. The increase in speed was accompanied by a decrease in median interpulse interval, consistent with the inverse relationship between average leader speed and

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119 median interpulse interval observed in the leaders of section 4.2. In one leader we found evidence of the increase in leader speed resulted from joining a newer (less aged) section of channel. A similar situation likely caused the increase in speed observed in the other leader. The role that the channel age plays in determining the electric field waveform of the following leader is explored in section 4.5. 4,4 Pulse Trains Present After Return Stroke Waveforms DE/dt radiation from subsequent leaders in this study usually ceased at the time of the return stroke. We have noted three cases where regularly occurring pulses were present prior to and some tens of microseconds after, the return stroke peak. Locations of pulses that arrived after the return stroke peak originated from several kilometers high, often near earlier sources of the channel to ground. Further investigation shows that pulses from similar locations were also present tens of microseconds prior to the return stroke, simultaneous to sources from the channel near ground. 4,4,1 Results Flash 2541323 . The subsequent leader of flash 2541323 was presented in section 4.3 as illustrative of a leader showing an increase in speed towards ground. The leader waveform was shown in Figure 4.21. Several dE/dt pulses can be seen up to 15 ps after the return stroke. The leader/retum stroke waveform at stations 2 5 is expanded in Figure 4.24. Timing offsets have been removed so that the return stroke peaks are aligned. Two sets of pulse alignments can be seen in this figure. The first is pulses whose sources are from the lowest part of the channel to ground. These share a common alignment with the return stroke peak and were broad, a result of conductivity effects

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dE/dt 120 Figure 4.24. Expanded time view of the subsequent leader of flash 2541323 at four stations. The small pulses marked before the return stroke share the same alignment with those occuring afterwards.

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121 over a finitely conducting ground ( Cooray and Lundquist, 1983; Le Vine et al., 1986; Cooray and Ming, 1994; Honma et al., 1998). Four pulses, occurring up to 15 ps after the return stroke peak, can be seen in Figure 4.24. These pulses had a different alignment than that of the return stroke peak and preceding leader pulses. Sources were located at 2.3 and 3.0 km high, near earlier sources of the leader, and are shown as “+” in Figure 4.25. A pulse that occurred just prior to the return stroke, but shared a common alignment with those that occurred after the return stroke, is marked in Figure 4.24. The small amplitude of this pulse made a location impossible, but the alignment suggests it originated near others 2-3 km high. Furthermore, the pulse is very narrow, unlike the other pulses around it, a result of less attenuation over a finitely conducting earth, meaning the pulse likely originated from a greater height. In fact, several other such sources were located tens of microseconds prior to the return stroke, each in the region 2 3 km high, near earlier sources along the channel. These source locations are also represented with “0” in Figure 4.25. Flash 2420760 . Flash 2420760 also exhibited pulses after the return stroke peak. The leader/retum stroke waveform is shown in Figure 4.26. Pulses are aligned with those occurring after the return stroke peak. Pulse sources present for 35 ps after the return stroke peak were located at a height of 1 .7 km. 4,4,2 Discussion Le Vine andKrider [1977] found radiation at 3 MHz from dart leaders often continued up to and through that of the return stroke. Source locations were not available and the origin of sources was unknown. We have shown that for wideband signals regular pulses

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z (km) z (km) 122 Figure 4.25. dE/dt source locations of flash 2541323. Locations of the subsequent leader to ground are shown as "O". Locations of sources prior to and after the return stroke are represented by "+".

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123 cs CO V~l H H H H C/5 C/5 C/5 C/5 (A T3 C o o o on O B • ^ H IP/HP Figure 4.26. dE/dt trace of the second leader/retum-stroke of flash 2420760.

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124 in the dE/dt waveform following subsequent strokes originated from sources several kilometers high, often near earlier regions of the channel to ground. In fact, we found that these sources were also present immediately prior to the return stroke, though more difficult to recognize due to the pulses associated with sources along the channel near ground. Rhodes etal. [1994] found the location of VHF radiation following a subsequent stroke shifted to a higher location, near earlier sources of the channel to ground. No activity was detected in this region prior to the stroke, but Rhodes et al. [1994] suggest it may have been masked by radiation from the channel to ground. The sources after the return stroke were located randomly with time. In our study, sources that occurred simultaneous to, and after the leader reached ground, appeared to progress more slowly than those from the main channel to ground, based upon their locations and the time between pulses. However, it was difficult to distinguish a channel followed by these sources and we were unable to estimate an average speed. 4,4.3 Conclusions Pulses present through the time of the return stroke originated from locations several kilometers high, often near earlier sources along the channel to ground. In one case the pulses ceased 15 ps after the return stroke peak, and in another case the pulses continued for at least 35 ps after the return stroke peak. Pulses that occurred after the return stroke peak in the dE/dt waveform were narrower than those from the channel to ground prior to the return stroke peak, a result of less conductivity effects from a finitely conducting earth. Differences in pulse waveshape were helpful in identifying pulses whose sources were from a region other than that of the leader tip near ground. The movement of these

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125 higher sources appeared to be slower than those along the channel to ground and their direction of progression was difficult to determine. 4,5 Leader Occurrences Schonland et al. [1935] found that higher dart leader speeds were associated with shorter interstroke intervals and slower speeds with longer intervals. Jordan et al. [1992] have shown a negative correlation between leader speed and the previous interstroke interval in natural lightning flashes in Florida. In addition, Winn [1965] found that laboratory sparks, similar to dart leaders, traveled slower along older, less ionized channels. In the current study we reported that subsequent leader speeds were inversely related to the median interpulse interval (see sections 4.2 and 4.3). It follows, therefore, that there may exist a relationship between the leader electric field waveform and the preceding inter-stroke interval. That relationship is the focus of this section. Recall that subsequent leaders in a previous channel, which do not exhibit regular pulses in the electric field waveform, characteristic of a dart-stepped leader, sometimes appear "chaotic" during the tens of microseconds prior to the return stroke [Weidman, 1982], Examples in the current study are seen in Figures 4.8 and 4.20. Weidman [1982], Rakov and Uman [1990b], and Izumi and Willett [1991] have also observed “chaotic” electric fields prior to subsequent strokes. These type of waveforms have typically been excluded from dart-stepped leader analysis in the past [Rakov and Uman, 1990b; Izumi and Willett, 1991], In the cases where the electric field of a subsequent leader/retumstroke is neither stepped nor "chaotic", it appears as a "normal" subsequent stroke [Izumi and Willett, 1991], No statistics such as those on dart-stepped leader occurrence [Rakov

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126 and Uman, 1990b] have been reported in the literature for "chaotic" or "normal" subsequent leaders. 4,5.1 Results Table 4.2 lists the interstroke intervals associated with several types of leaders identified in this study. Leaders that exhibited regular pulses, indicative of a dart-stepped leader, occurred after a geometric mean interstroke interval of 61 ms, prior to 12 second strokes. For dart-stepped leaders we required that pulse amplitudes be at least 20 % of the following return stroke peak. A similar interstroke interval, 77 ms, was found to precede dart-stepped leaders that followed strokes in new terminations (see column 4). Listed first is the order of the leader/retum-stroke in the overall flash sequence. In parentheses is the order of the leader/retum-stroke in the channel in which it occurred. Each leader preceded the second stroke in a channel, similar to those in column one. Seven leaders that exhibited regular pulses in the dE/dt waveform occurred after two or more strokes in the same channel. The interstroke interval preceding these leaders is listed in column five. The geometric mean interstroke interval was 140 ms, roughly twice the intervals found in columns one and four. Again, the first number indicates the order of the leader/retum-stroke in the overall flash sequence while the value in parentheses indicates its order in the channel. Leaders that showed no regular pulses (above 20 % of the return stroke peak) in the dE/dt waveform, e.g. Figures 4.8 and 4.20, occurred after a geometric mean interstroke interval of 23 ms. These intervals are listed in column two and only leaders that preceded second strokes were included for reasons that will be discussed later. Each of these leaders would be identified as either “chaotic”

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127 Table 4.2. Return stroke interval vs. leader characteristic. Leaders were classified as either dart-stepped (D-S), chaotic, or preceding a new termination to ground. All times in milliseconds. Stroke order in flash (stroke order in channel). Geometric mean intervals listed below each column. Second Strokes After NT After 2 RS D-S "Chaotic" New-Term D-S D-S 76 28 170 78 4(2) 107 5(3) 105 16 116 57 4(2) 118 4(3) 57 15 119 94 3(2) 144 3(3) 57 27 132 83 3(2) 117 4(4) 59 31 190 127 5(5) 60 27 68 465 4(4) 54 19 147 85 3(3) 54 19 77 50 25 111 51 32 174 69 28 62 59 19 61 23 117 77 140

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128 or “normal”. Included in the third column of Table 4.2 are the intervals preceding second strokes that occurred in new terminations to ground. Recall that leaders preceding new terminations were initially dart-stepped and later became stepped. These were analyzed in Chapter 3. The geometric mean interstroke interval prior to these leaders was 1 17 ms in 1 1 flashes. Again only leaders preceding the second stroke in a flash were included. We present two flashes to illustrate the relationship between leader characteristics, such as speed and electric field waveform, and the previous interstroke interval. Flash 2540223 Flash 2540223 occurred at 19:25:09 on 10 September, 19 km WSW of the central recording site. The flash comprised 20 records and 5 strokes in 308 ms and no records were missed due to our recording configuration. This flash exhibited several of the leader types listed in Table 4.2. All dE/dt source locations are plotted in Figure 4.27. The first sources in the flash were located 5.9 km high and progressed downward to 5.4 km during the next millisecond. At t = 47.0 ms the first stroke occurred, located at (-16 km, +7.3 km). Twenty-five milliseconds after the first stroke, the second stroke was colocated with the first. No leader was recorded prior to this stroke, save that during the pre-trigger delay. The dE/dt waveforms of the first two strokes are shown in the top two traces of Figure 4.28. Notice that fine structure following the first stroke lasted for longer than 140 ps, consistent with the results of Chapter 3 where the median duration of fine structure associated with first strokes exceeded 141 ps. The third stroke (third trace from the top in Figure 4.28) occurred in a new termination to ground at t = 144.0 ms and was located at (-16 km, +10.5 km), three kilometers directly north of the first two strokes.

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z (km) z (km) 129 X (km) Figure 4.27. Source locations of flash 2540223. First two strokes in same channel. Third stroke formed a new termination to ground. Fourth and fifth strokes in same channel as third stroke.

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130 M M Xfl E E E E E © VO VO VO r-' iri co o' K © o CN Cl IP/HP Figure 4.28. dE/dt waveform for the five return strokes of flash 2540223. Time from the beginning of flash is indicated to the right of each trace. Strokes 1 and 2 were in the same channel. Stroke 3 created a new termination to ground. Strokes 4 and 5 occurred in the new termination.

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131 Notice that fine structure lasted only 65 ns after the third stroke, indicative of a stroke in a new termination to ground that was preceded by a leader of the type described in Chapter 3. The fourth stroke (fourth trace from the top in Figure 4.28) occurred at t = 201.0 ms, or 57 ms after the third, and was co-located with the third stroke, that is, in the channel of the new termination. The entire dE/dt waveform of the fourth leader is shown in Figure 4.29. It appears that we missed the first dE/dt sources from the leader. The first sources we located were 4.2 km high. The leader speed was 12 x 10 6 m/s during the record 12, slowing to 6.7 x 10 6 m/s and 6.1 x 10 6 m/s during records 13 and 14 respectively. During the final record, 15, the leader speed was estimated to be 7 x 10 6 m/s. The overall leader duration exceeded 0.9 ms. The fifth stroke in the flash occurred at t = 308.0 ms and was preceded by the leader shown in Figure 4.30. This leader lasted 0.75 ms, shorter than that of the fourth leader, and was recorded in its entirety. The earliest leader sources were located 5.5 km high, 1.3 km above the earliest locations associated with the fourth leader. Source locations from 4.2 km to ground retraced those of the fourth leader. The fifth leader exhibited a speed of 14 x 10 6 m/s during record 17, and slowed down to 8.6 x 10 6 m/s, 7.8 x 10 6 m/s, and 6.2 x 10 6 m/s during records 18 20, respectively. Flash 2420289 This flash occurred at 17:00:04 on 29 August, 26 km SSW of the central recording site. The flash comprised 25 records in 97 ms, and it is possible that some activity was missed due to digitizer memory constraints. Five strokes, occurring in the same channel, were co-located during the flash. Source locations are shown in Figure 4.31. Sources prior to the first stroke are shown as “O” and were located beginning at a height of 5 km.

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132 CN co £ Cl CO £ 1^ CO £ in CO E % CN =tfc =tfc =tfc ON O o' o o' o o' O o' o CN <2 o CN o CN o CN IP/HP Figure 4.29. dE/dt waveform of the leader preceding the 4th stroke of flash 2540223. Time from the beginning of the flash is indicated to the right of each trace.

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133 t" 1-H C to £ 00 (A £ 0 \ C/5 £ o
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134 1 1 1 1 6 ° a o 0 f 4 o° o N o _° W* O & °4°o° ° 2 0 2k o 0 $
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135 During the next eight milliseconds source locations progressed downward, at an average speed of 6 x 10 5 m/s, terminating in the first return stroke at t = 8.0 ms. These sources were most likely associated with the stepped leader. The average speed is at the high end of observed stepped leader speeds, but not unreasonable (Schonland, 1956; Orville and Idone, 1982; Thomson et al., 1985). Fine structure in the dE/dt waveform followed the first stroke for at least 150 ps. The second stroke occurred at t = 34.4 ms and the leader/retum-stroke waveform is shown in the top two traces of Figure 4.32. The duration of the leader was 200 ps and sources were located along the channel to ground established by the first leader/retum-stroke. The average speed of the second leader was estimated at 32 x 10 6 m/s. This is at the upper end of observed dart-stepped speeds, but is similar to the value we found at the beginning of leaders in section 4.2. Note also the similarity in the waveform of the third leader to those in section 4.2 (see Figure 4.2 e.g.). The third stroke occurred at t = 56.3 ms and its leader/retum-stroke waveform is shown in the third trace from the top in Figure 4.32. This leader would be considered “chaotic”. Unfortunately, no locations were obtained during the leader itself. The fourth stroke occurred at t = 71.4 ms and was preceded by a leader lasting 130 ps. This is the shortest leader duration we have found in our data set thus far. The leader/retum-stroke waveform is shown in the fourth trace from the top in Figure 4.32. Leader sources were located starting at 6.8 km high and along the channel to ground. The estimated speed of the fifth leader was 50 x 10 6 m/s, the highest of any in this study. The fifth stroke occurred at t = 96.8 ms and its waveform is shown in the bottom trace of Figure 4.32.

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136 IP/HP

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137 4.5.2 Discussion Jordan et al. [1992] found that leader speed was negatively correlated to the previous interstroke interval. This was in agreement with earlier results of Schonland et al. [1935] and Winn [1965]. We have identified several types of leader electric field waveforms in the current study and found that these appear to be related to the previous interstroke interval. Leaders associated with “chaotic” electric fields occurred after a geometric mean interval of 23 ms prior to 12 second strokes. Examples of this type of leader waveform can be seen in Figure 4.28 (second trace from the top). Figure 4.32 (strokes 25) as well as Figure 4.8. Locations, and hence average speeds, were unavailable for most of the twelve “chaotic” leaders in the second column of Table 4.2 because either (1) pulses were difficult to align, or (2) only a small duration (tens of microseconds) of the leader waveform was recorded on some channels. However, two exceptions occurred in flash 2420289. The leader/retum-stroke sequences for strokes two and four (see Figure 4.32) provided a sufficient number of locations so that an average speed could be obtained for each leader. The average speeds of these two leaders were 32 x 10 6 m/s and 50 x 10 6 m/s respectively. These are the highest speeds of the current study and higher than those usually associated with dart-stepped leaders, and are consistent with those of dart leaders. These two leaders occurred after intervals of 26 ms and 16 ms respectively, relatively short interstroke intervals. Rakov and Uman [1990b] found a geometric mean interstroke interval of 60 ms for all 270 strokes in their study. Thomson et al. [1984] found a similar value, 69 ms. Jordan et al. [1992] report a maximum observed speed of 49 x 10 6 m/s for leaders that followed interstroke intervals of 0 30 ms. This is in good agreement with the current findings. Our findings suggest that “chaotic” leaders,

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138 associated with second strokes, occur after short interstroke intervals and are associated with high average speeds. A more extensive analysis is needed to confirm this hypothesis. The reason we limited our previous discussion on chaotic leaders to those associated with second strokes is because of the role that continuing current may play in conditioning the channel. Rakov et al. [1994] have shown that continuing current rarely flows after the first stroke in a flash. Therefore continuing current was unlikely present in any of the cases in the second column of Table 4.2. It is possible in later strokes in a flash that continuing current may occur for tens of milliseconds after a stroke, thus keeping the channel conductive longer so that relatively fast leaders might be associated with long interstroke intervals. In addition, Rakov and Uman [1990b] argue that channel conditioning, i.e. the number of strokes in a channel, will also affect the following leader characteristic. The more strokes that occur in a channel, the better conditioned that channel is, thus increasing the probability that fast subsequent leaders may follow at relatively long intervals, even in the absence of continuing current. Dart-stepped leaders that preceded second strokes occurred after a geometric mean interval of 61 ms, nearly three times the interval preceding “chaotic” leaders. Recall that dart-stepped leader speeds (section 4.2) varied between 1 x 10 6 m/s and 35 x 10 6 m/s. The overall average speed of these leaders was probably near 3 5 x 10 6 m/s, an order of magnitude slower than the two “chaotic” leaders described earlier. This is consistent with slower leader speeds being associated with longer interstroke intervals. Schonland [1956] suggested that a dart-stepped leader might occur after an unduly long inter-stroke interval. However, Rakov and Uman [1990b] found a geometric mean inter-stroke

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139 interval of 54 ms preceding dart-stepped leaders that occurred prior to the second stroke in flashes. This interval was not unduly long compared to the geometric mean interstroke interval of all 270 strokes in their study, 60 ms. We conclude, therefore, that second strokes preceded by a dart-stepped leader do not occur after an “unduly” long interval as suggested by Schonland [1956], but rather, after “typical” intervals, similar to the findings of Rakov and Uman [1990b]. We extend the preceding discussion of dart-stepped leader occurrence to those listed in the fourth column of Table 4.2. Each of the dart-stepped leaders in column four occurred prior to the second stroke in a channel after the creation of a new termination. The geometric mean interstroke interval prior to these strokes was 77 ms, not too different from that found in column one. Even though these leaders were the third or fourth in the overall flash sequence, they behaved similar to those in column one, i.e., they were both the second in a channel. Only four such strokes have been identified in our data set thus far, and more are needed to confirm the above findings. One other occurrence of dart-stepped leaders is noted in Table 4.2. The leaders listed in the fifth column occurred after two or more strokes in a channel. The geometric mean interval preceding these strokes was 140 ms, twice the interval of dart-stepped leaders preceding the second stroke in a flash (column one). We suggest a possible scenario to explain the observed differences. First consider the theory of Rakov and Uman [1990b] that successive strokes condition the channel. Two or more strokes occurring in a channel would be expected to condition that channel better than just one. Perhaps the leaders listed in the first column of Table 4.2, those occurring after just one stroke, occur in a relatively poorly conditioned channel and hence a dart-stepped leader is observed

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140 after a “typical” interstroke interval. The leaders in column five most likely occur in a better conditioned channel, since they occur after 2, 3, or 4 strokes in that channel. Here, “typical” intervals may support a dart leader and a relatively long interstroke interval may be required to produce a dart-stepped leader. In this case, Schonland’s [1956] view of an unduly long interval preceding a dart-stepped leader may have merit. The interval of 465 ms stands out in the fifth column and may have resulted from our failure to record an intervening stroke or the presence of a continuing current after the third stroke in the flash. We consider the latter to be the most likely scenario. 4,5.3 Conclusions Characteristics of subsequent leaders were analyzed with respect to the preceding interstroke interval. Dart-stepped leaders that preceded second strokes occurred after a “typical” interstroke interval of 61 ms while those that occurred after two or more strokes in a channel occurred after an interstroke interval more than twice as long, 140 ms. Channel conditioning was suggested as a possible reason for the difference in the preceding interval. Some subsequent leaders were not dart-stepped and appeared as either “chaotic” or “normal”. These leaders followed an interstroke interval of only 23 ms prior to second strokes. Two such leaders were found to travel at speeds of 32 x 10 6 m/s and 50 x 10 6 m/s, the highest in this study. 4.6 Summary Conclusions Subsequent leaders to ground, that appeared dart-stepped in the tens of microseconds prior to return strokes, were found to decrease in speed towards ground. Seven such leaders began with a mean speed of 16 x 10 6 m/s and decreased to 3 x 10 6 m/s near

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141 ground. During the final record (204.8 ns) of leaders, median interpulse intervals, at a threshold of 20 %, were 4.1 ps. During the first record of leaders, however, interpulse intervals were only 2.6 ps at a similar threshold. There was a negative correlation between average leader speed and median interpulse interval for dart-stepped leaders. This relationship was also true for two leaders that increased in speed when joining a newer section of channel. A “chaotic” or “normal” leader, rather than a dart-stepped leader, preceded some subsequent strokes. These leaders occurred after a relatively short interstroke interval of 23 ms and two leaders were found to exhibit the highest speeds of the current study.

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CHAPTER 5 COMPARISON OF PULSE TRAINS AND PULSE POLARITY REVERSALS 5.1 Introduction We introduce pulse trains that occur in IC discharges. A summary and discussion of characteristics of trains from IC discharges is presented in section 5.2. In section 5.3 we compare average speeds, median interpulse intervals, and average step lengths from pulse trains in each of three categories: ( 1 ) leaders preceding new terminations, ( 2 ) dart-stepped leaders, and (3) pulse trains in IC discharges. The phenomenon of pulse polarity reversal in IC pulse trains is explored in section 5.4. A summary of the chapter findings is given in section 5.5. 5,2 Pulse Trains in Intracloud Discharges Trains of pulses in the electric field waveform from lightning are not limited to cloudto-ground flashes. Krider et al. [1975] found an average of 5 6 (is between electric field pulses in trains from intracloud discharges. Trains of pulses lasted from 100 to 400 |is. Rakov et al. [1996] found that bursts, or trains, of electric field pulses occurred in both intracloud discharges and the intracloud portion of flashes to ground. The average interpulse interval from bursts in six flashes was between 6 . 1 4 s and 7.3 (is. The average duration of bursts was 117-235 tis. Pulse amplitudes often increased initially, and then 142

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143 decreased, in the study of Rakov et al. [1996], In addition, Rakov et al. [1996] noted a tendency for interpulse intervals to increase near the end of a burst. Millisecond-scale ramps, or K-changes, in the electric field from lightning occur during IC discharges and the intracloud portion of cloud-to-ground discharges ( Kitagawa and Brook, 1960; Kitagawa et al., 1962; Ogawa and Brook, 1964; Thottappillil et al., 1990; Rakov et al., 1996). Krider et al. [1975] hypothesized that the regular bursts of pulses observed in the electric field waveform of cloud discharges were related to Kchanges. Indeed, Rakov et al. [1996] found many pulse bursts occurred during electric field ramps characteristic of K-changes. Ogawa and Brook [1964] suggested that Kchanges were associated with dart like streamers travelling near speeds of 2 x 10 6 m/s. Shao et al. [1995] report speeds of K-processes between 10 6 and 10 7 m/s, similar to speeds of dart and dart-stepped leaders. Furthermore, the bursts recorded by Rakov et al. [1996] and Krider et al. [1975] occurred during the latter portion of discharges, supporting the view that they were associated with previously conditioned sections of the lightning channel, similar to dart and dart-stepped leaders. We investigated pulse trains that occurred in 1 1 cloud discharges. Median interpulse intervals and lengths of trains were similar to those of Krider et al. [1975] and Rakov et al. [1996], Using individual source locations, we calculate average speeds of trains in the manner described in Chapter 2. Speeds were 1.2 5.6 x 10 6 m/s, similar to dart-stepped leader speeds near ground ( Schonland ', 1956; Orville and Idone, 1982; this work. Chapter 4). Additionally, the median interpulse interval was nearly independent of threshold, allowing us to determine a “step length” as a measure of the average distance between consecutive pulse sources, assuming that there was no channel extension between steps.

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144 Step lengths were between 7 and 30 m; consistent with the length of photographically measured steps from dart-stepped leaders near ground ( Schonland , 1956; Orville and Idone, 1982). To our knowledge, these are the first estimates of speeds and step lengths from intracloud pulse trains. 5,2,1 Results We analyzed 35 pulse trains, each lasting 100 ps or more, that occurred in 11 cloud discharges. Of these 35 trains, 30 spanned only a single data record (204.8 ps). It is possible that pulses continued after the end of records, with pulse amplitudes being below the trigger threshold of our system. The remaining five trains spanned multiple data records. Unlike trains that occurred in channels to ground (Chapters 3 and 4), those in cloud discharges were difficult to place in context of the overall flash since there was no distinguishing event, such as the return stroke in a cloud-to-ground discharge, to serve as a reference. In addition, the gaps between our data records, due to the configuration of our recording system, made delineation of the flash structure very difficult. We chose, therefore, to focus on characteristics of pulse trains such as average speed, median interpulse interval, and the average step length defined here as the distance between consecutive pulse sources. A summary of the features of 35 IC pulse trains is presented in Table 5.1. Trains that spanned multiple records are in italics. Median interpulse intervals varied from 2.1 ps to 12.6 ps at a 30 % threshold, with a mean value of 5.3 ps. At a threshold of 20 %, the mean value of the median interpulse interval was 5.1 ps, not very different from its value at a 30 % threshold. In fact, the median interpulse interval varied little with threshold, in

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145 Table 5.1. Summary of intracloud pulse trains Flash Record Speed/10 6 % Error AT(30% AT(20%) As (30 %) Height ID # m/s m/s ps ps m (km) 2541375 17 1.6 29 3.9 X 7.1 5.5 19 1.4 16 7.65 6.95 11.5 6.2 20 3.4 9 4.63 4.65 15 6.9 21 1.9 16 4.35 X 9 5.5 24 1.2 24 3.18 X 6.7 6.4 2541378 10 2.5 8 6.75 7.15 14.6 7.4 11 2.0 68 4.88 4.88 8.9 6.5 12 2.5 15 3.48 3.4 9.2 6.5 15 2.3 11 3.85 3.58 10.6 6.7 24 3.3 28 4 3.4 13.8 7.0 2541813 9 4.8 5 4 3.58 20.5 6.5 11 3.6 5 4.03 3.95 14.6 6.6 12 2.8 19 X 5.38 X 6.2 2541949 6 2.4 25 3.2 2.9 8 6.5 9 5.4 31 3.35 2.7 20.4 6.8 10 5.6 19 3.23 3.05 18.5 6.5 12 2.2 13 7.45 6.13 16.1 7.0 2541173 10 1.5 48 4.58 5.2 11.3 6.0 14 3.9 12 5.25 5.28 21 7.6 IS 2.5 45 8.6 8.63 17.5 7.3 20 3.5 25 3.95 3.8 14.9 6.6 23/24 2.1 9 12.55 8.5 20.7 7.5 2541979 4 4.7 27 4.7 4.73 20 7.1 17 1.3 26 9.3 5.95 10.1 6.9 19 1.9 16 7.15 3.55 15 7.8 20 2.5 7 4.03 3.9 11.9 6.6 2541581 6 2.4 12 4 4.15 9 6.1 11 2.6 15 5.35 5.2 13.1 6.2 2541363 7a 5.4 28 2.13 2.13 12.7 7.2 7b 2.2 18 5.65 5.65 12 7.1 8 2.9 14 6.05 5.85 16.1 8.2 9 1.8 38 10.6 9.65 25.6 7.9 2442822 8 2.5 33 3.58 3.58 8 6.4 15 2.2 29 4.93 4.4 11.6 6.9 17 2.3 32 8.2 7.03 17.2 7.2 21 2.7 7 10.8 7.9 30.2 7.5 2541931 3 2.5 23 5.75 5.8 15.4 8.2 11 2.4 24 3.55 3.55 10.5 7.1 2541361 20 2.6 8 4.6 4.6 11 5.8 24 2.5 13 6.6 6.58 17.9 6.5 Mean 2.7 5.3 5.1 14 6.8

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146 contrast to our earlier findings for pulse intervals in the waveforms of dart-stepped leaders (Chapter 4). These values, 5.1 and 5.3 ps are similar to the average intervals of Krider et al. [1975] and Rakov et al. [1996]. The average speed was calculated in the manner described in Chapter 2, an average value found for each record (204.8 ps). Average speeds were 1.2 5.6 x 10 6 m/s with a mean value of 2.7 x 10 6 m/s. Multiplying the average speed of a train of pulses by its duration and dividing by the number of dE/dt crossings yields an estimate of the distance between consecutive pulse sources. We call this estimate the average step length. The number of dE/dt crossings was found using a 30 % threshold. Step lengths were 7 30 m with a mean of 14 m. We observed trains comprised entirely of pulses of positive polarity at all five stations as well as trains comprised of pulses of negative polarity. In addition, we recorded several trains with different polarities at different stations. We also noted both positive and negative polarity pulses in the dE/dt trace at a single station, similar to the observation of Rakov et al. [1996], A discussion of pulse polarities is reserved for section 5.4 of this chapter. Several examples of pulse trains that occurred in IC discharges are presented next. Flash 2541363 The dE/dt waveforms of two trains in flash 2541363 are illustrated in Figure 5.1. Records 8 and 9 were triggered consecutively (30 ps gap) and were considered one train. Sources were located 9 km west of the central recording site and are shown in Figure 5.2. Movement of sources was in the direction of the arrow shown. The average speed during record 7 was computed in two segments, designated a and b in Figure 5.1. The average speed over segment a, lasting 33 ps, was 5.4 x 10 6 ± 1.5 x 10 6 m/s, while that over

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dE/dt 147 Figure 5.1. dE/dt traces of two pulse trains in flash 2541363. Records 8 and 9 were triggered consecutively and were considered one train.

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148 Y (km) Figure 5.2. dE/dt source locations of flash 2541363.

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149 segment b, lasting 92 ps, was 2.2 x 10 6 ± 0.39 x 10 6 m/s. The average speeds determined from records 8 and 9 were 2.9 x 10 6 ± 0.42 x 10 6 m/s and 1.8 x 10 6 ± 0.69 x 10 6 m/s respectively. A graph depicting the median interpulse interval as a function of threshold is shown in Figure 5.3. Two curves, corresponding to segments a and b in Figure 5.1, are displayed for the train in record 7. Note particularly the lack of dependence of median interpulse interval on threshold for the curves corresponding to records 7 and 8 of the flash. This is in stark contrast to the dependence seen in the dart-stepped leaders of Chapter 4. Also notice that section a of record 7 had a median interpulse interval less than half that of section b, while its speed was more than twice as great. The average distance between dE/dt sources, or “step length”, over section a of record 7 was 12.8 m. A similar step length, 12.0 m, was found for section b. Thus the average step length remained nearly constant while the median interpulse interval increased by a factor of 2.5 and the average speed decreased by a like amount. Records 8 and 9 had average step lengths of 16.1 m and 25.6 m respectively. Flash 2541813 The dE/dt waveforms of two trains that occurred in the same channel 53 ms apart in flash 2541813 are shown in Figure 5.4. Records 11 and 12 were triggered consecutively and comprised a single train. Sources were located 10.6 km NW of the central recording site and are shown in Figure 5.5. Sources from the second train, “+”, retrace those of the first, “O”, except for a cluster near (-8.0, 7.5, 6.2) km. The average speed during record 9 was 4.8 x 10 6 ± 0.24 x 10 6 m/s. The average speeds of records 11 and 12 were 3.6 x 10 6 ±0.18 x 10 6 m/s and 2.8 x 10 6 ± 0.53 x 10 6 m/s respectively. A plot of the median

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150 Figure 5.3. Median interpulse interval vs threshold for the pulse trains of flash 2541363. Threshold ranges from 4 standard deviations above the noise level to 50 % of the largest dE/dt pulse in each train.

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dE/dt 151 4 _L Rec # 9 Rec# 11 Rec # 12 50 100 Time in microseconds 150 200 Figure 5.4. dE/dt traces of two pulse trains of flash 2541813. Records 1 1 and 12 were triggered consecutively and were considered one train.

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Z (km) Z (km) 152 8.4 8.2 -8 7.8 7.6 7.4 7.2 -7 X (km) Figure 5.5. dE/dt source locations for sources of records 9, 1 1, and 12 of flash 2541813. Sources of record 9 shown as "O", and those of records 1 1 and 12 as "+".

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153 interpulse interval vs. threshold is presented in Figure 5.6. Again, the median interpulse interval was nearly independent of threshold. Notice that between records 11 and 12 there was a decrease in speed accompanied by an increase in median interpulse interval, consistent with the relationship between leader speed and median interpulse interval we found for the dart-stepped leaders of Chapter 4. Average step lengths were 20.6 m and 15.6 m respectively for records 9 and 11. No step length was estimated for the train in record 12 since there were fewer than 5 crossings at a threshold of 30 %. Flash2541361 The dE/dt waveforms from two trains in flash 2541361 are shown in Figure 5.7. These trains differed from those in the first two flashes of this section because they were comprised of pulses of opposite polarity to those in Figures 5.1 and 5.4. In addition, the vertical component of source to source progression was upward. In other respects, the two trains were similar to those already presented. The speeds during records 20 and 24 were 2.6 x 10 6 ± 0.2 x 10 6 m/s and 2.5 x 10 6 ± 0.3 x 10 6 m/s respectively. Figure 5.8 shows a plot of median interpulse interval vs. threshold for each of the trains. Again, there was little dependence of interval on threshold. Step lengths were 11m and 18 m respectively for records 20 and 24. 5,2.2. Discussion The median interpulse interval from IC discharges was 5.1 ps at a 20 % threshold and 5.3 ps at a 30 % threshold respectively. These intervals are similar to the intervals between pulses in the electric field from IC pulse trains found by Krider et al. [1975] and

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154 Figure 5.6. Median interpulse interval vs. threshold for the trains of flash 2541813. Threshold ranges from 4 standard deviations above the noise level to 50 % of the largest dE/dt pulse in each train.

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dE/dt 155 Rec # 20 Rec # 24 Figure 5.7. dE/dt trace of two trains of flash 2541361.

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156 Figure 5.8. Median interpulse interval vs. threshold for trains of flash 2541361. Threshold ranges from 4 standard deviations above the noise level to 50 % of the largest dE/dt pulse.

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157 Rakov et al. [1996], Rakov et al. [1996] noted a tendency for pulse intervals to increase throughout a sequence. The first train of flash 2541363 illustrates this tendency. Note again record 7 in the top trace of Figure 5.1. Figure 5.9 summarizes the change in pulse interval with time. The first few pulses, at the beginning of the train, occur less than 2 ps apart. The time between pulses increases with time, approaching 6 ps near the end of the record. While not all IC pulse trains exhibited such an increase in interval with time, none showed a decrease in interpulse interval with time. The increase was most notable near the beginning of a train, such as record 7 of flash 2541363 (Figure 5.1), but was seen to a lesser degree in the latter portions of trains as well. Take for example record 1 1 of flash 2541813 (Figure 5.4). A plot of pulse interval vs. pulse number is shown in Figure 5.10 for record 11. There was a tendency for intervals to increase throughout the record. Notice that the smallest interval is near 3 ps. Intervals smaller than this were typically associated with the beginning of trains, such as in the top trace of Figure 5.1. In this respect, IC pulse trains were similar to dart-stepped leaders, in which the shortest intervals also occurred near the beginning of the leader. Krider et al. [1977] noted that pulse amplitudes often decreased during a sequence. Rakov et al. [1996], however, found that individual pulse amplitudes showed a tendency to first increase and then decrease throughout a sequence. Rakov et al. [1996] suggested the beginning of trains recorded by Krider et al. [1975] consisted of pulses with amplitudes that were too small to trigger their system, resulting in their missing the beginning of trains. We find variations in dE/dt pulse amplitudes during bursts. The train in record 7 of flash 2541363 (Figure 5.1) is an example of one that first increased in amplitude and then decreased. The beginning of the train was characterized by small

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158 c/i TD C o o
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159 Pulse number Figure 5.10. Interpulse interval vs. pulse number in record 1 1 of flash 2541813. A 20 % threshold was used to determine pulse intervals.

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160 pulses, separated by about 2 ps. Pulse amplitudes increased with time, as did the time between pulses, with pulse amplitudes again becoming smaller near the end of the record. Pulse amplitudes in record 9 of flash 2541813 (Figure 5.4) showed a clear tendency to become smaller towards the end of the record. We missed the beginning of this train and as a result, it appears like many of the trains of Krider et al. [1975], Pulse amplitudes of records 11 and 12 (comprising a single train) of flash 2541813 (Figure 5.4) exhibit several fluctuations in amplitude before decreasing near the end of the train in record 12. No further analysis of pulse amplitude is undertaken at this point because pulse amplitudes were found to be sensitive to channel orientation (see Figure 5.31 e.g.). Speeds of IC pulse trains ranged from 1.0 5.6 x 10 6 m/s with a mean value of 2.7 x 10 6 m/s. These speeds are similar to speeds of K-processes, 10 6 10 7 m/s, measured by Rhodes et al. [1994] and Shao et al. [1995], Unfortunately we lacked slow field records necessary to detect whether K-changes accompanied pulse trains. However, it is likely that some of the pulse trains were associated with K-changes as suggested by Krider et al. [1975] and confirmed by Rakov et al. [1996], Krider et al. [1975] also hypothesized that intracloud pulse trains were the result of an intracloud dart-stepped leader process. We find some evidence to support this theory. In addition to the fact that pulse intervals were similar to those of dart-stepped leaders near ground, speeds of IC pulse trains were in good agreement with those of dart-stepped leaders near ground (e.g. Schonland, 1956; Orville and Idone, 1982). Further evidence in support of this hypothesis can be found by examining flash 2541813. Recall Figure 5.5 showing the locations of sources from two pulse trains separated by 53 ms. Locations of sources in record 1 1 (“+”) retraced those in record 9 (“O”). Thus, pulse sources from the second train followed a previous channel,

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161 analogous to a dart-stepped leader that follows an existing channel to ground. Krider et al. [1975] and Rakov et al. [1996] also found IC trains to occur in the latter portion of discharges, suggesting the trains were associated with processes in old channels rather than with new breakdown. However, there were some differences between IC trains and dart-stepped leaders in our study and these are discussed in section 5.3. Since the median interpulse interval was nearly independent of threshold (see Figures 5.3, 5.6, 5.8), we found it convenient to define an average step length between consecutive pulse sources. Average step lengths were 7 — 30 meters with a mean value of 14 m. To our knowledge, these are the first reports of the average step length between pulse sources of intracloud pulse trains. Step lengths are consistent with those from dartstepped leaders near ground found by Schonland [1956], 7 25 m, and Orville and Idone [1982], 10 30 m. To see if there was any correlation between average step length and interpulse interval we plot the two quantities against each other in Figure 5.11. Each point on the graph represents measurements over a portion of a single record listed in Table 5.1. With the exception of record 7 of flash 2541363, pulse intervals were fairly constant during the portion of the record used to determine average step length. Median interpulse intervals were calculated using a threshold of 20 %. There appears to be some correlation between average step length and median interpulse interval, although there is a lot of scatter on the plot. We also investigated average step length vs. average speed. This relationship is shown in Figure 5.12. Correlation was worse than in Figure 5.11 (step length vs. median interpulse interval). An interesting relationship between average step length and interpulse interval is found in flash 2541363 (Figure 5.1). Recall that the train of record 7 was divided into two sections, a and b. The median interpulse interval

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162 J5 I C/3 V 00 cd c
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163 (s/ui) 9 oix paadg J3 s hJ cx
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164 increased by a factor of 2.5 from section a to b, and was accompanied by a corresponding decrease in speed by a factor of 2.5. Thus the average step length remained nearly constant at 12 13 m while both the average speed and median interpulse interval changed. The tendency for intervals to increase during a sequence suggests it might be instructive to investigate the relationship between pulse interval and average step length within individual trains to determine whether the step length remains nearly constant, as in flash 2541363, or changes over the course of the train. The determination is best made from the beginning of the train where pulses occur more frequently, and speeds are greater, thus allowing measurable changes in these quantities during a sequence. Unfortunately, we missed the beginning of most trains in Table 5.1 and more data must be obtained before a thorough study can be attempted. The existing data set may be sufficient for this once more flashes are analyzed for these features. The median interpulse interval during the trains in Table 5.1 did not decrease during any train, and often increased (see e.g. Figures 5.1, 5.9 and 5.10). All of the trains that spanned two records showed an increase in median interpulse interval across records. Conversely, no train exhibited an increase in speed while some were observed to decrease. Three of the four trains that spanned more than one record decreased in speed between consecutive records, the speed of the fourth remained essentially constant. Also, recall that the train in record 7 of flash 2541363 (Figure 5.1) decreased in speed while the median interpulse interval increased. Individual IC trains therefore exhibit an inverse relationship between average speed and median interpulse interval, similar to the dartstepped leaders of Chapter 4. A plot of median interpulse interval vs. speed for records in Table 5. 1 is shown in Figure 5.13. There appears to be a tendency for higher speeds to be

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10.0 165 [(s/ui 9 oix) psads] Soi

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166 associated with shorter interpulse intervals, although the correlation was worse than that associated with records of dart-stepped leaders (Figure 4.16), 0.28 compared to 0.53. 5.2.3 Conclusions Intracloud pulse trains were characterized by median interpulse intervals, average speeds, and average step lengths similar to those found in dart-stepped leaders near ground, supporting the hypothesis of Krider et al. [1975] that IC pulse trains are associated with an intracloud dart-stepped leader process. In one case we found sources to retrace locations active in a previous train, similar to the retracing of the channel to ground of dart-stepped leaders and leaders preceding new terminations. We have discussed, individually, trains of electric field pulses from (1) dart-stepped leaders (chapter 4), (2) leaders preceding new terminations (chapter 3), and (3) intracloud discharges. We now turn to a discussion of a comparison of some of the properties associated with each. We find that, despite similarities, several important differences do exist. These are explored in the next section. 5,3 Pulse Train Comparison Similarities in interpulse interval and average speed exist among the pulse trains described above. The time between electric field pulses from dart-stepped leaders are similar to the interval between pulses of intracloud pulse trains ( Krider et al., 1975; Krider et al., 1977, Rakov et al., 1996). In addition to similarities in the electric field signatures, there are reports of similar speeds for dart leaders and K-processes. Rhodes et al. [1994] found essentially no difference between dart leaders and K-processes, except

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167 the former had enough energy to reach ground. Shao et al. [1995] found speeds between 1 2 x 10 6 m/s and 2 4 x 10 7 m/s for dart leaders and K-processes. Additionally, Rhodes et al. [1994] and Shao et al. [1995] found that at VHF attempted leaders (those following a previous channel to ground but not reaching ground) often produced Kchange type fields and traveled at speeds similar to K-processes. They postulated that except for their greater extent, attempted leaders were similar to K-processes. Shao et al. [1995] argued that at VHF, dart leaders, attempted leaders, and K-changes are one in the same process. From the previous discussion and the results of Chapter 3, 4 and section 5.2, it follows that similarities exist between the three types of pulse trains we have identified. In this section we compare characteristics such as average speed and median interpulse interval for trains in each category. Among the similarities we find are a non-increase in speed and a tendency for pulse intervals to increase during a sequence. Some differences are noted as well, namely speeds at the beginning of trains, speeds and pulse intervals at common heights in channels to ground, and the dependence of pulse interval on threshold. 5.3.1 Average Speeds Krider et al. [1975] suggested that intracloud pulse trains were the result of an intracloud dart-stepped leader type process. Indeed, in section 5.2, we found that average speeds of intracloud trains were similar to those of dart-stepped leaders near ground. Recall also that the average speeds of leaders preceding new terminations (Chapter 3)

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168 were in good agreement with those of dart-stepped leaders near ground. The mean speed of 40 IC records was 2.7 x 10 6 m/s and the distribution of speeds is shown in Figure 5.14. Similarly, for 82 measurements, comprising seventeen leaders preceding new terminations, the mean speed was 3.1 x 10 6 m/s. The mean speed from 30 records in seven dart-stepped leaders was 8.0 x 10 6 m/s. Speeds of dart-stepped leaders were between 1.4 x 10 6 m/s and 35 x 10 6 m/s. The range of observed speeds was smaller in IC trains and leaders preceding new terminations, 1.2 5.6 x 10 6 m/s and 1.2 12 x 10 6 m/s respectively. The observed minimum speeds from trains in each category were similar, near 1 x 10 6 m/s. Upper limits, however, were quite different, as each dart-stepped leader exhibited a speed in excess of 10 x 10 6 m/s, greater than the speed observed in any record of an IC train and all but two records of leaders preceding a new termination to ground. The high dart-stepped leader speeds are about an order of magnitude greater than those measured near ground by Schonland [1956], but similar to the upper limit of dart-stepped leader speeds measured by Orville and Idone [1982] and dart-leader speeds of Rhodes et al. [1994] and Shao etal. [1995]. Recall that the highest speeds in dart-stepped leaders occurred during the first record (204.8 (j.s), corresponding to the beginning of the dE/dt waveform and the highest source locations of leaders. Consider again Figure 4.14 illustrating dart-stepped leader speed vs. height. In each leader, speed decreased with decreasing height and with time from the beginning of the leader. No leader increased in speed towards ground, except for two that joined old channels (section 4.3). This result was in agreement with the results of Schonland [1956] and Mach and Rust [1997]. A similar analysis for leaders preceding new terminations to ground, see Figure 5.15, shows that while three leaders exhibited an

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169 Figure 5.14. Histogram of speeds during IC records. Mean value shown.

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170 (uni) jqSi9 H Speed (xlO 6 m/s) Figure 5.15. Average speed vs. Height for leaders preceding new terminations.

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171 appreciable decrease in speed with decreasing height, most were nearly constant (within our measurement errors) during the dart-stepped leader phase. This could be a result of our failure to trigger on the start of such leaders, assuming they were similar to those in Figures 4.2 and 4.6. In each of the three leaders that decreased markedly in speed in Figure 5.15, the highest speed occurred during the first leader record. Figure 3.8 shows the dE/dt waveform of one such leader. Notice that even though the beginning of the leader was missed, it appears similar to that early in the dart-stepped leader (see Figure 4.2 e.g ). Only one of seventeen leaders increased in speed towards ground. The increase may be exaggerated since source locations were in the lowest kilometer of the channel were errors were largest. None of the IC trains in Table 5.1 exhibited an increase in speed. In fact, three of four IC trains that spanned multiple records decreased in speed between successive records, the speed of the fourth remained essentially unchanged (see Table 5.1). In addition, a decrease in speed over a short interval was noted during the first train of flash 2541363 (see Figure 5.1). Therefore, average speeds of pulse trains in each category did not increase, and often decreased, with time. Each of the three types of processes identified takes place in a previously ionized channel, similar to a dart leader prior to a subsequent stroke. Schonland [1935, 1956] found that dart leader speeds often decreased towards ground and never increased. All but four of the dart leaders of Orville and Idone [1982] decreased in speed, the increases for the other four (a factor of two) may have been apparent due to the use of a 2-D photograph. Winn [1965] describes luminous ionizing waves, similar to dart leaders, which decrease in velocity when traveling along defunct laboratory spark channels. A decrease in speed for the three processes described is therefore not unexpected.

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172 Shao et al. [1995] found that a change in the apparent conductivity along a channel affected the nature of the radiation of a breakdown event along that channel. They observed several breakdown events (dart leaders, M-components) that joined an earlier section of channel and subsequently increased in intensity at VHF. We found a similar situation to exist in the two subsequent leaders of section 4.3. Each of these leaders exhibited an increase in speed of nearly an order of magnitude. In one case, the leader was confirmed to have joined an earlier channel section, presumably with a higher conductivity, hence, the increase in speed. These are the only cases of measurable increases in speeds of the current study. Comparison of Figures 4.14 and 5.15 shows that dart-stepped leaders and leaders preceding new terminations spanned similar heights in our study. Although both occurred in existing channels to ground, the average speeds of dart-stepped leaders were noticeably faster than leaders preceding new terminations, at heights of 3 6 km. Each of the seven dart-stepped leaders of Table 4. 1 was observed to begin between 3-6 km high with a speed in excess of 10 x 10 6 m/s. Only three of seventeen leaders that preceded new terminations exhibited speeds near 10 x 10 6 m/s. Recall that we did not record the beginning of any leader preceding a new termination and it is possible that these leaders exhibited higher speeds prior to our recording them. We may also assume that if this were the case, these leaders began at greater heights than the dart-stepped leaders in Table 4.1. It is interesting to note that there was a large difference in the age of the channel followed by dart-stepped leaders vs. that followed by leaders preceding new terminations. The seven dart-stepped leaders occurred after a geometric mean interval of 69 ms from the preceding stroke. Seventeen leaders that preceded new terminations to

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173 ground occurred after a geometric mean interval of 119 ms from the preceding stroke, nearly twice as long as the interval preceding dart-stepped leaders. There is evidence for slower leader speeds following longer inter-stroke intervals. Schonland et al. [1935] found lower dart leader speeds with increasing time from the previous stroke and suggested this was a result of a decrease in the channel conductivity with time. Jordan et al. [1992] also found a tendency for lower leader speeds to be associated with longer preceding interstroke intervals. Data of Brook and Kitagawa [published in Winn, 1965] also support this finding. Winn [1965] also found that luminous waves, similar to dart leaders, decreased in velocity with increasing decay time when traveling along a 10 cm spark channel in atmospheric air. For completeness, a plot of average speed vs. height for IC pulse trains is shown in Figure 5.16. There appeared to be no relationship between source heights and average speeds of IC pulse trains. Average source heights from 35 records were between 5.5 km and 8.2 km high. It is interesting to note that this height range corresponds to the negative charge region of the cloud, 6-8 km high, in Florida thunderstorms [Krehbiel et al., 1983], No trains were observed at heights above 8.2 km, heights that might be associated with the positive charge region of the cloud. 5.3,2 Median interpulse intervals The electric field from both dart-stepped leaders and IC trains contain pulses that occur at regular intervals. Krider et al. [1977] found an average of 6.5 ps between electric field pulses of dart-stepped leaders 200 ps prior to return strokes in Florida. Krider et al. [1975] and Rakov et al. [1996] found averages of 6.1 ps and 6 7 ps

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174 oooooooooo o) oo h~' to id m cvi r-' o (uq) jq8p H Figure 5.16. Speed vs. height for IC pulse trains.

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175 respectively, between electric field pulses in IC trains. We have measured the median interpulse interval for waveforms associated with each of the three processes identified. Since the median interpulse interval for dart-stepped leaders was dependent on threshold, we chose one threshold, 20 %, at which to compare intervals. We chose 20 % because at this threshold there appeared to be a one-to-one correspondence between electric field pulses and their derivatives, thus allowing comparison with results in the literature for the time between electric field pulses. Figure 5.17 illustrates both E and dE/dt for a portion of each type of pulse train. Pulses in the E waveform had a corresponding dE/dt pulse, at a threshold of 20 %. Analysis of the E waveform proved difficult due to artificial low frequencies introduced through integration. Also note that electric field pulses, particularly those associated with IC trains, were not symmetrical, i.e., they had a sharper rise than fall. These are unlike the more symmetrical pulses measured by Krider et al. [1975], A separate analysis of median interpulse intervals at smaller thresholds is undertaken later in this section. Histograms of the number of records vs. the median interpulse interval for IC and leaders preceding new terminations are shown in Figures 5.18 5.20. The median interpulse interval for pulse trains in IC discharges had a mean value of 5.1 pis. The median interpulse interval for records of leaders preceding new terminations had a mean value of 7.6 pis. Each of these values is similar to the inter-pulse intervals for the trains of Krider et al. [1975], Krider et al. [1977], and Rakov et al. [1996], The mean value of median interpulse interval for dart-stepped leaders was 2.8 pis, however, interpulse intervals increased significantly with time. The median interpulse interval for the first record of dart-stepped leaders averaged 1.6 pis at a threshold of 20 %, and increased to 4. 1 pis during the last record. This latter value is in

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dE/dt dE/dt dE/dt 176 K L 70 80 90 100 110 120 Time in microseconds dE/dt E dE/dt E dE/dt E Figure 5.17. dE/dt and E traces of portions of an IC train, dart-stepped leader (DS) and leader preceding a new termination (NT).

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177 10 11 12 1 Interpulse interval (microseconds) J 14 15 Figure 5.18. Histogram of the interpulse interval in IC pulse trains. A threshold of 20 % was used to find intervals. The mean value is indicated on the graph.

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178 o b 4 5 6 7 8 9 10 11 12 13 14 15 Interpulse interval (microseconds) Figure 5.19. Histogram of the interpulse interval of pulse trains from leaders preceding new terminations to ground. A threshold of 20 % was used to find intervals. The mean value is indicated on the graph.

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179 | 0 1 I 10 11 12 13 14 15 Interpulse interval (microseconds) Figure 5.20. Histogram of the interpulse interval from dart-stepped leaders. A threshold of 20 % was used to calculate intervals. The mean value is indicated on the graph. Intervals were not homogeneous over the course of the leader (see text).

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180 better agreement with intervals from IC pulse trains and leaders preceding new terminations to ground. The average pulse intervals of Krider et al. [1977] from dartstepped leaders and those of Krider et al. [1975] and Rakov et al. [1996] from IC trains are similar to those from trains in each of the three categories of the current study if a threshold of 20 % is assumed and measurements are confined to the final record of dartstepped leaders. As we have seen, the median interpulse interval increased with time during dartstepped leaders. Median interpulse intervals for IC pulse trains also showed a tendency to increase with time, although more rapidly than dart-stepped leaders. The seven dartstepped leaders averaged 1.0 ms in duration and spanned between 4 and 7 records. Median interpulse intervals increased from an average of 1.6 ps to 4.1 ps over the course of leaders. In IC trains an increase in median interpulse interval was often noticeable within a single record (204 ps). Figures 5.9 and 5.10 are examples of such increases. The time between dE/dt crossings increased from less than 2 ps to near 6 ps during 200 ps in record 7 of flash 2541363 (see Figures 5.1 and 5.9). A smaller increase, from 4 ps to 5 ps, was seen in record 1 1 of flash 2541813 (Figures 5.4 and 5.10). While the median interpulse interval for dart-stepped leaders increased with successively later leader records, little systematic change was noticeable within a record. Figure 5.21 shows the time between dE/dt crossings vs. crossing number for records 19 22 of the second leader of flash 2541679 (Figure 4.2). The median interpulse interval is marked on each graph and increased between records. Little systematic change in interval was seen within any given record. Pulse trains associated with the dart-stepped leader portion of

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Interval (microseconds) Interval (microseconds) Interval (microseconds) Interval (microseconds) 181 Rec # 1 9 Rec # 20 Rec #21 Rec #22 Figure 5.21. Interpulse interval vs. pulse for the second leader in flash 2541679. The median interval between crossings is shown on each trace.

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182 leaders preceding new terminations showed no systematic change in interval either within an individual record or over several records. We find median interpulse intervals for dart-stepped leaders and IC discharges to systematically increase with time. The increase found in the case of IC trains is consistent with the findings of Krider et al. [1975] and Rakov et al. [1996], We provide microsecond-scale measurements of the dart-stepped leader for times greater than 200 p.s prior to the return stroke, the first such measurements. We find median interpulse intervals during dart-stepped leaders to increase with time, similar to those for IC trains. We now turn to a discussion involving the relationship between average speed and median interpulse interval. Average speed vs. median interpulse interval . The preceding discussions suggest a possible correlation between average speed and median interpulse interval in pulse trains, namely, a decreasing leader speed with an increasing median interpulse interval. Each of the seven dart-stepped leaders in Table 4.1 showed a decrease in speed towards earth accompanied by an increase in the median interpulse interval. This was summarized in Figure 4.15, where leader speed was plotted vs. median interpulse interval (@ 20 %) for each of the leaders of Table 4.1. A scatter plot of speed vs. median interpulse interval for all records in Table 4.1 (Figure 4.16) showed good correlation (R 2 = 0.53), especially when the two branches of flash 2541672 were taken into account. Pulse trains in cloud discharges also exhibited a decrease in speed and an increase in median interpulse interval. This was the case for three of the four trains that spanned multiple records as well as within the first train of flash 2541363 (see Figure 5.1). Figure 5.13 shows the relationship between speed and median interpulse interval for all records of cloud

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183 discharges. Overall, correlation was weaker (R 2 = 0.28) than in the case of dart-stepped leaders (R 2 = 0.53, see Fig. 4.16) and there was quite a bit of scatter. A similar plot for the dart-stepped portion of leaders preceding new terminations is shown in Figure 5.22. Correlation was similar to that of IC trains (Figure 5.13). Notice in Figure 4.16 that all five dart-stepped leader records, with median interpulse intervals greater than 4 ps, were associated with average speeds of less than 5 x 10 6 m/s while the average speeds of 15 of 19 leader records with intervals less than 4 ps exceeded 5 x 10 6 m/s. Figure 5.22 indicates that all 46 records of leaders preceding new terminations, with median interpulse intervals of 4 ps or greater, had average speeds less than 5 x 10 6 m/s, a result similar to that of dart-stepped leaders. Four of seven records of leaders preceding new terminations had interpulse intervals less than 4 ps and speeds greater than 5 x 10 6 m/s. All 23 records of intracloud trains, Figure 5.13, with intervals that exceeded 4 ps, had speeds less than 5 x 10 6 m/s. Only three of fourteen records with intervals less than 4 ps had speeds that exceeded 5 x 10 6 m/s, although the three did correspond to records with the smallest median interpulse intervals. We observed no trains, associated with any of the three processes, that consisted of pulses separated by 4 ps or greater, with an average speed in excess of 5 x 10 6 m/s. Dart-stepped leader records with speeds exceeding 5 x 10 6 m/s were almost always associated with median interpulse intervals less than 4 ps. IC pulse trains and leaders preceding new terminations rarely exhibited speeds greater than 5 x 10 6 m/s (3 of 40 and 4 of 53 records, respectively), and those that did were associated with median interpulse intervals less than 4 ps in each case. The reason we find so few records of IC pulse trains and leaders preceding new terminations with speeds greater than 5 x 10 6 m/s may be because we

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100 184 [(s/ui 9 oix) pasds] §oq

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185 appear to miss the beginning of these trains. Pulses occurring more frequently than every 4 pis were often associated with the beginning of trains (see Figures 4.2, 4.6, 5.1). Median interpulse interval vs. threshold . The median interpulse interval of dartstepped leaders was a sensitive function of the amplitude used to determine intervals. This is clearly visible in the median interpulse interval vs. threshold curves in Figures 4.4 and 4.7. The average median interpulse interval at a threshold of 8 % was 1.4 p.s for the dart-stepped leader records in Table 4.1. At a threshold of 20 % the average median interpulse interval doubled to 2.7 p.s. The reason for these differences was examined in the second leader of flash 2541679 (Figures 4.2, 4.4, 4.17). During the last record of the leader we found a median interpulse interval of 4.7 tis at a threshold of 20 %. At this threshold only the large pulses in Figure 4.17 contributed to the median interpulse interval. At a threshold of 8 %, the median interpulse interval during the same record was 2.0 ns, less than half its value at a 20 % threshold. Small pulses on one channel, responsible for this difference, often could be aligned with common pulses on another, indicating the pulses originated from locations near to the channel to ground. In contrast to pulse trains associated with dart-stepped leaders, little dependence was found between median interpulse interval and threshold for IC pulse trains (Figures 5.3 and 5.6). Consider the train of record 11 in flash 2541813 (Figure 5.4) again. The median interpulse interval between crossings was nearly independent of threshold (Figure 5.6). The median interpulse interval increased by only 10 % between thresholds of 8 50 %. Close examination of the leader waveform (Figure 5.23) shows no discernable pulses between the large, regularly occurring pulses, even at thresholds below 8 %. As another

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186 o in VO s IT) in o vn vn C/D •O C o o cfl O
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187 example, consider the train of record 20 in IC flash 2541361 (Figure 5.24). Again, no pulses other than the regularly occurring large pulses are found. A common feature among pulse trains in IC discharges was the lack of smaller pulses, the result being little dependence of median interpulse interval on threshold. Median interpulse intervals of leaders preceding new terminations to ground exhibited some dependence on threshold. Figure 5.25 shows a curve of median interpulse interval vs. threshold for record 13 of the leader preceding the new termination in flash 2541403 (see Figure 3.3 and Chapter 3 for analysis). There are two distinct regions on the plot. Between thresholds of 10 and 30 % the variation in median interpulse interval was relatively small within a record. At thresholds below 10 %, down to 4 %, the median interpulse interval decreases substantially from its value at 10 %. For example, the median interpulse interval in record 13 dropped from 4.4 ps at 10 % to 1.3 ps at 4 %. A closer look at the dE/dt waveform will reveal the reason for this. Inspection of Figure 5.25 reveals that many of the dE/dt pulses found at the lower threshold can be attributed to what appears to be the recovery of the dE/dt signal after large pulses, i.e., a dE/dt pulse following within about 2 ps of a large pulse. This was not the case in the dart-stepped leader of flash 2541679 (Figure 4. 17). Only a few of the dE/dt pulses in that case could be considered to be part of the recovery of a larger pulse. The smaller pulses present in the dart-stepped leader were interspersed between the larger pulses and could often be aligned with common pulses on other channels, the alignment being similar to that of the larger pulses, suggesting that the smaller pulses were radiated from a location near those of the larger pulses. The pulses associated with the “recovery” in the dE/dt waveform in Figure 5.25, often appear different at different stations. In this case it may be incorrect to consider

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188 IP/HP

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dE/dt dE/dt dE/dt dE/dt 189 Time in microseconds Figure 5.25. Expanded time view of a portion of the leader preceding the second stroke of flash 2541403.

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190 these crossings as coming from separate sources as they may be related to the source responsible for the larger pulse. Figure 5.26 shows the dE/dt waveform for the leader preceding a new termination in flash 2540666. This waveform appears similar to those of IC trains of this section. Median interpulse interval varied little with threshold, a vast majority of the crossings resulting from the large dE/dt pulses. Like the leader in flash 2541403, some larger pulses are associated with more than one crossing at a small threshold. These pulses, however, are again different from those in the dart-stepped leader of flash 2541679 as they do not appear to be associated with separate sources. There were differences in the median interpulse interval for trains in each category. Median interpulse intervals in IC trains were largely independent of threshold. Dartstepped leaders were characterized by median interpulse intervals that depended heavily on threshold. At the smallest threshold, dE/dt pulses were present that appeared to originate from the channel to ground. These smaller pulses were of insufficient amplitude so as to be included at thresholds of 20 30 %. Median interpulse intervals of leaders preceding new terminations to ground exhibited some dependence on threshold. In one case it appeared that the recovery of large dE/dt pulses produced dE/dt crossings at small thresholds. These crossings did not appear to be the result of a separate source, but rather, part of the preceding dE/dt pulse 5.3,3 Step lengths Optically determined lengths of individual steps of dart-stepped leaders near ground are on the order of tens of meters. Schonland [1956] found step lengths from 7 25 m. Orville andldone [1982] estimated step lengths between 10 30 m. No estimates of step

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dE/dt dE/dt dE/dt dE/dt 191 0 5 10 15 20 25 30 35 40 45 50 150 155 160 165 170 175 180 185 190 195 200 Figure 5.26. Expanded time view of a portion of the leader preceding the second stroke of flash 2420666.

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192 lengths are available from intracloud processes, such as the pulse trains recorded by Krider et al. [1975] and Rakov et al. [1996], We find average step lengths between consecutive pulse sources in intracloud trains to be 7 30 m, similar to those from dartstepped leaders near ground. Average step lengths were estimated by counting the number of dE/dt crossings at a 30 % threshold. The choice of a different threshold did not appreciably change these values since intervals in IC discharges were nearly independent of threshold. This was not the case, however, for the dart-stepped leaders of Chapter 4. Recall that the median interpulse interval increased with increasing threshold (see Figures 4.4 and 4.7 for example). Clearly the average step length, as we define it, will vary as a function of the threshold used to determine the number of dE/dt crossings. Average step lengths in dart-stepped leaders spanned 4 108 m at thresholds between 8 30 %, the upper limit much larger than values reported in the literature. Median interpulse intervals during the final record of dart-stepped leaders averaged 4.8 p.s at a threshold of 30 %. This value is similar to the average pulse interval of 5 6 p,s reported by Schonland [1956] and Krider et al. [1977] from dart-stepped leaders near ground. Using this threshold, the average step length during the final record of dart-stepped leaders would be 13 39 m. These step lengths are in good agreement with optical measurements of individual dart-step lengths near ground, 10 30 m (e.g., Schonland, 1956; Orville and Idone, 1982). It appears, therefore, that the large pulses (amplitudes at 30 % or larger) in the dE/dt waveform, 200 (is prior to return strokes, correspond to the optically observed steps in dart-stepped leaders. The presence of smaller pulses leads to more dE/dt crossings at lower thresholds, resulting in a smaller estimate of the average step length. Assuming a threshold of 8 %, step lengths would be only 4 12 m during

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193 the final record of leaders, 2-3 times smaller than those found using crossings at a 30 % threshold. The smaller pulses responsible for this difference appear to originate from sources near the channel to ground but may not be visible on optical records. Average step lengths in leaders preceding new terminations to ground were between 11 53 m using a threshold of 30 % to determine the number of dE/dt crossings. These are similar to those in cloud discharges mentioned above. Therefore, average step lengths, defined using a 30 % threshold, associated with trains in each of the three categories were similar if we again limit our measurements to the final record of dartstepped leaders. 5,3,4 Conclusions Pulse trains in this study were associated with three different processes. Two of these, dart-stepped leaders and leaders preceding new terminations, occurred in channels to ground, the third in IC discharges. Several common features were associated with each type of train. The first of these was a non-increase in speed. Dart-stepped leaders and IC trains often exhibited a noticeable decrease in speed with time. Leaders preceding new terminations were nearly constant in speed. Two dart-stepped leaders were observed to increase in speed (see section 4.3) as the result of joining a newer section of channel. Mean speeds of leaders preceding new terminations and IC trains were 3.1 x 10 6 m/s and 2.7 x 10 6 m/s respectively, similar to speeds of dart-stepped leaders observed optically near ground. Speeds of dart-stepped leaders of the current study near ground (lowest 1 km), were 3.6 x 10 6 m/s, in good agreement with those of the other two types of trains.

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194 Another common characteristic was an increase in the median interpulse interval with time. Both dart-stepped leaders and IC trains showed a systematic increase in median interval with time. Leaders preceding new terminations, however, exhibited no systematic change in median interpulse interval with time. The median interpulse interval in IC trains averaged 5.1 ps at a threshold of 20 % of the maximum pulse amplitude. A slightly higher value, 7.6 ps, was associated with leaders preceding new terminations to ground. Both of these intervals are similar to interpulse intervals in the literature. Median interpulse intervals, at 20 %, were 4.1 ps during the final record of dart-stepped leaders. This was slightly less than the interval found in IC trains, but also consistent with the time between dart-stepped leader steps near ground reported in the literature. We found an inverse relationship between average speed and median interpulse interval. Each of the seven dart-stepped leaders in Table 4.1 decreased in speed and exhibited an increase in the median interpulse interval. Likewise, trains in IC discharges decreased in speed, accompanied by an increase in the median interpulse interval. The relationship also proved valid for the two subsequent leaders that increased in speed in section 4.3. Each of these showed a decrease in median interpulse interval while increasing in speed. Scatter plots for records of each type of train showed the inverse relationship between average speed and median interpulse interval to different degrees. The best correlation was associated with dart-stepped leaders. Weaker correlation was seen in the case of IC trains and leaders preceding new terminations to ground. All three scatter plots were consistent with trains of pulses with median interpulse intervals greater than 4 ps (20 % threshold) being associated with speeds less than 5 x 10 6 m/s. All trains

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195 with average speeds exceeding 5 x 10 6 m/s were associated with median interpulse intervals less than 4 ps. Despite the similarities mentioned above, several important differences between pulse trains were found. While maximum average speed during IC trains was 5 x 10 6 m/s, several leaders preceding new terminations exhibited speeds near 10 x 10 6 m/s. The maximum speed in dart-stepped leaders was 35 x 10 6 m/s. In fact, the beginning of each dart-stepped leader was characterized by a speed greater than 10 x 10 6 m/s, greater than the speed observed in either of the other two types of trains. Median interpulse intervals associated with dart-stepped leaders varied both as a function of time and threshold. At a 20 % threshold, median interpulse intervals of dartstepped leaders averaged 4.1 ps near ground (lowest 1 km). However, at a similar threshold, intervals averaged only 1.6 ps near the beginning of leaders, half that near ground. This is the first report of the microsecond scale nature of the dart-stepped leader electric field more than 200 ps prior to the return stroke. Median interpulse intervals were much shorter earlier in the leader, and smaller than the shortest time between dartstepped leader steps quoted in the literature. Median interpulse intervals of dart-stepped leaders also varied as a function of threshold. Near the return stroke, median interpulse intervals averaged 4.1 ps at a threshold of 20 %, but just 2.2 ps at an 8 % threshold. Small pulses (less than 20 %) in the dE/dt waveform were responsible for this difference. The alignment of these smaller pulses suggested they originated from sources near to the channel to ground. In the case of IC trains, no such smaller pulses were present. Instead, median interpulse intervals were nearly constant as a function of threshold. Leaders preceding new terminations to ground sometimes exhibited an increase in median

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196 interpulse interval at small thresholds, although in those cases, the increase appeared to be the result of the “recovery” of larger dE/dt pulses. 5.4 Polarities of Pulses in Intracloud Pulse Trains 5.4.1 Introduction Workman et al. [1947], Smith [1957], and Krehbiel et al. [1979], have reported differences in measured electric field polarities from lightning at multiple stations. These measurements were made on the time scale of 1 100 ms. Krehbiel et al. [1979] attributed the difference in polarities to the movement and orientation of dipole charge centers. Differences in pulse polarities on the time scale of microseconds have also been reported ( Krider et al., 1975; Weidman and Krider, 1979; Rakov et al., 1996). Measurements of the electric field in each of these studies were made at a single station, so polarity differences at more than one station, or in relation to the orientation of the source, could not be determined. Weidman and Krider [1979] note both positive and negative polarity bipolar pulses while Rakov et al. [1996] found an almost equal number of positive and negative pulse trains. In addition, Rakov et al. [1996] noted a polarity reversal during a train. Weidman and Krider [1979] and Rakov et al. [1996] used the atmospheric electricity convention; a positive electric field change corresponded to the removal of negative charge overhead. We will employ a physics convention when deriving expressions for the electric field. An upward deflection of dE/dt corresponds to a negative value of the z component of the electric field in the equations to follow. We record intracloud pulse trains associated with different polarity pulses at different stations and also polarity reversals at a single station. Using a general theory, we develop

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197 a method to test current flow between pulse source locations to determine the most likely channels. We present an example illustrating differences in pulse polarities and the delineation of probable branches based on measured pulse polarities. 5,4.2 Theory and Method Theory, Consider an arbitrarily oriented linear channel carrying a conventional current /(r ', t) , flowing in the direction / as in Figure 5.27. If the source of dE/dt radiation arises from the current at the i 411 location, then the far-field expression for the electric field at the/* 1 station from this element is ( Thomson , 1999): £,(r,,0 = -^ | [/(?',/--)]•[/ -(/ R )R (5.1) 4 7T Ot J r K channel ~ ,dV_ R The far-field expression for the electric field dominates since the static field (a: — ) K and the induction field can be neglected at distances of several kilometers or more for frequencies greater than 1 MHz which are typical of the duration of the in-cloud pulses we investigate. Further, since the time tag used in calculating the source location occurs during the first 100 ns of the pulse, the maximum channel length for current flow is 30 m or less if current is the result of a wave that originates at /; and travels at or less than c. Since R is at least several kilometers for in-cloud sources, we can neglect changes in R and — over R the segment. Equation (5.1) hence becomes

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j 01 station Fig 5.27. Geometry used to derive the relationship between the measured derivative of the electric field at the ground and the current at the i* source.

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199 A A A y W -i£ 1 /(?'.' -Vi (5.2) channel where R tj =r J -r i . Note that the dependence of the retarded current time variation on R remains since it may be significant. For measurements on the surface of a perfectly conducting earth, the electric field has an additional contribution from the image current and is given by (e.g. Le Vine and Willett, 1992) E js {f j ,t) = 2[z-E j {r j ,t)]z (5.3) tied™, C (5.4) (5.5) channel where I(r t ) is assumed positive if conventional current flows in the direction of / . A A The polarity of the measured field is a product of the polarities of 0 {j • / and the term d R in brackets, — f I(r',t )dl' . For example, a typical return stroke, with dtc d~i c conventional current flowing up the channel, will produce a negative value for Ez in Equation 5.5 (an upward dE/dt deflection in waveshapes presented here). If the term in square brackets of Equation 5.5 has the same polarity in each of the five expressions for A A E, then the pulse polarity is dependent solely upon the polarity of the term 0 V • / since A A sin(0,. )> 0. Hence the polarity of 6 t] • / determines the polarity of the measured electric

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200 field, i.e., dE/dt and E peak polarity, which are the same (see Figure 5.17). It is possible A SK A for E = 0, and hence dE/dt = 0, if Q tj •/ = 0. In this case the vector / lies in the plane whose normal is 0 ^ . Note that is tangential to this plane but / • Ry is not necessarily zero. ^ « Y — f*. Method . We determine if a particular path / = /* = p — p is a possible direction for \ r k ~ r i\ a segment of the lightning channel passing through the point r j (the location found for the i* pulse). Note that r k is the location of the k* pulse where k can be any pulse number either before or after i. We test whether all measured pulse polarities for the i th pulse are consistent with that predicted by Equation 5.5. If all pulse polarities and Oy-I/t ’s can be determined unambiguously, there are four independent conditions for the d R five measurements, since the term — f I(f', t )dl' has an unknown, but assumed dt , J , c channel constant, polarity. A pulse polarity is considered indeterminate if there is no peak above the noise threshold (four standard deviations above the mean) on that channel. At most, one measurement in each set was excluded in this way. A more important problem arose when r t and r k were separated by a displacement comparable to their location errors. Specifically, if 6 jf is less than or equal to 0 {j • A/* , where A/* is the rms error in 4 > then the test condition is indeterminate. In other words, locations separated by distances less than the rms error in /* yielded no information concerning possible channel segments. We tested all possible combinations of current paths. This meant testing a particular segment twice by using , for the source at r t , and / fa , for the source at r k . «

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201 Each of these paths has a different physical interpretation, e.g. if k > i, current flowed in a new channel extension and if i > k then current flowed in a previously formed channel. Of particular interest were the cases in which measured pulse polarities were not consistent with current flow in the possible channel between two locations since these inconsistencies do not allow the existence of a possible lightning channel, hence limiting the choices for that channel. Pulse polarities were defined by the first dE/dt crossing above (or below) a threshold that was four standard deviations above the noise level on a particular channel. If no dE/dt deflection was noted above this threshold on a particular channel, an indeterminate polarity was the result. In some instances the dE/dt deflection started away from zero in one direction, not crossing the threshold, and turned in the other direction and crossed the threshold. An example is shown in Figure 5.28. This pulse was considered positive (dE/dt increasing downward) although it appears to have an initial deflection in the negative (upward) direction. 5,4,3 Results We present results from an intracloud pulse train to illustrate the dependence of observed pulse polarity on channel orientation for pulse trains that were associated with apparently unbranched channels. The discharge produced different polarity trains of dE/dt pulses at the five stations and also a change in polarity at a single station. Flash 2540071 Flash 2540071 occurred at 19:16:10 on day 254, seven kilometers SSW of the central recording site. The flash comprised 18 trigger records and spanned 326 ms. Figure 5.29

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202 1P/3P Figure 5.28. A positive dE/dt pulse (dE/dt is increasing downward).

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203 10 N 1 1 1 1 o d 1 c° <5°b ch \ a 1 1 1 -8 -7 -6 -5 -4 -3 Y (km) Figure 5.29. dE/dt locations of flash 2540071. Early processes shown as circles. The locations of the three pulse trains are shown as "diamonds" and labeled "ch".

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204 shows locations of all dE/dt sources. Sources during the first 246 ms of the flash are shown as “O” and spanned the first five records. These records contained single pulses and short bursts of pulses (< 100 ps). Locations from the first five records are labeled a d according to the order in which they occurred. The sixth trigger record occurred at t = 246 ms and marked the first of three co-located pulse trains. The trains were separated by 43 ms and 35 ms and spanned two, four and three records respectively. Locations of individual pulses are shown as “0” in Figure 5.29, the channel they followed labeled “ch”. The channel is expanded in Figure 5.30 and is divided into two segments, reflecting a large-scale change in channel direction. Two locations, A and B, one along each segment, have been marked. Each of the three trains had a source whose location was within 50 m of point A, and one within 50 m of point B. The dE/dt waveshapes of these sources are shown in Figure 5.31. Figure 5.31(a) shows waveshapes, corresponding to location A, recorded at each of the five stations for three different times, each window from a different pulse train. Notice the difference in pulse polarities among the five stations. All three trains produced pulses of positive polarity at stations 1, 2, and 3. At station 4, the dE/dt pulse polarity was negative in each case. The pulse polarity at station 5 was negative during the first two trains, and indeterminate during the third. The polarities at each of the five stations are consistent with a negative current flowing in the assumed channel through point A if the term in brackets in Equation 5.5 has the same polarity for each station. This means that the polarities at each station are those predicted A A a by Oy-l, if / is through point A as shown in Figure 5.30. The dE/dt waveforms corresponding to location B are shown in Figure 5.31(b). Again, pulse polarities were positive at stations 1, 2, and 3 during each pulse train. The polarity of the pulse at the

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Z (km) Y (km) 205 Figure 5.30. Locations of the three pulse trains in flash 2540071. Trains are marked with “O”, “0”, and “+” to represent the trains respectively. The most likely channel directions are drawn in.

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206 := A X 5 X 5 i (pjBMUMop 8uise3joui) uoipsgsp jp/gp r i X 5 ; 1 (pj'BMUMOp SuiSBSJOUl) UOip3[J3p jp/gp X 5 CO -o c
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207 (p.reAvuMOp §uisb3joui) uoposgsp jp/gp Figure 5.31 — continued.

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208 fourth station was again negative. Notice, however, the polarity of the pulse at the fifth station is now positive in each case. The measured polarities are again consistent with current flow along the channel through point B if the term in brackets of Equation 5.5 is the same at each station. The change in polarity of the pulse at station 5 is consistent with the new direction of the channel. The polarities are consistent with an assumed channel direction through point B, as shown in Figure 5.30. 5,4,4 Discussion Continuous channels . We can use Equation 5.5 and measured pulse polarities to test whether or not pulse sources may lie along a linear channel directed between two source A A locations. Since sin(0) is always of the same sign, the term 6 tj •/* is the determining factor in the pulse polarity, assuming the term in brackets of Equation 5.5 has the same polarity at each station. Determination of the integral term requires specific knowledge of the source current and even the polarity of the integral requires some knowledge of the current distribution. The polarity of pulse sources at two points along the channel (see Figures 5.30 and 5.31) were consistent with current flowing in the direction of the apparent channel, if the term in brackets in Equation 5.5 is assumed to have the same polarity at each station. This assumption is valid, for example, in the case of the transmission line model [Uman andMclain, 1970], In this special case the current wave travels at constant speed v that is equal to the speed of the extending channel and has the form V (5.6)

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209 and turns on at t = 0 at r t and does not turn off during the time of interest. Then Equation 5.5 becomes Ej,(f p t) = M o sm(O)(0 ir T)z [!--/•«»] c c c (5.7) which has a polarity that is independent of R. We tested whether or not the polarity of pulses in the three trains was consistent with current flowing in the linear channel between consecutive source locations. We found 66 % (66 out of 100) of the pulses were consistent with this view. A path was determined to be a possible section of the lightning channel only if pulse polarities were consistent with current flow in both directions along the linear channel between two consecutive locations, i.e. from location i to k and from location k to i. We did this since it is possible that current may flow in the direction of channel propagation or opposite to it. The requirement that the pulse polarity be consistent with a channel in two directions at a point is somewhat stringent and most likely accounts for the relatively small percentage (66 %) of pulses being consistent with a continuous channel. However, in this study we were primarily interested in pulses whose polarity was not consistent with a continuous channel. We investigate several of these cases later. We now examine sources that were associated with an indeterminate pulse polarity at a station. Indeterminate pulse polarities. In some instances a source produced no discemable pulse at one station. The threshold used in this determination was four standard deviations above the noise level on that particular channel. We see from Equation 5.5 that the electric field amplitude approaches zero when any of the following terms go to

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210 A A f zero: (a) sin(0), (b) 6 {j , or (c) the term in brackets. The first case, sin(0) , is ruled out, since this occurs only when the source is directly overhead of the station. This was not the case for any sources in this flash. The term in brackets approaches zero when the current is zero, but then no dE/dt pulse would be produced at any station. The remaining case is when G tj • l A is zero. This condition arises when /* lies in the plane with normal 0 ir As an example consider Figure 5.32 showing the first eight pulses of the second train. Beginning with the first pulse, we use equation 5.5 to solve for the polarity of the bracketed term with regard to station 1. Substituting this into the expression for E associated with measurements from stations 2 4 we find that all /* are consistent with the observed pulse polarities. This means that all paths, /* and l h were possible. Furthermore, the negative polarity of the bracketed term indicates that negative charge was moved in the direction of pulse-to-pulse propagation, or similarly, a conventional current flowed in the direction opposite to pulse-to-pulse propagation. Figure 5.33 represents the normal distance of locations 1-7 from a plane through pulse source 1 with normal 6 Xj . Sources 2-7 move away from the planes associated with stations 1 3, in the increasing 6 direction, consistent with negative pulse polarities (remember E is increasing downward in Figure 5.32). Sources 2-7 move away from the plane associated with station 4, in the decreasing 0 direction, consistent with a positive pulse polarity (negative deflection). However, sources did not deviate much from the plane referenced to station 5. Here l -0 i5 is approximately zero, consistent with the negligible deflection seen at station 5. Notice in Figure 5.32 that the dE/dt waveshape at station 5

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211 Figure 5.32. dE/dt waveforms measured at the five stations for the first eight pulses of the second train of flash 2540071 .

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212 Figure 5.33. Distance of sources 1 through 8 (Figure 5.3 1) from a plane containing the vector from location 1 to the respective station with normal in the theta direction (theta measured from the vertical). Distances are normal to the plane. Locations move in the increasing theta direction referenced to stations 1,2,3 and in the decreasing theta direction referenced to station 4. Locations are approximately in the plane referenced to station 5.

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213 changes at the 8 th source. This indicates a change in the channel direction and is discussed next. Branched channels. We now discuss some of the pulses whose polarities were not consistent with a channel between consecutive sources. Consider Figures 5.32 and 5.34 showing pulses from the second train. The locations of the first seventeen sources are shown in Figure 5.35. First, notice that the eighth source produced a negative field (positive deflection) at station 5, in contrast to the seven sources preceding it. The polarities associated with the eighth pulse were not consistent with current flowing in a channel between location seven and eight, and this path is shown dashed in Figure 5.35. We also found the path between locations 6 and 8 to be inconsistent with the observed polarities. Current flowing along the path between 5 and 8, however, would produce the observed polarities of the eighth pulse, suggesting that a branch may have occurred here. Another example of possible branching that was deduced from pulse polarities is seen in sources 11 17, shown in Figure 5.34. Paths, which were inconsistent with current flow producing the observed pulse polarities, are shown dashed in Figure 5.35. The path between locations 17 and 14 was consistent with a current flow producing the observed polarities but the paths 16-17 and 15-17 were not. Also, the path 13-14 was inconsistent with current flow producing the observed polarities. Notice here that the polarity of pulses 16 and 17 was the same at all five stations. Nonetheless, the path between 16 and 17 was inconsistent based upon equation 5.5. It was not necessary, therefore, to have differences in pulse polarities to discern possible branches. It was enough to test whether a particular path was consistent with the observed pulse polarities as predicted by Equation 5.5.

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214 T— CM CO MLO h1 — 1— 1— 1 — CO C 0 CO CO CO
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Z (km) 215 Figure 5.35. Expanded view of the early part of the second pulse train of flash 2540071. Paths which are not consistent with current flow based on the measured waveshapes are shown dashed. The most probable channel based on measured polarities is shown solid.

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216 Flash structure. The pulse trains of flash 2540071 are of further interest regarding the direction of charge movement. Each of the three trains was consistent with negative charge being moved in the direction of propagation. From 5.29 the direction of propagation is away from the probable flash origin, the region near sources labeled a. These results are in contrast to those provided by Shao et al. [1996], They found that Kprocesses moved negative charge towards the flash origin by retracing a previous channel. Successive K-processes started at further distances from the origin, thus extending the channel in a retrograde manner. Each pulse train in flash 2540071 extended the channel but did so in a manner opposite to that described by Shao et al. [1996], 5,4,5 Conclusions Differences in pulse polarities are examined and a method is developed to determine possible segments of the lightning channel. Using electromagnetic theory in conjunction with source locations and pulse source polarities we are able to distinguish possible branches in the lightning channel. Pulse polarities are related to channel geometry and reversals in pulse polarities are explained. 5.5 Summary and Conclusions In this chapter we investigated pulse trains in IC discharges and compared characteristics among the three types of trains identified in this study. Several similarities were found, among them a non-increase in speed and a tendency for interpulse intervals to increase with time. There was a negative correlation between average speed and

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217 median interpulse interval. This was strongest in the case of dart-stepped leaders. Among the differences in characteristics were maximum speeds and interpulse interval as a function of threshold. Dart-stepped leaders always began with speeds in excess of 10 x 10 6 m/s while pulse trains in IC discharges and leaders preceding new terminations rarely did so. This may be due in part to our failure to record the beginning of trains in the latter two categories. Further research is needed in this regard. Interpulse intervals in IC pulse trains were nearly independent of threshold while intervals in dart-stepped leaders were most sensitive to threshold.

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CHAPTER 6 RECOMMENDATIONS FOR FURTHER STUDY The data analyzed in this work involved only a small fraction of the data collected on days 242, 244 and 254 during the summer of 1992. As a result of this work, software programs have been developed to determine the locations and times of occurrence of dE/dt pulses at multiple stations, making it possible to process large amounts of data in a relatively short amount of time. In this chapter we suggest topics for further research using the current data set. Some topics follow up on the results of Chapters 3, 4, and 5 while others are suggestions based on the authorÂ’s observations in sifting through large amounts of data for the current study. 6,1 Pulse Trains Several topics investigated in this work deserve further study. Recall that we recorded the beginning of only one IC train and no leader preceding a new termination to ground. The beginning of dart-stepped leaders exhibited the highest speeds in this study and it is possible that IC trains and leaders preceding new terminations also began at similar speeds. An analysis of speed vs. interpulse interval for IC trains would be a productive avenue for investigation once sufficient IC trains (recorded in full) are obtained. Recall that the first pulse train in flash 1363 (Figure 5.1) exhibited a decrease in average speed and an 218

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219 increase in interpulse interval. This led to a nearly constant average step length. Full IC pulse train records will allow further investigation of a constant or changing step length since noticeable changes in speed and interpulse interval take place near the beginning of trains. Another topic of consideration for further work is that of “chaotic” leaders. Again, in most instances we record only 50 60 ps of these leaders (pretrigger data) prior to subsequent strokes. In two cases we were fortunate to record these in full and found these leaders to exhibit average speeds of 32 50 x 10 6 m/s. An analysis of the leader waveform would be of interest. Interpulse intervals in these leaders appeared to be on the order of one microsecond and amplitudes were several times smaller than dart-stepped leader pulses near return strokes. 6.2 Observations of Other Field Waveforms Small bursts of pulses often occurred prior to the first stroke in ground flashes. Weidman and Krider [1979] suggested that the bipolar pulses they record prior to the start of flashes were associated with preliminary breakdown occurring in the cloud. Pulses occurring at the beginning of flashes in this study were located between 5 7 km high (see e g. Figures 3.4 and 4.5). An example of the both the dE/dt and E field waveform at the start of a flash is presented in Figure 6.1. These appear to be different than the waveforms recorded by Weidman and Krider [1979] and an analysis of these types of pulses with regard to their location and movement may shed new light on the process of preliminary breakdown. We have also observed a single electric field pulse, often occurring several hundred of microseconds to a few milliseconds after a return

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220 UVHP a Figure 6. 1 . dE/dt and E waveforms at the start of a flash.

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221 stroke. The location of this pulse is in the cloud near heights of 6 9 km, often near earlier sources prior to the first stroke to ground. It is possible that these pulses may be associated with the initiation of M-components, an increase in channel luminosity and current following subsequent return strokes ( Malan and Schonland, 1937). Shao et al. [1995] observed M-components were usually initiated by fast moving negative streamers connecting to the upper extremity of the conducting channel to ground. In many cases a large spike, only a single data point wide (1 ns), occurred in the electric field waveform. The single pulse we record after subsequent strokes may be similar to that seen by Shao et al. [1995], Microsecond scale electric field pulses associated with M-components have also been recorded by Rakov et al. [1992] and a mechanism for the lightning Mcomponent put forth by Rakov et al. [1995], 6,3 Summary Conclusions It is the authorÂ’s opinion that this data set is far from exhausted. With the software developed in the course of this study, analysis of large amounts of data is possible in a relatively short period of time. Several topics that may provide fruitful results have been outlined in this chapter.

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223 Hager, W., and D. Wang, An analysis of errors in the location, current, and velocity of lightning, J. Geohpys. Res., 100, 25721-25729, 1995. Hofmann-Wellenhof, B. H. Lichtenegger, and J. Collins, Global Positioning System: Theory and Practice, SpringerVerlag, New York, 1993. Honma, N., F. Suzuki, Y. Miyake, M. Ishii, and S. Hidayat, Propagation effect on field waveforms in relation to time-of-arrival technique in lightning location, J. Geophys. Res., 103, 14141-14145, 1998. Idone, V., and R. Orville, Lightning return stroke velocities in the thunderstorm research international program (TRIP), J. Geophys. Res., 87, 4903-4915, 1982. Izumi,Y., and J. Willett, Catalog of absolutely calibrated, range normalized, wideband, electric field waveforms from located lightning flashes in Florida, Vol II: 8 and 10 August, 1985 data, Phillips Laboratory, Hanscom Air Force Base, MA, 1991. Jordan, D., V. Idone, V. Rakov, M. Uman, W. Beasley, and H. Jurenka, Observed dart leader speed in natural and triggered lightning, J. Geophys. Res., 97, 9951-9957, 1992. Jordan, D., V. Rakov, W. Beasley, and M. Uman, Luminosity characteristics of dart leaders and return strokes in natural lightning, J. Geophys. Res., 102, 22,025-22,032, 1997. Kitagawa, N., On the electric field change due to the leader process and some of their discharge mechanism. Pap. Metereol. Geophys. (Tokyo), 7, 400-414, 1957. Kitagawa, N., and M. Brook, A comparison of intracloud and cloud-to-ground lightning discharges, J. Geophys. Res., 65, 1189-1201, 1960. Kitagawa, N., N. Brook, and E. Workman, Continuing currents in cloud-to-ground lightning discharges, J. Geophys. Res., 67, 637-647, 1962. Krehbiel, P., M. Brook, R Lhermitte, and C. Lennon, Lightning charge structure in thunderstorms. Proceedings in Atmoshperic Electricity, 408-411, 1983. Krehbiel, P., M. Brook, and R. McCrory, An analysis of the charge structure of lightning discharges to ground, J. Geophys. Res., 84, 2432-2456, 1979. Krider, E., G. Radda, and R. Noggle, Regular radiation field pulses produced by intracloud lightning discharges, J. Geophys. Res., 80, 3801-3804, 1975. Krider, E., C. Weidman, and R. Noggle, The electric fields produced by lightning stepped leaders, J. Geophys. Res., 82, 951-960, 1977.

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225 Proctor, D., R. Uytenbogaardt, and B. Meredith, VHF radio pictures of lightning flashes to ground, J. Geophys. Res., 93, 12,683-12,727, 1988. Rakov, V., R. Thottappillil, and M. Uman, Electric field pulses in K and M changes of lightning ground flashes, J. Geophys. Res., 97, 9935-9950, 1992. Rakov, V., R. Thottappillil, and M. Uman, Mechanism of the lightning M component, J. Geophys. Res., 100, 25701-25710, 1995. Rakov, V., and M. Uman, Long continuing current in negative lightning ground flashes, J. Geophys. Res., 95, 5455-5470, 1990a. Rakov, V., and M. Uman, Some properties of negative cloud-to-ground lightning flashes versus stroke order, J. Geophys. Res., 95, 5447-5453, 1990b. Rakov, V., and M. Uman, Waveforms of first and subsequent leaders in negative lightning flashes, J. Geophys. Res., 95, 16,561-16,577, 1990c. Rakov, V., and M. Uman, Origin of lightning electric field signatures showing two return-stroke waveforms separated in time by a millisecond or less, J. Geophys. Res., 99, 8157-8165, 1994. Rakov, V., M. Uman, G. Hoffman, M. Masters, and M. Brook, Bursts of pulses in lightning electromagnetic radiation: observations and implications for lightning test standards, /£££' Trans. Electromagn. Compat., 38, 156-164, 1996. Rakov, V., M. Uman, and R. Thottappillil, Review of lightning properties from electric field and TV observations, J. Geophys. Res., 99, 10745-10750, 1994. Rhodes, C., X. Shao, P. Krehbiel, R. Thomas, and C. Hayenga, Observations of lightning phenomena using radio interferometry, J. Geophys. Res., 99, 13059-13082, 1994. Schonland, B., and H. Collens, Progressive lightning, Proc. R. Soc. London Ser. A, 143, 654-674, 1934. Schonland, B., D. Malan, and H. Collens, Progressive lightning II, Proc. R. Soc. London Ser. A, 152, 595-625, 1935. Schonland, B., D. Malan, and H. Collens, Progressive lightning, Pt. 6, Proc. R Soc. London Ser. A, 168, 455-469, 1938b. Schonland, B., The lightning discharge, Handb. Phys., 22, 576-628, 1956. Shao, X., P. Krehbiel, R. Thomas, and W. Rison, Radio interferometric observations of cloud-to-ground lightning phenomena in Florida, J. Geophys. Res., 100, 2749-2783, 1995.

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227 Wilson, C., Investigations on lightning discharges and on the electric field of thunderstorms, Philos. Trans. R. Soc. London Ser. A, 221, 73-115, 1920. Winn, W., A laboratory analogy to the dart leader and return stroke of lightning, J. Geophys. Res., 70, 3256-3270, 1965. Winn, W., T. Aldbridge, and C. Moore, Video tape recordings of lightning flashes, J. Geophys. Res., 78, 4515-4519, 1973.

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BIGRAPHICAL SKETCH Stephen Davis was bom in Cocoa Beach, Florida, in 1968. He graduated from Merritt Island High School in 1986 and attended the University of Florida. He was awarded a Bachelor of Science in Electrical Engineering degree in 1990, a Master of Science degree in Electrical Engineering in 1992, and the Doctor of Philosophy degree in Electrical Engineering in 1999. He is married to the former Michelle Hunter of St. Augustine, Florida, since 1996. 228

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I certify that I have read this study and that in my opinion it conforms to acceptable standards of scholarly presentation and is fully adequate, in scope and quality, as a dissertation for the degree of Doctor of Philosophy. £ yftp****^ Ewen M. Thomson, Chairman Associate Professor of Electrical and Computer Engineering I certify that I have read this study and that in my opinion it conforms to acceptable standards of scholarly presentation and is fully adequate, in scope and quality, as a dissertation for the degree of Doctor of Philosw^phy. Martin A. Uman Professor of Electrical and Computer Engineering I certify that I have read this study and that in my opinion it conforms to acceptable standards of scholarly presentation and is fully adequate, in scope and quality, as a dissertation for the degree of Doctor of Philosophy. — ^ — — > — Vladimir A. Rakov Professor of Electrical and Computer Engineering I certify that I have read this study and that in my opinion it conforms to acceptable standards of scholarly presentation and is fully adequate, in scope and quality, as a dissertation for the degree of Doctor of Philosophy. Gijs Bosman Professor of Electrical and Computer Engineering I certify that I have read this study and that in my opinion it conforms to acceptable standards of scholarly presentation and is fully adequate, in scope and quality, as a dissertation for the degree of Doctor of Philosophy. Bo Gustafsofi Associate Professor of Astronomy

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This dissertation was submitted to the Graduate Faculty of the College of Engineering and to the Graduate School and was accepted as partial fulfillment of the requirements for the degree of Doctor of Philosophy. August 1999 M. J. Ohanian Dean, College of Engineering Winfred M. Phillips Dean, Graduate School