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Properties of Natural Cloud-to-Ground Lightning Inferred from Multiple-Station Measurements of Close Electric and Magnet...

Permanent Link: http://ufdc.ufl.edu/UFE0021279/00001

Material Information

Title: Properties of Natural Cloud-to-Ground Lightning Inferred from Multiple-Station Measurements of Close Electric and Magnetic Fields and Field Derivatives
Physical Description: 1 online resource (437 p.)
Language: english
Creator: Jerauld, Jason E
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2007

Subjects

Subjects / Keywords: electromagnetics, leader, lightning, modeling, return, stepped, stroke
Electrical and Computer Engineering -- Dissertations, Academic -- UF
Genre: Electrical and Computer Engineering thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: This dissertation presents an examination of natural cloud-to-ground lightning in Florida, experimental data for which were acquired in 2002 to 2004. Several processes involved in natural lightning, in particular stepped leaders and first return strokes, were studied using the electric (E) and magnetic (B) fields and field derivatives (dE/dt and dB/dt) measured at distances ranging from about 50 m to 1 km. The experimental system used, known as the Multiple Station Experiment (MSE) system, consisted of six electric field sensors (bandwidth of 0.2 Hz to 4 MHz), two magnetic field sensors (10 Hz to 4 MHz), four dE/dt sensors (up to 20 MHz), and three dB/dt sensors (up to 20 MHz), spread around an area of about 0.5 kilometers squared. The system is located at the International Center for Lightning Research and Testing (ICLRT), and is operated by the University of Florida Lightning Research Group. Between 2002 and 2004, data were acquired for about 20 lightning flashes, including one consisting of both positive and negative strokes, all thought to have terminated on ground within or near the network. The channel locations were estimated by a 2-D time-of-arrival method, using the peaks of the return stroke dE/dt waveforms. The estimated locations were used in performing a statistical characterization of several field waveform parameters (such as the leader and return stroke electric field changes), and parameters of the leader channels (such as the line charge density, speed, and current) were estimated from the acquired waveforms using simple models. Further, new insights into the mechanisms of the stepped leader and ground attachment process were gained from the experimental data and associated modeling.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Jason E Jerauld.
Thesis: Thesis (Ph.D.)--University of Florida, 2007.
Local: Adviser: Uman, Martin A.
Local: Co-adviser: Rakov, Vladimir A.

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2007
System ID: UFE0021279:00001

Permanent Link: http://ufdc.ufl.edu/UFE0021279/00001

Material Information

Title: Properties of Natural Cloud-to-Ground Lightning Inferred from Multiple-Station Measurements of Close Electric and Magnetic Fields and Field Derivatives
Physical Description: 1 online resource (437 p.)
Language: english
Creator: Jerauld, Jason E
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2007

Subjects

Subjects / Keywords: electromagnetics, leader, lightning, modeling, return, stepped, stroke
Electrical and Computer Engineering -- Dissertations, Academic -- UF
Genre: Electrical and Computer Engineering thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: This dissertation presents an examination of natural cloud-to-ground lightning in Florida, experimental data for which were acquired in 2002 to 2004. Several processes involved in natural lightning, in particular stepped leaders and first return strokes, were studied using the electric (E) and magnetic (B) fields and field derivatives (dE/dt and dB/dt) measured at distances ranging from about 50 m to 1 km. The experimental system used, known as the Multiple Station Experiment (MSE) system, consisted of six electric field sensors (bandwidth of 0.2 Hz to 4 MHz), two magnetic field sensors (10 Hz to 4 MHz), four dE/dt sensors (up to 20 MHz), and three dB/dt sensors (up to 20 MHz), spread around an area of about 0.5 kilometers squared. The system is located at the International Center for Lightning Research and Testing (ICLRT), and is operated by the University of Florida Lightning Research Group. Between 2002 and 2004, data were acquired for about 20 lightning flashes, including one consisting of both positive and negative strokes, all thought to have terminated on ground within or near the network. The channel locations were estimated by a 2-D time-of-arrival method, using the peaks of the return stroke dE/dt waveforms. The estimated locations were used in performing a statistical characterization of several field waveform parameters (such as the leader and return stroke electric field changes), and parameters of the leader channels (such as the line charge density, speed, and current) were estimated from the acquired waveforms using simple models. Further, new insights into the mechanisms of the stepped leader and ground attachment process were gained from the experimental data and associated modeling.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Jason E Jerauld.
Thesis: Thesis (Ph.D.)--University of Florida, 2007.
Local: Adviser: Uman, Martin A.
Local: Co-adviser: Rakov, Vladimir A.

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2007
System ID: UFE0021279:00001


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f11116aac2af08a40cc73866ef726b176ea848d2













PROPERTIES OF NATURAL CLOUD-TO-GROUND LIGHTNING INFERRED FROM
MULTIPLE-STATION MEASUREMENTS OF CLOSE ELECTRIC AND MAGNETIC
FIELDS AND FIELD DERIVATIVES















By

JASON EDWARD JERAULD


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


2007






























2007 Jason Edward Jerauld



































To the memory of my father, Ronald E. Jerauld















ACKNOWLEDGMENTS

The work presented in this dissertation would not be possible without the assistance

of many people. I am very grateful for the guidance received from my committee chair

and co-chair, Dr. Martin Uman and Dr. Vladimir Rakov, as well as for the constructive

comments from my committee members Dr. Douglas Jordan, Dr. Timothy Anderson, and

Dr. Paul Gader. I also thank Keith Rambo, George Schnetzer, Michael Stapleton, Robert

Olsen III, Dr. Jens Schoene, Joseph Howard, Kathy Thomson, as well as everyone else

who contributed to this project.

This work was supported in part by U.S. DOT (FAA) Grant 99-G-043, NSF Grants

ATM-0003994 and ATM-0346164, the Florida Power and Light Corporation, the Florida

Gas Transmission Group, and by the Florida Space Grant Consortium.
















TABLE OF CONTENTS


ACKNOWLEDGMENTS ................

LIST OF TABLES ................

LIST OF FIGURES


page

iv

viii

*xvii


A B STR A C T . . . . . . . . .. . xliii

CHAPTER

1 INTRODUCTION AND LITERATURE REVIEW ................. 1
1.1 Introduction . . ... . . . . . 1
1.2 The Global Electric Circuit and the Electrical Structure of Thunderclouds 3


1.3 The Lightning Discharge Process ................
1.3.1 Introduction . . . . . .
1.3.2 Downward negative lightning discharges to ground .
1.3.3 Positive and bipolar lightning discharges to ground .
1.3.4 Rocket-triggered lightning . . . .
1.4 Measured Electric and Magnetic Field Waveforms from Natural
Negative First Strokes. . . . . . .
1.5 The International Center for Lightning Research and Testing at


Camp Blanding, Florida . . ..
1.6 1997-1999 Multiple Station Experiment .


4
4
6
..18
. . 23

. . 26
. . 1





... ... 26


. .. 3 1
. .. 3 4


2 EXPERIMENT DESCRIPTION .......................... 37
2.1 Experiment Overview . . . . . . . 37
2.2 Station Locations . . . . . . . 42
2.3 Control System . . . . . . . . 49
2.4 Fiber-Optic Links . . . . . . . 55
2.5 Digital Storage Oscilloscopes . . . . . . 62
2.6 Electric Field and dE/dt Measurements . . . . . 68
2.6.1 The flat plate antenna . . . . . . 68
2.6.2 Electric field measurements . . . . . 76
2.6.3 dE/dt measurements . . . . . . 86
2.7 Magnetic Field and dB/dt Measurements . . . . 89
2.7.1 The coaxial-loop magnetic field antenna . . . 91
2.7.2 Magnetic field measurements . . . . . 100
2.7.3 dB/dt measurements . . . . . . 107
2.8 Optical Measurements and Trigger System.... . . . 111










2.9
2.10
2.11
2.12


Other M easurements . ................
Video System . . . . . .
GPS Timing System . ................
One-Line Measurement Diagram . .........


3 DATA ...............................
3.1 Data Summary and Organization . . . ..
3.2 NLDN-Reported Parameters of Recorded Flashes . .
3.3 Data Calibration and Processing . ..........

4 DETERMINING THE LOCATION OF LIGHTNING EVENTS
4.1 M ethodology . ........
4 .2 R results . . . . . . .


. . 122
. . 125
. . 128
. . 129

......... 133
. . 133
. . 139
. . 148

. . . 152
. . 152
. . 155


5 ANALYSIS OF MEASURED WAVEFORMS. . . . 164
5.1 Comparison of Measured Electric Field and Numerically-Integrated
dE/dt Waveforms .... ........ . . . . ..164
5.2 Relative Azimuth Angles Between the Lightning Channel and
the Loop Sensor . . . .. . . . . 174
5.3 Description of Close Negative First Stroke Field and Field Derivative
W aveform s . . . . . . . . 177
5.4 Measurement of Waveform Parameters . . . . . 199
5.4.1 Electric field waveforms . . . . . 199
5.4.2 dE/dt and dB/dt waveforms . . . . . 202
5.4.3 Magnetic field waveforms . . . . . 204
5.5 Electric Field Waveform Parameters Versus Distance . ..... 207
5.6 Statistics on Measured Stepped Leader and First Return Stroke
Electric Field Waveform Parameters . . . 221
5.7 Statistics on Measured First Return Stroke dE/dt Waveform Parameters 230
5.8 First Return Stroke Magnetic Field Waveform Parameters . . 235
5.9 Lightning Channel Properties Inferred from Measured Electric
Field W aveform s . . . . . . . .239
5.9.1 Leader model . . . . . . . .239
5.9.2 Leader charge density, speed, and current inferred from
measured electric field waveforms.... . . . 241

6 MODELING OF MEASURED WAVEFORMS .................. 250
6.1 Calculation of Lightning Electric and Magnetic Fields . . . 250
6.2 Transmission-Line-Type Return Stroke Models ... . ...... 254
6.3 Effects of Field Propagation Over a Finitely Conducting Ground . 261
6.4 Modeling of Triggered-Lightning Strokes Having Characteristics
Similar to Natural First Strokes . . . . . . 265
6.4.1 Triggered-lightning flash S0123 . . . . 265
6.4.1.1 Experiment and data. . . . . .265
6.4.1.2 Modeling of S0123-3 . . . . .274










6.4.2 Interpretation of modeling results for SO 123-3 . . ..
6.4.3 Triggered-lightning stroke S9934-8 . . .
6.5 Modeling of First Return Stroke Field and Field-Derivative Waveforms .
6.5.1 First return stroke current waveforms . . .
6.5.2 Characterization of first return stroke fields and field derivatives
calculated with the transmission line model . .
6.5.3 Comparison of measured first return stroke fields and
field derivatives with those calculated using the transmission
line model ........... . . .....
6.6 Modeling of Stepped Leader Pulses. . .....
6.6.1 Triggered-lightning flash S0123 . .....
6.6.2 Natural flash MSE0303.. . .....


7 ANALYSIS OF NATURAL BIPOLAR FLASH MSE0202
7.1 General Flash Characteristics . . . .
7.2 First Positive Stroke Characteristics . .....
7.3 Subsequent Stroke Characteristics . . .


. . . 331
.. . 33 1
.. . 336
.. . 355


8 SUMMARY OF RESULTS AND RECOMMENDATIONS FOR FUTURE
RESEARCH ................... .............. .. 362
8.1 Summary of Results . . . . . . . .362
8.2 Improvements to the MSE System . . . . . 371
8.3 Recommendations for Future Research . . . . . 372


APPENDIX


A AMPLITUDE CALIBRATION FACTORS FOR RECORDED DATA .


. 374


LIST OF REFERENCES ................................ 378


BIOGRAPHICAL SKETCH . ................... .


S. 283
S. 287
S. 291
S. 292

S. 294


S. 311
S. 321
S. 322
S. 326


. 393















LIST OF TABLES
Table page

1-1 Parameters of downward negative lightning derived from channel-base
current measurements. Note the rise times reported here are
likely to be biased towards larger values and rates of rise to
toward lower values due to the limited time resolution of the
data in the study . . . . . . . 15

2-1 List of MSE stations and associated measurements, for the 2002-2004
experim ents . . . . . . . . 38

2-2 Typical MSE measurement configuration settings for the 2002-2004
experim ent . . . . . . . . 41

2-3 MSE station locations, measured in 1999 with a differential
GPS (DGPS) receiver, having a nominal accuracy of a few meters.
For Stations 4 and 9, measurements were performed at both
the E-field and B-field antennas. . . . . . 45

2-4 MSE station locations, measured in 2004 with a Garmin Etrex
Venture hand-held GPS receiver with WAAS, having a nominal
accuracy of a few meters. For stations with multiple sensors,
the coordinates were measured at the location of the dE/dt antenna . 45

2-5 MSE station locations, measured in 2005 with a Garmin Etrex
Venture hand-held GPS receiver with WAAS, having a nominal
accuracy of a few meters. For stations with multiple sensors,
the coordinates were measured at the approximate center of
the station . . . . . . . . 46

2-6 Locations of rocket launchers used at the ICLRT facility, some
measured on multiple occasions with different GPS receivers. .. . 47

2-7 MSE station locations, as well as other landmarks, given in
Camp Blanding coordinates (CBC). Corresponding state plane
coordinates (SPC) are obtained by adding 99750 and 621500
to the east (X) and north (Y) CBC values, respectively. . . 48

2-8 MSE fiber-optic link summary . . . . . 56









2-9 OTDR measured optical lengths and corresponding time delays
for armored fiber-optic cables used in the MSE network. . . 63

2-10 Digital storage oscilloscopes (DSOs) used in the MSE system.
Specific oscilloscope configurations for data obtained by the
MSE system are given in Tables 3-3 and 3-4...... . . 63

2-11 Salient characteristics of the MSE electric field measurements. .. . 85

2-12 Salient characteristics of the MSE dE/dt measurements. Note
that the PIC controller attenuation setting, Gpic, varied between
2002 and 2004 . . . . . . . 89

2-13 Salient characteristics of the MSE B-field measurements. Note
that the PIC controller attenuation setting, Gplc, varied between
2002 and 2004 . . . . . . . 107

2-14 Salient characteristics of the MSE dB/dt measurements. Note
that the in-line attenuation setting, Gatt, varied between 2002
and 2004. Note that the measurements at Station 1 were offline
in 2004 due to water damage . . . . . . 109

2-15 Current measurements recorded on the MSE Yokogawa DL716
digitizer (Scope 19) . . . . . . . 124

2-16 Orientations of video cameras in the MSE network. . . . 126

3-1 List of natural cloud-to-ground flashes recorded by the Multiple
Station Experiment (MSE) system, along with the corresponding
digitizer data file names. All flashes lowered negative charge
to ground unless otherwise noted. Flash times given with microsecond
precision were obtained from the GPS timing system discussed
in Section 2.11 or the NLDN (see Section 3.2). Flash times
given with minute precision were obtained from video or oscilloscope
records and should be considered approximate and accurate
within a few minutes . . . . . . . 135

3-2 List of rocket-triggered flashes recorded by the Multiple Station
Experiment (MSE) system, along with the corresponding launcher
locations and digitizer data file names. All flashes lowered negative
charge to ground unless otherwise noted. Flash times given
with microsecond precision were obtained from the GPS timing
system discussed in Section 2.11. Flash times given with minute
precision were obtained from video or oscilloscope records
and should be considered approximate and accurate within a
few m minutes . . . . . . . . 136









3-3 Digitizer configuration for natural flashes recorded by the MSE
network. Sampling rate for Scope 19 is 10 MHz.. . . . 137

3-4 Digitizer configuration for rocket-triggered flashes recorded
by the MSE network. Sampling rate for Scope 19 is 10 MHz. .. . 138

3-5 NLDN-reported parameters for natural flashes MSE0201 through
M SE 0208 . . . . . . . . 144

3-6 NLDN-reported parameters for natural flashes MSE0209 through
M SE 0302 . . . . . . . . 145

3-7 NLDN-reported parameters for natural flashes MSE0303 through
M SE 0406 . . . . . . . . 146

3-8 NLDN-reported parameters for natural flashes MSE0407 through
M SE 04 12 . . . . . . . . 147

4-1 Location results for the first stroke of classical-triggered flash
FPL0213. Results are given for each combination of three stations.
The locations are given in "Camp Blanding Coordinates" (CBC),
which can be converted to State Plane Coordinates (SPC) by
adding 99750 and 621500 m to the east and north values, respectively.
The ground-truth location is (637, 459). . . . . 158

4-2 Location estimates (ground strike points) for natural first return
strokes recorded by the MSE network, obtained with the 2-D
TOA technique, using the time difference of arrival of features
(typically the peak) of the measured dE/dt waveforms. In cases
where four dE/dt stations were available, typically the four individual
location solutions (from four sets of three stations) were averaged
to obtain the estimated location. The locations are given in "Camp
Blanding Coordinates" (CBC), which can be converted to State
Plane Coordinates (SPC) by adding 99750 and 621500 m to
the east and north values, respectively. . . . . 160

4-3 Location results for the first stroke of natural negative flash
MSE0303, estimated using the 2-D TOA technique. Results
are given for each combination of three stations. The locations
are given in "Camp Blanding Coordinates" (CBC), which can
be converted to State Plane Coordinates (SPC) by adding 99750
and 621500 m to the east and north values, respectively. . . 161









4-4 Location results for the first stroke of natural negative flash
MSE0210, estimated using the 2-D TOA technique. Results
are given for each combination of three stations. The locations
are given in "Camp Blanding Coordinates" (CBC), which can
be converted to State Plane Coordinates (SPC) by adding 99750
and 621500 m to the east and north values, respectively . .


. 162


5-1 Amplitude scaling factors for the electric field derivatives (dE/dt)
measured at Stations 4 and 9, estimated by comparing measured
electric field (E) with numerically-integrated dE/dt. Scaling
factors were estimated for each of the storm days in which both
E and dE/dt were available. . . . . ........ 173

5-2 Relative azimuth angles, 4, between the location of the lightning
channel and the locations of the north-south oriented loop sensors
at Stations 1, 4, and 9, for each of the natural first strokes recorded
by the MSE system. Also given is the secant of each angle,
which is an amplitude scaling factor that can be applied to B
and dB/dt waveforms measured that station...... . . 176

5-3 Relative azimuth angles, 4, between the locations of the ICLRT
rocket launchers and the locations of the north-south oriented
loop sensors at Stations 1, 4, and 9. Also given is the secant
of each angle, which is an amplitude scaling factor that can
be applied to B and dB/dt waveforms measured that station.
... . . . . . . . . 176


5-4 Parameters of the best-fit power-law equations (of the form
IAEL(r) = Arb) for the measured leader electric field change
versus distance for 14 natural negative first strokes. R2 is the
coefficient of determination. The equations were obtained for
AEL in kV m 1 and r in meters.. . .............

5-5 Parameters of the best-fit power-law equations (of the form
AEL(r)| =Arb) for the measured leader electric field change
versus distance for 29 strokes (first and subsequent) in 6 natural
negative flashes. R2 is the coefficient of determination. The
equations were obtained for AEL in kV m 1 and r in meters. .

5-6 Parameters of the best-fit power-law equations (of the form
AEL(r) = Arb) for the measured leader electric field change
versus distance for 32 strokes in triggered-lightning flashes
FPL0208 through FPL0331 (8 flashes total). R2 is the coefficient
of determination. The equations were obtained for AEL in kV
m 1 and r in meters . ...................


. .. 209





. 210







. 211









5-7 Parameters of the best-fit power-law equations (of the form
AEL(r) = Arb) for the measured leader electric field change
versus distance for 16 strokes in triggered-lightning flashes
FPL0336 through FPL0403 (5 flashes total). R2 is the coefficient
of determination. The equations were obtained for AEL in kV
m 1 and r in m eters . . . . . . .212

5-8 Parameters of the best-fit linear equations (of the form THpw(r)
= Ar+b) for the measured stepped-leader/first-return-stroke
electric field half-peak width versus distance for 14 natural negative
first strokes. R2 is the coefficient of determination. The equations
were obtained for THPW in uts and r in meters. . . . 217

5-9 Parameters of the best-fit linear equations (of the form THpw(r)
= Ar+b) for the measured leader/return-stroke electric field
half-peak width versus distance for 29 strokes (first and subsequent)
in 6 natural negative flashes. R2 is the coefficient of determination.
The equations were obtained for THPW in pts and r in meters. .. . 218

5-10 Parameters of the best-fit linear equations (of the form THpw(r)
= Ar+b) for the measured leader/return-stroke electric field
half-peak width versus distance for 32 strokes in triggered-lightning
flashes FPL0208 through FPL0331 (8 flashes total). R2 is the
coefficient of determination. The equations were obtained for
THPW in pts and r in meters . . . . . .219

5-11 Parameters of the best-fit linear equations (of the form THpw(r)
= Ar+b) for the measured leader/return-stroke electric field
half-peak width versus distance for 16 strokes in triggered-lightning
flashes FPL0336 through FPL0403 (5 flashes total). R2 is the
coefficient of determination. The equations were found for THPW
in ts and r in m eters . . . . . . .220

5-12 Statistics on the distances at which stepped-leader/first-stroke
electric fields were measured. The data were sorted by distance
into 100 m bins, beginning with 100 200 m, except for the
last bin, which contains one value measured at a distance greater
than 1000 m. All units are meters. . . . . . .222

5-13 Statistics on the first-stroke stepped leader electric field change,
AEL. The data were sorted by distance into 100 m bins, beginning
with 100 200 m, except for the last bin, which contains one
value measured at a distance greater than 1000 m. . . . 222









5-14 Statistics on the first return stroke electric field change at 20 his,
AER-20. The data were sorted by distance into 100 m bins, beginning
with 100 200 m, except for the last bin, which contains one
value measured at a distance greater than 1000 m. . . . 223

5-15 Statistics on the first return stroke electric field change at 100 his,
ER 100. The data were sorted by distance into 100 m bins,
beginning with 100 200 m, except for the last bin, which contains
one value measured at a distance greater than 1000 m. . . 223

5-16 Statistics on the first return stroke electric field change at 1000 his,
AER 1000. The data were sorted by distance into 100 m bins,
beginning with 100 200 m, except for the last bin, which contains
one value measured at a distance greater than 1000 m. . . 224

5-17 Summary of the mean values of AE, AER, and THPW. The data
were sorted by distance into 100 m bins, beginning with 100 200 m,
except for the last bin, which contains one value measured at
a distance greater than 1000m . . . . . .224

5-18 Statistics on the distances at which stepped-leader/first-stroke
electric fields were measured. The data were sorted by distance
into bins of increasing size, beginning with 100 200 m. All
units are m eters . . . . . . . .226

5-19 Statistics on the first-stroke stepped leader electric field change,
AEL. The data were sorted by distance into bins of increasing
size, beginning with 100 200 m. . . . . . .227

5-20 Statistics on the first return stroke electric field change at 20 his,
AER-20. The data were sorted by distance into bins of increasing
size, beginning with 100 200 m. . . . . . .227

5-21 Statistics on the first return stroke electric field change at 100 his,
AER-100. The data were sorted by distance into bins of increasing
size, beginning with 100 200 m. . . . . . .227

5-22 Statistics on the first return stroke electric field change at 1000 his,
AER-1000. The data were sorted by distance into bins of increasing
size, beginning with 100 200 m. . . . . . .227

5-23 Statistics on the electric field stepped-leader/first-stroke field
waveform half-peak width, THPw. The data were sorted by distance
into 100 m bins, beginning with 100 200 m, except for the
last bin, which contains one value measured at a distance greater
than 1000 m . . . . . . . . 228









5-24 Statistics on the distances at which first stroke dE/dt waveforms
were measured. The data were sorted by distance into 100 m
bins, beginning with 0 100 m, except for the last bin, which
contains one value measured at a distance greater than 1000 m.
All units are meters . ...................

5-25 Statistics on the first return stroke dE/dt peak. The data were
sorted by distance into 100 m bins, beginning with 0 100 m,
except for the last bin, which contains one value measured at
a distance greater than 1000 m. No scaling factors were applied
to the data . . . . . . . .

5-26 Statistics on the first return stroke dE/dt peak, based only on
scaled data obtained at Stations 4 and 9. The data were sorted
by distance into 100 m bins, beginning with 100 200 m, except
for the last bin, which contains one value measured at a distance
greater than 1000 m. . ..................

5-27 Statistics on the first return stroke dE/dt half-peak width, THPW.
The data were sorted by distance into 100 m bins, beginning
with 100 200 m, except for the last bin, which contains one
value measured at a distance greater than 1000 m. Note that
THPW was not calculated for waveforms with saturated peaks..


. . 230






. 231






. 232






. 233


5-28 Statistics on the first return stroke dE/dt 30-90% rise time, T3o090.
The data were sorted by distance into 100 m bins, beginning
with 100 200 m, except for the last bin, which contains one
value measured at a distance greater than 1000 m. Note that
T30-90 was not calculated for waveforms with saturated peaks. .. . 234

5-29 Initial peak, BEW,i, and maximum peak, BEW,max values of the
return stroke magnetic field waveforms (east-west component
only) measured at Stations 4 and 9, for 14 negative first strokes
recorded by the M SE system . . . . . . 236

5-30 Parameters of the return stroke magnetic field waveforms measured
at Stations 4 and 9, for 14 negative first strokes recorded by
the MSE system. The quantities Bi and Bmax are the values BEW,i
and BEW,max, respectively, given in Table 5-29, scaled by the
appropriate values given in Table 5-2 (in order to account for
the relative orientation between the lightning channel and the
magnetic field loop sensor) . . . . . . 237









5-31 Statistics on the measured parameters of the first return stroke
magnetic field waveforms recorded by the MSE system. The
data were sorted by distance into bins of increasing size, beginning
w ith 100 200 m . . . . . . . .238

5-32 Stepped-leader charge density (p), speed (v), and current (I
= pv) estimates for 14 natural negative first strokes. For both
p and v, the values given are the means of the values calculated
at each station, along with the standard deviation. . . . 243

5-33 Subsequent-leader charge density (p), speed (v), and current
(I = pv) estimates for 23 negative subsequent strokes in 6 natural
flashes. For both p and v, the values given are the means of
the values calculated at each station, along with the standard
deviation . . . . . . . . .245

6-1 Parameters of the current and current derivative waveforms
used for modeling event MSE0211 using the one-wave and
two-wave transmission line models. The first five items are
the parameters used in generating a first stroke current derivative
(dl/dt) waveform from Equation 6.30. The remaining six items
are some measured parameters of the generated current and
dl/dt waveforms. Ipeak is the peak current, Isf is the approximate
maximum slow front current amplitude, Tsf is the approximate
duration of the slow front, (dl/dt)peak is the maximum value
of the dl/dt waveform, (dl/dt),f is the approximate maximum
slow front dI/dt amplitude, and (dl/dt)thpw is the half-peak
width of the dl/dt waveform . . . . . . 313


6-2 Parameters of the one-wave and two-wave transmission line
models used for modeling event MSE0211. Hj is the height
of the junction, V,p is the speed of the upward wave, Vdown is
the speed of the downward wave, vref is the speed of the reflected
wave, and F is the current reflection coefficient at ground ..

7-1 Location results for the first (positive) stroke of natural bipolar
flash MSE0202, estimated using the 2-D TOA technique. Results
are given for each combination of three stations. The locations
are given in "Camp Blanding Coordinates" (CBC), which can
be converted to State Plane Coordinates (SPC) by adding 99750
and 621500 m to the east and north values, respectively .

7-2 Distances to various locations within the MSE network from
the first (positive) stroke channel of natural bipolar flash MSE0202,
the location of which was estimated using the 2-D TOA technique
(see Table 7-1 and Figure 7-3) ........... . .....


. 313


. 334




. 336









7-3 Parameters of natural bipolar flash MSE0202. . . .


7-4 Parameters of the measured electric field waveforms for the
first (positive) stroke of natural bipolar flash MSE0202. . . 344

7-5 Parameters of the measured dE/dt waveforms for the first (positive)
stroke of natural bipolar flash MSE0202. . . . . 351

A-1 Amplitude calibration factors for MSE data recorded in 2002,
organized by date. For some days, not all data were recorded.
. . . . . . . . . 3 7 5

A-2 Amplitude calibration factors for MSE data recorded in 2003,
organized by date. For some days, not all data were recorded.
. . . . . . . . . 3 7 6

A-3 Amplitude calibration factors for MSE data recorded in 2004,
organized by date. For some days, not all data were recorded.
. . . . . . . . . 3 7 7


337















LIST OF FIGURES
Figure page

1-1 Four primary types of cloud-to-ground (CG) lightning flashes.
A) Downward negative. B) Upward negative. C) Downward
positive. D) Upward positive. Only the initial leader is shown
for each type . . . . . . . . 6

1-2 Sequence events in a natural negative cloud-to-ground lightning
flash.......... .. ....... ... ......... 7

1-3 Average negative first- and subsequent-stroke current waveshapes
each shown on two time scales, A and B. The lower time scales
(A) correspond to the solid curves, while the upper time scales
(B) correspond to the broken curves. The vertical (amplitude)
scale is in relative units, the peak values being equal to negative
unity .. . . . . . ... .. 16

1-4 Waveforms of the current measured on tower bottom for the
first stroke (A) and two subsequent strokes (B and C) in a flash
in South A frica . . . . . . . 17

1-5 Illustration of the types of bipolar discharges. A) Type 1. B)
Type 2. C) Type 3. D) Type 4 . . . . . 22

1-6 Typical vertical electric field intensity (A) and azimuthal magnetic
flux density (B) waveforms for first (solid line) and subsequent
(broken line) return strokes (leader waveforms not shown) at
distances of 1, 2, 5, 10, 15, 50, and 200 km. Time scales are
in m icroseconds . . . . . . . 27

1-7 Electric field waveforms of (a) a first return stroke, (b) a subsequent
stroke initiated by a dart-stepped leader, and (c) a subsequent
return stroke initiated by a dart leader, showing the fine structure
both before and after the initial field peak. Each waveform is
shown on two time scales, 5 us per division (labelled 5) and
10 us per division (labeled 10). The fields are normalized to
a distance of 100 km. Leader pulses (L), slow front (F), and
fast transition (R) are indicated. . . . . . 29


xvii









1-8 An example of dE/dt (A) and E (B) produced by a first return
stroke at a distance of about 36 km over the Atlantic Ocean.
The propagation path was almost entirely over salt water. . . 31

1-9 Sketch of the ICLRT facility at Camp Blanding, Florida, during
2002-2004. Approximate locations ofMSE field sensors (see
Section 2.1) are also shown. . . . . . . 32

1-10 The tower rocket launcher . . . . . . 33

1-11 The mobile rocket launcher in its rest position. . . . 34

1-12 The Launch Control trailer. A) View from the south-east. B)
View from the north-west. Photos courtesy of Brian DeCarlo. .. . 35

2-1 Diagram illustrating the operation of the MSE system in 2002-2004. 39

2-2 Sketch of the MSE system during the 2002-2004 experiments.
Objects, except for the MSE field stations and the optical sensors,
are approximately to scale . . . . . . 40

2-3 The MSE control system in the Launch Control trailer. The
control center is also used for rocket-triggered lightning operations.
A) Above the counter. B) Below the counter. Photos courtesy
of Brian D eCarlo . . . . . . . 50

2-4 Electric field mill located a few meters west of the Launch Control
trailer . . . . . . . . . 5 1

2-5 Flowchart representation of the MSE software control algorithm. .. 52

2-6 The PIC controller. A) Front view. B) Side view. . . . 53

2-7 Diagram of how a PIC controller is connected to other elements
of a measurement system . . . . . . 53

2-8 A typical measurement configuration utilizing a PIC controller. .. . 54

2-9 PIC RF unit enclosure mounted with a solar cell. . . . 55

2-10 Measured frequency response of PIC controller #39. The frequency
response was measured for each attenuation setting. The dashed
lines indicate the ideal attenuation values. . . . . 56

2-11 Measured frequency response of three Opticomm MMV-120
fiber-optic links used in the MSE network. . . . . 58


xviii









2-12 Digital storage oscilloscopes in the Launch Control trailer. The
models of some DSOs are labeled. Note that this picture was
taken in 2005 and this is not how the DSOs were arranged in
the 2002-2004 MSE system . . . . . . 64

2-13 Flat plate antenna used in E-field and dE/dt measurements. The
sensing element is the circular portion of area a 0.155 m2 surrounded
by an annular air gap. The remainder of the structure is the antenna
housing, grounded via a 3-m ground rod. The wire screen surrounding
the sensor and attached to the grounded housing serves to reduce
the enhancement of the electric field by the antenna. . . . 69

2-14 Detailed mechanical drawing of the aluminum flat plate antenna
used in the M SE . . . . . . . 70

2-15 Diagram of an installation of a MSE measurement utilizing
a flat-plate antenna . . . . . . . 71

2-16 Picture of a MSE measurement utilizing a flat-plate antenna. .. . 72

2-17 Frequency-domain equivalent circuit, using a Norton equivalent
current source, of a flat-plate antenna sensor feeding a load
(represented by ZL) . . . . . . . 75

2-18 Integrator capacitor assembly used in the MSE. A) Closed Pomona
box. B) Box open to show interior . . . . . 79

2-19 Measured (solid line) and ideal (dashed line) test circuit responses
for integrating capacitor unit #09 (0.209 tF)...... . . 81

2-20 Schematic of the high-impedance amplifier used in the MSE
electric field measurements . . . . . . 82

2-21 Measured frequency response of amplifier #2...... . . 83

2-22 Diagram of a MSE electric field measurement. . . . 83

2-23 Inside of a metal enclosure containing the electronics for an
MSE electric field measurement . . . . . 84

2-24 Diagram of a MSE dE/dt measurement. . . . . 88

2-25 Inside of a metal enclosure containing the electronics for an
M SE dE/dt measurement . . . . . . 88









2-26 Square loops of 50 Q coaxial cable in PVC pipe. A) Crossed-loop
measurement. B) Single-loop measurement. Metal enclosures
housing measurement electronics are located near each antenna. .. 91

2-27 Frequency-domain Thevenin equivalent circuit of a coaxial-cable
loop antenna. The circuit consists of an ideal open-circuit voltage,
Voop(co), in series with source impedance, Z,, and load impedance
Z L . . . . . . . . . 9 4

2-28 Diagram (A) and equivalent circuit (B) of a differential-output
coaxial loop antenna with both ends of the cable terminated
in 50 . . . . . . .... . 9 8

2-29 Diagram (A) and equivalent circuit (B) of a single-ended output
coaxial loop antenna with both ends of the cable terminated
in 50 . . . . . . .... . 9 9

2-30 Example active integrator circuit. . . . . . 102

2-31 Active integrator circuit used in the MSE magnetic field measurements. 103

2-32 Measured frequency responses of the active integrators used
in the MSE magnetic field measurements....... . . 104

2-33 Diagram of a MSE magnetic field measurement. . . . 105

2-34 Inside of a metal enclosure containing the electronics for an
MSE magnetic field measurement. . . . . . 105

2-35 Diagram of a MSE dB/dt measurement. . . . . 109

2-36 Corrected (relative to Jerauld, 2003) schematic of the MSE
optical sensor circuit . . . . . . . 111

2-37 Sketch of the optical sensor cover installed in 2003. . . . 113

2-38 Diagram of a MSE optical measurement....... . . 114

2-39 Optical measurement assembly, located at the south-west corner
of the MSE network. A) Closed measurement box. B) Open
m easurem ent box. . . . . . .. ...... 115

2-40 Diagram of trigger configuration A. . . . . . 118

2-41 Diagram of trigger configuration B-1. Configurations B-2 and
B-3 are obtained by moving the switch to positions 2 and 3,
respectively . . . . . . . . 119









2-42 Diagram of trigger configuration C. . . . . . 120

2-43 Trigger circuit used in the MSE system. . . . . 121

2-44 Frame of video from the MSE video recording system. Each
quadrant is an individual camera view with the labels corresponding
to the locations indicated on Figure 2-2. . . . . 128

2-45 Accutime GPS antenna associated with the Datum bc627AT
GPS timing card. The antenna is mounted on the south end
of the Launch Control trailer . . . . . . 129

2-46 One-line diagram for the MSE electric and magnetic field measurements. 130

2-47 One-line diagram for the MSE dE/dt and dB/dt measurements. .. . 131

2-48 One-line diagram for the MSE optical measurements. . . 132

3-1 Map showing the locations of NLDN sensors in and around
the Florida region, as of late 2003. The approximate location
of Camp Blanding is also shown. . . . . . 139

3-2 Calibration signal acquired on a LeCroy oscilloscope. From
top to bottom, the three horizontal lines indicate the calculated
positive level, offset (DC level), and negative level, respectively. .. 150

4-1 Location of the first stroke of altitude-triggered flash FPL0205,
which terminated on Instrumentation Station 1 (IS1), estimated
using the 2-D TOA technique. The peaks of the first-stroke
dE/dt waveforms measured at Stations 1, 4, and 9 were used
in calculating the time differences. The top image shows all
four stations (colored boxes), the calculated solution (black
x), and the actual location (gray x). The bottom image is a
zoom of the top image around the intersection of the two hyperbolas.
... . . . . . . . . . 1 5 6

4-2 Location of classical-triggered flash FPL0213, which terminated
on the tower launcher (TL), estimated using the 2-D TOA technique.
The peaks of the dE/dt waveforms measured at Stations 1, 4,
and 8 were used in calculating the time differences. The top
image shows all four dE/dt stations (colored boxes), the calculated
solution (black x), and the actual location (gray x). The bottom
image is a zoom of the top image around the intersection of
the tw o hyperbolas . . . . . . . 157









4-3 Location results for the first stroke of natural negative flash
MSE0303, estimated using the 2-D TOA technique. The peaks
of the dE/dt waveforms measured at Stations 1, 4, 8, and 9 (locations
indicated by the colored boxes) were used in calculating the
time differences. Each of the four plots (each corresponding
to one combination of three stations) shows the two hyperbolas
defined by the station locations and measured time differences,
the intersection of which (each indicated by a black x) represents
the individual location solution. The coordinates of each location
estimate are given in Table 4-3. The gray box indicates the
location of the tower rocket launcher (TL). . . . . 161

4-4 Location results for the first stroke of natural negative flash
MSE0210, estimated using the 2-D TOA technique. The peaks
of the dE/dt waveforms measured at Stations 1, 4, 8, and 9 (locations
indicated by the colored boxes) were used in calculating the
time differences. Each of the four plots (each corresponding
to one combination of three stations) shows the two hyperbolas
defined by the station locations and measured time differences,
the intersection of which (each indicated by a black x) represents
the individual location solution. The coordinates of each location
estimate are given in Table 4-4. The gray box indicates the
location of the tower rocket launcher (TL). . . . . 163

5-1 Comparison of directly-measured E (blue curves) and integrated
dE/dt (red curves) at Station 4 (A) and Station 9 (B), for the
first stroke of natural flash MSE0201. No scaling has been applied
to the integrated dE/dt waveforms. . . . . . 168

5-2 Comparison of directly-measured E (blue curves) and integrated
dE/dt (red curves) at Station 4 (A) and Station 9 (B), for the
first stroke of natural flash MSE0201. The waveforms are the
same as those shown in Figure 5-1, except that the red curves
were each scaled by the indicated scale factor in order to match
the corresponding blue curves. . . . . . 169

5-3 Comparison of directly-measured E (blue curves) and integrated
dE/dt (red curves) at Station 4 (A) and Station 9 (B), for the
first stroke of natural flash MSE0303. The red curves were each
scaled by the indicated scale factor in order to match the corresponding
blue curves . . . . . . . . 170


xxii









5-4 Comparison of directly-measured E (blue curves) and integrated
dE/dt (red curves) at Station 4 (A) and Station 9 (B), for the
fifth stroke of natural flash MSE0303. The red curves were
each scaled by the indicated scale factor in order to match the
corresponding blue curves . . . . . . 171

5-5 Comparison of directly-measured E (blue curves) and integrated
dE/dt (red curves) at Station 4 (A) and Station 9 (B), for the
first stroke of triggered flash FPL0321. The red curves were
each scaled by the indicated scale factor in order to match the
corresponding blue curves . . . . . . 172


5-6 Plan-view diagram illustrating the relative azimuth angle between
a lightning channel and a north-south oriented loop sensor . .


. 175


5-7 Plot of the secant function versus angle in degrees. The inset
shows the same plot ranging from 0 to 80 degrees . ...

5-8 Example first-stroke electric field waveform for natural flash
MSE0410, displayed on a 20 ms time scale. The waveform
was measured at Station 6, which was about 260 m from the
channel . . . . . . . .

5-9 Overlayed first-stroke electric field waveforms for natural flash
MSE0410, displayed on a 5 ms time scale .. .......


. . 177


5-10 Example first-stroke electric field waveform for natural flash
MSE0410, displayed on a 200 uts time scale. The waveform
was measured at Station 6, which was about 260 m from the
channel. Some features of the waveform are labeled. . . 179

5-11 Example first-stroke electric field waveform for natural flash
MSE0410, displayed on a 50 uts time scale. The waveform was
measured at Station 6, which was about 260 m from the channel.
Some features of the waveform are labeled...... . . 180

5-12 Electric field waveforms, measured at six stations, for the first
stroke of natural flash MSE0410. Each waveform is displayed
on a 50 uts time scale. The estimated distance to the channel
is given on each plot . . . . . . . 182

5-13 Overlayed first-stroke electric field waveforms for natural flash
MSE0410, displayed on a 50 uts time scale. Each waveform
was vertically shifted so that it would begin with zero amplitude
and horizontally shifted so that the fast transition occurs at time
zero . . . . . . . . . 183


xxiii









5-14 Electric field waveforms from eight first return strokes, all measured
between 100 and 200 m of the channel. Each waveform is displayed
on a 200 uts time scale, with time zero corresponding the the
fast transition of the waveform. The waveforms are sorted by
distance, which is given on each plot . . . . 184

5-15 Electric field waveforms from eight different first return strokes,
all measured between 100 and 200 m of the channel. Each waveform
is displayed on a 100 uts time scale, with time zero corresponding
the the fast transition of the waveform. The waveforms are sorted
by distance, which is given on each plot. . . . . 185

5-16 Electric field waveforms from eight different first return strokes,
all measured between 100 and 200 m of the channel. Each waveform
is displayed on a 25 uts time scale, with time zero corresponding
the fast transition of the waveform. The waveforms are sorted
by distance, which is given on each plot. . . . . 186

5-17 Electric field waveforms from eight different first return strokes,
all measured between 200 and 300 m of the channel. Each waveform
is displayed on a 100 uts time scale, with time zero corresponding
the fast transition of the waveform. The waveforms are sorted
by distance, which is given on each plot. . . . . 187

5-18 Electric field waveforms from eight different first return strokes,
all measured between 300 and 400 m of the channel. Each waveform
is displayed on a 100 uts time scale, with time zero corresponding
the fast transition of the waveform. The waveforms are sorted
by distance, which is given on each plot. . . . . 188

5-19 Electric field waveforms from eight different first return strokes,
all measured between 400 and 500 m of the channel. Each waveform
is displayed on a 100 uts time scale, with time zero corresponding
the fast transition of the waveform. The waveforms are sorted
by distance, which is given on each plot. . . . . 189

5-20 First-stroke electric field (A) and magnetic field (B) waveforms
for natural flash MSE0303, displayed on a 20 uts time scale.
The waveforms were both measured at Station 9, which was
about 265 m from the channel. Only the east-west component
of the azimuthal magnetic field was measured. The waveforms
were shifted in time so that the fast transition occurs at time
zero . . . . . . . . . 190


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5-21 Magnetic field waveforms (east-west component only) from
eight different first return strokes, all measured between 100
and 300 m of the channel. Each waveform is displayed on a
00 uts time scale, with time zero corresponding the fast transition
of the waveform. The waveforms are sorted by distance, which
is given on each plot . . . . . . . 191

5-22 Magnetic field waveforms (east-west component only) from
eight different first return strokes, all measured between 300
and 400 m of the channel. Each waveform is displayed on a
100 uts time scale, with time zero corresponding the fast transition
of the waveform. The waveforms are sorted by distance, which
is given on each plot . . . . . . . 192

5-23 dE/dt waveform from the first stroke of natural flash MSE0303,
displayed on a 20 uts (A) and a 5 uts (B) time scale. The waveforms
were measured at Station 8, which was about 126 m from the
channel. The waveform was shifted in time so that the peak
occurs at time zero. Some features of the waveforms are labeled.
... . . . . . . . . . 1 9 3

5-24 dE/dt waveforms from eight different first return strokes, all
measured between 70 and 300 m of the channel. Each waveform
is displayed on a 100 uts time scale, with time zero corresponding
the peak of the waveform. The waveforms are sorted by distance,
which is given on each plot. . . . . . . 194

5-25 dE/dt waveforms from eight different first return strokes, all
measured between 70 and 300 m of the channel. Each waveform
is displayed on a 25 uts time scale, with time zero corresponding
the peak of the waveform. The waveforms are sorted by distance,
which is given on each plot. . . . . . . 195

5-26 dE/dt waveform from the first stroke of natural flash MSE0303,
displayed on a 15 uts time scale. The waveforms were measured
at Station 8, which was about 126 m from the channel. The
waveform was shifted in time so that the peak occurs at time
zero. The secondary pulse and following negative pulses are
labeled. Note that this is the same dE/dt waveform as shown
in Figure 5-23 . . . . . . . 196

5-27 North-south (A) and east-west (B) components of dB/dt, measured
at Station 1, at a distance of about 72 m from the first stroke
channel of flash MSE0203. Each waveform is displayed on
a 25 uts time scale, with time zero corresponding the peak of
the waveform. Note that both waveforms are slightly saturated. .. . 196









5-28 North-south (A) and east-west (B) components of dB/dt, measured
at Station 1, at a distance of about 72 m from the first stroke
channel of flash MSE0203. Each waveform is displayed on
a 10 uts time scale, with time zero corresponding the peak of
the waveform. Note that both waveforms are slightly saturated. .. . 197

5-29 North-south (A) and east-west (B) components of dB/dt, measured
at Station 1, at a distance of about 96 m from the first stroke
channel of flash MSE0207. Each waveform is displayed on
a 25 uts time scale, with time zero corresponding the peak of
the waveform. Note that both waveforms are slightly saturated. .. . 197

5-30 North-south (A) and east-west (B) components of dB/dt, measured
at Station 1, at a distance of about 96 m from the first stroke
channel of flash MSE0207. Each waveform is displayed on
a 10 uts time scale, with time zero corresponding the peak of
the waveform. Note that both waveforms are slightly saturated. .. . 198

5-31 Example first-stroke electric field waveform illustrating the
measured leader field change parameters. A) Overall electric
field waveform on a 20 ms time scale. B) Expansion of the waveform
shown in (A), on a 2.5 ms time scale. . . . . . 201

5-32 Example first-stroke electric field waveform illustrating the
measured return stroke field change parameters. The top plot
(A) shows the three measured return-stroke field changes and
the bottom plot (B) shows in detail the measurement of the parameter
AER-100. The quantity ER 100 is the value of the electric field
at 100 ts from the 5% value of AE 10. .... . . . 203

5-33 Example first-stroke dE/dt waveform illustrating the measured
waveform parameters. The top plot (A) shows the measured
peak value along with the corresponding 30, 50, and 90 percent
values. The bottom plot (B) shows the measured half-peak width
(THpw) and 30-90 percent rise time (T30-90). .. . . 205

5-34 Example first-stroke magnetic field waveform (east-west component
only) illustrating the measured waveform parameters. The top
plot (A) shows the measured maximum peak value (BEW,max)
along with the corresponding 50 percent value and the measured
half-peak width (THpw) The bottom plot (B) shows the measured
initial peak value (BEW,i) and corresponding 30-90 percent rise
tim e (T ,30-90) . . . . . . . .206


xxvi









5-35 Example first-stroke magnetic field waveform (east-west component
only) illustrating a case where the measured half-peak width
(THpw) is not uniquely identified. . . . . . 207

5-36 Leader electric field change plotted versus distance for the first
strokes of flashes MSE0201, MSE0203, MSE0205, MSE0209,
MSE0211, MSE0301, MSE0303, and MSE0401. Included on
each plot is the best-fit power-law equation of the form |AEL(r)
=Arb along with the corresponding coefficient of determination
(R2) . . . . . . ...... ... ... 213

5-37 Leader electric field change plotted versus distance for the first
strokes of flashes MSE0403, MSE0404, MSE0407, MSE0409,
MSE0410, MSE0411. Included on each plot is the best-fit power-law
equation of the form IAEL(r) =Arb along with the corresponding
coefficient of determination (R2). . . . . . 214

5-38 Stepped-leader/first-return-stroke electric field half-peak width
plotted versus distance for the first strokes of flashes MSE0201,
MSE0203, MSE0205, MSE0209, MSE0211, MSE0301, MSE0303,
and MSE0401. Included on each plot is the best-fit power-law
equation of the form THpw(r) Ar+b along with the corresponding
coefficient of determination (R2). . . . . . 215

5-39 Stepped-leader/first-return-stroke electric field half-peak width
plotted versus distance for the first strokes of flashes MSE0403,
MSE0404, MSE0407, MSE0409, MSE0410, MSE0411. Included
on each plot is the best-fit power-law equation of the form THpw(r)
SAr+b along with the corresponding coefficient of determination
(R 2) . . . . . .. .. . . 2 16

5-40 Mean leader electric field change plotted versus mean distance
within each 100 m bin. The vertical bars indicate the range of
values within each bin. Also given is the best-fit power law
equation and the corresponding coefficient of determination
(R 2) . . . . . . . ... 2 2 5

5-41 Mean leader electric field change plotted versus mean distance
within each non-uniform bin. The vertical and horizontal bars
indicate the range of values within each bin. Also given is the
best-fit power law equation and the corresponding coefficient
of determination (R2) . . . . . . .228


xxvii









5-42 Mean return stroke electric field change plotted versus mean
distance within each non-uniform bin. The three plots (A, B,
and C) correspond to the return stroke field changes measured
at 20, 100, and 1000 ts, respectively. The vertical and horizontal
bars on each plot indicate the range of values within each bin.
Also given is the best-fit power-law equations and the corresponding
coefficients of determination (R2). . . . . . .229

5-43 Illustration of the geometry involved in calculating the electric
and magnetic fields at horizontal distance r from a descending
leader (speed v) using the electrostatic and magnetostatic approximations,
respectively. The ground is assumed to be perfectly conducting.
. . . . . . . . . 2 3 9

5-44 Estimated leader (A) charge density, (B) velocity, and (C) current,
each plotted versus the NLDN-reported return stroke peak current,
for 13 negative first strokes. NLDN current was not available
for one event (MSE0404). (D) is a scatter plot of estimated
charge density versus velocity. Also given on each plot is the
best-fit linear equation and corresponding coefficient of determination
(R2). Note that for simplicity the charge density and current
values are presented as positive values. . . . . 244

5-45 Estimated leader (A) charge density, (B) velocity, and (C) current,
each plotted versus the NLDN-reported return stroke peak current,
for 15 negative subsequent strokes (in 5 natural flashes) in which
NLDN currents were available. (D) is a scatter plot of estimated
charge density versus velocity. Also given on each plot is the
best-fit linear equation and corresponding coefficient of determination
(R2). Note that for simplicity the charge density and current
values are presented as positive values. . . . . 247

5-46 Estimated leader charge density plotted versus the NLDN-reported
return stroke peak current, for 14 negative subsequent strokes
(in 4 natural flashes) for which NLDN currents were available.
These data are the same as in Figure 5-45, except that one data
point (corresponding to stroke 2 of flash MSE0301) was excluded
as an outlier. Also given is the best-fit linear equation (on the
reduced data set) and corresponding coefficient of determination
(R2). Note that for simplicity the charge density and current
values are presented as positive values. . . . . 248


xxviii









6-1 Illustration of the geometry involved in calculating electric and
magnetic fields on ground at horizontal distance r from a straight
and vertical antenna of length H = H -HB over a perfectly
conducting ground plane . . . . . . .253

6-2 Illustration of the transmission line model used to model the
return stroke process, along with the corresponding current
versus time waveforms at ground (z' = 0) and at two heights
zl an d z2. . . . . . . . . 2 55

6-3 Electric and magnetic fields calculated at a distance ofD = 1
km using an implementation of the transmission line (TL) model.
Shown top to bottom are current, vertical electric field, and
azimuthal magnetic field. For each result, the total field and
individual field components are shown. Parameters used in the
calculation are given in the top panel. Note that the field time
scales are normalized to account for the propagation delay. . . 257

6-4 Plot of Equation 6.21 (top) and its derivative (bottom), which
can be used in simulating the channel-base current in engineering
return stroke m odels . . . . . . .258

6-5 Plots of the function Swait (0, r, t, c) evaluated at r = 10 m, 100 m,
and 1 km, assuming a ground conductivity c = 0.001 S -m.
. . . . . ... 2 6 3

6-6 dE/dt waveforms calculated at (A) 10 m, (B) 100 m, and (C)
1 km, using the single-wave transmission line model. The input
current is that shown in Figure 6-4 and the assumed return stroke
speed is 108 m Is. The blue curves are the waveforms calculated
assuming a perfectly conducting ground (cy = ) and the red
curves are the waveforms calculated assuming a ground conductivity
a = 0.001 S m . . . . . . . .264

6-7 Monochrome video frame (A) and framing camera image (B)
recorded from the SATTLIF trailer for stroke 3 of triggered-lightning
flash SO 123. The framing camera image has been thresholded
for enhancement. Estimated heights are labeled on each image. .. . 268

6-8 Numerically-integrated dI/dt, dB/dt at 15 m, and dE/dt at 15
and 30 m waveforms for stroke 3 of triggered-lightning flash
SO 123. Positive current indicates positive charge moving upward
(negative charge lowered to ground) and the electric field polarity
is consistent with the atmospheric electricity sign convention.
Time zero indicates the trigger point of the digitizer. . . . 270


xxix









6-9 dl/dt, dB/dt at 15 m, and dE/dt at 15 and 30 m waveforms for
stroke 3 of triggered-lightning flash SO 123. Positive current
indicates positive charge moving upward (negative charge lowered
to ground) and the dE/dt polarity is consistent with the atmospheric
electricity sign convention. Time zero indicates the trigger point
of the digitizer . . . . . . . .271

6-10 dE/dt waveforms measured at Station 1, approximately 160
m from the first-stroke channel of natural negative flash MSEO410.
The middle and bottom plots show zooms of the final leader
step and slow front, respectively. The dE/dt polarity is consistent
with the atmospheric electricity sign convention. Note the fast-transition
peak is saturated . . . . . . . .273

6-11 Numerically-integrated versions of the first-stroke dE/dt waveforms
(measured about 160 m from the channel) presented in Figure
6-10, for natural flash MSEO410. The middle and bottom plots
show zooms of the final leader step and slow front, respectively.
Electric field polarity is consistent with the atmospheric electricity
sign convention. Note the dE/dt peak saturates at time 67.4
sus, thus the integrated waveform should be considered distorted
after that tim e . . . . . . . .274

6-12 Field derivatives calculated using the single-wave transmission
line model (TLM) at a speed of 108 m s 1 with dI/dt as input
and current originating at ground level for stroke 3 of triggered-lightning
flash SO 123. The field derivatives were calculated assuming
a perfectly conducting ground. Model-predicted results are compared
with measured waveforms. Note that the time scales are not
the same as in Figure 6-9 . . . . . . 276

6-13 Electrostatic, induction, and radiation field components (defined
by the formula of Uman et al., 1975) for dE/dt at 30 m, calculated
using the single-wave transmission line model (TLM) at a speed
of 108 m s 1 with dI/dt as input and current originating at ground
level, for stroke 3 of triggered-lightning flash SO 123. The total
field (sum of the three components) is also shown and is the
same as that in Figure 6-12 (the lower right panel). The field
derivative was calculated assuming a perfectly conducting ground.
The time scale corresponds to those in Figure 6-12. . . . 278









6-14 Field derivatives calculated using the two-wave transmission
line model (TLM) with dI/dt as input and current originating
at a height of 6.5 m, for stroke 3 of triggered-lightning flash
SO123. Model parameters are given in the upper-left panel and
the model-predicted results are compared with measured waveforms.
Hj is the height of the junction point (origin of the upward and
downward waves), F is the reflection coefficient at ground, and
v,p and Vdown are the speeds of the upward and downward waves,
respectively. The field derivatives were calculated assuming
a perfectly conducting ground. Model-predicted results are compared
with measured waveforms. The time values on the horizontal
axes correspond to those in Figure 6-12. . . . . 279

6-15 Field derivatives calculated using the two-wave transmission
line model (TLM) with dI/dt as input and current originating
at a height of 6.5 m, for stroke 3 of triggered-lightning flash
SO123. The model results are the same as presented as in Figure
6-14, but plotted on an expanded time scale around the fast
transition. Model parameters are given in the upper-left panel
and the model-predicted results are compared with measured
waveforms. Hj is the height of the junction point (origin of
the upward and downward waves), F is the reflection coefficient
at ground, and v,p and Vdown are the speeds of the upward and
downward waves, respectively. The field derivatives were calculated
assuming a perfectly conducting ground. Model-predicted results
are compared with measured waveforms. The time values on
the horizontal axes correspond to those in Figures 6-12 and
6- 14 . . . . . . . . . 2 8 0

6-16 Contributions from upward (dotted curve) and downward (solid
gray curve) waves to the model-predicted dE/dt waveform at
30 m, calculated using the two-wave transmission line model
(TLM) with dI/dt as input and current originating at a height
of 6.5 m, for stroke 3 of triggered-lightning flash SO123. The
total field (sum of the two components) is also shown (solid
black curve) and is the same as that in Figures 6-14 and 6-15
(the lower right panel in each figure). The field derivative was
calculated assuming a perfectly conducting ground. Model-predicted
results are compared with measured waveforms. The time scale
corresponds to those in Figures 6-12 and 6-14..... . .281


xxxi









6-17 Electric fields at 100 km calculated using the single and two-wave
transmission line (TL) models, assuming propagation over a
perfectly-conducting ground, for stroke 3 of triggered-lightning
flash S0123. Integrated dI/dt was used as input to both models
and model parameters are the same as used in the calculations
shown in Figures 6-12 (for single-wave model) and 6-14 (for
two-wave model). The time scale has been normalized to account
for the propagation over 100 km and corresponds to the time
values in Figure 6-8. The electric field waveform for the single-wave
model has the same shape as that of current (see Figure 6-8),
as follows from Equation 6.19. . . . . . 282

6-18 Field derivatives at 15 m, calculated using the two-wave transmission
line model (TLM) with dI/dt as input and current originating
at a height of 2 m, for stroke 8 of triggered-lightning flash S9934.
Model parameters are given in the lower-left panel and the model-predicted
results are compared with measured waveforms. Hj is the height
of the junction point (origin of the upward and downward waves),
F is the reflection coefficient at ground, and V,p, Vdown, and
Vref are the speeds of the upward, downward, and reflected waves,
respectively. Note that the peak of the measured dE/dt waveform
is slightly saturated . . . . . . .288

6-19 Still photograph of triggered-lightning flash S9934. The camera
was located on top of the SATTLIF trailer and faced east. The
(apparent) channel loop and height of the 2-m strike object are
labeled on the im age . . . . . . .289

6-20 (A) dI/dt waveform obtained from Equation 6.30 with the parameters
ac = 120 x 109 kAt 1is, c2 = 10 x 109 kAt 1is, Tpeak = 4 x 106 s,
y= 55 x 10-9 s, and 3 = 0.05. The inset shows an expansion
of the waveform around the peak of the dl/dt waveform. (B)
Current waveform obtained by numerically-integrating the dI/dt
waveform shown in (A) . . . . . . .294

6-21 Electric and magnetic fields and their derivatives calculated
at 50 m using the single-wave transmission line model. It is
assumed that the ground is perfectly conducting. The input
current is that shown in Figure 6-20 and the assumed return
stroke velocity is 1.5 x 108 m Is. For a given plot, the total
field or field derivative is indicated by the black curve. The
electrostatic, induction, and radiation field components are indicated
by the blue, red, and green curves, respectively. Time has been
normalized to account for propagation delay. . . . . 296


xxxii









6-22 Electric and magnetic fields and their derivatives calculated
at 100 m using the single-wave transmission line model. It is
assumed that the ground is perfectly conducting. The input
current is that shown in Figure 6-20 and the assumed return
stroke velocity is 1.5 x 108 m Is. For a given plot, the total
field or field derivative is indicated by the black curve. The
electrostatic, induction, and radiation field components are indicated
by the blue, red, and green curves, respectively. Time has been
normalized to account for propagation delay. . . . . 297

6-23 Electric and magnetic fields and their derivatives calculated
at 500 m using the single-wave transmission line model. It is
assumed that the ground is perfectly conducting. The input
current is that shown in Figure 6-20 and the assumed return
stroke velocity is 1.5 x 108 m Is. For a given plot, the total
field or field derivative is indicated by the black curve. The
electrostatic, induction, and radiation field components are indicated
by the blue, red, and green curves, respectively. Time has been
normalized to account for propagation delay. . . . . 298

6-24 Electric and magnetic fields and their derivatives calculated
at 50 m using the two-wave transmission line model. The effects
of field propagation over a finitely conducting ground have been
ignored. The initiation point of the current is 30 m and the current
reflection coefficient at ground (F) is 0.5. The velocity of all
waves is 1.5 x 108 m -s. The input current is that shown in
Figure 6-20, scaled by 1/(1+F) a 0.67. For a given plot, the
total field or field derivative is indicated by the black curve.
The electrostatic, induction, and radiation field components
are indicated by the blue, red, and green curves, respectively.
Time has been normalized to account for propagation delay. . . 299

6-25 Electric and magnetic fields and their derivatives calculated
at 100 m using the two-wave transmission line model. The effects
of field propagation over a finitely conducting ground have been
ignored. The initiation point of the current is 30 m and the current
reflection coefficient at ground (F) is 0.5. The velocity of all
waves is 1.5 x 108 m -s. The input current is that shown in
Figure 6-20, scaled by 1/(1+F) a 0.67. For a given plot, the
total field or field derivative is indicated by the black curve.
The electrostatic, induction, and radiation field components
are indicated by the blue, red, and green curves, respectively.
Time has been normalized to account for propagation delay. . . 300


xxxiii









6-26 Electric and magnetic fields and their derivatives calculated
at 500 m using the two-wave transmission line model. The effects
of field propagation over a finitely conducting ground have been
ignored. The initiation point of the current is 30 m and the current
reflection coefficient at ground (F) is 0.5. The velocity of all
waves is 1.5 x 108 m -s. The input current is that shown in
Figure 6-20, scaled by 1/(1+F) w 0.67. For a given plot, the
total field or field derivative is indicated by the black curve.
The electrostatic, induction, and radiation field components
are indicated by the blue, red, and green curves, respectively.
Time has been normalized to account for propagation delay. . . 301

6-27 dE/dt waveforms calculated at 100 m using the single-wave
(blue curve) and two-wave (red curve) transmission line models.
The input current for both models is that shown in Figure 6-20,
but scaled by 1/(1+F) a 0.67 for the two-wave model. The model
parameters for the single-wave and two-wave models are the
same as used for Figures 6-21 and 6-24, respectively. Time
has been normalized to account for propagation delay. . . 302

6-28 dE/dt waveform (black curve) calculated at 100 m using the
two-wave transmission line model. Also given are the contributions
to to the field from the upward (blue curve), downward (red
curve), and reflected (green curve) waves. The input current
and model parameters are the same as used for Figure 6-27.
Time has been normalized to account for propagation delay. . . 303

6-29 Electric (left column) and magnetic (right column) fields calculated
at 50, 100, and 500 m using the single-wave (blue curves) and
two-wave (red curves) transmission line models. The input current
for both models is that shown in Figure 6-20, but scaled by
1/(1+F) w 0.67 for the two-wave model. The model parameters
for the single-wave and two-wave models are the same as used
for Figures 6-21 and 6-24, respectively. Time has been normalized
to account for propagation delay. . . . . . 304

6-30 Electric field waveform (black curve) calculated at 50, 100,
and 500 m using the two-wave transmission line model. Also
given are the contributions to to the field from the upward (blue
curve), downward (red curve), and reflected (green curve) waves.
The input current and model parameters are the same as used
for Figure 6-24. Time has been normalized to account for propagation
d elay . . . . . . . . 3 0 5


xxxiv









6-31 Electric field waveforms calculated at 10 m using the single-wave
(blue curve) and two-wave (red curve) transmission line models.
The input current for both models is that shown in Figure 6-20,
but scaled by 1/(1+F) a 0.67 for the two-wave model. The model
parameters for the single-wave and two-wave models are the
same as used for Figures 6-21 and 6-24, respectively. Time
has been normalized to account for propagation delay. . . 306

6-32 Electric field waveform (black curve) calculated at 10 m using
the two-wave transmission line model. The electrostatic, induction,
and radiation field components are indicated by the blue, red,
and green curves, respectively. The input current and model
parameters are the same as used for Figure 6-24. Time has been
normalized to account for propagation delay. . . . . 307

6-33 Electric field waveforms calculated at 100 km using the single-wave
(blue curve) and two-wave (red curve) transmission line models.
The input current for both models is that shown in Figure 6-20,
but scaled by 1/(1+F) a 0.67 for the two-wave model. The model
parameters for the single-wave and two-wave models are the
same as used for Figures 6-21 and 6-24, respectively. Time
has been normalized to account for propagation delay. . . 307

6-34 Electric (left column) and magnetic (right column) fields calculated
at 50, 100, and 500 m using the two wave transmission line
model. The blue curves represent the field calculated assuming
no propagation effects and the red curves represent the field
calculated assuming a ground conductivity of 0.001 S m1
The input current for both models is that shown in Figure 6-20,
with the amplitude scaled by 1/(1+F) a 0.67. The model parameters,
with the exception of the assumed ground conductivity, are
the same as used for Figure 6-24. Time has been normalized
to account for propagation delay. . . . . . 309

6-35 dE/dt (left column) and dB/dt (right column) waveforms calculated
at 50, 100, and 500 m using the two wave transmission line
model. The blue curves represent the field derivative calculated
assuming no propagation effects and the red curves represent
the field calculated assuming a ground conductivity of 0.001
S m 1. The input current for both models is that shown in Figure
6-20, with the amplitude scaled by 1/(1+F) a 0.67. The model
parameters, with the exception of the assumed ground conductivity,
are the same as used for Figure 6-24. Time has been normalized
to account for propagation delay. . . . . . 310


xxxV









6-36 Current waveforms (A), along with the corresponding derivatives
(B), used for modeling the first return stroke of natural flash
MSE0211. The blue curves indicate the waveforms originating
from ground for the one-wave transmission line model, while
the red curves indicate the waveforms originating from the junction
point for the two-wave model. . . . . . .312

6-37 dE/dt waveforms calculated at three distances using the one-wave
(blue curves) and two-wave (red curves) transmission line models.
The calculated waveforms are compared with the corresponding
measured waveforms (black curves). The source current waveforms
are shown in Figure 6-36, and parameters of the current waveforms
and of the models are given in Tables 6-1 and 6-2, respectively.
It is assumed that the fields are not influenced by propagation
effects. Note that the source current waveforms are different
for the two models. No dE/dt data were recorded at Station
9 due to equipment error. . . . . . . 315

6-38 dB/dt waveforms calculated at two distances using the one-wave
(blue curves) and two-wave (red curves) transmission line models.
The calculated waveforms are compared with the corresponding
measured waveforms (black curves). The source current waveforms
are shown in Figure 6-36, and parameters of the current waveforms
and of the models are given in Tables 6-1 and 6-2, respectively.
Note that both the east-west (EW) and north-south (NS) components
of the field were measured and calculated at Station 1, while
only the east-west component was measured at Station 4. It
is assumed that the fields are not influenced by propagation
effects. Note that the source current waveforms are different
for the two models. No dB/dt data were recorded at Station
9 due to equipment error. . . . . . . 316

6-39 Electric field waveforms calculated at five distances using the
one-wave (blue curves) and two-wave (red curves) transmission
line models. The calculated waveforms are compared with the
corresponding measured waveforms (black curves). The source
current waveforms are shown in Figure 6-36, and parameters
of the current waveforms and of the models are given in Tables
6-1 and 6-2, respectively. It is assumed that the fields are not
influenced by propagation effects. Note that the source current
waveforms are different for the two models. No E-field data
were recorded at Station 6 due to equipment error.... . ..... 317


xxxvi









6-40 Electric and magnetic field waveforms calculated at two distances
using the one-wave (blue curves) and two-wave (red curves)
transmission line models. The calculated waveforms are compared
with the corresponding measured waveforms (black curves).
The source current waveforms are shown in Figure 6-36, and
parameters of the current waveforms and of the models are given
in Tables 6-1 and 6-2, respectively. It is assumed that the fields
are not influenced by propagation effects. Note that the source
current waveforms are different for the two models. . . . 318

6-41 dE/dt waveforms calculated at three distances using the two-wave
transmission line model (red curves) The calculated waveforms
are compared with the corresponding measured waveforms
(black curves). The assumed ground conductivity is 0.004 S -m.
The two-wave TL model parameters are the same as used in
calculating the waveforms of Figure 6-37, but the source current
waveform is different with a peak of about 19 kA. No dE/dt
data were recorded at Station 9 due to equipment error. . . 319

6-42 dB/dt waveforms calculated at two distances using the two-wave
transmission line model (red curves) The calculated waveforms
are compared with the corresponding measured waveforms
(black curves). Note that both the east-west (EW) and north-south
(NS) components of the field were measured and calculated
at Station 1, while only the east-west component was measured
at Station 4. The assumed ground conductivity is 0.004 S -m.
The two-wave TL model parameters are the same as used in
calculating the waveforms of Figure 6-38, but the source current
waveform is different with a peak of about 19 kA. No dB/dt
data were recorded at Station 9 due to equipment error. . . 320

6-43 Current waveform used for modeling the leader step of triggered-lightning
stroke S 123-3. The waveform was generated using Equation
6.31 with the parameters Io = 5.5 kA, rl = 0.536, n = 2, Ti =
50 ns, and z2 = 250 ns . . . . . . 324


xxxvii









6-44 Field derivatives calculated at 15 and 30 m for the leader step
of triggered-lightning stroke S0123-3. The assumed current
derivative waveform (which is the derivative of the current waveform
shown in Figure 6-43) propagated upward from an initial height
of 12 m at a constant speed of 1.5 x 108 m Is. The amplitude
of the current derivative waveform decayed exponentially with
height, with a decay constant of 22 m. The calculated waveforms
(blue curves) are compared with the corresponding measured
waveforms (black curves). The initial values of the calculated
waveforms were vertically shifted to match the initial values
of the corresponding measured data. Time zero corresponds
to the beginning of the step waveforms. . . . . .325

6-45 Current waveform, along with its derivative, used for modeling
the leader step preceding the first stroke of natural flash MSE0303. .327

6-46 dE/dt waveforms calculated at four distances for the leader step
preceding the first stroke of natural flash MSE0303. The assumed
current derivative waveform (shown in Figure 6-45) propagated
upward from an initial height of 30 m at a constant speed of
1.7 x 108 m Is. The amplitude of the current derivative waveform
decayed exponentially with height, with a decay height constant
of 22 m. The calculated waveforms (blue curves) are compared
with the corresponding measured waveforms (black curves).
The distances labeled on each plot indicate the estimated distance
to the ground strike point. Time zero corresponds to the beginning
of the step waveforms . . . . . . .328

6-47 dB/dt waveforms calculated at three distances for the leader
step preceding the first stroke of natural flash MSE0303. The
assumed current derivative waveform (shown in Figure 6-45)
propagated upward from an initial height of 30 m at a constant
speed of 1.7 x 108 m Is. The amplitude of the current derivative
waveform decayed exponentially with height, with a decay height
constant of 22 m. The calculated waveforms (blue curves) are
compared with the corresponding measured waveforms (black
curves). At Station 1, both the east-west (EW) and north-south
(NS) components of dB/dt were calculated, while only the east-west
components were calculated at Stations 4 and 9. The distances
labeled on each plot indicate the estimated distance to the ground
strike point. Time zero corresponds to the beginning of the step
w aveform s . . . . . . . . .329


xxxviii









7-1 Electric (A) and magnetic (B) fields from natural bipolar flash
MSE0202, displayed on a 800 ms time scale. Time 0 indicates
the trigger point of the digitizer. The distance to the first-stroke
channel is about 290 m. The distance to the second and third
stroke channels is on the order of 500 m to 1 km. Note that only
the east-west component of the horizontal magnetic field was
measured, with the polarity reversal between strokes 1 and 2
(both positive) in B being due to the fact that the two strokes
were on roughly opposite sides of the loop antenna. In contrast,
the polarity reversal in A and B between strokes 2 and 3 (having
the same location) is due to the fact that the two strokes transported
charge of opposite polarity (positive and negative, respectively).
. . . . . . . . . 3 3 2

7-2 Map of the MSE network showing the estimated locations (each
indicated by an x) of the first (positive) and five subsequent
(one positive and at least three negative) strokes of natural bipolar
flash MSE0202. The first stroke location was estimated using
the 2-D TOA technique, while the general area of the subsequent
strokes was estimated from video records....... . . 333

7-3 Location results for the first (positive) stroke of natural bipolar
flash MSE0202, estimated using the 2-D TOA technique. The
initial peaks of the dE/dt waveforms measured at Stations 1,
4, 8, and 9 (locations indicated by the colored boxes) were used
in calculating the time differences. Each of the four plots (each
corresponding to one combination of three stations) shows the
two hyperbolas defined by the station locations and measured
time differences, the intersection of which (each indicated by
a black x) represents the individual location solution. The coordinates
of each location estimate are given in Table 7-1. The gray box
indicates the location of the tower rocket launcher (TL). . .335

7-4 Frame of video (inverted gray-scale) showing the first (positive)
stroke channel (thick black line) of natural bipolar flash MSE0202,
located approximately 680 m from the camera. The left portion
of the image is obscured by a rain shield placed over the window.The
bottom vertical portion of the channel is partially obscured by
the "Test house structure," which is located about 60 m from
the camera, and is barely visible in the image. Although the
channel appears to terminate on the structure, it does not, as
the channel and structure are separated by about 600 m. The
camera was facing approximately south-west. IS1 = Instrumentation
Station 1, where the camera was located. . . . . 338


xxxix









7-5 First (positive) stroke electric field waveforms from natural
bipolar flash MSE0202. The time scale is 130 ms. Time 0 indicates
the trigger point of the digitizer. The measurement at Station
10 was not functioning. Distances to each station are given in
Table 7-2 . . . . . .. . ....

7-6 First (positive) stroke electric field waveforms from natural
bipolar flash MSE0202. The time scale is 5 ms. Time 0 indicates
the trigger point of the digitizer. The measurement at Station
10 was not functioning. Distances to each station are given in
Table 7-2 . . . . . .. . ....

7-7 First (positive) stroke electric field waveforms from natural
bipolar flash MSE0202. The time scale is 40 ts. The measurement
at Station 10 was not functioning. Distances to each station
are given in Table 7-2 ............... . .....


7-8 Leader electric field changes plotted versus distance for the
first (positive) stroke of natural bipolar flash MSE0202. Also
plotted is the best fit power-law equation of the form AEL(r)
Arb ... .

7-9 Return stroke electric field waveform measured at Station 2,
for the first (positive) stroke of natural bipolar flash MSE0202.
Several waveform parameters are labeled on the figure . .

7-10 First (positive) stroke electric and magnetic field waveforms,
both measured at Stations 4 and 9, from natural bipolar flash
MSE0202. Only the east-west component of the magnetic fields
were measured. The time scale is 3 ms. The distance to the
measurement station is labeled on each plot ..

7-11 First (positive) stroke electric and magnetic field waveforms,
both measured at Stations 4 and 9, from natural bipolar flash
MSE0202. Only the east-west component of the magnetic fields
were measured. The time scale is 200 ts. The distance to the
measurement station is labeled on each plot ..


. 342



. . 343






. . 345






. . 346


7-12 First (positive) stroke electric and magnetic field waveforms,
both measured at Stations 4 and 9, from natural bipolar flash
MSE0202. The time scale is 40 ps. Only the east-west component
of the magnetic fields were measured. The distance to the measurement
station is labeled on each plot. . . . . . .346


. 339






. 340




. 341









7-13 Overlayed electric (blue curves) and magnetic (red curves) field
waveforms, measured at Station 4 (A) and Station 9 (B), from
the first (positive) stroke of natural bipolar flash MSE0202.
The time scale is 25 ts. Only the east-west component of the
magnetic fields were measured. The distance to the measurement
station is labeled on each plot. . . . . . .347

7-14 Electric field measured at a distance of 45 km by the Los Alamos
Sferics Array (LASA). The waveform is displayed on a (A)
2 ms, (B) 1.5 ms, and (C) 500 uts time scale. The amplitude
of the waveform has been normalized to its initial peak. Time
zero corresponds to the beginning of the fast transition. The
data is provided courtesy of Los Alamos National Laboratories
(L A N L ). . . . . . . . . .348

7-15 Magnetic field measured at 280 m (blue curve), overlayed with
the electric field measured at a distance of 45 km (red curve).
Time zero corresponds to the beginning of the fast transition.
The distant data was measured by the Los Alamos Sferics Array
(LASA) and is provided courtesy of Los Alamos National Laboratories
(L A N L ). . . . . . . . . .349

7-16 First (positive) stroke dE/dt waveforms from natural bipolar
flash MSE0202. The time scale is 200 ts. Time 0 indicates
the trigger point of the digitizer. The distance to the measurement
station is labeled on each plot. . . . . . .349

7-17 First (positive) stroke dE/dt waveforms from natural bipolar
flash MSE0202. The time scale is 40 ts. Time 0 indicates the
trigger point of the digitizer. The distance to the measurement
station is labeled on each plot. . . . . . .350

7-18 First (positive) stroke dE/dt waveforms from natural bipolar
flash MSE0202. The time scale is 10 ts. The distance to the
measurement station is labeled on each plot. ..... . . .350

7-19 First (positive) stroke dB/dt waveforms from natural bipolar
flash MSE0202. The time scale is 10 ts. Note that both the
east-west (EW) and north-south (NS) components of the field
were measured and calculated at Station 1, while only the east-west
component was measured at Station 4. The measurement at
Station 9 was not functioning. The distance to the measurement
station is labeled on each plot. . . . . . .352









7-20 dE/dt (blue curves) and dB/dt (red curves) waveforms measured
at Station 1 (A) and Station 4 (B), for the first (positive) stroke
of natural bipolar flash MSE0202. The time scale is 7 ts. The
amplitudes have been normalized and the corresponding dE/dt
and dB/dt waveforms at a given station have been overlayed.
Each of the waveforms was also filtered with a three point moving
average filter, in order to reduce noise. The distance to the measurement
station is labeled on each plot. . . . . . .352

7-21 dE/dt waveform measured at Station 9 from the first (positive)
stroke of natural bipolar flash MSE0202. The time scale is 4 ts.
The distance to the measurement station is labeled on the plot.
. . . . . . . . . 3 5 4

7-22 Second (positive) stroke electric field waveforms from natural
bipolar flash MSE0202. The time scale is 55 ms. The measurement
at Station 10 was not functioning. . . . . . .356

7-23 Second (positive) stroke electric field waveforms from natural
bipolar flash MSE0202. The time scale is 5 ms. The measurement
at Station 10 was not functioning. . . . . . .357

7-24 Second (positive) stroke electric field waveforms from natural
bipolar flash MSE0202. The time scale is 37 ts. The measurement
at Station 10 was not functioning. . . . . . .359

7-25 Third (negative) stroke electric field waveforms from natural
bipolar flash MSE0202. The time scale is 10 ms. The measurement
at Station 10 was not functioning. . . . . . .360

7-26 Third (negative) stroke electric field waveforms from natural
bipolar flash MSE0202. The time scale is 2 ms. The measurement
at Station 10 was not functioning. . . . . . .361















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 NATURAL CLOUD-TO-GROUND LIGHTNING INFERRED FROM
MULTIPLE-STATION MEASUREMENTS OF CLOSE ELECTRIC AND MAGNETIC
FIELDS AND FIELD DERIVATIVES

By

Jason Edward Jerauld

August 2007

Chair: Martin A. Uman
Co-Chair: Vladimir A. Rakov
Major: Electrical and Computer Engineering

This dissertation presents an examination of natural cloud-to-ground lightning in

Florida, experimental data for which were acquired in 2002 to 2004. Several processes

involved in natural lightning, in particular stepped leaders and first return strokes, were

studied using the electric (E) and magnetic (B) fields and field derivatives (dE/dt and

dB/dt) measured at distances ranging from about 50 m to 1 km. The experimental system

used, known as the Multiple Station Experiment (MSE) system, consisted of six electric

field sensors (bandwidth of 0.2 Hz to 4 MHz), two magnetic field sensors (10 Hz to

4 MHz), four dE/dt sensors (up to 20 MHz), and three dB/dt sensors (up to 20 MHz),

spread around an area of about 0.5 km2. The system is located at the International Center

for Lightning Research and Testing (ICLRT), and is operated by the University of Florida

Lightning Research Group. Between 2002 and 2004, data were acquired for about 20

lightning flashes, including one consisting of both positive and negative strokes, all

thought to have terminated on ground within or near the network. The channel locations

were estimated by a 2-D time-of-arrival method, using the peaks of the return stroke dE/dt

waveforms. The estimated locations were used in performing a statistical characterization


xliii









of several field waveform parameters (such as the leader and return stroke electric field

changes), and parameters of the leader channels (such as the line charge density, speed,

and current) were estimated from the acquired waveforms using simple models. Further,

new insights into the mechanisms of the stepped leader and ground attachment process

were gained from the experimental data and associated modeling.


xliv















CHAPTER 1
INTRODUCTION AND LITERATURE REVIEW

1.1 Introduction

This dissertation represents the embodiment of six years of work by the author. The

goal is to expand on the knowledge of natural cloud-to-ground lightning, and in particular

natural first return strokes, by examining the close lightning electromagnetic environment.

A number of studies [Weidman andKrider, 1978; Lin et al., 1979; Krehbiel, 1981;

Cooray and Lundquist, 1982; Rakov and Uman, 1990c; Rakov et al., 1994; Krider et al.,

1996; Murray et al., 2005] have focused on relatively distant (from 1 to over 100 km)

measurements of lightning electromagnetic fields, but there currently exists no detailed

study (only a few relatively brief reports, including Beasley et al., 1982; Rakov et al.,

1998, 2003b) of the electromagnetic environment of natural first strokes within several

hundred meters of the lightning channel. While there have been several studies of close

electromagnetic fields from artificially-initiated (rocket-triggered) negative lightning

[Rubinstein et al., 1995; Rakov et al., 1998; Uman et al., 2000; Crawford et al., 2001;

Rakov et al., 2001; Uman et al., 2002; Schoene et al., 2003a,b; Miki et al., 2002; Kodali

et al., 2005], these triggered flashes lack the initial downward stepped leader and first

return stroke which are characteristic of natural negative cloud-to-ground lightning. First

return strokes differ from natural-subsequent and triggered-lightning strokes in several

other ways, as outlined below.

First stroke channels typically contain branches, unlike the channels of subsequent
and triggered-lightning strokes, especially the latter.

Measured channel-base currents from first return strokes in both negative and
positive flashes have a median peak of about 30 kA, compared to 12 to 15 kA for
subsequent and triggered-lightning strokes.









First strokes (excluding any following continuing current) typically transfer
about 5 to 10 C of charge to ground, compared to about 1 C for subsequent and
triggered-lightning strokes.

The structure of the electric and magnetic field waveforms of first strokes is
typically more complex than those of subsequent and triggered-lightning strokes
[Lin et al., 1979; Weidman andKrider, 1978].

First strokes are thought to be typically associated with upward-connecting leaders
having lengths on the order of tens of meters or more (for strokes to flat terrain)
[Golde, 1947; Wagner, 1967; Orville andldone, 1982], compared to typical lengths
of 20 m or less for subsequent and triggered-lightning strokes [Idone, 1990; Wang
et al., 1999a], although very few estimates of upward leader lengths have been
reported.

The Multiple Station Experiment (MSE) system, which was constructed at the

International Center for Lightning Research and Testing (ICLRT), at Camp Blanding,

Florida, was designed to measure the close (within a few hundred meters) electric and

magnetic fields and field derivatives from natural lightning. The MSE system operated

from 2002 to 2004, and consisted of six electric field (E) measurements, four electric

field derivative (dE/dt) measurements, two magnetic field (B) measurements and four

magnetic field derivative (dB/dt) measurements. The sensors were spread around an area

of about 0.5 km2. Waveforms measured at each stations were transmitted via fiber-optic

links to a central location, where they were digitized and stored. The network was

activated and deactivated by a computer, based upon the output of an electric field mill

(which measures the ambient electric field at ground). The digitizers were triggered when

the simultaneous output of two optical sensors, viewing the network from its opposite

corners, both exceeded a predetermined threshold. This was done so that data were

obtained only for flashes within or near the boundary of the network.

Between 2002 and 2004, data were acquired for 27 natural cloud-to-ground flashes.

All flashes lowered negative charge to ground except one flash that consisted of two

positive strokes followed by three or more negative strokes. Of the 26 negative flashes,

about 20 are thought to have terminated on ground within or near the boundary of









the network. In addition, data were acquired for 19 rocket-triggered lightning flashes.

Analysis and modeling of these data are used to gain insights into several lightning

processes, such as stepped leaders and first return strokes.

1.2 The Global Electric Circuit and the Electrical Structure of Thunderclouds

Before discussing the lightning discharge process (Section 1.3), it is useful to

provide a succinct overview of the "global electric circuit." The Earth-atmosphere system

can be crudely modeled as a lossy spherical capacitor [Uman, 1974], with the inner and

outer shells consisting of the Earth's surface and the electrosphere, respectively. The

latter is the region of the atmosphere just above 60 km characterized by an exponential

increase in conductivity due to the presence of free electrons [Roble and Tzur, 1986;

Reid, 1986]. According to this model, the Earth's surface is negatively charged, having

a total magnitude of roughly 5 x 105 C, while an equal positive charge is distributed

throughout the atmosphere [Rakov and Uman, 2003]. Little charge resides on the

electrosphere shell. The capacitor is considered lossy because there is a fair-weather

(the term "fair weather" indicates a lack of thunderstorm conditions) leakage current

density of about 2 x 10 12 A m 2 between the shells due to the weakly-conducting

atmosphere. This leakage current would neutralize all the charge on Earth in roughly 10

minutes if there were no mechanism to replenish this charge. This recharging mechanism

is generally thought to be the action of thunderstorms, with lightning being primarily

responsible for lowering negative charge to ground and thus replenishing the charge on

the Earth's surface. This is the so-called "classical" view of atmospheric electricity, and

is undoubtedly a gross simplification, but provides adequate insight for the following

discussion.

The cumulonimbus, commonly referred to as the thundercloud, is the charge

source for most of the lightning on Earth. The meteorological and detailed electrical

characteristics are beyond the scope of this work, though the latter will be briefly outlined

here. The idealized gross charge distribution of the cumulonimbus is generally modeled









as a triple structure (vertically stacked point charges) with positive charge at the top,

negative in the middle, and an additional, smaller positive at the bottom. The top two

charges are usually specified to be equal in magnitude and on the order of 40 C, forming

a dipole. The lower positive charge is generally an order of magnitude smaller and may

not be present at all. In Florida and New Mexico, the three charge centers are generally

located at heights of 12 km, 7 km, and 2 km, respectively, above sea-level. These cloud

charge locations and magnitudes have been estimated by a variety of remote [Krehbiel,

1986] and in situ methods [Simpson and Scrase, 1937]. The mechanisms of charge

separation within the cumulonimbus are complex but basically involve the electrification

of individual hydrometeors (atmospheric water in any form) and a process that separates

these charged hydrometeors by their polarity, such as the convection mechanism [Moore

et al., 1989] and the graupel-ice mechanism [Jayaratne et al., 1983].

1.3 The Lightning Discharge Process

1.3.1 Introduction

Uman [1987] defines lightning as a transient, high-current electric discharge whose

path length is measured in kilometers. This definition is very general, as there is a

significant variety in the types of lightning discharges. The most common sources of

lightning is the electric charge separated in ordinary thunderstorm cumulonimbuss) clouds

[Uman, 1987], although other non-thunderstorm situations exist that are able to produce

lightning (or at least long electrical sparks), such as sand storms, volcano eruptions, and

nuclear explosions [Rakov and Uman, 2003]. Further, thunderstorm-related lightning

can be divided into cloud-to-ground (occurring between cloud and Earth), intracloud

(occurring within a single cloud), intercloud (occurring between thunderclouds), and

cloud-to-air (occurring between cloud and clean air outside the cloud) discharges, with

the latter three often grouped together by the umbrella term "cloud flash" or "cloud

discharge." These cloud discharges make up the majority (perhaps 75%) of all lightning

discharges [Rakov and Uman, 2003] and pose a significant threat to aircraft. Further,









there exist transient luminous events (TLE) observed in the middle and upper atmosphere,

such as sprites, jets, and elves. Lightning discharges are apparently also not confined to

the planet Earth, as a variety of remote and in situ measurements [Little et al., 1999] have

been interpreted as evidence for lightning on the planets Venus, Jupiter, Saturn, Uranus,

and Neptune.

Although there is significant interest in cloud discharges and other transient optical

phenomena in the atmosphere, especially the latter in recent years, cloud-to-ground (CG)

discharges remain the most-studied and best-understood type of lightning, primarily

because of the relative difficulty in studying cloud discharges compared to CG discharges.

CG lightning also poses the most significant threat to life and property (aside from

aircraft), so from a practical point of view (e.g., lightning protection) the study of CG

lightning is more important. CG lightning can be further subdivided into four categories,

illustrated in Figure 1-1, based upon the direction of the initial leader and the polarity

of cloud charge lowered to ground. It is worth noting that others [Uman, 1987] define

the four categories based upon the direction of the initial leader and the polarity of the

charge on the leader, which yields opposite-polarity labels for Types 2 and 4 shown in

Figure 1-1. A leader can be defined as a self-propagating discharge creating a channel

with electrical conductivity on the order of 104 S m 1 (compared to 10 14 S m 1for air

at sea level). All CG lightning discharges involve an initial leader initiated from either the

cloud or the ground (or a ground-based object), and this leader can carry either positive

or negative charge. The propagation of the leader is due to the ionization dielectricc

breakdown) of the air resulting from the high electric field at the tip of the leader. The

electric field required for electrical breakdown of dry air between two parallel plane

electrodes at sea level is about 3 MV m 1 and decreases with decreasing pressure (e.g.,

higher altitudes) and with the presence of hydrometeors [Rakov and Uman, 2003].

Downward negative lightning accounts for roughly 90% of all CG lightning world

wide, with positive downward lightning accounting for most of the remaining 10%,







6

++ + ++ + + ++
+ ++ + + + ++ + + +



A B +



Downward Negative Upward Negative

++ + + + + + +
++ ++ +/ ++ + + + + +
S + + + + + + +


C + D




Downward Positive Upward Positive

Figure 1-1. Four primary types of cloud-to-ground (CG) lightning flashes. A) Downward
negative. B) Upward negative. C) Downward positive. D) Upward positive.
Only the initial leader is shown for each type. Adapted from Rakov and
Uman [2003].


although there is significant local variability. Upward lightning is relatively rare and

is typically initiated from objects on mountain tops and tall man-made objects on flat

terrain, such as communication towers, where the ground-based object enhances the

electric field (present due to an overhead thundercloud) around the tip of the object and

an upward leader is initiated. Since downward negative CG lightning is by far the most

common type of discharge, it is thus the most extensively studied, and will be the primary

focus of the remainder of the discussion, except for Section 1.3.3.

1.3.2 Downward negative lightning discharges to ground

In downward negative lightning the initial leader, referred to as the stepped leader, is

initiated from within the cloud, via a process known as initial breakdown (or preliminary

breakdown). Clarence andMalan [1957] suggested that initial breakdown is a vertical

discharge between the main negative and lower positive charge centers, having a duration


















II,


-- -

,'-,\
-10 5 10


| f -100 /s 1 C -lo /s



Descending Attachment (100 ps) (tens of ms) Downward Upward
stepped at 15 ms Upward No-current negative subsequent
leader first interval dart return
at 10 ms return leader stroke
stroke


Figure 1-2. Sequence events in a natural negative cloud-to-ground lightning flash.


of 2 to 10 ms, although more recent studies [Krehbiel et al., 1979; Proctor et al., 1988;

Rhodes andKrehbiel, 1989] suggest that initial breakdown can be viewed as a sequence

of channels extending in seemingly random directions from the cloud charge source

[Rakov and Uman, 2003]. Initial breakdown is also characterized by a series of pulses

generally thought to mark a transition from the initial breakdown to the stepped leader.

These pulses have been observed in both wide-band [Weidman andKrider, 1979] and

VHF [Beasley et al., 1982] electric field waveforms from distant (some tens to hundreds

of kilometers) lightning, and typically have a bipolar shape, a total duration of 20 40 ts,

and an interpulse interval of 70 130 uis [Rakov and Uman, 2003]. Brook andKitagawa

[1960] and Isikawa [1961] also reported similar observations of optical radiation

apparently associated with initial breakdown pulses. Interestingly, the characteristics of

initial breakdown associated with CG lightning are apparently different than those of









cloud discharges [Kitagawa andBrook, 1960]. The lightning initiation mechanism in

thunderclouds is probably complex and is relatively poorly understood, as evidenced by

the observation that the maximum values of the large-scale electric fields generated in

thunderclouds are of insufficient magnitude to explain the initiation of lightning, leading

Gurevich et al. [1997] to suggest that runaway electrons play a role in the mechanism.

After initial breakdown, the negatively-charged stepped leader propagates towards

an area of positive charge, which is typically the base of the cloud for CG lightning. The

leader is referred to as "stepped" because it has been observed optically to propagate in

a discrete (discontinuous) manner through the virgin air. After exiting the visible cloud

the CG leader descends towards ground, typically exhibiting many branches. Figure 1-2

illustrates the lightning discharge process after the stepped leader has exited the visible

cloud.

The first optical observations of stepped leaders were obtained with streak cameras

[Schonland, 1938; Schonland et al., 1938a,b; Schonland, 1956; Berger and Vogelsanger,

1966; Orville andldone, 1982], named so because the film is literally "streaked" across

the aperture at high speed (on the order of 50 m s 1), resulting in a time-resolved image

of lightning processes. More-recent studies, such as Chen et al. [1999], have used

electronic systems, such as the ALPS system [Yokoyama et al., 1990], consisting of a

16 x 16 array of photo-diodes with the resulting optical waveforms recorded digitally, to

image stepped leaders. In addition, both wide-band and VHF electric field measurements

have been used to estimate stepped leader speeds [Beasley et al., 1983; Thomson, 1985;

Proctor et al., 1988]. A typical value of stepped leader speed, averaged over a few

kilometers of channel, is 2 x 105 m s 1, with some evidence to suggest the stepped

leader accelerates as it approaches ground [Schonland, 1938; Schonland et al., 1938a,b;

Schonland, 1956; Nagai et al., 1982]. The mean step duration and interval are 1 uts and

20 50 uts, respectively [Rakov and Uman, 2003], with a mean overall leader duration of

about 35 ms [Rakov and Uman, 1990c]. Using this mean leader duration and an assumed









channel length of 7 km (reasonable height for the negative charge center in Florida),

the resulting estimated stepped leader speed is 2 x 105 m s 1 a value consistent with

the observations discussed above. Each step is also associated with an impulse current

inferred to be on the order of 1 kA or greater.

The step-formation mechanism for negative lightning stepped leaders has been

inferred from measurements of long laboratory sparks [Gorin et al., 1976]. In these long

spark experiments, the formation of each step is associated with a brief illumination of the

channel behind the leader tip, assumed to be due to a pulse propagating up the channel on

a time scale too short to be resolved in the experiment. For natural lightning, Chen et al.

[1999] observed luminosity waves associated with individual steps that propagated in the

direction opposite to that of the advancement of the leader. Charge is likely deposited

on the stepped leader channel by the step-formation process, involving the dielectric

breakdown of the air in front of the leader tip (and probably involving the propagating

pulse described above), as well as a steady current (average of 100 200 A, Rakov and

Uman 2003) flowing from the cloud charge source to the leader tip via the conducting

leader channel. The charge deposited by the former process has apparently not been

quantified.

Williams and Brook [1963] estimated average stepped-leader currents in two flashes

to be 50 A and 63 A using remote magnetic field measurements. Thomson [1985],

using electric fields measured in Florida, inferred currents ranging from 100 A to 5 kA

for 62 stepped-leaders near ground, along with corresponding line charge densities

(for 10 events) ranging from 0.7 to 32 x 10 3 C m 1. Further, Krehbiel [1981], using

multiple-station electric field measurements in Florida, estimated final stepped leader

currents in the range of 200 A to 3.8 kA with a mean of 1.3 kA. Brook et al. [1962],

using a single-station electric field measurements in New Mexico and a point charge

approximation, estimated the total charge deposited on 24 stepped-leader channels to

range from 3 to 20 C with a mean of 6 C. Krehbiel et al. [1979], using multiple-station









electric field measurements, estimated charges ranging from 5 to 20 C for four stepped

leaders. Proctor et al. [1988], using multiple-station VHF measurements, estimated

total stepped leader charges ranging from 3.6 to 57 C, with a median of 11 C. Out of the

total 15 events, 5 events were reported to have stepped-leader charges between 5 and

15 C. Proctor [1997] later reported that stepped-leader line charge density in so-called

lower-origin flashes (beginning at 1 to 7.4 km above mean sea level), for both cloud and

cloud-to-ground discharges, was about 10 3 C m 1, consistent with the estimates of

Thomson [1985]. Assuming a total stepped-leader charge of 5 C and a channel length

of 7 km, the corresponding line charge density is about 0.7 x 10 3 C m 1 a value

consistent with the above estimates. The stepped leader process can be viewed as a

mechanism by which charge is removed from the cloud and deposited along a channel

extending between cloud and ground. Based on the above observations (and many

others), Rakov and Uman [2003] suggest that "the stepped-leader channel is likely to

consist of a thin core (probably less than 1 cm in diameter) that carries the longitudinal

channel current, surrounded by a radially formed corona sheath (that stores the leader

charge) whose radius is typically several meters."

About 35 ms after the stepped leader is initiated, and when the leader tip is still some

hundreds of meters above ground, several upward positive leaders (UPLs) are initiated

from objects on the ground and each propagate toward the negative stepped leader

channel or one of its branches (though the distinction between the main channel and a

branch is not clear until attachment actually occurs). This is considered the beginning

of the lightning attachment process. The potential of the stepped-leader tip, relative

to ground, is estimated to be some tens of megavolts [Bazelyan et al., 1978], which

is probably a significant fraction of the cloud potential [Rakov and Uman, 2003]. An

UPL is initiated when the electric field at ground, due to the charge on the downward

stepped leader, exceeds that required for dielectric breakdown. The UPL deposits positive

charge along the upward-propagating channel, although the breakdown mechanism is









considerable different than that of negative leaders [Gorin et al., 1976]. The presence

of objects protruding above ground (e.g., buildings and trees) enhances the electric

field from the downward leader, such that an UPL is initiated earlier from a protruding

object than from the surrounding terrain. The UPL that makes the final connection with

the downward stepped leader is referred to as the upward connecting leader or upward

connecting discharge, in order to make the distinction between that leader and possibly

many upward unconnected discharges.

The speed and average current of both connecting and unconnected upward positive

leaders has been estimated to be about 105 m s-1 and 100 A, respectively very similar

to parameters measured for the downward stepped leader although there is considerably

less data available for the UPL process. Yokoyama et al. [1990], using the ALPS optical

imaging system, observed upward-connecting leaders in six discharges to a 80 m

telecommunications tower in Japan, and estimated average upward propagation speeds

ranging from 0.8 to 2.7 x 105 m s-1. For an event estimated to have an average upward

connecting leader speed of about 0.8 x 105 m s1, Yokoyama et al. [1990] estimated a

corresponding average downward leader speed of 2.9 x 105 m s-1. Wang et al. [2001]

observed an upward connecting leader (with the ALPS system) advancing a distance

of about 88 m over 53 uts, thus having an average speed of 1.7 x 106 m s 1, that was

initiated when the downward stepped leader (estimated to have an average speed of

4 x 106 m s 1) was at a height of about 300 m.

There exist very few estimates of upward connecting leader lengths in the literature.

The upward connecting leaders (initiated from a tall tower) measured by Yokoyama

et al. [1990] ranged from 25 to over 150 m. Berger and Vogelsanger [1966] inferred

the presence of an upward connecting leader having a length of at least 40 m from a

streak photograph, although the leader itself was apparently too faint to be imaged.

Orville andldone [1982] inferred from streak camera records upward connecting leader

lengths of about 20 and 30 m for two upward connecting leaders in Florida. It is expected









that upward connecting leaders from tall structures should generally be longer than

leaders from flat terrain (due to the increased field enhancement of the former and hence

earlier initiation relative to the latter). Golde [1947] and Wagner [1967] both presented

a sketch of a streak camera photograph attributed to D. J. Malan, in which the stepped

leader appears to end about 50 m above flat terrain, implying the (unimaged) upward

connecting leader was about 50 m in length. Upward connecting leader lengths have

also been inferred from still photographs, where the height of the junction point (where

the connection between the upward and downward leaders is established) is estimated

by a split or loop in the channel Hagenguth [1947]; Golde [1967], the presence of both

upward and downward branching in a section of channel [Orville, 1968e], or an abrupt

change in channel shape near the ground. The photograph of Hagenguth [1947] indicates

an upward connecting leader length between 3 and 9 m above a patch of weeds in a lake,

while that of Golde [1967] indicates a length about 9 m above a chimney of unspecified

length. Orville [1968e] estimated an upward connecting leader length of about 12 m

above the top of a 7 m European ash tree. According to Rakov and Uman [2003], the

process by which the extending plasma channels of the upward and downward leaders

make contact is called the break-through phase or final jump, and is thought to involve the

accelerated extension of the two plasma channels inside the so-called "common streamer

zone," formed when the streamer zones ahead of each leader tip come in contact. The

break-through phase is perhaps one of the most poorly understood aspects of lightning,

and in fact has never been directly observed in lightning.

When the two leaders combine to form a single channel, a large potential

discontinuity exists at the junction point since the stepped-leader channel above the

junction point is at some tens of megavolts and the upward leader channel below is

roughly at ground potential. This large potential discontinuity then propagates in both

directions from the attachment point (typically a few to some tens of meters above

ground), with the upward wave propagating towards the cloud. The downward wave,









upon reaching the ground, reflects and propagates back up the channel towards the cloud.

This situation is analogous to short-circuiting one end of a charged transmission line, with

one conductor at high potential relative to the other. The upward-propagating wave is

known as the return stroke (specifically thefirst return stroke), and it serves to neutralize

(lower to ground) most or all of the charge deposited by the stepped leader. The entire

process by which the stepped leader propagates down from the cloud and the return stroke

wave propagates back up, neutralizing the charge deposited by the stepped leader, is

referred to as a leader/return-stroke sequence. Just as the leader can be thought of as a

mechanism that removes charge from the cloud and distributes it along a vertical channel,

the return stroke can be thought of as a process that removes the charge deposited on the

channel, lowering it to ground. Hence, the complete leader/returns-stroke sequence can be

considered a two-stage process by which negative cloud charge is lowered to Earth.

The return stroke is responsible for the impressive visual and auditory effects, as

well as the damage and personal injury, associated with lightning. The speed of this wave,

averaged over the lower few hundred meters of channel, has been optically estimated to

be on the order of 108 m s 1 [Schonlandet al., 1935; Schonland, 1956; Boyle and Orville,

1976; Mach andRust, 1989a] and observed to decrease (by 25% or more according to

Idone and Orville, 1982 over the visible channel) with height. Schonlandet al. [1935],

using streak photography, found that typically the speed at the visible top of the main

channel was about half that at the channel base (0.5 vs. 1 x 108 m s 1).

Currents from first return strokes in negative downward lightning have been

measured on tall towers, with the most complete characterization being the result of

the work of K. Berger, who measured currents (using a resistive shunt) on top of two

70 m towers on the summit of Mount San Salvatore in Lugano, Switzerland [Berger,

1955a,b, 1962, 1967a,b, 1972, 1980; Berger and Vogelsanger, 1965, 1969; Berger and

Garbagnati, 1984; Berger et al., 1975]. The results of Berger et al. [1975], an analysis

of 101 return strokes in negative downward flashes, are still used to a large extent as the









primary reference source for lightning research [Rakov and Uman, 2003]. Figure 1-3

shows average negative first- and subsequent-stroke current waveshapes as reported by

Berger et al. [1975], and were obtained by normalizing the individual current waveforms

to their respective peak values, aligning all the waveforms to the 0.5 peak point on the

initial rising portion, and calculating the average. Figure 1-4 shows current waveforms

for a first and two subsequent strokes, measured at the base of a 60 m tower in South

Africa using a current transformer, presented by Eriksson [1978a]. The first stroke

current waveforms in both Figures 1-3 and 1-4 have a characteristic concave shape in the

initial rising portion, apparently not present or very pronounced in subsequent strokes.

This concave front, often called the "slow front" is generally attributed to the upward

connecting leader [Rakov and Uman, 2003, pp. 144], although this certainly has not been

demonstrated and, in fact, is argued against in this dissertation.

Parameters of downward negative lightning, derived by Berger et al. [1975] from

channel-base currents, are given in Table 1-1. First-stroke currents have a median peak of

about 30 kA, rise time (labeled front duration in Table 1-1) of about 5.5 his, and duration

of (half-peak width) about 75 his. Interesting, both the total and so-called impulse charge

(charge Q is equal to the time integral of the channel-base current I, i.e. Q = fldt)

associated with first strokes is about 5 C, similar to that estimated to be deposited on the

stepped-leader channel. This observation is not unexpected, since the return stroke wave

neutralizes (lowers to ground) most, if not all, of the charge deposited on the stepped

leader channel. The maximum dl/dt observed for first strokes was estimated by Berger

etal. [1975] to have a median value of about 12 kA uts.

After a no-current interval of a few to some hundreds of milliseconds (typically

some tens of milliseconds) one more more negative subsequent leader/return-stroke

sequences may, but do not always, follow the first the typical number of strokes per

flash being 3 to 5. According to Rakov andHuffines [2003], approximately 80% of

downward negative flashes contain more than one stroke. The term "subsequent" refers

















Table 1-1. Parameters of downward negative lightning derived from channel-base
current measurements. Adapted from Berger et al. [1975]. Note the rise
times reported here are likely to be biased towards larger values and rates of
rise to toward lower values due to the limited time resolution of the data in the
study.


Parameters
Peak current (minimum 2 kA)
First strokes
Subsequent Strokes
Charge (total charge)
First strokes
Subsequent strokes
Complete flash
Impulse charge (excluding
continuing current)
First strokes
Subsequent strokes
Front duration (2 kA to peak)
First strokes
Subsequent strokes
Maximum dI/dt
First strokes
Subsequent strokes
Stroke duration (2 kA to half peak
value of the tail)
First strokes
Subsequent strokes
Action integral (fI2dt)
First strokes
Subsequent strokes
Time interval between strokes
Flash duration
All flashes
Excluding single-stroke flashes


Units
kA


Percentage exceeding tabulated value
Sample Size 95% 50% 5%


1.1
0.22


1.8
0.22


4.5
0.95


kA gts 1


6.0 x 103
5.5 x 102
7


0.15
31


5.5 x 104
6.0 x 103
33


13
180


5.5 x 105
5.2 x 104
150


1100
900











0 16 32 48 64 80 us-B


80 160 240 320 400 us-A
First Strokes


0 8 16 24 32 40 s -B
0.0

-0.2
A
-0.4

-0.86


-1.0
0 20 40 60 80 100 ps-A
Subsequent Strokes


Figure 1-3. Average negative first- and subsequent-stroke current waveshapes each shown
on two time scales, A and B. The lower time scales (A) correspond to the
solid curves, while the upper time scales (B) correspond to the broken curves.
The vertical (amplitude) scale is in relative units, the peak values being equal
to negative unity. Adapted from Berger et al. [1975].


to any stroke after the first and the two terms (first and subsequent) serve to clearly

distinguish to two types of return strokes. Flashes triggered using the rocket-and-wire

technique (Section 1.3.4) are comprised only of strokes that are similar, if not identical to,

subsequent strokes in natural negative lightning, with the first stroke being replaced by

a process involving the destruction of the thin metal triggering wire. Subsequent strokes

are typically characterized by a leader speed of about 107 m s 1 [Schonland et al., 1935;

McEachron, 1939; Hubert andMouget, 1981; Idone et al., 1984; Jordan et al., 1992;

Mach andRust, 1997] and a lack of observable stepping; these subsequent leaders being

referred to as "dart" leaders. The difference between leaders preceding first and and those

preceding subsequent return strokes is due to the first return stroke pre-conditioning the











0 10 20 30 40
0- -- 1---1----1 --1-

24- A

48 First Stroke

72
10 20 30 40

i Time, ps
24- B Second Stroke
0
48

72
10 20 30 40
0 i *

24 C Third Stroke

48



Figure 1-4. Waveforms of the current measured on tower bottom for the first stroke (A)
and two subsequent strokes (B and C) in a flash in South Africa. Adapted
from Eriksson [1978a].


channel, i.e., leaving a warm, low density air path for the dart leader to follow. Assuming

a reasonable channel length of about 7 km, and the typical dart leader speed of 107 m s1,

the estimated leader duration is about 0.7 ms. Dart leader charges and currents have been

estimated to be on the order of 1 C [Brook et al., 1962] and 1 kA [Idone and Orville,

1985], respectively. Some subsequent leaders, known as "dart-stepped" leaders, exhibit

properties of both dart and stepped leaders.

Upward positive connecting leaders associated with subsequent strokes are thought

to have lengths ranging from a few to some tens of meters. Orville andldone [1982]

and Idone et al. [1984] both inferred upward connecting leaders of roughly 20 30 m

in length for a few events, although Orville andldone [1982] reported that they did

not observe any evidence of upward connecting leaders in association with 21 other









subsequent strokes. Further, Idone [1990], using photographic recordings, inferred an

upper bound for the length of an upward connecting leader in rocket-triggered lightning

(whose strokes are similar to natural subsequent strokes) to be on the order of 10 20 m.

Wang et al. [1999a], using the ALPS optical system, inferred the existence of two upward

connecting leaders in rocket-triggered lightning having lengths of 7 11 m and 4 7 m.

Natural negative subsequent return strokes typically have peak currents at ground of

about 10 to 15 kA and lower about one fifth the charge of first strokes (see Table 1-1).

The current rise time and duration are also typically an order of magnitude shorter than

for first strokes. Subsequent return stroke propagation velocity is similar to that for first

strokes, on the order of 108 m s 1 [Boyle and Orville, 1976; Hubert andMouget, 1981;

Idone and Orville, 1982; Idone et al., 1984; Willett et al., 1988, 1989a; Mach and Rust,

1989a; Olsen et al., 2004] with optical intensity (assumed to be positively correlated with

current) and optical rise time decaying with height [Jordan and Uman, 1983; Jordan

etal., 1995, 1997].

1.3.3 Positive and bipolar lightning discharges to ground

As mentioned in Section 1.3.1, downward positive cloud-to-ground lightning

accounts for about 10% of all cloud-to-ground lightning worldwide, although there is

significant local and seasonal variability. For example, positive discharges may account

for the majority of flashes in winter storms (60% in December according to Hojo et al.,

1989), while negative lightning is dominant in summer thunderstorms. Brook et al. [1982]

reported that positive flashes account for about 40% of cloud-to-ground flashes in winter

storms in Japan. Using NLDN data from 1992-1995, Orville and Silver [1997] reported

that the monthly percentage of positive flashes over the contiguous United States ranged

from about 3% in August 1992 to about 25% in December 1993. In a similar study using

NLDN data from 1995-1997, Orville andHuffines [1999] reported monthly percentages

of positive flashes ranging from about 6% in July 1995 to about 25% in January 1996.

These observations suggest that winter storms are more conducive to the production









of positive flashes than summer storms. There is evidence [Fuquay, 1982] that there

is a tendency for positive lightning to occur during the dissipating phase of individual

thunderstorms, regardless of the season.

Since the overall occurrence of positive lightning is relatively low compared with

negative lightning, it has been observed less, and thus it is relatively poorly understood.

Further, triggering positive lightning return strokes using the rocket-and-wire technique

(Section 1.3.4) has been generally unsuccessful, with only a few cases documented in the

literature [Wang et al., 1999; Idone et al., 1987; Jerauld et al., 2004]. Idone et al. [1987]

and Jerauld et al. [2004] each document triggered-lightning flashes consisting of of a

negative initial stage and one or more negative strokes followed by a positive stroke.

Rakov and Uman [2003] list five observed properties that are thought to be

characteristic of positive lightning discharges.

1. Positive flashes are usually composed of a single stroke (99.6 percent according
to Lyons et al., 1998), whereas about 80 percent of negative flashes contain two
or more strokes [Rakov andHuffines, 2003]. Further, Ishii et al. [1998] observed
that subsequent strokes in multiple-stroke positive flashes in winter storms in Japan
always create a new termination on ground.

2. Positive return strokes tend to be followed by continuing currents that typically last
for tens to hundreds of millisecond [Rust et al., 1981; Fuquay, 1982], which are
likely responsible for the unusually large charge transfers associated with positive
flashes [Brook et al., 1982].

3. Electric field measurements appear to indicate that positive return strokes are
preceded by significant in-cloud activity lasting, on average, in excess of 100 or
200 ms [Rust et al., 1981; Fuquay, 1982].

4. Positive discharges have been reported [Fuquay, 1982] to involve long horizontal
channels, up to 10 km in extent.

5. Time-resolved optical images indicate that positive leaders appear to move through
virgin air either continuously or in a stepped fashion, in contrast to negative leaders,
which are always optically stepped. Further, distant electric and magnetic fields
from positive discharges are less likely to exhibit clearly-identifiable step pulses
immediately prior to the return stroke waveform than are first strokes in negative
lightning.









Berger and Vogelsanger [1966] obtained the only available streak image of a downward

positive leader, which was identified as positive solely on the basis of the similarity of

the luminous characteristics of its leader to those identified positive leaders developing

upward from instrumented towers. The propagation speed of the leader increased from

4 x 105 to 2.5 x 106 m s 1 as it approached ground. This leader was not observed to

branch, although Fuquay [1982] published a still photograph of a positive flash that

does show branches. The mechanism for the positive leader has been inferred from

laboratory long-spark experiments, similar to that done for negative leaders. According

to Gorin et al. [1976], the positive leader in a long spark can move either continuously

or intermittently, the intermittent form being viewed as a kind of stepping, although not

necessarily of the same nature as the stepping in lightning negative leaders.

Berger et al. [1975], using currents measured on instrumented towers, reported

that the median charge transfer by positive flashes (80 C) is about an order of magnitude

greater than that by negative flashes (7.5 C, see Table 1-1), while the median peak

currents were similar (35 versus 30 kA, respectively). As discussed above, this difference

in charge transfer is likely due to the continuing currents observed to follow positive

strokes. However, the five percent peak current level for positive flashes is 250 kA (that

is, five percent of the flashes studied by Berger et al. [1975] exceeded 250 kA), much

higher than the five percent value of 80 kA for negative first strokes in the same study.

Unlike negative discharges, the positive discharges studied Berger et al. [1975] consist

of both microsecond-scale waveforms similar to those for negative lightning (see Figures

1-3 and 1-4) as well as millisecond-scale waveforms with rise times up to hundreds of

microseconds. Rakov and Uman [2003] hypothesize that the latter type of waveforms are

characteristic of tall objects capable of generating very long upward connecting leaders,

thus the distribution of positive lightning peak currents published by Berger et al. [1975]

may not be applicable to objects of moderate height on flat ground.









Very little experimental data exist on positive return stroke speeds, although

what is available indicates the typical speed is on the order 108 m s 1. Mach andRust

[1993], using photoelectric measurements, reported average return stroke speeds of

0.8 x 108 m s 1 for four positive natural-lightning return strokes. The speeds were

averaged over channel segments 332 to 433 m long. The triggered positive return stroke

reported by Idone et al. [1987] (third stroke of an eight-stroke flash, the other seven being

negative) had an optically-estimated speed of about 108 m s-1, with the seven negative

strokes having speeds ranging from 0.9 to 1.6 x 108 m s 1. The speeds reported by

Idone et al. [1987] were averaged over a channel segment of length 850 m near ground.

Jerauld et al. [2004], using a very crude method based on estimated leader charge density

(obtained from electric fields measured at multiple stations) and measured channel-base

current, estimated a positive return stroke speed of 0.92 x 108 m s-1. The positive stroke

was the second in a two-stroke rocket-triggered flash, with the previous stroke and the

initial stage both lowering negative charge to ground.

Bipolar lightning is defined as a flash that lowers both positive and negative charge

to ground. The little available data on bipolar lightning seems to indicate that the majority

of bipolar flashes are initiated by upward leaders from tall objects [Berger, 1978]. In the

data of Berger [1978], obtained between 1963 and 1973 at Mount San Salvatore, bipolar

flashes accounted for 72 out of 1196 observed flashes (6 percent). Rakov [2005], based

on a review of literature, states that bipolar flashes may not occur less often than positive

flashes, at least when tall objects are involved, with bipolar flashes constituting 6 to 14%

of summer lightning in Europe and the United States and 3 to 33% of winter lightning in

Japan.

Bipolar lightning can be grouped into three categories, illustrated in Figure 1-5,

based on the characteristics of the current polarity reversal. Type 1 bipolar events involve

a polarity reversal during the initial stage of an upward or classical rocket-triggered

lightning discharge. Type 2 events involve a change in polarity between the initial











Type 1 A
S (Upward Flash)

Time

Initial Stage Negative RS Negative RS

Positive RS
Type 2 B
S (Upward Flash)

STime

Initial Stage

Positive RS
Type 3a C\
(Upward Flash)

Time

Initial Stage Negative RS

Positive RS
D


Type 3b T
(Downward Flash)
Negative RS

Figure 1-5. Illustration of the types of bipolar discharges, based upon the classifications
given by Rakov and Uman [2003]. A) Type 1. B) Type 2. C) Type 3. D) Type
4.


stage and following return strokes. Type 3 events involve a polarity reversal between

return strokes. Further, Type 3 events are grouped into two sub-categories, with Type

3a events being upward or rocket-triggered lightning discharges, while Type 3b events

are downward cloud-to-ground flashes having no initial stage. Types 1, 2, and 3a are all

upward or rocket-triggered lightning discharges, while Type 3b is the only downward

cloud-to-ground event. This is only a rough categorization and some flashes may belong

to more than one group. Events of Type 1 have been reported by McEachron [1939],

Davis and Standring [1947], Horii [1982], Hubert et al. [1984], Akiyama et al. [1985],

Laroche et al. [1985], and Liu and Zhang [1998], with the latter four events being

rocket-triggered lightning discharges. Events of Type 2 have been reported by Berger

and Vogelsanger [1966], Berger [1978], Nakahori et al. [1982], and Fernandez [1997],

with the latter two events being rocket-triggered lightning discharges. Events of Type









3a have been reported by McEachron [1939], Berger and Vogelsanger [1965], Idone

et al. [1987], Schulz andDiendorfer [2003], and Jerauldet al. [2004], with the events

described by Idone et al. [1987] and Jerauld et al. [2004] being rocket-triggered lightning

discharges. As of the time of this writing, no well-documented Type 3b bipolar flash has

been presented in the literature.

1.3.4 Rocket-triggered lightning

The rocket-and-wire technique is a method of artificially initiating a cloud-to-ground

lightning flash. The technique involves launching a small rocket that extends upward a

thin conducting wire, which can be grounded or ungrounded. If the wire is grounded,

the flash is usually referred to as "classical" triggered lightning. Triggering with an

ungrounded wire, having a gap of some hundreds of meters or more between the bottom

of the conducting wire and ground, is usually referred to as "altitude" triggered lightning.

In cases where the gap is only a few meters or less, it is typically not referred to as

altitude triggering. The primary difference between the two techniques is that the altitude

method is capable, to a degree, of reproducing a stepped leader followed by a first

return stroke, whereas the classical method is not. In both cases, usually negative cloud

charge is lowered towards ground, with very few documented cases of positive triggered

lightning using either method (see Section 1.3.3). The rocket is typically constructed from

fiberglass or plastic and is about 1 m in length. The triggering wire is Kevlar-reinforced

copper or steel of diameter about 0.2 mm and the spool can be mounted on either the

rocket or the ground. The rocket is launched when thunderstorm conditions are deemed

adequate, although these conditions may vary by region. At the Camp Blanding lightning

research facility (Section 1.5), the following three conditions are thought to be necessary

for successful triggering.

*A static electric field measured at ground having magnitude in excess of
-5 kV m 1. If multiple field measurements at different locations are used, it
is highly desired that each measurement be roughly equal, likely indicating an
extensive charge layer overhead.









A thundercloud directly overhead and preferably not the edge of a storm.

Lightning activity within a few kilometers, preferably with flashes occurring at
intervals of one minute or so. This usually occurs during the end of the storm, after
the major lightning activity where flashes occur every few seconds.

Classical triggered lightning. The initial speed of the rocket is about 200 m s1,

and when the rocket reaches about 300 m, a positively-charged upward leader (assuming

a negative cloud charge source overhead) is initiated from the tip of the wire. This

leader has an average speed of about 105 m s-1, similar upward leaders discussed in

Section 1.3.2. The upward leader current vaporizes the triggering wire and the gap

between the bottom of the leader and the ground is bridged, establishing the initial

continuous current (ICC) which has a duration of some hundreds of milliseconds. The

combined upward-leader and ICC processes are referred to as the initial stage (IS)

of rocket-triggered lightning and is similar to the initial stage observed for upward

flashes from tall towers [Miki et al., 2005]. After a no-current interval of some tens of

milliseconds, a downward-propagating negatively-charged dart leader traverses the gap

between cloud and ground at an average speed of about 107 m s1. When this dart leader

makes contact with ground, an upward return stroke wave propagates up towards the

cloud at a speed of roughly 108 m s-1. After an interval of some tens to hundreds of

milliseconds, more strokes may follow. These leader/return-stroke sequence are thought

to be very similar, if not identical to, subsequent dart-leader/return-stroke sequences in

natural negative lightning. The primary distinction between natural lightning and classical

rocket-triggered lightning is that the stepped-leader/first-return-stroke sequence in natural

lightning is replaced by initial stage (the upward positive leader, involving destruction of

the triggering wire, and initial continuous current) in classical triggered lightning.

Altitude triggered lightning. In contrast to classical-triggered lightning,

altitude-triggered lightning involves an ungrounded triggering wire. The bottom of

the conducting triggering wire is typically isolated from a grounded "intercepting

wire" by insulating Kevlar cable. The grounded intercepting wire and insulating Kevlar









cable have lengths on the order of some tens and hundreds of meters, respectively.

Unintentional altitude triggering can also occur as a result of accidental breakage of the

wire during classical triggering. Since the triggering wire is ungrounded, the presence of

a strong electric field (due to the overhead cloud charge source) results in the initiation

of a bidirectional (positive charge up and negative charge down) leader from opposite

ends of the wire. Upward positive leaders in altitude-triggered lightning are very faint

and hence difficult to image with streak cameras [Rakov and Uman, 2003], although they

have been imaged with photoelectric techniques, such as the ALPS system [Chen et al.,

2003]. The downward leader, initiated from the bottom of the wire, exhibits stepping

as it propagates through the virgin air. Lalande et al. [1998] estimated individual step

lengths of 3 5 m and a mean interstep interval of 21 uts for an altitude-triggered event,

compared with corresponding mean values of 3 50 m and 30 50 uts reported by

Berger and Vogelsanger [1969] for 19 downward negative stepped leaders in natural

lightning. Lalande et al. [1998] inferred from still photographic records the presence

of an upward connecting leader (initiated from the top of the 50 m intercepting wire) of

length 20 m. The corresponding current record, measured at the base of the intercepting

wire, suggested the upward connecting leader was stepped, with interstep intervals on the

order of 20 ts.

When contact is made between the downward-stepped and upward-connecting

leaders, the return stroke is initiated. However, this return stroke is dissimilar from both

natural first and subsequent strokes, as well as strokes in classical-triggered lightning.

The current waveform measured at ground appears to be "chopped" soon after reaching

its peak value, and its width is appreciably smaller than that of the following return

strokes. This phenomenon is presumably due to the return stroke front (having a speed

on the order of 108 m s 1) catching up with the upward-moving leader tip (which is still

propagating towards the cloud at a speed of about 105 m s-1) after 10 uts or so, producing

an opposite-polarity downward-moving reflected current wave that "chops" the current









waveform measured at ground. This return stroke is referred to as an "initial-stage"

return stroke [Rakov and Uman, 2003] or a "mini" return stroke [Chen et al., 2003].

The leader/return-stroke sequences that follow this initial-stage stroke are thought to be

similar those in classical triggered lightning. Although the altitude-triggering technique

reproduces some features observed in natural stepped leaders and first return strokes,

the complexity of the triggering process (e.g. the bidirectional leader and the reflected

initial-stage return stroke wave) often makes it difficult to interpret the resulting data.

More details of observations from altitude-triggered lightning can be found in Laroche

et al. [1991], Lalande et al. [1998], Rakov et al. [1998], and Chen et al. [2003].

1.4 Measured Electric and Magnetic Field Waveforms from Natural Negative First
Strokes

Figure 1-6 shows "typical" electric and magnetic fields ranging from 1 to 200 km

from negative return strokes, published by Lin et al. [1979], which are drawings based

upon many measurements obtained in Florida. The initial rising portion and peak of

the fields at each distance is due to the radiation component and decreases inversely

with distance in the absence of significant propagation effects [Lin et al., 1980]. After

some tens of microseconds, the electric and magnetic fields within a few kilometers are

dominated by the electrostatic and induction components, respectively. Beyond 50 km or

so, the both the electric and magnetic field waveshapes are bipolar and dominated by their

respective radiation components.

Several studies have been conducted to examine first stroke electric fields in the

range of tens to hundreds of kilometers (e.g. Weidman andKrider, 1978 in Florida and

Arizona and Cooray andLundquist, 1982 in Sweden). First-stroke fields can be separated

temporally into two phases illustrated in Figure 1-7a the first being the so-called

"initial slow front," or simply "slow front," described by Weidman andKrider [1978]

as an initial portion or front which rises slowly for 2 8 ts to about half the peak field

amplitude. After the slow front follows an abrupt transition to peak, typically referred
















A


Electric Field Intensity


r= 1.0 km

Ramp
300 VIm
-T-


r =2.0 km

Initial Peak Ramp
100 V/m
-

0 50 100 150 170
Time, ps
r = 5.0 km
-L_
Initial Peak




r=10km

20 VIm




r=15km
5.V./m Zero Crossing



r = 50 km


S 100 150
0 0 -- 170
Time, ps
r = 200 km


Figure 1-6.


B


Magnetic Flux Density


Hump





r = 1.0 km


Half Value


-r^
WTrir-- ....


r= 2.0 km

Initial Peak


10100


Time, ps
r = 5.0 km


.L Hump
2x107 t


r=10km

Haf Value



r = 15 km
r=15km





r =50 km

Zero Crossing
II OI

0 50
Time, ps
r=200km


Typical vertical electric field intensity (A) and azimuthal magnetic flux
density (B) waveforms for first (solid line) and subsequent (broken line)
return strokes (leader waveforms not shown) at distances of 1, 2, 5, 10, 15,
50, and 200 km. Time scales are in microseconds. Adapted from Lin et al.
[1979].









to as the "fast transition," having a 10-90% rise time of 0.2 uts or less when the field

propagation was over seawater, according to Weidman andKrider [1978] (Weidman and

Krider 1980a give a 10-90% rise time of 0.1 uts over seawater). The shape of the front

is typically concave in both measured currents and distant fields, although Weidman and

Krider [1978] do report some convex shaped fronts. The relative amplitude of the slow

front and total peak field for first strokes is reported by Weidman andKrider [1978] to be

0.4-0.5, while Cooray andLundquist [1982] and Master et al. [1984] give ratios of about

0.4 and 0.3, respectively. The corresponding first-stroke slow front durations are 4, 2.9,

and 5 his, respectively.

Weidman andKrider [1978] report that subsequent strokes preceded by dart leaders

also exhibit slow fronts, although they are generally smaller than those of first strokes,

with the front amplitude to total field peak ratio being about 0.2. These subsequent stroke

field fronts are also of shorter duration, having a mean of 0.6 0.9 ts. Interestingly,

subsequent strokes preceded by dart leaders were reported to have fast transitions to peak

field similar to those of first strokes, indicating the primary distinction between first and

these subsequent strokes fields is the slow front. Finally, slow fronts from subsequent

strokes preceded by dart-stepped leaders are also reported by Weidman andKrider

[1978] to have front amplitude to peak field ratios similar to those of first strokes, but a

mean duration of 2.1 ts, in between those of first (mean of 4 uts) and subsequent strokes

preceded by dart leaders (mean of 0.6 0.9 uts).

The origin of the slow front observed in distant fields is unknown, but is often

assumed to be related to the slow front observed in directly-measured currents (see

Section 1.3.2) and attributed to the upward connecting leader, an interpretation we

argue against in this dissertation. Weidman andKrider [1978] attempted to reproduce

the measured field fronts by modeling a single upward connecting discharge with both

velocity and current rising exponentially to peak (both having the same time constant),

justified by observations of exponential increases in upward streamer velocity in long


















-20 -15 -10 -5 0 5 10 15 20


5
L F

First
(a) R a
C
L L L L 10

SI I r I I I I i



10 L L LF S

5 Subsequent
Lu (b) R With Dart-Stepped
a Leader
L L L L L L FL V b
10





R a


(C) c Subsequent With
R a Dart Leader

10
I H I I I I I I I I I I I
-60 -40 -20 0 20 40 60 80
Time, ps


Figure 1-7. Electric field waveforms of (a) a first return stroke, (b) a subsequent stroke
initiated by a dart-stepped leader, and (c) a subsequent return stroke initiated
by a dart leader, showing the fine structure both before and after the initial
field peak. Each waveform is shown on two time scales, 5 us per division
(labelled 5) and 10 us per division (labeled 10). The fields are normalized to
a distance of 100 km. Leader pulses (L), slow front (F), and fast transition
(R) are indicated. Adapted from Weidman andKrider [1978].









laboratory sparks [Wagner, 1960], but according to Weidman andKrider [1978] this

assumption is not critical. In their model, the initial upward velocity in all cases was set to

105 m s-1. In their Figure 13a, electric fields at 100 km were calculated by constraining

the final velocity to be 107 m s-1 and varying the maximum current from 1 to 40 kA, with

the final discharge length being 21.4 m in all cases. In their Figure 13b, the final current

was held at 10 kA, and the maximum upward velocity ranged from 106 to 108 m -1.

The final upward discharge lengths ranged between 3.9 and 144.6 m. While the shapes

and durations of the calculated fields were similar to their measured data, the calculated

field amplitudes tended to be much smaller than the measured 5 V m 1 at 100 km, for

reasonable upward channel lengths and currents; "reasonable" being defined as a final

length of less then 30 m and a final current of about 10 kA.

Submicrosecond measurements of distant first-stroke electric field derivative (dE/dt)

waveforms propagating over ocean water, where propagation effects are assumed to be

minimal, have also been reported [Le Vine et al., 1989; Willett et al., 1990; Krider et al.,

1996; Murray et al., 2005; Willett et al., 1998]. An example from Krider et al. [1996] is

given in Figure 1-8. Murray et al. [2005] compared 131 directly-measured E waveforms

(sampled with 100 ns resolution) with corresponding integrated dE/dt waveforms (10 ns

resolution) and concluded that the fine structure of the integrated dE/dt waveforms,

especially during the onset of the slow front, is significantly more complex than those

of the corresponding directly-measured E waveforms. They further hypothesized that

the electromagnetic environment near the points(s) where lightning leaders attach to the

surface is often more complicated than what would be produced by a single current pulse

propagating up a single channel.

There have been few reported observations of fields and field derivatives at distances

less than 1 km from natural first strokes. Heidler andHopf [1998] reported measurements

of both E and dE/dt for several hundred natural flashes at distances ranging from 0.7

to 14 km. It is not stated how many first-stroke waveforms were measured at distances










150 Sept. 5, 1984
20.56.49.78 UT
S1 Range = 36 km
a 100 -

A ? 50 90 ns

300 400 500 ns
"V 0
100 200

-50-





10V/m B



I I
5 Vs


Figure 1-8. An example of dE/dt (A) and E (B) produced by a first return stroke at a
distance of about 36 km over the Atlantic Ocean. The propagation path was
almost entirely over salt water. Adapted from Krider et al. [1996].


ranging from 0.7 to 1 km, although Heidler andHopf [1998] reported that about 80

return strokes (the distinction is not made between first and subsequent) were measured at

less than 2 km.

In contrast with natural first strokes, there have been several studies examining the

very close (less than 1 m and up to some tens of meters) electromagnetic environment of

rocket-triggered lightning, such as Uman et al. [2000], Miki et al. [2002], and Schoene

et al. [2003a]. Recall from Section 1.3.4 that all strokes in classical rocket-triggered

lightning are thought to be very similar to natural negative subsequent strokes.

1.5 The International Center for Lightning Research and Testing at Camp
Blanding, Florida

The lightning-triggering facility at Camp Blanding, Florida was established in 1993

by the Electric Power Research Institute (EPRI) and Power Technologies, Inc. (PTI). In











Office Building Instrument NE Optical Sensor
Station

d Blast Wall
71


V Ground Plane-
SATTLIF Station 2
_Underground
Launcher
dE/dt dB/dt X 2 Station 5 Launch
Stationtation5 Control
Station 1
E

.9 Test House La nc
S Launch
Tower


S d] dB/dt

dE/dt
Station 4


Test Runway


Station 6


SW Optical Sensor
4 ----

Military Container

Flat Plate dE/dt Antenna
Coaxial Loop B Antenna
Station


N



~ m00


SCoaxial Loop dB/dt Antenna

Flat Plate E Antenna


Figure 1-9. Sketch of the ICLRT facility at Camp Blanding, Florida, during 2002-2004.
Approximate locations of MSE field sensors (see Section 2.1) are also shown.


1994, the University of Florida (UF) Lightning Research Group assumed operation of the

facility. It has since been known as the International Center for Lightning Research and

Testing (ICLRT). Since 2005, the ICLRT has been operated jointly by UF and the Florida

Institute of Technology (FIT). Experiments on natural and rocket-triggered lightning

are conducted year-round, though the primary months of activity are May-September.

During 1995-2002, over 40 researchers (excluding UF faculty, students, and staff) from

13 countries representing 4 continents have performed experiments at Camp Blanding

concerned with various aspects of atmospheric electricity, lightning, and lightning

protection [Rakov et al., 2005].


Test
3-Phase
Distribution
Lines


dE/dt

Station 8


E

Station 10







































Figure 1-10. The tower rocket launcher.


The ICLRT (located approximately 29.94'N, 82.03'W) occupies an area of

roughly 1 km2 on the Camp Blanding National Guard base, located in north central

Florida. A diagram of the facility is shown in Figure 1-9. Rocket-triggered lightning

operations are conducted from two fixed launchers: one located on an 11 m wooden

tower located roughly in the center of the site, pictured in Figure 1-10, and the other

(currently non-operational) located underground, in the north-west section of the site,

and surrounded by a 70 x 70 m2 buried metal screen (ground plane). A third, mobile,

launcher is fixed to the arm of a utility "bucket" truck and can be positioned virtually

anywhere within the site. The mobile launcher is pictured in Figure 1-11. All launchers

are equipped with resistive shunts for measuring the lightning channel-base current.































Figure 1-11. The mobile rocket launcher in its rest position.


Launcher controls, along with video and data acquisition equipment are housed

in the shielded "Launch Control" trailer, pictured in Figure 1-12, which is located

about 60 m north of the launch tower. The trailer is situated under a system of grounded

catenary wires and is surrounded by a buried metal counterpoise, both of which serve to

protect the trailer from lightning. During triggering operations, the Launch Control trailer

is disconnected from the power grid and power is supplied by a diesel generator. Rakov

et al. [2005] give a review of triggered and natural lightning experiments conducted at the

ICLRT between 1993 and 2003.

1.6 1997-1999 Multiple Station Experiment

The original Multiple Station Experiment (MSE) system was installed at the ICLRT

in 1997 and operated through 1999 [Crawford et al., 2001; Jerauld et al., 2003b]. This

network consisted of ten stations (numbered 1-10) spread about the ICLRT facility,

with the vertical electric field (E) measured at all ten stations and the two components

(north-south and east-west) of the azimuth magnetic induction (B) measured at two




















4


Figure 1-12. The Launch Control trailer. A) View from the south-east. B) View from the
north-west. Photos courtesy of Brian DeCarlo.

stations (yielding a total of 4 B-field measurements). Data were transmitted from the
sensors to Launch Control trailer (see Section 1.5) via Nicolet Isobe 3000 fiber-optic
links having a nominal bandwidth of DC-15 MHz. Waveforms at the fiber-optic receiver
outputs were digitized on a Nicolet Multipro digitizer at 10 MHz with 12-bit vertical
resolution. A continuous 51.2 ms record (40 ms pretrigger) was acquired for each event
- enough typically for only one stroke per flash. The digitizers were triggered from the
combined output of the two crossed-loop magnetic field sensors, configured such that


U 'MR







36

the system would likely trigger only on flashes within or near the network. The two

crossed-loop sensors also provided rudimentary direction-finding capabilities. Remote

measurement electronics were powered from 12 V lead-acid batteries that required

constant monitoring and replacing. The present MSE system was implemented in 2002

and is described in the next chapter.















CHAPTER 2
EXPERIMENT DESCRIPTION

2.1 Experiment Overview

The 1997-1999 MSE system is described briefly in Section 1.6. In 2002, the MSE

network was reorganized and upgraded to include electric and magnetic field derivative

measurements (dE/dt and dB/dt, respectively), as well as optical measurements and video

coverage. Two of the original ten stations were removed (although the station numbering

system was kept the same) and some of the remaining stations were moved to different,

but nearby, locations. Each of the crossed-loop B-field measurements was downgraded

to a single-loop configuration, reducing the total number of B-field measurements from 4

to 2. Further, two of the remaining eight E-field measurements were converted to dE/dt

measurements (reducing the total number of E measurements from 10 to 6), along with

the addition of two new dE/dt measurements (yielding a total of 4 dE/dt measurements).

Four new dB/dt measurements were also installed. Field-derivative measurements are

desirable in addition to directly-measured fields because of the higher bandwidth of the

former. However, due to limited dynamic range (e.g., limited amplitude resolution due

to digitizer noise), time-integrated field derivatives typically cannot totally substitute for

directly-measured fields.

Unlike the previous experiment, the system was controlled by a computer and

automatically enabled (armed) by sensing the ambient electrostatic field at ground (via

a device known as an electric field mill), and was triggered by the simultaneous output

from the two optical sensors viewing the network from its opposite corners. This optical

triggering scheme was used in order to limit the acquired data to flashes occurring within

or very close to the network. Video coverage from four sites is used to help determine

the location of the lightning within the network as well as the geometry of the lightning







38

Table 2-1. List of MSE stations and associated measurements, for the 2002-2004
experiments.

Station Measurements
1 dE/dt, dB/dt (N-S and E-W components)
2 E-Field
4 E, B (E-W component), dE/dt, dB/dt (E-W component)
5 E-Field
6 E-Field
8 dE/dt
9 E, B (E-W component), dE/dt, dB/dt (E-W component)
10 E-Field
NEOb Optical
SWOC Optical
a) Stations 3 and 7 were removed prior to the 2002 experiment. b) Abbreviation for
"north-east optical," c) Abbreviation for "south-west optical."


channel. GPS-accurate timing is used to correlate data recorded at the ICLRT with that

of other systems, such as the National Lightning Detection Network, or NLDN [Jerauld

et al., 2005]. The operation of the field measuring system is illustrated in Figure 2-1.

Table 2-1 lists the sensors installed at each station for the 2002-2004 experiment. Figure

2-2 is a sketch showing the layout of the MSE network.

The electric and magnetic field and optical waveforms were sampled continuously

for 0.4, 0.8, or 1.6 s at 10 MHz, with 12 bits per sample, on a Yokogawa DL716 digital

storage oscilloscope (DSO). The upper frequency response of the electric and magnetic

field measurements was limited to 4 MHz (-3 dB) by the internal low-pass filter of the

DL716. The field derivative data (dE/dt and dB/dt) were sampled at 50, 100, or 200 MHz,

with 8 bits per sample, on a LeCroy LT344 or LT374 DSO. The upper frequency response

of these measurements was limited to 20 MHz by the internal low-pass filters of the

LeCroy digitizers. Unlike the Yokogawa DSO, the LeCroys did not sample continuously

but rather the memory was divided into "segments," meaning that within a given flash

a 5 ms window was acquired each time the digitizer was triggered. Details of the

measurement configurations are presented in Table 2-2 and in Sections 2.6, 2.7, 2.8, and

3.1.





















U)


E~ >


0.. ) =
cEU) 0

LL


IIIL
II IO
0 0PY
1 0-O
LL LL ccE


((D


Figure 2-1. Diagram illustrating the operation of the MSE system in 2002-2004.


WI
-I


I-

0'
CC I


I-I
ZI
01
~I
ZI
0 1
01
zII





Cu
II


I
I
II










a).
-cr








40





S I E
4-D












0 o___ __













(0 ,1 t0 m -1- on.
s 0
Uco
00












1-1
-O 0





Figure 2-2. Sketch of the MSE system during the 2002-2004 experiments. Objects,






z o scale.
Ch cc


C cuO(D

70 ( 0


iU Wa U / ) o
-J 0 1O 0 c









0 LU1 I-
D C ) r.
LMo< CD Ii


















to scale.








41

Table 2-2. Typical MSE measurement configuration settings for the 2002-2004
experiment.







a
00




o
0 C3

N











N N -
N N NO
a -N A 0







W6 o0 0 C*
b6a a*











ti00 a N C ~



Cn\ ON 00N ^ ^ b




8) t o -S
"T T c:0 ^ '
S S -o |








^l U ^ *o
u -3 a |
S""" 8 0^n** 8>


+- a^ *'r' c '0 '









During summer 2005, the MSE network was additionally supplemented with ten

x-ray (energetic radiation) sensors, forming the basis of the Thunderstorm Energetic

Radiation Array (TERA). This new MSE/TERA network is a collaborative project

between the University of Florida and the Florida Institute of Technology. During

spring/summer 2006, an additional ten x-ray and four dE/dt sensors were installed at

new locations within the ICLRT facility. The new network is the responsibility of Ph.D.

student Joseph Howard, whose work involves time-of-arrival analysis of x-ray and dE/dt

pulses from close natural lightning.

2.2 Station Locations

Locations of measuring stations, as well as other relevant landmarks (such as

rocket launchers for triggering lightning) within the ICLRT facility, were measured

with Global Positioning System (GPS) receivers. Several surveys have been performed,

the first being in 1999 with a receiver utilizing differential GPS (DGPS). DGPS differs

from standard GPS in that, in addition to satellite navigation signals, the receiver also

acquires correction signals from a ground-based reference station, improving the location

accuracy to within a few meters. Without DGPS, location errors were on the order

of 100 m before selective availability (SA) an intentional error introduced into the

signals used by civilians was deactivated in 2000, decreasing the error to 10 or 20 m.

Accuracy can likely be increased by time averaging the measured coordinates, although

this assumes the errors are random with zero mean (i.e., no bias) and the errors in latitude

and longitude are independent. Some time-averaged location measurements (averaging

time ranging from a few hours to several days) were also acquired with a CNS brand

GPS receiver (no DGPS). A recent alternative to DGPS is the Wide Area Augmentation

System (WAAS), which is being developed by the Federal Aviation Administration

(FAA) and Federal Department of Transportation (FDOT) for aviation navigation, as

GPS alone does not meet FAA requirements. Similar to DGPS, WAAS consists of

ground-based reference stations that correct for GPS errors and send the message to









an enabled receiver. Unlike DGPS, the reference stations do not broadcast directly to

the receiver, but rather to special WAAS satellites in orbit. A WAAS-enabled receiver

acquires the satellite signals and corrects the data, which theoretically increases location

accuracy to better than 3 m 95% of the time. Currently, WAAS is only available in North

America. A WAAS-enabled Garmin eTrex Venture GPS receiver was used to perform two

GPS surveys, one in 2004 and another in 2005, consisting of all the MSE stations as well

as other landmarks. A few additional measurements were also performed in 2006.

Latitude and longitude are typically given in decimal degrees or degrees-minutes-seconds

format, neither of which are convenient for linear measurements. Fortunately, a Cartesian

coordinate system, known as the State Plane Coordinates System (SPCS), was developed

by the U.S. National Geodetic Survey (NGS). Each state is divided into up to five zones

and the curved surface of each zone is projected onto a planar surface, with the projection

method being dependent on the geometry of the zone in question. Zones generally follow

political boundaries, such as counties, and no zone occupies more than one state. The

ICLRT resides near the western edge of Clay county, in the north-west region of the

"Florida East" zone. Different zones are necessary because an ellipsoid surface cannot

be projected onto a planar surface without some amount of distortion; the goal of the

SPCS was to minimize the distortion. The system is designed to have a maximum linear

error of 1 in 10,000, meaning that if a line is measured to be 10,000 units (e.g., meters)

in state plane coordinates, the actual length may be in error by as much as one unit.

While coordinates in each zone are very accurate and ideal for local surveying, owing to

the small zone sizes, state plane coordinates are not well suited for regional or national

mapping tasks. Each set of state plane coordinates is independent with its own origin,

usually, but not always, two million feet west of the zone's central meridian (north-south

line running approximately down the center of the zone) and some distance (there is no

standard) south of the zone's southern-most point. This guarantees that all coordinates

within the zone are positive. X distances run east-west and are typically called "eastings"









because distances are measured east of the origin. Y distances run north-south and are

referred to as "northings" because distances are measured north of the origin. Thus, the

SPC system forms a right-hand Cartesian coordinate system with the Z axis pointing

away from the surface of the Earth.

Latitude and longitude coordinates can be converted to SPCs via the utility on the

website http://www.ngs.noaa. gov/TOOLS/spc. html provided by the NGS. Using

state plane coordinates, distances can be calculated easily using Euclidean geometry. For

each location, the coordinates obtained via GPS were converted to SPCs. For locations

with multiple GPS measurements (e.g., DGPS and Garmin), each set of coordinates

were converted to SPCs and were averaged. Coordinates considered inconsistent or

measured in error were not included in the average. The resulting SPC values are very

large relative to the size of the ICLRT facility, owing to the location of the SPC origin

discussed above. Therefore, 99750 m and 621500 m were subtracted from the X and Y

SPC values, respectively, creating so called "Camp Blanding Coordinates" (CBC), which

are more convenient than the corresponding SPC values. The values were chosen so that

the western-most location of interest (the South-West Optical measurement) would have

an X value of approximately 200 m in CBC, while the southern-most location of interest

(Station 9) would have a Y value of approximately 200 m in CBC. The value of 200 m

was chosen somewhat arbitrarily, although it was hoped that most flashes recorded by the

MSE system would be found to have positive CBC values.












Table 2-3. MSE station locations, measured in 1999 with a differential GPS (DGPS)
receiver, having a nominal accuracy of a few meters. For Stations 4 and 9,
measurements were performed at both the E-field and B-field antennas.


Latitude ['N]
29.94347234
29.94404460

29.94329562
29.94328196
29.94323225
29.94160838


Longitude ['W]
82.03497685
82.03197909

82.02931170
82.02937771
82.03248203
82.03561998


SPC North [m]
622052.231
622113.062

622027.722
622026.265
622023.446
621846.163


SPC East [m]
100085.517
100375.501

100632.273
100625.887
100326.136
100021.563


8 29.94145723 82.03053364
9 (E-field) 29.94026821 82.03396553
9 (B-field) 29.94022270 82.03399469
10 29.94068532 82.02925378
a) Optical measurements were not in use in 1999. b)
c) Station moved prior to the 2002 experiment.


621824.988 100512.473
621696.160 100179.954
621691.140 100177.093
621738.310 100635.270
Station removed prior to the 2002 experiment.


Table 2-4. MSE station locations, measured in 2004 with a Garmin Etrex Venture
hand-held GPS receiver with WAAS, having a nominal accuracy of a few
meters. For stations with multiple sensors, the coordinates were measured at
the location of the dE/dt antenna.


Station Latitude ['N]


1
2
4
5
6
8
9
10
NEO
SWO


29.94346
29.94406
29.94330
29.94323
29.94178
29.94149
29.94029
29.94074
29.94438
29.94100


Longitude ['W]
82.03497
82.03199
82.02937
82.03249
82.03535
82.03052
82.03397
82.02924
82.02898
82.03631


SPC North [m]
622050.857
622114.779
622028.258
622023.204
621864.953
621828.609
621698.579
621744.359
622147.643
621779.323


SPC East [m]
100086.166
100374.463
100626.649
100325.364
100047.800
100513.823
100179.544
100636.655
100665.374
99954.336


a) Stations 3 and 7 were removed prior to the 2002 experiments.


Station
1
2
3b
4 (E-field)
4 (B-field)
5
6C
7b


























Table 2-5. MSE station locations, measured in 2005 with a Garmin Etrex Venture
hand-held GPS receiver with WAAS, having a nominal accuracy of a few
meters. For stations with multiple sensors, the coordinates were measured at
the approximate center of the station.


Station Latitude ['N]


1
2
4
5
6
8
9
10
NEO
SWO


29.94348
29.94404
29.94330
29.94323
29.94180
29.94147
29.94025
29.94070
29.94441
29.94099


Longitude [W]
82.03498
82.03195
82.02932
82.03249
82.03539
82.03055
82.03394
82.02919
82.02906
82.03632


SPC North [m]
622053.083
622112.527
622028.215
622023.204
621867.205
621826.418
621694.119
621739.882
622151.038
621778.223


SPC East [m]
100085.221
100378.305
100631.476
100325.364
100043.958
100510.906
100182.400
100641.442
100657.681
99953.361


a) Stations 3 and 7 were removed prior to the 2002 experiments.











47













Table 2-6. Locations of rocket launchers used at the ICLRT facility, some measured on

multiple occasions with different GPS receivers.


m oo


O





\OO


m ^

I 11 CI
10 I'D


\D OC










wrc ',D



- (--


U3 c3 ~
000 0


0 Q~ e~


00
00


0

0

0
hD
(N






0
4^


0
b,







0
03











20



0
0
S.
(U
-s

b,
L,
&<
(U~


i fe






13


c 0




ca c

^ s







c3


0


0


-E

0
~









~-c3








04 5






0 b)
0C





00


0003


'0
.0





o







U


0


0
0
CL.
ccl







0

B
m





0
e














o
M- 0










v


-0
- 0
^


0

0



*0
,.


0




0

0
-J



.,..

"O
VI
,.






















' 0
E
0
^-1
hi

(U







0-
-~0







oa


0
o -
h h


o g





















Table 2-7. MSE station locations, as well as other landmarks, given in Camp Blanding
coordinates (CBC). Corresponding state plane coordinates (SPC) are obtained
by adding 99750 and 621500 to the east (X) and north (Y) CBC values,
respectively.

Location CBC East (X) [m] CBC North (Y) [m]
Station 1 335.635 552.057
Station 2 626.090 613.456
Station 4 878.804 529.477
Station 5 575.621 523.285
Station 6" 295.879 366.079
Station 8 762.401 326.672
Station 9 430.972 196.349
Station 10 887.789 240.850
NEO 911.527 649.340
SWO 203.848 278.773
Tower launcher 636.923 458.901
SATTLIF underground launcher 380.617 600.525
Mobile launcher 2002b
Mobile launcher 2003a 399.865 432.963
Mobile launcher 2003b 399.865 424.963
Mobile launcher 2003c 1068.773 419.000
a) DGPS measurement was not included in the SPC average,
since Station 6 was moved between 1999 and 2002.









2.3 Control System

The MSE network is automatically enabled by a central control computer, pictured

in Figure 2-3, running a custom LabView application written by Robert Olsen, a Ph.D.

student at the University of Florida. The output of an electric field mill (sensing the

quasi-static electric field at ground, which can be used as an indicator of thunderstorm

conditions) is digitized on the computer using a National Instruments data acquisition

card. The field mill is pictured in Figure 2-4. If the electric field exceeds a certain value

(typically 2 kV m 1), control commands are sent over a 900 MHz RF link to the

instruments in the field and the instruments are activated (that is, power is supplied to

the fiber-optic transmitters and other measurement electronics). In addition, each of the

digitizers is configured over a GPIB or Ethernet interface. Activating the network is a

multi-step process by which instruments are powered up, calibration signals (generated

in the field and transmitted over the fiber-optic links) are recorded on the digitizers, each

of the PIC controllers is set to its proper voltage attenuation setting, and the digitizers

are armed. Once this process is complete the network is ready to acquire data. If the

field falls below the threshold value for ten minutes, the network is disarmed, using a

procedure that is essentially the inverse of the arming procedure. This automated system

allows the network to acquire data while no personnel are on site, with the added benefit

of saving battery power. A flowchart representation of the MSE control algorithm is

shown in Figure 2-5.

The primary components of the control system are the control computer and a device

known as a PIC controller. The PIC controller (named so because it contains a PIC brand

16F873-207SP microcontroller) was designed by Michael Stapleton and Keith Rambo.

Each PIC controller is given a unique two-digit hexadecimal identifier and thus can be

controlled individually by the control computer. A PIC controller is pictured in Figure

2-6 and a diagram of a typical PIC controller installation is given in Figure 2-7. Figure

2-8 shows a photograph of a typical PIC controller installation.


















Nt1
w /n

i,^ / .^ i i :l m r1


U--^F ^^^^k 0l 6 0.
.6011 0 '6^y 0
0rrrrco miute0Ir 00
Oications display comuter i
adio Rocket display1
^^^^^^^^^^^^^^launcher^^^


Figure 2-3. The MSE control system in the Launch Control trailer. The control center is
also used for rocket-triggered lightning operations. A) Above the counter. B)
Below the counter. Photos courtesy of Brian DeCarlo.































Figure 2-4. Electric field mill located a few meters west of the Launch Control trailer.

As shown in Figures 2-7 and 2-8, all of the measurement electronics are housed

in a shielded metal enclosure in order to minimize the electromagnetic coupling from

the lightning. The output of the sensor (e.g. a flat plate or loop antenna) is fed into the

box via a BNC bulkhead feed-through connector and is connected to the input of the

PIC controller. The output of the PIC controller is then connected to the fiber-optic

transmitter. The PIC controller is capable, depending on the command, of attenuating

the signal (by certain fixed amounts, such as -20 dB) or injecting a 0.5 V, 100 Hz,

square-wave calibration signal into the fiber-optic transmitter. Similarly, the PIC

is powered from the 12 V battery and, when commanded, it supplies power to the

transmitter and other measurement electronics. Command and responses are sent and

received optically over 1 mm diameter plastic fiber, which is connected to a 900 MHz

RF transceiver outside of the shielded metal enclosure (pictured in Figure 2-9), again

in order to minimize any electromagnetic coupling to the measurement electronics

from the lightning. The RF transceiver unit was powered by a 12 V battery which was


























Disarm
Digitizers






Run
Calibration
Procedure




Y

_N


Figure 2-5. Flowchart representation of the MSE software control algorithm.






















BNC
Connectors



Plastic Fiber.
Connectors


- Battery Connectors



Power Connector
for Measurement
Electronics




LCD Display
Connector


Hexadecimal
Switches


Figure 2-6. The PIC controller. A) Front view. B) Side view.




In-line Terminator


Data Fiber


Bulkhead
Feed-through
BNC Connector


Metal Enclosure


Plastic Control Fiber


Figure 2-7. Diagram of how a PIC controller is connected to other elements of a
measurement system.




















































Figure 2-8. A typical measurement configuration utilizing a PIC controller.









Solar Cell Enclosed in "Chicken Wire" Mesh








Antenna

Metal Box
Containing
PIC RF Unit





Plastic Fiber

Figure 2-9. PIC RF unit enclosure mounted with a solar cell.


continuously charged by a 10 W solar cell. The control computer is also connected to a

900 MHz transceiver (see Figures 2-1 and 2-3), and thus the computer exercises control

over the MSE network measurements via the 900 MHz link.

Figure 2-10 shows the frequency response of a PIC controller. The frequency

response was measured for each attenuation setting.

2.4 Fiber-Optic Links

Fiber-optic links were used to transmit the analog data from all sensors in the field

to the Launch Control trailer, where they were digitized and stored. Three different types

were used in the MSE system. This section presents a detailed description of all types of

links. Thirteen Opticomm MMV-120C fiber-optic links were used along with one Nicolet

Isobe 3000 fiber-optic link and four Meret MDL288DC fiber-optic links. Table 2-8 gives

a brief summary of the characteristics of each type of link.

Opticomm MMV-120C. The Opticomm MMV-120C fiber-optic links utilize

frequency modulation (FM) with a carrier frequency of 70 MHz and operate at an optical













PIC 39, 0 dB






--
L


102 104 106
Frequency, Hz


1.00

0.95

0.90

0.85
10


0.55

0.50

> 0.45

0.40

10


0.22

0.20


* ** ** ** *


102 104
Frequency, Hz


0.75

0.70

0.65

0.60

0.55
1C


0.34

0.32

0.30

0.28

0.26

1C


102 104 106
Frequency, Hz
PIC 39, -10 dB


102 104 106
Frequency, Hz


Frequency, Hz


Figure 2-10. Measured frequency response of PIC controller #39. The frequency
response was measured for each attenuation setting. The dashed lines
indicate the ideal attenuation values.





Table 2-8. MSE fiber-optic link summary.


Signal to
noise
ratio (approx)
59 dB
60 dB
40 dB


Nominal
-3 dB
bandwidth
DC 30 MHz
DC 15 MHz
DC 20 MHz


Transmitter
Input
Resistance
68 kM
1 MQ
50 Q


Receiver
Output
Resistance
50 Q
50 Q
50 Q


Input
Range
1V
Selectable
0.5 V


Output
Range
(in 50 0)
1 V
1 V
0.5 V


0


"'' "' N :'


Frequency, Hz
PIC 39, -14 dB
I ..I ..




- . -i


0.18

0.16

0.14
10


Type
Opticomm
Nicolet
Meret


PIC 39, -3 dB


-


)0


. ..i .-.





E -


)0


0


,I









wavelength of 1310 nm. The Opticomm links were intended by the manufacturer to be

used as video fiber-optic links and therefore had an input and output resistance of 75 Q

(the standard resistance for video equipment). This was not appropriate for the MSE,

which is almost exclusively a 50 Q system. Therefore, the input resistance was modified

to 68 kQ by the manufacturer. A high input resistance has the advantage of being able

to be lowered any desired value by simply adding an in-line terminator. The value of

68 kQ was not chosen arbitrarily; it was the highest value the manufacturer could achieve

without sacrificing the performance of the link. In addition, the output resistance was

modified to 50 Q from 75 Q. Finally, the low frequency cutoff was modified to DC from

5 Hz (-3 dB) by the manufacturer. The manufacturer lists the signal-to-noise ratio to

be about 67 dB, however this value is acquired using the short-haul RS-250C standard

in which the signal is low-pass filtered with a cut-off frequency of about 5 MHz. Thus,

67 dB may not be an accurate representation of the true signal-to-noise ratio over the

entire bandwidth. In practice the actual signal-to-noise ratio over the entire bandwidth is

several dB lower than the value obtained under the short-haul RS-250C standard. Figure

2-11 shows plots of the measured frequency response for three Opticomm MMV-120

fiber-optic links used in the MSE system.

The Opticomm links utilize 62.5/125 utm (core/cladding) graded index multi-mode

fiber-optic cable. Optical Cable Corporation (OCC) BX series water resistant armored

cables with ST connectors were used with the Opticomm links. Each armored cable

consists of two armored outer jackets surrounding either four (BX-04 series) or six

(BX-06 series) sub-cables. Each sub-cable is Kevlar reinforced. The sub-cables, which

are color coded, are twisted around a strength member running through the center of the

cable.

Nicolet Isobe 3000. The Nicolet Isobe 3000 fiber-optic links have an input

resistance of 1 MQ and utilize a combination of amplitude modulation (AM) and

pulse-width modulation (PWM). The input range of the transmitter is selectable from









Opticomm Fiber-Optic Links

1.10 -
Opticomm #2
Opticomm #4
c: 1.05 -- Opticomm #6 ..:
D -,:
= .. ... ...... .' =

> 1.00- _---- -


S0.95


0 0.90

I-,I 1111111 I, I I I I I I 1111111 I I I 1111111 I,, ,I 1111111 I l
102 103 104 105 106 107
Frequency, Hz

Figure 2-11. Measured frequency response of three Opticomm MMV-120 fiber-optic
links used in the MSE network.

0.1 V, 1 V, and 10 V. In addition, the gain and offset of the link can be manually
adjusted at the receiver end. The output range of the receiver is fixed at 1 V regardless
of the selected input range. For example, if a 5 V signal is connected to the transmitter
set to the 10 V input range, the corresponding voltage at the output of the receiver
will be 0.5 V. Therefore, the Isobe fiber-optic link effectively attenuates the signal by
-20 dB (0.1 V/V) when the transmitter is set to the 10 V range. Similarly, when the
transmitter is set to the 0.1 V range, the link introduces a gain of 20 dB (10 V/V).
The Isobe links were used with 200 ptm multi-mode Kevlar reinforced duplex
fiber-optic cables with SMA connectors, arranged in six-fiber armored cables, and
manufactured by OFS Fitel Corporation. The individual sub-cables are color coded and
twisted around a strength member. Each Isobe link requires two fibers; hence each cable
can supply three links. SMA connectors were used as before. These cables have only a









single layer of armor and were vulnerable to water intrusion through any opening in the

armor. Therefore, care must be taken to protect the ends of the cable from the elements.

Meret MDL288DC. The Meret MDL288DC fiber-optic links utilize amplitude

modulation (AM) and operate at an optical wavelength of 820 nm. Unlike the Opticomm

and Isobe links, the Meret transmitters are not stand-alone units; they must be mounted

on a circuit board. The advantage of this design, however, is that any electronics

associated with a measurement such as a preamplifier or an active integrator can be

incorporated in the same circuit as the fiber-optic transmitter. In the early 1990s,

George Schnetzer designed and built several different types of units incorporating

the Meret transmitters. The three most common units included an active integrator,

a high-impedance preamplifier, or a differential preamplifier. Although the Meret

transmitter itself has a nominal frequency response from DC to 35 MHz, the other circuit

components lower the upper limit. For example, the units which incorporated an active

integrator are limited to 10 MHz, while the units with a differential preamplifier are

limited to 20 MHz. The 20 MHz differential input units are the only type used in the

MSE, and the other types will not be discussed further.

In practice, the Meret links suffer from high noise and from DC offset drift. This is

corrected by utilizing AC coupled active low-pass filters at the output of the receivers.

The low frequency response is limited to about 1.5 Hz (-3 dB) by the AC coupling. In

addition, the filters can provide gain which is adjusted by a potentiometer. These filters

were designed to be paired with specific types of Meret units. For example, the 20 MHz

(-3 dB) low-pass filters were designed to be used with the differential input units.

The Meret links have been used in previous ICLRT experiments with 50/125 ftm,

although they will operate using the 62.5/125 utm OCC fiber. The Meret fiber-optic

transmitters use SMA0906 connectors, which would be difficult to terminate in the

field. Conversely, the ST and SMA connectors used with the Opticomm and Isobe links,

respectively, were relatively easy to terminate in the field. Therefore, the fibers were









terminated with ST connectors, as with the Opticomm links, and 3 m patch cords were

used to convert the ST connectors to SMA0906 connectors. The insertion loss for an

individual patch cord ranged from about -0.5 to -1.5 dB, with two patch cords needed

for each link. Furthermore, in previous experiments, the Meret links were used with a

fiber length of about 100 m, however they will operate at length of over 500 m using the

62.5/125 um fiber. An optical loss of over several dB can be introduced by using such

long fiber lengths, but the links are still usable. The maximum signal-to-noise ratio was

measured experimentally to be about 40 dB by connecting a transmitter and receiver

together with two patch cords and a 1 m length of 62.5/125 tm fiber. Since the signal

level decreases with increasing fiber length, the signal-to-noise ratio for any link in the

field will be less than the maximum value of 40 dB.

Fiber-optic delays. It is important to know the time delays associated with each

fiber-optic link so that all waveforms can be properly aligned when performing data

analysis. Furthermore, it is desirable to know the time delays to within one sample

(digitization) point. If each of the fiber-optic links is of the same type and uses the same

length of fiber, the relative delays between each of the waveforms will be identical.

However, the MSE utilized three different types of links with many different lengths of

fiber, so accurate time delay measurements are critical. The total delay of a fiber-optic

link is determined by two factors; electronic delays and fiber delays. Electronic delays

constitute any delays that arise from the transmitter and receiver electronics themselves.

Fiber delays are due to the propagation of light in the fiber-optic cable at a finite speed,

which is slower than the speed of light. In general, the time delay of a link can be

modeled as a constant delay (due to the electronics) plus a delay that is a linear function

of fiber length.

Each armored cable was cut and terminated in the field, so the length of each

cable could not be measured directly. Therefore, the optical length of each fiber was

measured with an Agilent E6000C Optical Time-Domain Reflectometer (OTDR). The









OTDR measures the length of the cable by sending a pulse of light down the fiber and

measuring the time it takes for the pulse to be reflected back to the light source. The

distance resolution of the OTDR is inversely proportional to the pulse width of the light

source (since the OTDR is actually measuring time); hence a narrow pulse will yield a

more precise measure of fiber length. In addition, when used with multi-mode fiber, the

distance resolution of the OTDR will be limited by modal dispersion in the fiber, whereby

the width of a pulse of light is widened due to multi-modal propagation in the fiber.

The optical length in meters of a fiber, 1, is given by

1 Ctmeas
1= (2.1)
2N

The quantity c is the speed of light in a vacuum, equal to 3 x 108 m S 1 and tmeas

is the measured round-time of the light pulse emitted by the OTDR. The quantity N is

supplied by the manufacturer of the fiber and is typically referred to as the group index,

and is defined as the ratio of the speed of light in a vacuum to the speed of light in the

fiber. In practice this value is often slightly different from the index of refraction of the

glass which is used to make the fiber.

The one-half scaling factor is included because tmeas is the measured round-trip

time, not the one-way time. The group index is supplied by the manufacturer and must

be programmed into the OTDR. If the wrong value of N is used, the optical length

measurement will be incorrect. The optical length measurement can be corrected if both

the correct value of N and the incorrect value of N used during the measurement are

known. The fiber delay, tfiber, can be found by rearranging equation 2.1

1 NI
tfiber = tmeas (2.2)
2 c

Hence, the time delay of the fiber optic cable is proportional to both the I and N. The

OCC and OFS Fitel fiber-optic cables (both armored and unarmored) have values ofN









of 1.483 and 1.429, respectively. The corresponding fiber delays are 4.943 ns m 1 and

4.763 ns m1, respectively.

The optical lengths, and hence time delays, of all fibers in the MSE network were

measured using the OTDR. The OTDR was set to generate a 5 ns wide pulse at 1310 nm

for the OCC armored fiber and 850 nm for the OFS fiber with the measurement being

averaged over one minute. Table 2-9 gives the measured optical length and corresponding

time delay for each fiber. The time delays were calculated by using Equation 2.2. Only

the fibers currently in service were tested; any unused fibers in an armored cable bundle

were not. Each armored cable is uniquely identified by the location it was run to, such as

Station 1, for example. Each individual fiber is uniquely identified by the combination

of the cable identifier and the color of the fiber in that cable, such as Station 1 Blue, for

example. The OFS fibers are grouped into pairs (such as Tower Yellow/Red for example)

since the Nicolet Isobe links each require two fibers. At the time of this writing, the

delays due to the electronics have not been measured, and hence only the fiber delays are

given.

2.5 Digital Storage Oscilloscopes

This section describes the digital storage oscilloscopes (DSOs) used in the MSE

system. Two types of DSOs were used. The first type was a Yokogawa DL716, which

was used to record continuous long-duration (on the order of 1 s) electric and magnetic

field and optical waveforms at a sampling rate of 10 MHz. The second type was a LeCroy

LT344 Waverunner or LT374 Waverunner2, which was used to record short duration (on

the order of a few milliseconds) electric and magnetic field derivative waveforms at a

sampling rate of 50, 100, 200, or 250 MHz. Note that a LeCroy LT344 was used for the

dB/dt measurements in 2002, but replaced with an LT374 in 2003. Each oscilloscope

used at the ICLRT is given a unique identifier. The oscilloscopes used in the MSE system

are listed in Table 2-10, and some oscilloscopes are pictured in Figure 2-12. Specific









Table 2-9. OTDR measured optical lengths and corresponding time delays for armored
fiber-optic cables used in the MSE network.


Fiber designation
Station 1 Blue
Station 1 Orange
Station 1 Green
Station 2 Brown
Station 4 Blue
Station 4 Green
Station 4 Gray
Station 4 Orange
Station 5 Brown
Station 6 Brown
Station 8 Blue
Station 9 Blue
Station 9 Brown
Station 9 Gray
Station 9 Orange
Station 10 Brown
SW Optical Brown
NE Optical
Orange / Blue


Cable
Type
OCC
OCC
OCC
OCC
OCC
OCC
OCC
OCC
OCC
OCC
OCC
OCC
OCC
OCC
OCC
OCC
OCC


Measurement
dE-1
dB-1N
dB-1E
E-2
dE-4
E-4
B-4N
dB-4N
E-5
E-6
dE-8
dE-9
E-9
B-9N
dB-9N
E-10
SWO


OFS NEO


OTDR measured
length [m]
499.7
500.0
500.0
129.2
288.7
289.0
289.0
289.3
105.8
521.5
357.2
617.2
617.5
616.2
616.2
527.8
652.9


421.2


Corresponding
time delay [ns]
2470
2472
2472
639
1427
1429
1429
1430
523
2578
1766
3051
3052
3046
3046
2609
3227


2006


Table 2-10.


Digital storage oscilloscopes (DSOs) used in the MSE system. Specific
oscilloscope configurations for data obtained by the MSE system are given in
Tables 3-3 and 3-4.


DSO type
LeCroy LT344
LeCroy LT344

Yokogawa DL716
LeCroy LT374
LeCroy LT374


Use
dE/dt waveforms
dB/dt waveforms
E, B, and
Optical waveforms
dE/dt waveforms
dB/dt waveforms


Sampling
rate [MHz]
250
50 or 100

10
200
50 or 200


Comment
Only used on 8/24/2004
Only used in 2002




Only used after 2002


oscilloscope configurations for data obtained by the MSE system are given in Tables 3-3

and 3-4. The below paragraphs give specifics on the operation of each type of DSO.

Yokogawa DL716. The Yokogawa DL716 is a 16 channel DSO with a maximum

bandwidth of 4 MHz (-3 dB) and a maximum sampling rate of 10 MHz, with 12-bit

vertical resolution. The DL716 is capable of a maximum record length of 16 megasamples


DSO ID
16
17

19
20
21











SsaYokogawa
DL716





LeCroy
LT374


LeCroy
LT344












Figure 2-12. Digital storage oscilloscopes in the Launch Control trailer. The models of
some DSOs are labeled. Note that this picture was taken in 2005 and this is
not how the DSOs were arranged in the 2002-2004 MSE system.

per channel when all 16 channels are used simultaneously. At the maximum sampling

rate of 10 MHz, the maximum record length is 1.6 s when all 16 channels are used.

Therefore, the DL716 is ideal for recording a continuous full-flash record of lightning

electric and magnetic fields. Since each sample is recorded with 12-bit resolution, two

bytes (16 bits or one word) are required to store each sample (four bits are thrown away).

Therefore, a 1.6 s record sampled on all 16 channels at 10 MHz requires 256 megawords

or 512 megabytes.

Each DL716 channel can be set from 5 mV per division to 20 V per division with

a maximum peak-to-peak input voltage range of 250 V. The input resistance of each









channel is 1 MQ shunted with 30 pF of input capacitance, either AC or DC coupled. In

addition, each channel can be individually configured with an internal low-pass filter

having a -3 dB cutoff at 500 Hz, 5 kHz, 50 kHz, or 500 kHz.

The DL716 is equipped with 9.2 GB of internal storage and many acquired

waveforms can be stored in the digitizer itself. The DL716 is also equipped with an

external SCSI hard disk connector so that more storage can be added. Waveforms can

be moved to and from the DL716 over a 10Base-T Ethernet connection using the File

Transfer Protocol (FTP).

The DL716 can be configured over an IEEE 488.2 (GPIB) bus and supports a robust

command set. Almost every setting can be manipulated over GPIB, therefore the DL716

can be configured and armed remotely. The DL716 can be automatically configured

for an experiment by a PC with a GPIB interface card and appropriate software such as

National Instruments LabView by either issuing a series of commands or loading a set of

predefined settings from the hard disk of the DSO.

The DL716 can be triggered by any of the 16 channels or by an external TTL

level trigger input. Furthermore, complex triggering schemes can be generated by OR

triggering any combination of the 16 channels with the trigger level and slope of each

channel capable of being set individually.

One major disadvantage of the DL716 is that, for long records (several hundred

milliseconds or more), it takes up to 15 minutes to write the data from memory to disk.

During this interval, the digitizer cannot trigger and hence no new lightning data can be

recorded.

Each time the DL716 is triggered, the waveforms recorded on all active channels

are saved to a single binary file (having the extension ".WVF") that is paired with an

ASCII header file (having extension ".HDR"). The file names are set by the LabView

control program (see Section 2.3) via the GPIB interface. File names for lightning data

are typically are of the form "DMMDDXXX.HDR" and "DMMDDXXX.WAV," where









MA is the month, DD is the day, and XXXis a number from 000 to 999, the latter number

beginning at 000 and increasing with each data file saved on a given day. File names for

calibration data are of the form "CAMMDDXXX.HDR" and "CMMDDXXX.WAV."

LeCroy LT344 Waverunner. The LeCroy LT344 is a four channel DSO with a

maximum bandwidth of 500 MHz at a maximum sampling rate of 500 MHz with 8-bit

vertical resolution. The LT344 is capable of a maximum record length of one megabyte

per channel when all four channels are in use. Since a sample is recorded with 8-bit

resolution, one byte is required to store each sample; hence the total record length is one

megasample per channel. At the maximum sampling rate of 500 MHz, the maximum

record length is 2 ms. Typically the LT344 is not used to acquire a single continuous

record but rather is used in segmented memory mode. In segmented memory mode, the

acquisition memory is divided into multiple segments and a separate trigger is required

to record each segment. For example, if five segments are used, the acquisition memory

is divided into 200 kilosamples per segment per channel. Segmented memory mode is

useful when acquisition memory is limited and multiple events are to be recorded with

the time length of each event being very small relative to the length of time between

events. Segmented memory mode is ideal for recording the electric and magnetic field

waveforms (or their time-derivatives) from individual return strokes. Typically, the return

stroke waveforms occur on a tens of microseconds time scale while the time between

return strokes is on the order of tens to hundreds of milliseconds [Uman, 1987]. When

pre-trigger is used, the pre-trigger setting applies to each segment of the acquisition. For

example, if 10% pre-trigger is used, the first 10% of each segment record consists of data

before that segments trigger point.

The input resistance of each LT344 channel can be set to 50 Q or 1 MQ, either AC

or DC coupled. Each channel can be set from 2 mV per division to 10 V per division with

a maximum RMS input voltage of 5 V and 280 V when 50 Q and 1 MQ input resistance









are used, respectively. In addition, each channel can be individually configured with an

internal low pass filter of value 25 MHz or 200 MHz (-3 dB).

The LT344 is equipped with a PCMCIA Type III slot, which is used to add storage

such as a hard drive or a compact flash card which come in a variety of sizes. A 128 MB

compact flash card was used in the LT344; hence a maximum of 32 waveforms could be

stored if one megabyte was used per channel and all four channel were in use for each

acquisition. Waveforms can be moved to and from the DSO over a 10Base-T Ethernet

connection or the GPIB bus using LeCroy Scope Explorer software. Unlike the DL716,

the LT344 does not support FTP and uses a proprietary protocol for file transfers.

The LT344 can be configured over GPIB or Ethernet and supports a robust command

set. Similar to the DL716, the LT344 can be configured and armed remotely.

The LT344 can be triggered from any of the four channels or from an external

trigger input, and complex triggering schemes are available as with the DL716. Unlike

the DL716, the external trigger input is not TTL, and the trigger level and slope can

be adjusted. In addition, the input resistance and coupling of the trigger input can be

adjusted.

Each time the LT344 is triggered, the waveforms recorded on each of the active

channels are each saved to an individual binary file. Unlike the DL716, the header

information is stored in the same binary file as the waveform data. File names for

lightning data are of the form "ACX.YYY" where X is the channel number and YYY is a

number from 000 to 999, the latter number beginning at 000 and increasing with each

data file saved on a given day. File names for calibration data are of the form "SCX.YYY."

LeCroy LT734 Waverunner2. The LeCroy LT374 Waverunner2 is the successor

of the LT344 Waverunner DSO. The LT374 is essentially identical to the LT344, except

that the maximum sampling rate is 2 GHz, the maximum acquisition memory is four

megabytes per channel and the input filters are selectable from 20 MHz and 200 MHz (-3

dB).









2.6 Electric Field and dE/dt Measurements

This section describes the measurement of the vertical component of the electric

field, E, and its time derivative, dE/dt, in the MSE system. As shown in Table 2-1,

E-fields were measured at Stations 2, 4, 5, 6, 9, and 10, while dE/dt was measured at

Stations 1, 4, 8, and 9. All E-field and dE/dt waveforms presented herein are the vertical

component of the electric field, that is, the component of the electric field or dE/dt

vector normal (perpendicular) to the surface of the Earth. This is because, for a perfectly

conducting ground, boundary conditions state that the horizontal (tangential to the

ground) component of the E-field is zero. However, the soil conductivity in many parts of

the world, including the ICLRT where this experiment was conducted (Rakov et al. 1998

report a value of 2.5 x 10 4 S m 1), is relatively poor, and thus the horizontal component

of the E-field will likely be non-zero. Nevertheless, the vertical component remains that

which is dominant and of interest here. The E-field sensors described in the following

sections measure only the vertical component of the field, regardless whether or not a

horizontal component is present. Hence the term "E-field measurement" implies "vertical

component of electric field measured at ground level."

2.6.1 The flat plate antenna

E and dE/dt sensors used in the MSE system are aluminum flat plate antennas placed

essentially flush with the Earth, as shown in Figure 2-13. The antenna consists of a

hollow rectangular aluminum housing with a circular portion of the top face isolated

from the remainder of the top face of the structure by a 0.6 cm-wide annular air gap

surrounding it. The circular portion of the antenna has a diameter of about 0.444 m and

a corresponding area of 0.155 m2 (Jerauld, 2003 gives an area of 0.16 m2). The circular

portion is kept electrically isolated by this annular gap and six nylon standoffs which are

used to mount it to the bottom (ground) of the housing. The circular portion is the sensor

while the remainder of the housing is connected to a 3-m long ground rod by a short

length of 12 AWG wire and a lug mounted on the side of the housing. The underside


























Figure 2-13. Flat plate antenna used in E-field and dE/dt measurements. The sensing
element is the circular portion of area a 0.155 m2 surrounded by an annular
air gap. The remainder of the structure is the antenna housing, grounded via
a 3-m ground rod. The wire screen surrounding the sensor and attached to
the grounded housing serves to reduce the enhancement of the electric field
by the antenna.

of the circular plate is connected to the center conductor of a female BNC connector

mounted to the side of the housing by an approximately 20 cm length of 16 AWG wire.

The inductance of a 20 cm length of 16 AWG wire is approximately 10 nH. The outer

conductor of the BNC connector is connected to the grounded aluminum housing.

Therefore, the voltage measured across the BNC connector is the voltage which appears

between the circular plate and the grounded antenna housing. A detailed mechanical

drawing of the antenna is shown in Figure 2-14.

The antenna housing was placed on the ground surface. In order to simulate a flat

ground, pieces of wire mesh screen which extended from each side of the antenna were

attached to the top of the the four sides of the metal antenna housing. One portion of the

screen was about one meter in length while the others were about a third of a meter in

length. The electronics for each electric field or electric field derivative measurement was

placed in a metal Hoffman enclosure (also known as a Hoffman box) which was buried

underground about one meter from the antenna. Each hole was about a half a meter








70








TOP VIEW
22 "
------- ----------------------------------
@ @ @/
Drain Hole @





) 8.75 "






6"1













SFemale BNC
2 Ground Rod Attach Lug Connector


11 "

2 3/16 r YNylon Connection Point
|3t DnpEdge *Stand off and Plate
23/16 Sn S ff ne en"C

CROSS SECTION

Figure 2-14. Detailed mechanical drawing of the aluminum flat plate antenna used in the
MSE. Adapted from Crawford [1998].









Wire Screen
Reflective Insulation
\ Fiber-optic Cable
Flat Plate Antenna


Metal

Cable


Ground Rod

Figure 2-15. Diagram of an installation of a MSE measurement utilizing a flat-plate
antenna.

deep and the Hoffman box was placed on a shelf angled downward so as to drain any

water acquired in the hole away from the box. Furthermore, pieces of wood were used

to secure the box in the hole. The Hoffman box was placed underground so that it would

be protected from the external environment and the area surrounding the antenna would

be as flat as possible. In addition, a piece of reflective insulation was placed over the

hole to protect the electronics from the heat of the sun. The 1 m length of screen covered

the hole and the insulation. A length of 50 Q coaxial cable with male BNC connectors

connected the antenna to a female BNC bulkhead feed-through connector mounted to

the side of the Hoffman box. This cable was enclosed in metal shield braid which was

secured to the male BNC connectors on each end of the cable by metal hose clamps.

Therefore, the shield braid and the Hoffman enclosure are electrically connected to the

grounded antenna housing. This configuration served to electromagnetically shield the

coaxial cable and electronics, minimize the electric field enhancement of the antenna, and

protect the electronics from the external environment. A drawing of this configuration and

a corresponding picture of an MSE measurement are shown in Figures 2-15 and 2-16,

respectively. This configuration is very similar to that described by Crawford [1998].





























Figure 2-16. Picture of a MSE measurement utilizing a flat-plate antenna.

The Thevenin or Norton equivalent circuit for a flat-plate antenna can be derived by

considering the boundary on a perfectly conducting (oy = ) surface.



D-. = p, (2.3)

The quantity D is the electric displacement vector at the surface and is expressed

in units of C m 2, is the unit vector normal to the surface, and ps is the surface charge

density and is also expressed in units of C m Hence, D h = D, is the component of

the electric displacement which is normal to the surface. If the conducting surface is

parallel to the ground, then the the normal component of the electric displacement is the 2

component in the Cartesian or cylindrical coordinate systems, and the boundary condition

becomes

D, =Dz = ps (2.4)

Note that since the surface is considered a perfect conductor, the electric displacement

inside of the conductor and the tangential component of the electric displacement along









the surface of the conductor are both zero. If the medium above the plate (air) is linear,

isotropic, homogeneous, and non-conducting, then

Dz = Ez (2.5)

The quantity Ez is the magnitude of the component of the electric field which is

normal to the surface of the plate (expressed in units of V m 1) and e is the permittivity

of the dielectric medium. For air, the value of eo is essentially that of free space

(8.85 x 10 12 F m 1). Therefore, the expression for ps can be written as


Ps = CoEz (2.6)

If the surface charge density is uniform (which will be the case if the smallest

wavelength comprising Ez is much greater than the plate diameter), then the total charge

can be found by multiplying the surface charge density by the area of the plate. The

boundary condition specifies that if the magnitude of the normal component of the

electric field is uniform over the surface of the plate, then surface charge density along

the plate must also be uniform. For a circular plate, the electric field along the surface of

the plate can be considered non-uniform when the plate diameter is larger than about a

sixteenth of a wavelength. If the highest frequency component of Ez is 30 MHz then the

smallest wavelength will necessarily be 10 m. One sixteenth of a wavelength is 0.625 m,

which is larger than the 0.444 m diameter of the plates used in the MSE.

If the electric field is uniform across a plate of area Aplate, then the total charge on

the plate can be expressed as

Qplate = coAplateEz (2.7)

The Norton equivalent short circuit current, i(t), is the time derivative of the charge.

d d dEz(t) (.
i(t) = Qpliate(t) = d [EoAplateEz(t)] = EOAplate dz(t) (2.8)
dt dt it









Hence, the flat-plate antenna in the presence of a uniform time-varying electric field

can be viewed as a current source whose magnitude is proportional to the time derivative

of the normal component of the electric field, in parallel with the source impedance of

the antenna. This Norton equivalent current source is the basis of the equivalent circuit.

The Thevenin equivalent voltage, which yields the same results, could also be used by

performing a simple transformation. The equivalent circuit analysis is often performed in

the frequency domain. However, a solution can be found directly in the time domain by

solving a first-order differential equation. The relationship between the time domain and

the frequency domain is given by the Fourier transform. The Fourier transform, X(m), of

a time-domain signal, x(t), is


F {x(t)} = X(m) = x(t)e-Otdt (2.9)

Differentiation with respect to time in the time domain corresponds to multiplication

by the complex number jo in the frequency domain. Therefore, the expression for the

magnitude of the Norton equivalent current source in the frequency domain becomes


I(o) = oApiatejoEz,(C) (2.10)

The quantity Ez(c) designates that the normal component of the electric field is now a

function of angular frequency CO and not time.

The Norton equivalent circuit in the frequency domain is shown in Figure 2-17.

The current source is placed in parallel with the source impedance, Zs, and the load

impedance, ZL. The source impedance is the impedance of the antenna itself and the load

impedance is the impedance of any external elements connected to the plate. In general,

the source and load impedances can be resistive, capacitive, inductive, or a combination

of the three.












I( ) T Z, ZL




Figure 2-17. Frequency-domain equivalent circuit, using a Norton equivalent current
source, of a flat-plate antenna sensor feeding a load (represented by ZL).

If the output of the antenna is taken as the voltage across the load impedance, then

the expression for the output voltage in the frequency domain is


Vaout () = I(o)Zotatal = I(Z) (Z |ZL) = j10~ AplateEz() Z -s ZL (2.11)

The source impedance, Z,, is determined by the capacitance of the antenna itself,

Cant
1
Zs = (2.12)
]wCant
The capacitance of the flat plate antennas used in the MSE was measured to be

about 80 pF. Any inductance and resistance of the antenna is considered negligible and

ignored. The impedance of the length of wire connecting the circular plate to the BNC

connector is given by R, + j0mL, where R, is the resistance of the wire and L, is the self

inductance. Assuming that R, is approximately zero and Lis 10 nH (as given above),

then the impedance of the wire is about 2 Q at 30 MHz. The capacitive impedance of the

antenna at the same frequency is about 66 Q, much larger than the impedance of the wire.

Whether the antenna acts as a E-field or dE/dt sensor depends on the load

impedance, ZL. The two cases are discussed individually in the following two sections.









2.6.2 Electric field measurements

If the antenna is to act as an E-field sensor, the load impedance, ZL-E, is the

impedance of a capacitor, Cit, connected in parallel with a resistance, R.

1 R R R
ZL-E = I R 1=jR" (2.13)
-joCit R + 1 + joRC,,t
jOCJ"nt

Ci,t is referred to as an integrating capacitor since it serves to integrate the current

induced on the surface of the plate in response to the external time-varying electric field.

In the time domain, a voltage, vc(t), across a capacitor, C, is proportional to the integral

of the current, ic(t), flowing though that capacitor.


c(t)=1 ic()d (2.14)

Since, by Equation 2.8, the short-circuit current is proportional to dE/dt, the integral

of the current (that is, the voltage across the capacitor) is proportional to E. Since the

antenna capacitance and the integrating capacitance are in parallel, we can combine them

into one term, C = Cant + Cit, having a corresponding impedance of 1/jo(Cat + Cint).

Hence, the total impedance, Ztotal = Zs, I ZL, is given by

R R
Ztotal = + jO (Cat +Ct) 1 +jcoC (2.15)

Substitution of Equation 2.15 into Equation 2.11 yields


R
Vout-E (C) = I(O)Ztotal = jcoioApiateEz(co) R (2.16)
1 + jcRC
Further, dividing Equation 2.16 by the quantity joaRC yields

cOAplate
Vout-E ) 0Apate 1 = I Ez(m) (2.17)
C 1 + jaRC )

The resistance, R, is the input resistance of an amplifier or fiber-optic transmitter.

The quantity jo/(1/RC + jo) is the form of a single-pole high-pass filter with a -3 dB









point (the frequency at which the magnitude of the output equals 0.707 times the input) of

1
C= RC (2.18)


If co> oo, then Equation 2.17 simplifies to

V0^ E(OI) plateE
Vout-E (CO) = AplateEz(C) (2.19)

If the frequency content of the time domain electric field, Ez(t), satisfies the

condition o > 1/RC, then the time domain output voltage of the antenna, V,t-E (t), is

given by

Vot -E(t)= AateE(t) (2.20)
C
Equation 2.20 represents the ideal time domain response (gain) of a flat-plate

electric field antenna. The output voltage of the antenna is directly proportional to the

vertical component of the electric field at ground. Further, the output voltage is directly

proportional to the area of the antenna and inversely proportional to the integrating

capacitance. The load resistance does not affect the gain of the ideal flat-plate electric

field antenna.

The general time domain case, with no frequency constraints, has been considered

by Jerauld [2003]. Starting from Equation 2.17, it can be shown that the general

time-domain output voltage is given by

,Olate IAplate t ft
Vout-E(t) AateE (t) RA e Re Ez(l)eRdl (2.21)
C RC2

The above expression is valid for an arbitrary electric-field, Ez(t), with no frequency

constraints. The antenna output voltage consists of two terms, the first of which is equal

to that given by Equation 2.20. This is the output of an ideal flat-plate electric-field

antenna. The second term is the effect of the non-ideal low-frequency response of the

antenna. As R approaches infinity, the second term approaches zero and the output

approaches that of an ideal flat-plate electric-field antenna. This can also be seen by









considering the frequency-domain expression for the antenna output voltage and allowing

R to approach infinity. The same argument can be applied to allowing the quantities RC

and RC2 to approach infinity. IfC alone is allowed to approach infinity then in the limit

the output voltage will be zero. However, L'Hopital's Rule can be invoked, and it can be

seen that the second term will decrease to zero before the first. Therefore, it can be said

that for very large values of C, the antenna output voltage will be approximately that of

an ideal antenna, with very low gain. Of course, "very large" and "very low" are relative

terms which are determined by the requirements of the experiment.

The antenna output voltage given in Equation 2.21 can be specified exactly if the

electric field waveform is specified exactly. The response of the antenna to a step function

of the form of Equation 2.22 is of particular interest since it can be used to crudely

approximate the electric field waveform from a lightning return stroke.



E,(t) = Eou(t) (2.22)

The unit step function, u(t), is defined as

1 t>o
u(t) = (2.23)
0 t<0

As shown by Jerauld [2003], substituting 2.22 into Equation 2.21 yields


Plate
ut-E(t) = E Eoe RC (2.24)

The term RC is known as the decay time constant and is typically denoted by T. The

time constant is the inverse of mo.

1
S= RC (2.25)
(oO

When the electric field is a step-function, the output of the antenna at time t = T is

a factor of 1/e less than it was at time t = 0. Therefore, the output of the antenna is only









Pomona Box


Male BNC
Connector


Female BNC
Connector


Captors Conected in Parallel
Capacitors Connected in Parallel


Figure 2-18. Integrator capacitor assembly used in the MSE. A) Closed Pomona box. B)
Box open to show interior.


valid for a short period of time relative to T. This is exactly what is expected since the

response of the electric field flat-plate antenna is that of a high-pass filter in the frequency

domain.

For times 0 < t < z, the output of the antenna, given a step-function input of

amplitude E0, becomes


/ oAplate 0
Vout-E(t) = -Apla
C


(2.26)


Equation 2.26 gives the expected output of an ideal flat-plate electric field antenna.

The conclusion is that if the electric fields to be measured are on a time scale much less

than that of the time constant, then the antenna output should match that of an ideal

antenna. If this condition is not satisfied, then the output will be distorted due to the

non-ideal low-frequency response of the antenna.









Figure 2-18 shows an integrating capacitor assembly built by George Schnetzer. The

chosen value of the integrating capacitance was about 0.2 rF, which is much greater than

the capacitance of the antenna, and hence the latter can be ignored. Multiple capacitors

were placed in parallel in a small box with BNC connectors. The capacitors were placed

in parallel in order to minimize the lead inductance of the individual capacitors. This

parasitic lead inductance, L, is in series with the integrating capacitance, Cit, and results

in a resonance at angular frequency mR.

1
OR = (2.27)

The effect of this resonance is a deviation from the high-frequency response of the

capacitor. Each of the integrating capacitors used in the MSE network were verified to

have the ideal capacitor frequency response up to at least 5 MHz. Figure 2-19 shows

the measured and ideal frequency response of one of the integrating capacitor units.

The operating range of each integrating capacitor was tested by placing the capacitor

in parallel with the 50 Q input of an oscilloscope and feeding it with a 1 V sinusoidal

voltage source having a 50 Q source resistance. The expected magnitude response of this

circuit is given by Equation 2.28.

1
Vcap (() = (2.28)
1 + (25mCint)2

The load resistance, R, is typically the input resistance of an amplifier or a fiber-optic

transmitter. The input resistance of the Opticomm MMV-120C fiber-optic transmitter

(described in Section 2.4) is 68 kQ. This yields decay time constants ofRCint = 13.6 ms.

Since the MSE system is intended to measure the electric fields from stepped leaders

and first return strokes in natural lightning, the time constant should be much larger

than the typical stepped leader duration of 35 ms [Rakov and Uman, 2003]; preferably

0.5 s or larger, and hence a larger time constant is desired. Therefore, an amplifier with

high input resistance was constructed in order to increase the decay time constant, since









- IrIUjYIdLIIIy IJdpydUILUI *ufU

c 1.00


Measured
Ideal \
cr 0.10

V) '_ -
_,
0 -
o -
C 0.01



.- , ,,,, I 1 ,,,, I .l, ,,,,,, , ,,,,,I , ,,,, I ,,,,1 ,, ,
4 5



101 10 10 3 104 105 106 107
Frequency, Hz

Figure 2-19. Measured (solid line) and ideal (dashed line) test circuit responses for
integrating capacitor unit #09 (0.209 rF).

increasing the integrating capacitance further could result in further resonance problems.

An amplifier with an input impedance of 5.1 MQ and a gain of 2 was designed by Keith

Rambo and George Schnetzer. The resulting time constant, T, is approximately 1 s,

corresponding to a low-frequency -3 dB point of about 0.16 Hz. A schematic of the

amplifier is shown in Figure 2-20 (the power supply circuitry is omitted for simplicity).

The amplifier is powered from a 12 V battery. The amplifier ground is at 6 V above

the negative battery terminal in order to bias the AD825 op-amp with 6 V. Therefore,

if a single battery were to be used to power all of the electronics in the measurement, the

output of the amplifier would float 6 V above the common ground which is far above the

maximum input range of the fiber-optic transmitter. In order to alleviate this problem,

both the input and output of the amplifier would have to be AC coupled (by a DC

blocking capacitor), or the amplifier would have to be powered by a separate battery than

the remainder of the electronics. The second option was chosen since it was desirable to













AD825 -o OUT
IN o-

5.1 MK2




Figure 2-20. Schematic of the high-impedance amplifier used in the MSE electric field
measurements.

keep the low-frequency roll-off of the measurement to a minimum. The amplifier was

connected to a separate 12 V battery through a relay. The control circuit of the relay

was connected to the primary measurement battery (through the PIC controller) and the

load circuit of the relay was connected to the separate 12 V battery. Therefore, when

the PIC controller supplies power to the electronics in the measurement, it also connects

the amplifier to its battery via the relay. Hence, the amplifier is not powered when the

measurement is turned off. The measured frequency response of one of the amplifiers is

shown in Figure 2-21.

A diagram of an MSE electric field measurement is shown in Figure 2-22 and a

picture of the metal enclosure and associated electronics is given in Figure 2-23. The

antenna is placed on the ground and the electronics are enclosed in a metal Hoffman

enclosure (indicated by the dashed line). In order to eliminate ground loops, all electronic

components were isolated from each other and the metal box by pieces of plastic and

Styrofoam. The integrating capacitor, Cint 0.2 rF, enclosed in a Pomona box, is directly

connected to the female BNC connector mounted to the inside of the Hoffman box.

The other end of the Pomona box is connected to the input of the amplifier (having gain

Gamp = 2 and input resistance R = 5.1 MQ) via a short length of 50 Q coaxial cable. Note

that this cable is not terminated in its characteristic impedance of 50 Q. However, the















2.0



1.5



1.0



0.5


102 103 104 105 106 107
Frequency, Hz

Figure 2-21. Measured frequency response of amplifier #2.


PIC Controller PIC Controller
Supplies Power to Supplies Power to
Amplifier Relay Fiber-optic Transmitter


Flat-plate
Antenna


Hi-Z


PIC Controller


Amplifier PIC
Controller
Battery Battery
12V 12V

Integrating Capacitor in a Metal Box
Metal Enclosure


50 n In-line Terminator


Figure 2-22. Diagram of a MSE electric field measurement.


Fiber-optic
Cable
































Figure 2-23. Inside of a metal enclosure containing the electronics for an MSE electric
field measurement.

length of the cable is short enough that reflections in the cable should not be a problem.

The output of the amplifier is connected to the input of a PIC controller (see Section 2.3).

The output of the PIC controller is connected to an Opticomm MMV-120C fiber-optic

transmitter terminated in 50 Q. Since the PIC controller is terminated in 50 Q, it can be

thought of as a 50 Q in-line attenuator of value Gpc.

Using the expression for the ideal output voltage of the electric field flat-plate

antenna, the expression for the voltage at the input of the fiber-optic transmitter is


VFOT-E(t)= -pte GampGpcEz (t) (2.29)
c-int

The above expression assumes that the output voltage of the antenna can be

approximated by the ideal output and the gain of the amplifier is flat in the frequency

range of interest.







85

Table 2-11. Salient characteristics of the MSE electric field measurements.
Station Cit [vtF] T [s] Nominal gain [kV m 1V']
2 0.230 1.17 83.8
4 0.202 1.03 73.6
5 0.228 1.16 83.1
6 0.204 1.04 74.4
9 0.198 1.01 72.2
10 0.210 1.07 76.5


Substituting the values Apate = 0.155 m2, Cint 0.2 kF, Gamp = 2, and GpC = 1

into Equation 2.29 yields


FOT-E) = 1.37 x 10 5)E(t) (2.30)

Equation 2.30 indicates that an electric field of 1 V m 1 at the surface of the plate

will result in 1.37 x 10 5 V at the input of the fiber-optic transmitter. Equivalently, 1 V at

the input of the fiber-optic transmitter corresponds to an electric field of about 73 kV m 1

at the surface of the plate.

Table 2-11 gives the integrating capacitance, time constant, and nominal gain (units

per volt) values for each of the MSE stations where electric field measurements were

located. The gain values are referred to as "nominal" since they do not account for any

variation in the gain of the fiber-optic links, which are ideally unity.

The Opticomm fiber-optic transmitter was connected to a receiver in the Launch

Control trailer by a length of 62.5 utm fiber-optic cable. The output of the receiver

was connected to a Yokogawa DL716 digitizer by a length of 50 Q coaxial cable and

terminated in 50 Q. The digitizer configuration is discussed in Section 3.1. The voltage at

the input of the digitizing oscilloscope is equal to the voltage present at the input of the

fiber-optic transmitter modified by the fiber-optic link. The method of accounting for the

presence of the fiber-optic link in the recorded data is discussed in Section 3.3. The actual

measurement gain values, which include the non-ideal gain values of the fiber-optic links,

are given in Appendix A.









2.6.3 dE/dt measurements

Referring to Equation 2.11, if the antenna is to act as an dE/dt sensor, the load

impedance, ZL-dE, is a resistance, R.


ZLdE =R (2.31)


The source impedance is that of the capacitance of the antenna, as given by Equation

2.12. The corresponding output voltage in the frequency domain, Vout-dE (C), is given by

R
Vout-dE(CO) = I(CO)Ztotal = jCioAplateEz(CO) 1 RC (2.32)
1 + jKLRCant

Note that Equation 2.32 is of the exact same form as Equation 2.16, except that the

latter also includes an integrating capacitance, Cint. Since the antenna is now viewed from

the point of view of a dE/dt sensor, Equation 2.32 can be rearranged to yield


Vout-dE(CO) = I(C)Ztotal = oAplateR jC cEOEz(Co) (2.33)
1 + JcoRCant

The quantity jwEz,(o) represents the time-derivative of the electric field in the

frequency domain. The quantity 1/(1 + jomRCant) is the form a single-pole low-pass filter

in the frequency domain with a -3 dB point of

1
Coo = (2.34)
RCant

Note that Equation 2.34 is of the exact same form as Equation 2.18. However, from

the point of view of a dE/dt sensor, coo represents a high-frequency roll-off, where as from

the point of view of an electric field sensor, it represents a low-frequency roll-off.

If co < coo, then Equation 2.33 simplifies to


Vout-dE(Co) = oARjcoEz(co)


If the frequency content of the time domain electric field derivative, dEz(t)/dt,

satisfies the above condition, then the time domain output voltage of the antenna,









Vout-dE(t), is given by

Vout-dE(t) = oAR (t) (2.35)
dt

Equation 2.35 represents the ideal time domain response of a flat plate dE/dt

antenna. The output voltage of the antenna is directly proportional to the vertical

component of the electric field derivative at ground. Further, the output voltage is directly

proportional to the area of the antenna and the load resistance. The antenna capacitance

does not affect the gain of the ideal flat plate dE/dt field antenna.

As with an electric field measurement, the flat plate antenna was connected directly

to the female BNC bulkhead feed-through connector mounted to the side of the Hoffman

enclosure. Inside the Hoffman box, a short length of 50 Q coaxial cable connected

the end of the bulkhead feed-through BNC connector inside of the box to the input

of a PIC controller (see Section 2.3). The output of the PIC controller is connected to

an Opticomm MMV-120C fiber-optic transmitter terminated in 50 Q. Since the PIC

controller output is terminated in 50 Q, the PIC controller appears to be a 50 Q in-line

attenuator of value GPIC to the antenna. Therefore, the load resistance, R, is 50 Q. In

order to eliminate ground loops, all electronic components were isolated from each other

and the metal box by pieces of plastic and Styrofoam. A diagram of the configuration is

presented in Figure 2-24 and a picture of the metal enclosure and associated electronics is

given in Figure 2-25.

The capacitance of the 0.155 m2 flat-plate antennas was measured to be about 80 pF.

Therefore, using Equation 2.34, the -3 dB bandwidth of the response is

1 1
CO = = 2.5 x 108 s (2.36)
RCant (50 Q) (80 pF)

This corresponds to a frequency of fo 40 MHz. Since the dE/dt measurements

were to be band-limited to 20 MHz (-3 dB) via anti-aliasing filters at the digitizers inputs,

the response of the antenna can be considered uniform over the complete frequency range

of interest. Therefore, Equation 2.35 can be used to approximate the voltage output of the



















Fiber-optic
Cable


Metal Enclosure

Figure 2-24. Diagram of a MSE dE/dt measurement.


Figure 2-25. Inside of a metal enclosure containing the electronics for an MSE dE/dt
measurement.







89

Table 2-12. Salient characteristics of the MSE dE/dt measurements. Note that the PIC
controller attenuation setting, Gpic, varied between 2002 and 2004.

Date range Gpic Nominal gain [kV m1 -s 1 V1]
07/09/2002 0.197 74.0
07/19/2002- 07/20/2002 0.316 46.1
08/02/2002- 06/14/2004 0.501 29.1
06/23/2004 08/24/2004 0.707 20.6


dE/dt antenna. The expression for the voltage at the input of the fiber-optic transmitter is

dEz (t)
VFOT-dE(t) = oAplateRGIC dE(t (2.37)

Several different values of Gpic were used in the dE/dt measurements between

2002 and 2004. These values are summarized in Table 2-12 below, along with the

corresponding nominal gain (kV m 1 1s-1 per volt) of the measurements. Since each

of the four dE/dt measurements (located at Stations 1, 4, 8, and 9) were configured

identically, the values given in Table 2-12 apply to any of the dE/dt measurement in the

MSE network.

The Opticomm fiber-optic transmitter was connected to a receiver in the Launch

Control trailer by a length of 62.5 utm fiber-optic cable. The output of the receiver was

connected to a LeCroy LT374 digitizer and terminated in 50 Q by a length of 50 Q

coaxial cable. The digitizer configuration is discussed in Section 3.1. The voltage at

the input of the digitizing oscilloscope is equal to the voltage present at the input of the

fiber-optic transmitter modified by the fiber-optic link. The method of accounting for the

presence of the fiber-optic link in the recorded data is discussed in Section 3.3. The actual

measurement gain values, which include the non-ideal gain values of the fiber-optic links,

are given in Appendix A.

2.7 Magnetic Field and dB/dt Measurements

This section describes the measurement of the magnetic induction, B, otherwise

known as the magnetic flux density, and its time derivative, dB/dt, in the MSE network.

In a linear, homogeneous, and isotropic medium, such as air, the magnetic induction, B









(units of Wb m 2 or T) is related to the magnetic field, H (units ofA m 1) by


B=jH (2.38)


The quantity p is the permeability of the medium. The value of u for air is very close

to that of free space, uo = 4n x 10 7 1.257 x 106 H m-1. Since and R differ by only

a constant, the term "magnetic field" is often used to refer to either H or B.

As shown in Table 2-1, the magnetic field was measured at Stations 4 and 9,

while its time derivative, dB/dt, was measured at Stations 1, 4, and 9. All B-field and

dB/dt waveforms presented herein are the component of the the magnetic field which

is tangential to the surface of the Earth, which is the only component that exists for a

perfectly conducting ground. In this study, B-fields were measured with loops of 50 Q

coaxial cable, with the voltage induced on the cable being proportional to the component

of the magnetic field derivative (dB/dt) normal to the plane of the loop, as given by

Faraday's law (and discussed in detail in the following section). If the plane of the loop is

placed perpendicular to the ground, then the component of the tangential magnetic field

that is normal to the plane of the loop will be sensed by the loop. Note that in only the

case where the tangential magnetic field is completely normal to the plane of the loop

will the total tangential field be sensed. In general, this will not be the case, and thus

two orthogonal loops (referred to as a "crossed-loop" measurement, shown in Figure

2-26) are required to sense the total tangential magnetic field. For both the magnetic

field and dB/dt at Stations 4 and 9, only the east-west component of the tangential field

was measured, that is, each measurement consisted of only one coaxial loop whose plane

was oriented north-south. For the dB/dt measurements at Station 1, both the north-south

and east-west components of the tangential field were measured in a crossed-loop

configuration.








































Figure 2-26. Square loops of 50 Q coaxial cable in PVC pipe. A) Crossed-loop
measurement. B) Single-loop measurement. Metal enclosures housing
measurement electronics are located near each antenna.

2.7.1 The coaxial-loop magnetic field antenna

The loop antennas used in the MSE network consist of square loops of 50 Q coaxial

cable. These loops, such as those shown in Figure 2-26, were enclosed in PVC pipe to

protect the cable from the sun and rain.

The Thevenin or Norton equivalent circuit of a coaxial loop antenna can be derived

by first considering Faraday's Law.


Id- j (2.39)
/ dt









The quantity is the electric-field vector, ds is a differential length about an

arbitrary closed path C, and ( is the magnetic flux through the surface defined by the

closed path C and is expressed in units of Wb. Faraday's Law states that the line integral

of the electric field about an arbitrary closed path C is equal to the negative of the

time-derivative of the magnetic flux through the surface defined by C. The magnetic flux

is defined as

S= iB.da (2.40)

As stated above, B is the magnetic induction (or magnetic flux density) vector and

da is a differential area on an arbitrary open surface S, with da being normal to S. B is

expressed in units of Wb m 2 or T. Therefore, ( is equal to the surface integral of the

magnetic induction over the open surface S. Since the open surface S is defined by the

closed path C, then Equation 2.39 can be re-written as

d
tE -ds = -- S-da (2.41)
c dtJs

Moreover, if the medium is stationary, then both C and S will be stationary, and the

expression can be further simplified to

IdB-t
E ds= a (2.42)
c sdt

Hence, if the medium is stationary, then the line integral of the electric field about

the closed path C is equal to the negative of the surface integral (taken over the surface

bounded by C) of the time derivative of the magnetic induction.

If the magnetic field is uniform over the entire surface and the entire surface lies in

the same plane, then the expression further simplifies to

d dB.no
S- ds = -Aloop dB = -Aioop d (2.43)

The quantity Aloop is the total area of the surface and h is the unit vector normal to

the surface. Hence, the line integral of the electric field about the closed path C is equal









to the negative of the area of the surface bound by C times the time derivative of the

magnitude of the normal component of magnetic field through the surface. The above

expression is only valid if the magnetic field is uniform over the entire surface of interest

and the surface lies in a single plane. If B is a component of an electromagnetic wave,

then the expression is only valid if the longest dimension of the surface is much smaller

than a sixteenth of a wavelength.

It is important to note that the quantity Bnorm denotes the component of the magnetic

field normal to the plane of the loop. If the plane of the loop is oriented perpendicular

to the surface of the Earth, as is done in the MSE network, then the component that is

normal to the plane of the loop is tangential to the surface of the Earth. Thus, as stated

above, it is the tangential component of the magnetic field that is sensed by the MSE loop

antennas.

The term on the left-hand side of Equation 2.43 is defined as the electromotive

force, or EMF, and is expressed in units of V. This can be interpreted by saying that if

a perfectly conducting wire placed along the path C is broken, the voltage measured

between the two open ends of the wire is equal the time-derivative of the normal

component of magnetic field through the surface bound by the wire times the area

bounded by the wire. Hence, a loop of wire can be used to sense the component of the

magnetic field which is normal to the plane of the loop. The open circuit voltage, vioop(t),

of a broken loop of wire in the presence of a time-varying magnetic field is given by


vip = ds Alop dBnorm (t (2.44)
Vp = ic dt

A wire-loop antenna in the presence of a uniform time-varying magnetic field can

be viewed as a voltage source whose magnitude is proportional to the time derivative

of the component of the magnetic field which is normal to the plane of the loop. This

is the Thevenin equivalent (open circuit) voltage of a loop antenna and the basis of the














Voop ) 'w Z,



Figure 2-27. Frequency-domain Thevenin equivalent circuit of a coaxial-cable loop
antenna. The circuit consists of an ideal open-circuit voltage, ,oop (o), in
series with source impedance, Zs, and load impedance ZL.

equivalent circuit. As with the electric-field antenna, the circuit analysis for the magnetic

field antenna will be performed in the frequency domain.

The frequency domain Thevenin equivalent (open circuit) voltage source of a wire

loop antenna is given by

Vloop(Co) -jcoAloopBnorm(C) (2.45)

The voltage source is in series with source impedance, Zs, and load impedance, ZL,

as shown in Figure 2-27. The source impedance is the impedance of the antenna itself

and the load impedance is the impedance of any external elements connected to the loop.

In general, the source and load impedances can be resistive, capacitive, inductive, or a

combination of the three. If the output of the antenna is taken as the voltage across the

load impedance, then the expression for the output voltage in the frequency domain is

ZL ZL
Vo () = Lioop (CO) = ZL -J loopBnorm (C) (2.46)
Z + ZL Z + ZL

The output voltage of the antenna in the frequency domain is -joAAloopBnorm(Ci),

scaled by the frequency-dependent quantity ZL/ (Zs + ZL). The frequency-independent

gain of the antenna is A1oop.

Typically the source impedance is considered a resistance, RIoop, in series with an

inductive reactance, jaLloop. Therefore, the source impedance is


Zs = Rloop + j0Lloop


(2.47)









The load impedance is considered a resistance, Rload, and hence

ZL = Rload (2.48)

Substituting the expressions for the source and load impedances (Equations 2.47 and

2.48) into the expression for the frequency-domain output voltage of the loop antenna

(Equation 2.46) yields


Vout(0) = Aoop Road jpBnorm () (2.49)
\j(Lloop + Rloop + Rload /

Equation 2.49 can be rearranged to yield


Vout(0 = -AloopRload 1 j(cBnorm (() (2.50)
R1oop + Road I i CO ( oop )

oRloopRRloadl
The quantity 1/ (1 + j(Rloo+l-oad) is the form of a first order low-pass filter with a

-3 dB frequency (the frequency at which the output is equal to 0.707 times the input) of

Rloop +Rload (2.51)
Lloop

For frequencies Co < coo, Equation 2.50 simplifies to


Vout (CO) = A lopRload joBnorm (C) (2.52)
Rloop + Rload

If the frequency content of the time domain magnetic field derivative, dB(t)/dt,

satisfies the above condition, then the time domain output voltage of the antenna, ot (t),

is given by
Vo, (t)= AloopRload dBnorm(t) (2.53)
Rloop + Rload dt
Equation 2.53 gives the ideal time domain response of a loop antenna. The general

time domain case, with no frequency constraints, has been considered by Jerauld [2003].

Starting from Equation 2.50, it can be shown that the general time domain output voltage









is given by

VO (t RloadAloop dBnorm(t)
Vout(t) = -
Rloop + Rload dt
RloadAloop Lloop \ln- 1 d(n)Bnorm (2.54t))
Rloop + Rload 2 Rloop Rload dt (n)
n-2 I

The first term in Equation 2.54 is identical to Equation 2.53, the ideal time domain

response of the loop antenna. The second term is the manifestation of the upper frequency

response limit in the time domain. The second term will become zero if Loop = 0, which

corresponds to coo = .

Both the B-field and the dB/dt measurements utilize square loops of 50 Q coaxial

cable, as described above. The coaxial cable is placed in 3 inch PVC pipe to help keep a

rigid shape and protect the cable from the sun and rain. The inner conductor of the cable

is the actual wire comprising the loop antenna. The outer shield is necessary to keep

current from being induced on the inner conductor by an external electric field. The outer

shield of the cable can be thought of another loop of wire placed at almost exactly the

same spatial location as the inner conductor. Therefore, identical voltages will be induced

on the inner conductor and the shield of the coaxial cable. As discussed in the previous

section, the voltage output of a wire-loop antenna is measured between the two ends of

the wire with the expression describing the ideal output voltage given by Equation 2.53.

In practice, since the antenna is constructed from coaxial cable, it is convenient to use

coaxial cable connectors (such as BNC or SMA connectors) and measure the voltage

difference across the connectors at the two ends of the cable. The output voltage would

then be the difference between the measured voltages across the connectors at the two

ends of the cable.


(2.55)


VOWt (t) = [Vi, I(t) Vo, I(t) I [Vi,2 (t) Vo,2 (t) I









The subscripts ic and oc refer to the inner and outer conductor, respectively. The

subscripts 1 and 2 refer to the two ends of the coaxial cable. This configuration is the

basis of a differential output coaxial loop antenna.

However, this configuration poses a problem since Equation 2.55 can be rearranged

to yield

out (t) = [Vic (t) Vic2 (t)] [Voc (t) Voc2 (t)] (2.56)

As mentioned previously, the induced voltage on the inner conductor and the outer

shield are almost identical, therefore the output voltage of the differential coaxial antenna,

as shown in Equation 2.56, would be close to zero. However, if the shield from the two

ends of the cable is soldered together at the output of the antenna, then vocal (t) will be

equal to Voc2(t) and Equation 2.56 reduces to



Vout (t) = Vic1 (t) Vic2 (t) (2.57)

This is simply the voltage difference between the two ends of the inner conductor

of the coaxial cable. Although soldering the shield together at the base of the antenna

alleviates one problem, it introduces another. Once the shield is soldered together, the

outer shield of the cable forms a closed loop. If any current is induced on this loop by

either an external electric or magnetic field, an unwanted magnetic field will necessarily

be induced perpendicular to the loop. This induced magnetic field will distort the external

magnetic field to be sensed. Therefore, a small gap is placed in the shield to inhibit any

shield current and hence prevent any unwanted magnetic fields from the shield. Typically

this gap is placed at the top of the loop, as pictured in Figure 2-28.

In practice, each end of the coaxial cable is terminated in its characteristic

impedance, which is 50 Q for all MSE loop antennas. This termination usually takes

the form of the input resistance of the inputs of a differential amplifier that the the

antenna is connected to. Since the output is taken across both ends of the cable, the load

resistance, Rload, is 100 Q, as shown in Figure 2-28.










External
Loop Resistance
Rloop


Gap in Shield
Coaxial Cable Shield
(Outer Conductor)
Inner Conductor
Shield Soldered
Together


"h
Input
Terminal

50n


Differential Output
Voltage Taken Across
B Lloop Rloop 100 Load



Vloop l ,
50 Q
0,-


Input
STerminal

50 Q


\/
Load Resistors
Rlod = 100 Q
Differential Amplifier Input


Figure 2-28. Diagram (A) and equivalent circuit (B) of a differential-output coaxial loop
antenna with both ends of the cable terminated in 50 Q.


The corresponding expressions for the ideal time-domain output voltage and -3 dB

bandwidth of a differential output coaxial antenna with both ends terminated in 50 Q are


(2.58)


S100Aloop dBnorm(t)
Rloop + 100 dt


Rloop + 100 (2.59)
coo = (2.59)
Lloop

The value of L1oop is determined by the geometry of the antenna and Rloop, the

total resistance of the loop antenna including its inherent resistance and any externally

added resistance, is determined by the desired bandwidth of the antenna. If no external

resistance is added to the antenna, Rloop is the resistance of the inner conductor of the

cable, which is very close to zero. Both Rloop and Lloop affect the gain and bandwidth

of the antenna, as shown by Equations 2.58 (Lloop is a function of Aloop), and 2.59,


r -\


^.










External
Loop Resistance
A Rloop

-----------IW------------
Single-Ended Output
B R Voltage Taken Across
Gap in Shield Rloop 50 n Resistor
Coaxial Cable Shield
(Outer Conductor) 50 n
Inner Conductor\ V
Shield Soldered 50 0
Together


-------- ----------------


Input
Terminal

50 n % 50 n
S Single Ended
Resistor Soldered -Amplifier Input
to Shield Load Resistors
Rload = 100 2

Figure 2-29. Diagram (A) and equivalent circuit (B) of a single-ended output coaxial
loop antenna with both ends of the cable terminated in 50 Q.


respectively. Decreasing R1oop or increasing Aloop (since increasing Aloop increases

L1oop) increases the gain of the antenna. However, these same modifications decrease the

bandwidth of the antenna. Therefore, there is a gain/bandwidth trade-off associated with a

coaxial loop antenna.

A coaxial loop antenna can also have a single-ended output, meaning the output

voltage is taken from only one end of the cable. Like the differential-output antenna, each

end of the cable is terminated in its characteristic impedance, which is 50 Q for all MSE

loop antennas. However, the output voltage is measured across only one end of the cable

and the 50 Q termination on that end of the cable takes the form of the input resistance

of an amplifier. The other end of the cable is terminated by soldering a 50 Q resistor

between the inner conductor and the outer shield. This soldering is usually located at the

base of the antenna. This configuration is shown in Figure 2-29.









The equivalent circuit is the same as the differential-output antenna, however the

output is taken across only one of the 50 Q resistors, hence the gain of the antenna is

halved. However, Rload is still considered to be 100 Q since both resistors affect the

bandwidth. Therefore, the expression for the ideal time-domain output voltage of a single

ended coaxial loop antenna is


vt(t) 1 100OAoop dBnorm(t) (2.60)
2 Rloop + 100 dt

The -3 dB bandwidth of the antenna is the same as for the differential-output

loop antenna, given in Equation 2.59. It should be noted that a measurement utilizing

a single-ended configuration is somewhat easier to implement than a differential

configuration since a differential amplifier is not required. However, the advantage of

the differential configuration is that it has high common-mode noise rejection.

2.7.2 Magnetic field measurements

The MSE magnetic field antennas were square single-ended coaxial loop antennas

of area 0.533 m2, terminated in 50 Q. The antennas were arranged in orthogonal

crossed-loop pairs as shown in Figure 2-26. No external resistance was added to the

loop, hence Rloop is approximately zero. Rload, as stated previously, was 100 Q due to

the 50 Q terminations at each end of the cable. The output of the loop was taken from

the base of the antenna and connected to a female BNC feed-through connector mounted

to the side of a Hoffman box located on the ground approximately one meter away. In

order to eliminate ground loops, all electronic components were isolated from each

other and the metal box by pieces of plastic and Styrofoam. The end of the feed-through

connector inside of the box was connected, via a short length of 50 Q coaxial cable, to the

input of an active integrator with input resistance 50 Q. This 50 Q input resistance is the

termination of the output end of the antenna coaxial cable. As stated previously, the 50 Q

termination of the other end of the cable consists of a resistor soldered directly into the

cable at the base of the antenna. Therefore, assuming that the frequency range of interest









lies within the region where the response of the antenna is flat and substituting Rloop = 0

into Equation 2.60, the time-domain output voltage of this antenna is given by


1 dBnorm (t) (2.61)
Vout-B(t)= -mAloop (2.61)

The inductance of this loop is approximately 4 urH and the corresponding -3 dB high

frequency limit is coo = 2.5 x 107 s 1 or fo = 4 MHz.

The active integrator is an essential part of a magnetic field measurement for it

integrates the voltage output of the loop antenna (which is proportional to dB/dt) and

gives an output which is proportional to the magnetic field. The response of an ideal

active integrator is given by



Vint(t) = Vin(t)dl (2.62)
Jl=0
In practice, active integrators never have an ideal response. Figure 2-30 shows an

example active integrator. An ideal active integrator would only have a capacitor in the

feedback loop of the op-amp, however the resistor is required to have a DC feedback

path. If this were not present, the active integrator would integrate the small DC offset

voltage present at the input of the op-amp until the output saturated.

This feedback resistor has the effect of limiting the low-frequency response of the

active integrator, which can be viewed in the time domain as introducing a decay time

constant into the system. The decay time constant of the example active integrator is

given by



= R2C1 (2.63)

In addition, the output of an active integrator is not just the integral of the input,

but the integral of the input multiplied by a constant. This constant is referred to as the

integration constant, kint, and is expressed in units of s-1. For the example integrator, kint

















Input Rout
Output


R3




Figure 2-30. Example active integrator circuit.

is given by
1
kint = (2.64)
R1C1
The upper-frequency limit of the active integrator is typically determined by the

op-amp. The upper and lower limits of the frequency response are the points in which the

magnitude response of the integrator deviates from kit/m (the ideal magnitude response

of an active integrator).

Therefore, the output of the active integrator shown in Figure 2-30, assuming an

ideal op-amp, is given by


Vint(t) = kint( vin(t)dl e V-i R1C (t)dl e R2C1 (2.65)

Analogous to the passive integration used with a flat plate electric field antenna, for

times t << the time domain output of the active integrator reduces to

S1 ort
int (t) = kint vin (t) dl- vin (t) dl (2.66)
J=0 RIC1 J=o












51 kI


51 n
Inp ut 2 5 .1 k 2 2 tF
51n 51n
S> H0032CG Output
S1 kI 27 pF HOO32CG
1 kI $ 27 pF



Figure 2-31. Active integrator circuit used in the MSE magnetic field measurements.


The active integrators used in the MSE B-field measurements were designed and

built by George Schnetzer. Two units were constructed and are the same units that were

used in the 2000 experimental configuration described by Rakov et al. [2001] and the

schematic is shown in Figure 2-31. This active integrator was also powered by a single

12 V battery, and a DC-DC converter was used to obtain 12 V needed to power the

op-amp.

The input and output resistance of the active integrator is 50 Q. The integrator

consists of two inverting states, and hence the integration constant is positive. The first

stage performs the actual integration while the second stage provides a gain of ten. The

two stages are AC coupled by a 22 rF capacitor. The value of kint is for each unit is

roughly equal to 2.5 x 105 s1. This value takes into account the gain often introduced

by the second stage. Table 2-13.

The decay time constant for each unit was measured to be approximately 15 ms,

which is not far from the value of 20 ms determined from the integrator circuit. The

lower frequency limit of the integrator was measured to be about 10 Hz, which is

consistent with the measured time constant. The upper frequency limit was measured to

be approximately 5 MHz. The measured frequency responses of the two active integrators

used in the MSE magnetic field measurements are given in Figures 2-32.






104

S4 MSE B-field Active Integrators
S 104

S103 1 -' Station 4
S -- Station 9
a> 102

0 101

10

nz 10-1
O -2

10 1 2 3 4 5 6 7
10 102 103 104 105 106 10
Frequency, Hz

Figure 2-32. Measured frequency responses of the active integrators used in the MSE
magnetic field measurements.

Inside the metal Hoffman enclosure (shown near the antennas pictured in Figure
2-26), the output of the active integrator was connected to the input of a PIC controller by
a short length of 50 Q coaxial cable. The output of the PIC controller was then connected,
via another short length of cable, to the input of an Opticomm MMV-120C fiber-optic
transmitter. The output of the PIC controller was then terminated in 50 Q. The equivalent
circuit of the PIC controller is a 50 Q in-line attenuator of value Gpic. A diagrams of
an MSE magnetic field measurement is given in Figure 2-33 and a picture of the metal
enclosure and associated electronics is given in Figure 2-34.
If it is assumed that magnitude response of the antenna is flat and the active
integrator integrates properly over the frequency range of interest of the magnetic













PIC Controller
Supplies Power to
Active Integrator


PIC Controller
Supplies Power to


Active


Fiber-optic Cable


50 Q In-line Terminator


Metal Enclosure

Figure 2-33. Diagram of a MSE magnetic field measurement.


Figure 2-34. Inside of a metal enclosure containing the electronics for an MSE magnetic
field measurement.


Loop Antenna









field to be sensed, then the expression for the voltage present at the input of the fiber-optic

transmitter, VFOT B(t), is given by



VFOT-B(t) = IAloopkintGpIc RFOT Borm(t (2.67)
2 Rout +RFOT

The term RFOT / (Rout +RFOT) is the voltage division between the output resistance

of the active integrator, Rout, and the input resistance of the fiber-optic transmitter or

in-line terminator, RFOT. The output of the fiber-optic receiver was connected to a

Yokogawa DL716 digitizer, and terminated in 50 Q. Substituting the values Aloop =

0.533 m2, kint 2.5 x 105 s 1, Rout = 50 Q, and RFOT = 50 Q, into Equation 2.67 yields


VFOT-B(t) -33313GpicBorm(t) (2.68)

Two different PIC attenuation values were used in the MSE magnetic field

measurements from 2002 to 2004. These values are given in Table 2-13, along with

the corresponding integrator constants and nominal gain values at each station. The gain

values are referred to as "nominal" since they do not account for any variation in the gain

of the fiber-optic links, which are ideally unity.

The Opticomm fiber-optic transmitter was connected to a receiver in the Launch

Control trailer by a length of 62.5 uim fiber-optic cable. The output of the receiver

was connected to a Yokogawa DL716 digitizer by a length of 50 Q coaxial cable and

terminated in 50 Q. The digitizer configuration is discussed in Section 3.1. The voltage at

the input of the digitizing oscilloscope is equal to the voltage present at the input of the

fiber-optic transmitter modified by the fiber-optic link. The method of accounting for the

presence of the fiber-optic link in the recorded data is discussed in Section 3.3. The actual

measurement gain values, which include the non-ideal gain values of the fiber-optic links,

are given in Appendix A.

Finally, it is worth noting that the negative signs present in the nominal units/volt

given in Table 2-13 are somewhat arbitrary. The negative sign results from the negative







107

Table 2-13. Salient characteristics of the MSE B-field measurements. Note that the PIC
controller attenuation setting, Gpic, varied between 2002 and 2004.

Date range
07/09/2002-06/14/2004 06/23/2004-08/24/2004
Nominal units/volt Nominal units/volt
Station Loop area k,,t [s-1] Gatt [T V 1] Gatt [ptT V1]
4 0.533 2.6 x 105 0.316 -91.3 0.707 -40.8
9 0.533 2.35 x 105 0.316 -101.1 0.707 -45.2


sign present in Faraday's Law (Equation 2.39). However, the polarity of the waveform

recorded on the oscilloscope is also related to the orientation of the loop antenna relative

to the lightning channel. In other words, the same lightning channel located on opposite

sides of the loop will result waveforms of identical amplitude and opposite polarity. The

negative sign has been kept through the derivation for completeness.

2.7.3 dB/dt measurements

The MSE dB/dt measurements utilized square loops of 50 Q coaxial cable with

differential outputs, which are described in Section 2.7.1. Two of the antennas consisted

of a single loop while a third consisted of an orthogonal crossed loop pair, yielding

a total of four loops. The single-loop antennas have physical areas of approximately

0.120 m2 and 0.108 m2. These antennas were used to measure dB/dt in previous triggered

lightning experiments, such as those described by Uman et al. [2002] and Schoene et al.

[2003a,b]. The crossed loop antenna was constructed during the summer of 2002 by

George Schnetzer and each of the orthogonal loops has a physical area of approximately

0.151 m2.

Unlike the loops used for the magnetic field measurements, a 470 Q resistor was

soldered into the loop in order to increase the bandwidth of the sensor at the expense of

gain. Hence, R1oop = 470 Q. Like the magnetic field antennas, each end of the cable was

terminated in 50 Q, yielding Rload = 100 Q.









Therefore, when dB/dt is expressed in units of Wb m 2 s1 (or in equivalent units of

T s-1), the time-domain output voltage of this antenna is given by


Vout-dB(t)= -(0.175)Alop dBnort (2.69)

The inductance of each of the loops is approximately 1.2 urH and the corresponding

-3 dB bandwidth, as given by Equation 2.51, is coo = 4.75 x 108 s 1 orfo 75 MHz.

The differential outputs of the loop were taken from the base of the antenna and

the end of each cable was connected to a female BNC bulkhead feed-through connector

mounted to the side of a Hoffman box located on the ground approximately one meter

away from the antenna. The two lengths of cable were twisted together in order to

minimize the voltage induced on the cables by the magnetic field. Inside of the box,

one of the feed-through connectors was connected directly to a 50 Q in-line attenuator

of value Gatt whose output was connected to the input of a PIC controller by a short

length of 50 Q coaxial cable. The output of the PIC controller was connected to the

non-inverting input of a Meret differential input fiber-optic transmitter (see Section 2.4)

with an input resistance of 50 Q. The other BNC feed-through connector was connected

directly to another 50 Q in-line attenuator of value Gatt whose output was connected

to the inverting input of the Meret fiber-optic transmitter. Typically, the PIC controller

is used to provide programmable attenuation to a measurement. However, the PIC

controller has only one input and is thus not compatible with sensors having differential

outputs. While it was possible to use two PIC controllers to provide attenuation, it proved

more cost effective to use in-line attenuators. The disadvantage of this configuration

is that an operator must physically change the attenuators in order to manipulate the

full-scale range of the measurement. The calibration function of the PIC controller,

however, could still be used and this is why the output of the PIC controller is connected

to the non-inverting input of the Meret fiber-optic transmitter. A description of the

PIC controller is given in Section 2.3. Figure 2-35 shows a diagram of a MSE dB/dt











50 n


Differential Output
Loop Antenna


PIC Controller
Supplies Power to
Fiber-optic Transmitter


PIC Controller


Fiber-optic
Cable


Metal Enclosure


Figure 2-35. Diagram of a MSE dB/dt measurement.

Table 2-14. Salient characteristics of the MSE dB/dt measurements. Note that the
in-line attenuation setting, Gatt, varied between 2002 and 2004. Note that
the measurements at Station 1 were offline in 2004 due to water damage.

Date range
07/09/2002-06/14/2004 06/23/2004-08/24/2004
Station Loop area Gatt Nominal gain [T s 1 V 1] Gattd Nominal gain [T s 1 V1]
la 0.151 0.519 -72.9 Offline Offline
Ib 0.151 0.519 -72.9 Offline Offline


4 0.120 0.517 -92.1 1
9 0.108 0.517 -102.3 1
a) North-south oriented loop. b) East-west oriented loop. c) Measured value of the 50 Q
in-line attenuator. d) External attenuation was removed.


-47.6
-52.9


measurement. In order to eliminate ground loops, all electronic components were isolated

from each other and the metal box by pieces of plastic and Styrofoam.

If it is assumed that magnitude response of the antenna is flat over the frequency

range of interest, then the expression for the differential voltage present at the input of the

fiber-optic transmitter, VFOT-dB(t), is given by


VFOT-dB(t) = -(.175)AloopGattdBorm"(t) (2.70)
dt









The loop areas, attenuation settings, and corresponding nominal gain values

for the four dB/dt measurements are given in Table 2-14. However, unlike the

Opticomm MMV-120C and Nicolet Isobe 3000 fiber-optic links, the Meret links, in this

configuration, cannot be assumed to have a nominal gain of one. The gain of the Meret

links is strongly related to the quality of the fiber termination with a poor termination

resulting in high attenuation. Hence, the nominal gain values given in Table 2-14 are

of little use, and the gain of the fiber-optic link must be estimated experimentally.

The method of accounting for the presence of the fiber-optic link in the recorded data

is discussed in Section 3.3. The actual measurement gain values, which include the

non-ideal gain values of the fiber-optic links, are given in Appendix A.

The output of the fiber-optic receiver was connected to the input of an AC coupled

active low-pass filter (discussed in Section 2.4) with an input resistance of 50 Q by a

length of 50 Q coaxial cable. This filter is discussed in Section 2.4. The output of filter

was connected to the input of a LeCroy LT344 or LT374 oscilloscope by a short length

of 50 Q coaxial cable and terminated in 50 Q. The digitizer configuration is discussed in

Section 3.1.

Finally, it is worth noting that the negative signs present in the nominal gain given

in Table 2-14 are somewhat arbitrary. The negative sign results from the negative sign

present in Faraday's Law (Equation 2.39). However, the polarity of the waveform

recorded on the oscilloscope is also related to the orientation of the loop antenna relative

to the lightning channel. In other words, the same lightning channel located on opposite

sides of the loop will result waveforms of identical amplitude and opposite polarity. In

addition, for a given lightning location, reversing the connections to the differential input

fiber-optic transmitter will also reverse the waveform polarity. The negative sign has been

kept through the derivation for completeness.










c O 1 0.1 pF
C30807E
PIN Photo
Diode
45 V -
45Vo Output

1 kM





Figure 2-36. Corrected (relative to Jerauld, 2003) schematic of the MSE optical sensor
circuit.

2.8 Optical Measurements and Trigger System

Two optical measurements were used in the MSE as a part of the system to trigger

the digitizers to record lightning data. Since the optical measurements were originally

intended to be only used as part of the digitizer triggering system, their outputs were

not calibrated. There is nevertheless significant scientific value in even the uncalibrated

optical waveforms. One sensor was placed at the north-east corer of the ICLRT site

facing south-west and the other was placed on the south-west corner of the site facing

north-east. The two measurements were designated "North-East Optical" (NEO) and

"South-West Optical" (SWO), respectively. The optical detectors themselves are simple

circuits consisting of a reverse biased EG&G C30807E N-type silicon PIN photodiode in

series with a 1 kQ resistor. The output of the circuit is taken across the resistor, as shown

in Figure 2-36. The C30807E is reverse biased at 45 V, with a corresponding dark current

of 1 nA. Further, the C30807E is designed to sense wavelengths in the 400 to 1100 nm

region. It should be noted that an incorrect circuit is given by Jerauld [2003].

The optical sensor circuit was mounted against the inside of a metal Hoffman

enclosure with a small hole drilled in it just large enough for the lens of the PIN

photodiode. A cylindrical piece of PVC of diameter 14 cm and length 6.5 cm was









mounted on the outside of the Hoffman enclosure centered on the photodiode. The

inner wall of the PVC and the circular section of the Hoffman enclosure surrounding

the photodiode were painted black. A piece of Plexiglas was mounted to the open end

of the PVC section and was entirely covered by black electrical tape except for an

approximately 1 to 2 mm wide horizontal slit across the center. The purpose of the slit

was to limit the amount of light received by the optical sensor and to limit the elevation

angle from which light could be detected by the optical sensor. Therefore, a very bright

light source at a relatively low elevation angle was required to produce a significant

voltage at the output of the optical sensor. The slit did not limit the azimuth angle at

which light could hit the optical sensor, although the length of the PVC pipe did.

During the 2002 season, the electrical tape comprising the slit was replaced several

times due to deterioration from the rain and sunlight. In September of 2002, the electrical

tape was replaced with black paint, which is more resilient to the environment. The

width of this slit was never measured precisely or fabricated uniformly. In 2003 it was

decided to replace the circular piece of Plexiglas with glass and replace the paint and

electrical tape with a cover milled from copper-coated fiberglass. The cover was milled

using a "Protomat" machine normally used for milling circuit boards at the ICLRT. The

copper-coated fiberglass boards are a few millimeters thick and, again, normally used for

producing circuit boards. Creating a precise and uniform slit-width was easy with the

milling machine. The slit width was increased to 4 mm in order to increase the probability

of triggering the system on natural subsequent strokes (which are significantly less bright

than first strokes). The cover was painted with black paint and mounted to the circular

piece of glass with water-tight silicone. The cover/glass combination was then mounted

to the end of a piece of 4 inch diameter PVC pipe, approximately 7.5 cm long. This

pipe was then fitted inside the piece of pipe mounted to the Hoffman box containing

the optical sensor. Hence, the elevation view was increased by widening the slit and the

azimuth view was decreased by decreasing the diameter and increasing the length of the



























Figure 2-37. Sketch of the optical sensor cover installed in 2003.

pipe. For the south-west optical sensor, the slit is 4 mm x 95 mm (taking into account

the slit-length reduction due to the thickness of the pipe) and the pipe is approximately

7.6 cm long, yielding, at 1 km distance, elevation and azimuth views of about 65 m and

1.2 km, respectively. The length of the pipe is slightly different for the north-east optical

sensor, and hence the view is slightly different. A sketch of the new optical sensor cover

is shown in Figure 2-37.

Any light shining on the lens of the PIN photo-diode will result in a current through

it, with that current being superimposed on the quiescent current. The output of the sensor

is taken as the voltage between the terminals of the resistor and is connected, through

the capacitor, to an amplifier having a gain often and an input resistance of 1 MQ.

This amplifier is identical to that described in Section 2.6 except for the gain and input

resistance. The output of the amplifier is connected to the input of a PIC controller whose

output is connected to the input of a fiber-optic transmitter (not terminated in 50 Q). A

diagram of an MSE optical measurement is shown in Figure 2-38 and a corresponding

picture is shown in Figure 2-39.









PIC Controller PIC Controller
Supplies Power to Supplies Power to
Amplifier Relay Fiber-optic Transmitter

Hi-Z Amplifier PIC Controller
-10 7 ^Fiber-optic
G- amp = 10 GPIC = 1 Fiber-optic
Transmitter Fiber-optic
Cable

Amplifier PIC
Controller
BatteryBattery
12 V12
12 V
Optical Sensor
Mounted to
Metal Enclosure ----------------------------------------------------------
Metal Enclosure

Figure 2-38. Diagram of a MSE optical measurement.


Due to limited resources, two different types of fiber-optic links were used with

the two different optical measurements. Since the measurements were originally

intended primarily to serve as a trigger source, this was not thought to be a problem.

The sensor located on north-east corner of the network was coupled to a Nicolet Isobe

3000 fiber-optic link while the sensor located on the south-west corer was coupled

to an Opticomm MMV-120C fiber-optic link. The two optical measurements were

digitized continuously for 400, 800, or 1600 ms at 10 MHz on channels 9 and 10 of the

Yokogawa DL716 digital storage oscilloscope. The optical waveforms are band-limited

to 4 MHz (-3 dB) by the anti-aliasing filter associated with the DL716 digitizer. Detailed

descriptions of the fiber-optic links and the DL716 digitizer are given in Sections 2.4 and

2.5, respectively.

Figures 2-40, 2-41, 2-42 show different trigger configurations used in the MSE

system. In all three configurations, the outputs of the fiber-optic receivers from the

north-east and south-west optical measurements were fed into the input of an "AND"

trigger circuit, which was designed and built by Mr. George Schnetzer. This circuit,

depicted in Figure 2-43, is designed to output a logic-level pulse when the two inputs


































Metal Enclosure


Figure 2-39. Optical measurement assembly, located at the south-west corner of the MSE
network. A) Closed measurement box. B) Open measurement box.









simultaneously exceed the 100 mV trigger threshold. Thus, the output only goes high

when light simultaneously observed by the two optical sensors is of sufficient brightness.

Since the two optical sensors view the network from opposite covers, this condition

should only be satisfied when a lightning terminates on ground within or very near the

MSE network. The purpose of this "AND" trigger system is to record data for only close

flashes and exclude distant flashes. If the system triggers on a distant flash (the data of

which are of limited value due to the limited dynamic ranges of the measurements),

the oscilloscopes would not be able to record data from close flashes while saving the

previous data (a process that can take up to 15 minutes for the Yokogawa DL716), hence

it is necessary to exclude distant flashes. In trigger configuration A (Figure 2-40), used

primarily in 2002, the output of the trigger circuit is connected to the external trigger

inputs of each of the oscilloscopes, as well as being recorded on channel 16 of the

Yokogawa DL716. In addition, the trigger output was connected to an "OR" circuit, the

output of which was connected to the GPS timing card discussed in Section 2.11. The

other input to the OR circuit was a trigger pulse derived from the current measurement

used in rocket-triggered lightning experiments. Thus, GPS time stamps could be obtained

from both natural and rocket-triggered lightning. Unfortunately, it was found that for

some rocket-triggered lightning flashes, only the LeCroy oscilloscopes would trigger,

while the Yokogawa would not. The reason for this problem is unknown, but it is

hypothesized that optical waveforms barely exceeding the trigger threshold of the AND

circuit resulted in relatively narrow trigger pulses, which were of insufficient duration

to trigger the Yokogawa digitizer (the minimum required duration of the trigger pulse is

500 ns).

Trigger configuration B (Figure 2-41) was designed to eliminate the problems

with configuration A, as well as add more flexibility to the trigger setup. The switch

box, shown in the lower-left corer of Figure 2-41, is a manual switch allowing the

operator to select from three different trigger sources: the optical AND trigger, a trigger









derived from the high-level current measurement in rocket-triggered lightning, and a

trigger derived from the low-level current measurement in rocket-triggered lightning.

The three switch positions, respectively, allow the MSE system to be triggered from

natural lightning, return strokes in rocket-triggered lightning (some of which are not

bright enough to trigger the AND circuit), and the initial stage in rocket-triggered

lightning (which typically begins some hundreds of milliseconds before any return

stroke). As before, the AND trigger and the high-level current trigger were connected

to an OR circuit, whose output was connected to the GPS timing card. The output of

the switch box was connected only to the external trigger input of a LeCroy DSO. The

trigger output of this digitizer was then connected to the trigger inputs of the other two

oscilloscopes. This configuration ensures that all of the oscilloscopes trigger when the

first one triggers. The latter two scopes were configured to trigger only when the width

of the input pulse exceeded 800 ts, since the LeCroy was prone to randomly outputting

spurious noise on its trigger-out, which would otherwise trigger the other oscilloscopes.

The result of this pulse-width requirement is that the data recorded on Scopes 19 and 20

are displaced in time -0.8 and -1 ms, respectively, relative to the data recorded on Scope

21. Compensating for these time shifts is discussed in Section 3.3.

Trigger configuration C (Figure 2-42) is similar to configuration B, except that the

switch box was removed and the inputs to the OR circuit were a trigger derived from

the low current measurement and the trigger output of the Yokogawa DL716 (which was

itself triggered the same as in configuration B). As a result of the trigger pulse width

requirement discussed above, the GPS time stamps obtained in this configuration are

offset by +0.8 ms relative to the true time. As with configuration B, data recorded on

Scopes 19 and 20 are displaced in time -0.8 and -1 ms, respectively, relative to the data

recorded on Scope 21.































NE Optical AND trigger
100 mV in
SW Optical +5 V out






Trigger from high
current measurement

bc627at
GPS OR
card


DL716


Ch 9 (1 Mn)


Ch 10 (1 MQ)


Ch 16(1 MQ)


Ext trig in (TTL)


Scope 20 LeCroy LT374


Ext trig in
+1 V (1 Mn)



Scope 17 LeCroy LT344


Ext trig in
+1 V (50 n)


Figure 2-40. Diagram of trigger configuration A.



























NE Optical

SW Optical


Figure 2-41. Diagram of trigger configuration B-1. Configurations B-2 and B-3 are
obtained by moving the switch to positions 2 and 3, respectively.






























NE Optical

SW Optical


Trigger from low
current measurement


Scope 19 Yokogawa DL716

Ch 9 (1 Mn)

Ch 10(1 Mn)

Ch 15(1 Mn)

Trig out (TTL)

Ch 16 trig in
+0.5 V (50 )
0.8 ms pulse width

Scope 20 LeCroy LT374


Figure 2-42. Diagram of trigger configuration C.




























































51 kQ
51k5
w 15kt pk
I kF


Figure 2-43. Trigger circuit used in the MSE system.


TRIGGER

OUT
:10 k









2.9 Other Measurements

In addition to the electric field (E), magnetic field (B), field-derivative (dE/dt and

dB/dt), and optical measurements, several other measurements were incorporated into the

MSE network at various times between 2002 and 2004. These additional measurements

are described below.

Current measurements. Almost all rocket-triggered lightning experiments

conducted at the ICLRT employ a measurement of the lightning channel-base current.

The current is typically measured at a convenient location somewhere on or near the

metal rocket launcher with a non-inductive resistor (often referred to as a shunt) or a

current transformer. A shunt is placed in series with the current path while the current

transformer (which has a toroidal shape) encircles the current-carrying conductor. In both

cases, the output voltage of the sensor is directly proportional to the current. Whether one

uses a shunt or current transformer depends on the physical constraints of the system and

the desired measurement range and bandwidth.

Due to dynamic range constraints of the fiber-optic links and digitizers, the channel

base current is typically measured on two amplitude scales. One scale referred to as

the "high current" measurement and is designed to sense currents up to some tens of

kiloamperes, typically associated with lightning return strokes. The other scale is the

"low current" measurement and is designed to sense currents from tens of amperes to a

few kiloamperes, typically associated with the long duration currents (tens to hundreds

of milliseconds) of the initial stage of classical-rocket triggered lightning, as well as

continuing currents following return strokes. The two current measurements are identical,

except for the attenuation assigned to each of the PIC controllers. The details of these

current measurements are found in Schoene [2006].

Since the MSE system was used to acquire data from rocket-triggered lightning, as

well as from natural lightning, it was decided to record one or more of the channel-base

current measurements (all sensed with shunts) on the Yokogawa DL716 digitizer









used in the MSE system (in addition to the digitizers assigned to the triggered-lightning

experiment). These measurements were typically only activated during triggered-lightning

experiments, and no current data were obtained for natural lightning flashes. The only

exception to this were current measurements on the tower rocket launcher, set up in the

second half of 2002, and were specifically designed to obtain data on induced currents

from nearby natural lightning strikes. This specific measurement configuration is

described in detail in Jerauld [2003]. In some cases, the triggered-lightning initial stage

current needed to be diverted to a path different from the following return strokes at the

tower launcher. In these cases, an interceptor conductor was mounted above the tower

launcher and high and low currents were measured for both the interceptor conductor

(return strokes) and the rocket launcher (initial stage currents), as described in Schoene

[2006]. The tower launcher and interceptor conductor are shown in Figure 1-10.

Rocket-triggered lightning flashes recorded by the MSE between 2002 and 2004

were triggered at the tower rocket launcher or at the mobile rocket launcher (positioned in

several different locations at the ICLRT). The locations of the rocket launchers are given

in Tables 2-6 and 2-7. Details of the rocket-triggered lightning experiments, including

whether the lightning current was injected into a test object (such as as the test power

line) and whether the initial-stage current was bypassed, are given in Schoene [2006]

(for the 2002-2004 power line experiments) and DeCarlo [2006] (for the 2004 test house

experiment).

Table 2-15 lists the currents recorded on the MSE Yokogawa DL716 (Scope 19) for

days in which rocket-triggered lightning experiments were conducted (see Table 3-2 for

a list of triggered-lightning flashes recorded by the MSE system and Table 3-4 for the

corresponding digitizer configurations).

"Fast" electric field measurement. In addition to the electric field measurements

described in Section 2.6, one additional measurement was installed at Station 5 in

late summer 2004. This measurement was referred to as the "fast" electric field at







124

Table 2-15. Current measurements recorded on the MSE Yokogawa DL716 digitizer
(Scope 19).

Launcher Current Scope 19
Date range location recorded channel
07/09 08/02/2002 Tower High tower 11
Low tower 12
07/14/2003 Tower Low tower 11
07/31/2003 Mobile 2003a Low 11
08/02/2003 Mobile 2003b Low 11
08/15/2003 Mobile 2003c Low 11
06/23 07/24/2004 Tower High interceptor 11
Low interceptor 12


Station 5, or "FE-5." The purpose of this measurement was to measure the electric field

with a system having higher upper-frequency response than the standard MSE E-field

measurements. Station 5 was chosen because it is near the center of the MSE network and

relatively close to the tower rocket launcher.

FE-5 consisted of a circular flat plate antenna having a diameter of 0.5 m,

corresponding to an area of about 0.196 m2 (larger than the standard MSE antennas

having an area of about 0.155 m2). The antenna was placed adjacent to the existing

E-5 antenna and attached to a nearby 3 m ground rod. The grounds of the two antennas

were not intentionally connected together, though it is possible that their wire mesh

screens (which are grounded) overlapped (it is uncertain). As with the standard MSE

E-field measurements, the output of the antenna was connected to an underground metal

enclosure via a length of 50 Q coaxial cable enclosed in metal shield braid. Inside the

enclosure, the female bulkhead BNC connector was connected to a 72 nF capacitor

assembly built by Ph.D student Joseph Howard. The capacitor consisted of seven 10 nF

capacitors in parallel (in order to reduce parasitic inductance) and had a measured

upper-frequency response of about 10 MHz. The capacitor was in parallel with the 1 MQ

input resistance of an Nicolet Isobe 3000 fiber-optic transmitter, yielding a time constant

of about 72 ms. The nominal gain of the antenna (not accounting for variation in the

gain of the fiber-optic link) is about 41.5 kV m 1 V1. Unlike the standard MSE E-field









measurements, no buffer amplifier was placed between the capacitor and the fiber-optic

transmitter. The transmitter was connected to a receiver by about 70 m of 200 utm duplex

fiber-optic cable.

The waveforms from the FE-5 measurement were recorded on channel 13 of Scope

19 (Yokogawa DL716; sampling rate of 10 MHz) and channel 1 of Scope 21 (LeCroy

LT344; sampling rate of 20 MHz) and data were obtained for this measurement on

7/14/2004, 7/24/2004, and 8/24/2004. See Chapter 3 for a list of MSE data, as well as a

description of the digitizer configurations for the given days.

2.10 Video System

A Cohu 1300 Series CCD camera was placed in each of four buildings known as

Instrumentation Stations (identified as IS1-IS4 on Figure 2-2) and oriented to maximize

video coverage of the site. However, the orientation of each camera, which is given in

Table 2-16, was limited by the location of the windows in the Instrumentation Stations.

Video signals were transmitted over Opticomm MMV-110 video fiber-optic links to

the Launch Control trailer and the receiver outputs were connected to the inputs of a

quad-view security monitor. The monitor combined the four video signals into a single

quad display, reducing the resolution of each video by a factor of four. The combined

video signal was fed from the monitor output into the input of a Sony SR2000 TIVO

digital video recorder (DVR). No audio was recorded. The four video signals were not

generator locked (gen-locked), meaning that the horizontal and vertical timing of the

individual video signals were not synchronized to a single reference signal. An attempt

was made in 2002 to supply a reference signal (which the cameras can accept as an

auxiliary input) to each of the cameras via fiber-optic links, but it was not clear whether

it worked properly. It is unclear what effect the lack of synchronization has on the

combined quad signal, but it should be understood that some information is lost. During

2002 and 2003, there was no way to automatically arm the DVR, hence it was set to

continuous loop recording and video was saved after each event. This worked reasonably







126

Table 2-16. Orientations of video cameras in the MSE network.
Camera location Approximate camera orientation
Instrumentation Station 1 (IS1) South by south-west
Instrumentation Station 2 (IS2) South-west
Instrumentation Station 3 (IS3) South-east
Instrumentation Station 4 (IS4) East


well during the summer months, when personnel were on-site on a regular basis, but

proved impractical during the rest of the year, when the site was largely unattended. In

2004, an attempt was made to automate the process by installing an after-market network

adapter and controlling the DVR with a LabView program, integrated into the main

control program. The automated DVR operated reasonably well, although at times the

device would stop responding to commands, reducing its effectiveness. Despite these

limitations, between 2002 and 2004 (no video device was used in 2005), some form of

video was acquired for about half of the flashes recorded. A frame of video from this

system is shown in Figure 2-44.

On the DVR, videos were digitized at 30 frames per second with 720 x 480

resolution using MPEG-2 compression. The video is interlaced, meaning that each frame

is separated into two fields, with the odd field containing the odd-numbered horizontal

lines of the frame and the even field containing the even lines. The two fields are also

known as upper and lower fields, with the order the fields are displayed referred to as the

field dominance. The field dominance can vary depending on the video format and the

equipment used to capture and play it. An alternative to interlaced video is progressive

scan, which consists of 30 non-interlaced frames per second. The fields have half the

vertical resolution (360 lines as opposed to 720) and are recorded/displayed at 60 fields

per second, yielding an effective frame rate of 30 frames per second. Video was extracted

from the DVR either by directly copying the MPEG files over an Ethernet connection

or connected the DVR's analog video output to a JVC Mini DV recorder/player and

re-digitizing the video over an IEEE-1394 (known commercially as Firewire) interface









using Adobe Premiere software. Theoretically, the first method is superior to the latter,

since there is no analog stage, but in practice this made little difference due to the

relatively poor quality of the video and high quality of the JVC unit. Further, extracting

the digital video from the DVR was often difficult, since it was not designed for that

task and hence 3rd party software was necessary. Once extracted, the video files can be

manipulated using a variety of software packages, such as Avidemux (used by the author).

To double temporal resolution (at the expense of vertical resolution), video frames can be

separated into odd and even fields. This is often necessary because return strokes (having

a duration of typically only a few hundred microseconds) are often recorded by only one

field in a given frame, with such events often missed if played back normally.

In practice, video usefulness is often limited by the reduced resolution, relatively

poor temporal resolution (compared to the time scale of lightning processes), effects

of rain, and the lack of synchronization between the different video frames in the quad

display. For some flashes the channel is generally unambiguous, while for other events

it is obscured by rain and haze, yielding only a bright blob or sometimes a point of light

near the ground. Further, in cases where a channel struck near a camera location, induced

effects often ruin the video signal. The lack of synchronization between the individual

videos in the quad display also introduces ambiguity. The effects of these limitations

are often compounded when multiple channel termination points are present, as is not

uncommon with natural lightning. Nevertheless, in most cases the video records provide

a rough indication of the termination point of the channel (or, more likely, can be used

to rule out certain locations and/or support locations determined from other methods), as

well as provide an indication if the flash had multiple strike points. Interstroke intervals

obtained from field records can be correlated with luminous events in the video records

(limited to 16.7 ms video field resolution).

























Figure 2-44. Frame of video from the MSE video recording system. Each quadrant is
an individual camera view with the labels corresponding to the locations
indicated on Figure 2-2.

In addition to the four Cohu cameras, Sony stand-alone digital video (DV) and 8

mm cameras were placed out in the field during triggered lightning operations. On a few

occasions video and/or audio was recorded by these cameras from MSE flashes.

2.11 GPS Timing System

A Datum bc627AT GPS timing card, installed in a computer, was used to provide

trigger times with microsecond accuracy. The bc627AT consists of a Datum bc620AT

time and frequency module and a GPS receiver core. The bc627AT determines time

and position by measuring the time of arrival of the signals from GPS satellites in orbit.

The GPS timing card was connected to an Accutime antenna (pictured in Figure 2-45)

mounted on the south end of the Launch Control trailer by about 50 feet of RS-422 cable.

An 7-pin round Conxall connector mates to the base of the Accutime antenna and a D

connector on the other end of the cable mates with the timing card. The cable was fed

into the trailer via a hole in the bottom of the south end. The exposed cable outside of

the trailer was enclosed in metal shield braid, and the shield braid was connected to the

ground of the trailer.




























Figure 2-45. Accutime GPS antenna associated with the Datum bc627AT GPS timing
card. The antenna is mounted on the south end of the Launch Control trailer.

The output of the trigger circuit was fed into an input of the card and the time was

latched into a set of internal registers when a system trigger (discussed in Section 2.8)

occurred. The card was specifically designed to have less than 100 ns delay between the

rising edge of the trigger signal and latching of the time. Software written by the author

in Microsoft Visual C++ (utilizing a software development kit purchased from Datum)

interfaced with the card and logged all of the trigger times on the host computer. Since

the time is latched automatically in hardware when a trigger event occurs, the accuracy

of event timing is independent of the software. However, the software did introduce a

period of a few milliseconds after each trigger in which no additional triggers could be

recorded. However, since typical lightning interstroke intervals are on the order of tens of

milliseconds or more, this was considered acceptable.

2.12 One-Line Measurement Diagram

Figures 2-46, 2-47, and 2-48 give so-called "one-line diagrams" for the 2002-2004

MSE experiment. The one-line diagrams give the basic configuration of each of the

measurements in a simple graphical form. For each line in a given diagram, the sensor











E-2
0.230 uF
AMP PIC OB FOT ST-2 FOR L Scope 19-1
2 I L2X "L OPT-2 2--OPT-2 10MHz


E-4
0.202 uF
-AMP PICOD FOT ST-4 FOR L Scope 19-2
2 I L2X "L OPT-3 2 OPT-3 ^ 10MHz


E-5
0.228 uF
AMP PIC 26 FOT ST-5 FOR L Scope 19-4
2 I L2X "L OPT-6 OPT-6 [ 10MHz


E-6
0.204 uF
AMP PIC 14 FOT ST-6 FOR L Scope 19-5
I L2X ~ OPT-7 Brown OPT-7 10MHz


E-9
0.198 uF
AMP PIC 18 FOT ST-9 FOR L Scope 19-6
2 I L2X "L OPT-9 r^^OPT-9 50 10MHz


E-10
0.210 uF
-- -AMP PIC01D -0 FOT ST-10 FOR L-5 Scope 19-8
2 I L2X "_ OPT-12 OPT-12 "_ 10MHz


B-4N


Q ACTIVE INT PIC OE FOT ST-4 FOR Scope 19-3
k = 2.60E5 OPT-4 G OPT-4 10 MHz


B-9N


Q ACTIVE INT PIC 3B FOT ST-9 FOR Scope 19-7
k = 2.35E5 OPT-10 G OPT-10 _Q 10 MHz



Figure 2-46. One-line diagram for the MSE electric and magnetic field measurements.


(e.g., flat plate or loop antenna) is shown on the left and the digitizer channel is on on the

right, and in between the particular electronics for that measurement (e.g., amplifier or


active integrator) are shown.
















dE-1


ST-1


Figure 2-47. One-line diagram for the MSE dE/dt and dB/dt measurements.





























NEO


swo


Trigger to all Scopes


Figure 2-48. One-line diagram for the MSE optical measurements.















CHAPTER 3
DATA

The purpose of this chapter is to present an overview of the natural and rocket-triggered

lightning data recorded by the MSE network from 2002 to 2004. Section 3.1 gives listings

of the flashes recorded, a summary of data recorded for each flash, as well as some details

of the oscilloscope and trigger-system configurations for each of the events. The reader

is referred to Appendix A for a list of calibration values for each storm day (one or more

flashes may occur during any given storm day). Section 3.2 discusses parameters for each

flash (when available), such as ground-strike location and peak current, reported by the

U.S. National Lightning Detection Network (NLDN) [Cummins et al., 1998; Jerauld

et al., 2005]. Section 3.3 discusses the calibration and processing of the raw data recorded

on the oscilloscopes. Finally, Section 5.1 discusses the comparison between measured

electric field and numerically-integrated electric field derivative waveforms at Stations 4

and 9, the two stations at which both E and dE/dt waveforms were measured.

3.1 Data Summary and Organization

Lists of natural and rocket-triggered lightning flashes recorded by the MSE network

are given in Tables 3-1 and 3-2, respectively. Each flash is given a unique identifier

which indicates the type of flash and in what year it was recorded. For example, flash

"MSE0201," the first entry in Table 3-1, was the first natural flash recorded in 2002 (the

prefix "MSE" being used for natural flashes). Data were obtained from 11 natural flashes

in 2002, and hence the flash ID of the last event is "MSE0211." For rocket-triggered

lightning data (Table 3-2), the prefixes of the flash IDs correspond to the organization

funding the particular experiment. The prefix "FPL" stands for "Florida Power and Light"

(see Schoene, 2006), while the prefix "LSA" stands for "Lightning Safety Alliance"

(see DeCarlo, 2006). The times given to six decimal places in Tables 3-1 and 3-2









were obtained from the GPS timing system and should have an accuracy of a few

microseconds. Other times were obtained from the oscilloscope files or video records

and should be considered accurate within a few minutes. Also included in Tables 3-1 and

3-2 are the names of the files containing the data for each natural and triggered-lightning

event recorded by the MSE system. The oscilloscope models corresponding to each

scope ID, as well as the file naming system for each type of oscilloscope, are discussed in

Section 2.5. Data were sorted by storm day and oscilloscope ID such that, for example,

the data from Scope 19 obtained for flash MSE0201 would be stored in the folder

"/072002/Scope 19/".

Tables 3-3 and 3-4 give the trigger configuration and oscilloscope configurations

for each of the natural and triggered lightning flashes recorded by the MSE system. The

trigger configurations correspond to those discussed in Section 2.8. For the oscilloscopes,

the sampling rate, record length, and pre-trigger are given for each event. In addition, for

the LeCroy oscilloscopes (Scopes 17, 20, and 21), the number of segments recorded are

also given.









135







Table 3-1. List of natural cloud-to-ground flashes recorded by the Multiple Station
Experiment (MSE) system, along with the corresponding digitizer data file
names. All flashes lowered negative charge to ground unless otherwise noted.

Flash times given with microsecond precision were obtained from the GPS
timing system discussed in Section 2.11 or the NLDN (see Section 3.2). Flash

times given with minute precision were obtained from video or oscilloscope
records and should be considered approximate and accurate within a few
minutes.


Scope 19 Scope 20 Scope 17/21

Time (UT) file name file name file name
19:39:30.712167 D0720000.WVF ACX.001 ACX.001

20:05:28.989697 D0804000.WVF ACX.004 ACX.004
18:00:44.071711 D0830000.WVF ACX.002 ACX.002
18:01:37.992834 No data ACX.003 ACX.003
18:13:55.826994 D0830001.WVF ACX.004 ACX.004
20:40:59.256337 D0915000.WVF ACX.002 ACX.002

20:41:30.726628 No data ACX.003 ACX.003
21:18:14.425065 D0915001.WVF ACX.004 ACX.004
14:29:05.611539 D1110000.WVF ACX.005 ACX.005
14:31:42.561464 No data ACX.006 ACX.006
18:49:58.599998 D1224000.WVF ACX.003 ACX.003
18:56:28.493531 D0618000.WVF ACX.002 ACX.002

19:39:16.726401 D0618001.WVF ACX.003 ACX.003
21:05:59.012944 D0718000.WVF ACX.005 ACX.005
20:50:46.774935 D0721000.WVF ACX.007 ACX.007
20:59:10.737710 D0721001.WVF ACX.009 ACX.009
00:37:29.797563 D0613000.WVF ACX.003 ACX.003

00:38:50.546749 No data ACX.004 ACX.004
15:49:41.490158 D0623000.WVF ACX.002 ACX.002
23:12:01.349973 D0630000.WVF ACX.001 ACX.001
19:25:07.945792 D0711000.WVF ACX.007 ACX.007
19:59:17.027378 D0711001.WVF ACX.008 ACX.008

20:08:00.593216 D0711002.WVF ACX.009 ACX.009
20:53:25.390812 D0711003.WVF ACX.010 ACX.010
20:57:45.124385 D0711004.WVF ACX.011 ACX.011
17:38:30.931683 D0715000.WVF ACX.001 ACX.001
21:45:53:668976 D0824000.WVF ACX.001 ACX.001

21:46:38.660209 No data ACX.002 ACX.002


Comment


2 positive strokes


Flash ID

MSE0201

MSE0202
MSE0203
MSE0204
MSE0205
MSE0206

MSE0207
MSE0208
MSE0209
MSE0210
MSE0211
MSE0301

MSE0302
MSE0303
MSE0304
MSE0305
MSE0401

MSE0402
MSE0403
MSE0404
MSE0405
MSE0406

MSE0407
MSE0408
MSE0409
MSE0410
MSE0411

MSE0412


Date

07/20/2002

08/04/2002
08/30/2002
08/30/2002
08/30/2002
09/15/2002

09/15/2002
09/15/2002
11/10/2002
11/10/2002
12/24/2002
06/18/2003

06/18/2003
07/18/2003
07/21/2003
07/21/2003
06/14/2004

06/14/2004
06/23/2004
06/30/2004
07/11/2004
07/11/2004

07/11/2004
07/11/2004
07/11/2004
07/15/2004
08/24/2004

08/24/2004











136







Table 3-2. List of rocket-triggered flashes recorded by the Multiple Station Experiment

(MSE) system, along with the corresponding launcher locations and digitizer

data file names. All flashes lowered negative charge to ground unless

otherwise noted. Flash times given with microsecond precision were obtained

from the GPS timing system discussed in Section 2.11. Flash times given with

minute precision were obtained from video or oscilloscope records and should

be considered approximate and accurate within a few minutes.


0





o -a
0 a
on

on
-r z


0 0 0 0 0 0 0~


0

o Q



-3

o Q





o o
o o

o o






ci
0


ci
o i
0 00



o *t








- c


o o o 0i


0 0 0 0 0 0 0 0 0 0

S0 0 00 i ri
0 0 D CD CD C 0 -
0 C t t t t t t 00 00


- ci
i N

3 3
FL FL


ri ci

&< < &
[_FL, [L [












137







Table 3-3. Digitizer configuration for natural flashes recorded by the MSE network.

Sampling rate for Scope 19 is 10 MHz.






S o
0 ...









-


0a





C-fl--------~-C]- -c,,,, C]- --C- -- C
^ *
-a
H "
8, 8
W P .i .i .i .i .i .i rl .i .i .i .i rl .i .i .i .i i .i .i .i .i .i r i i


0







. . . . . . .






- 't] -C]- -- --- -
000 00 00 00 00 00 00 00 00 00 00 00 00 0
V ~ ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( (


o o
N N







z


0D 0 '0 '0 0 0 '0
(N N (N (N (N (N




^o o Co Co Co C C
00 00 0000 00 00


0 o 0 C C C C C C





'0 00 00 00 00 00 00 00 00
O C- C- C- C- C- C C C
o o CCC
N 0 0 0 0


U U U U u u u U U U U U


o o

.t .t
o, o


o o
.t .t
o, o


C> C C
C -
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C C C


lon
0 0


o o


0 o 0
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(N (N (N




'0 0 '0
00 00 00


o o
N N

o o
C]C]Z

'0 0 ^3
00 00
z


0 0f0 0 0 0 0 0 0 00
I' o- x C -
C] .] .] .] .] .] .] .] .] .] ('T

o o C C C C C C C C C












138







Table 3-4. Digitizer configuration for rocket-triggered flashes recorded by the MSE

network. Sampling rate for Scope 19 is 10 MHz.


0\ 0\ 0\ 0\ 0\














0
0 0 0>0 0 0
Sa) V a) aI






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-85" -80' -75*
ORockwood' Leno r
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35 35*
oR irsellille
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tle Beach
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O aa

Gulf of -,i. 'I m Bay
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Naple
Dmdstead
25* 25*


-85 -80' -75
km
0 200 400

Figure 3-1. Map showing the locations of NLDN sensors in and around the Florida
region, as of late 2003. The approximate location of Camp Blanding is also
shown.


3.2 NLDN-Reported Parameters of Recorded Flashes

Since 1989, the U.S. National Lightning Detection Network (NLDN) has provided

lightning data covering the contiguous United States. Over 100 sensors, employing

magnetic direction finding (MDF) and time of arrival (TOA) technology, are distributed

over the contiguous United States, and these sensors relay data back to a central site

where the data are analyzed to locate and characterize cloud-to-ground lightning events.

A map showing the locations of NLDN sensors in the Florida region, as of late 2003, is

found in Figure 3-1. During 2001- 2003 a network-wide upgrade was underway and was

near completion at the end of 2003. A detailed discussion of the NLDN upgrade is found

in Cramer et al. [2004], Cummins et al. [2004], and Cummins et al. [2006].

The optimum lightning location is computed using a generalization of the X2

minimization technique described by Hiscox et al. [1984]. For each stroke location, an

error ellipse is computed based on the assumptions about the sensors angle and timing









accuracy. Spatial and temporal grouping rules are used to assign detected strokes to

flashes before providing the real-time flash data to the end user. The data are processed

in real-time and are generally available to users in about 30 seconds. Reprocessed data,

corrected for errors in sensor calibration and communications delays, are generally

available within a few days and are archived. It should be noted that the NLDN only

reports data if the shapes of the recorded waveforms are characteristic of return strokes in

natural, cloud-to-ground lightning.

Cummins et al. [1998], using their detection efficiency model, estimated flash

detection efficiency to be on the order of 80 to 90 %, depending on the region, for flashes

having peak currents of 5 kA and larger. The detection of only one stroke of a flash is

required for a flash to be detected. Cummins et al. [1998] estimated stroke detection

efficiency to be roughly 50 percent for the overall network, based on a comparison of

the average NLDN stroke multiplicity of about 2 (observed for two years after the 1995

NLDN upgrade) and the average stroke multiplicity of 3 to 4 reported by Thomson et al.

[1984]. Rakov andHuffines [2003] estimated the NLDN stroke detection efficiency to

be roughly 40% and 20% (corresponding flash detection efficiencies 78% and 62%) for

Florida and New Mexico, respectively. In doing so, they used stroke counts in 1995-2001

NLDN data and "ground-truth" electric field and optical observations found in the

literature. Note that the latter detection efficiency estimates are based on relatively small

samples and involve an assumption that the detection efficiency for first strokes is the

same as that for subsequent strokes, although first strokes typically have larger peak

currents than subsequent ones and therefore should be associated with higher detection

efficiency than subsequent strokes.

A 50% error ellipse is calculated for each stroke location reported by the NLDN.

This ellipse defined as a confidence region for which there is a 50% probability that the

actual stroke location lies within the area circumscribed by the ellipse, with the center of

the ellipse being the most-probable (reported) stroke location. Hence, the semi-major axis









of the 50% ellipse is usually viewed as the median (50%) location error. Corresponding

error ellipses for any probability level (e.g. 90%) can be derived by multiplying the

semi-major and semi-minor axes of the 50% ellipse by an appropriate scaling factor.

The two-dimensional Gaussian distribution of errors in latitude and longitude is based

on the assumption that the random errors in sensor time and angle measurements

are uncorrelated and their distributions are approximately Gaussian [Cummins et al.,

1998]. Strokes located within a group of several sensors typically have relatively small

near-circular error ellipses, whereas strokes detected by only 2 or 3 sensors typically have

very large, elongated ellipses. A stroke detected by only two sensors, when that stroke is

located near the line joining the two sensors (base line), typically has an elongated ellipse

whose major axis is along the base line.

The median stroke location accuracy has been theoretically estimated to be

about 500 m over much of the United States, based on the calculated 50 percent error

ellipses, which assume that the distributions of angle and time errors are Gaussian

[Stansfield, 1947; Cummins et al., 1998]. Detailed discussions of these models, along

with assumptions used, are found in Cummins et al. [1995, 1998].

As described in Cummins et al. [1998], return-stroke peak currents are estimated

from peak magnetic field signal strengths measured by the individual NLDN sensors.

During the 2002-2004 period in which MSE data were obtained, a power-function

attenuation of signal with distance was assumed, in order to account for propagation

effects, with the exponent (derived empirically by Orville, 1991a) equal to -1.13. The

raw signal strengths measured by individual sensors were normalized to 100 km using

this power relationship. The range-normalized signal strength (RNSS) values, from

all reporting stations within 625 km (to exclude signals with polarity reversals due to

ionospheric reflection), are averaged and converted to a peak current estimate (Ipeak)

using the empirical linear relationship (obtained using the triggered-lightning data of









Idone et al., 1993)

peak = 0.185 RNSS. (3.1)

Prior to the 1995 upgrade (see Cummins et al., 1998), a different regression equation

(also obtained using the data of Idone et al., 1993) was used which contained an intercept

value of 5.2 kA. The intercept of the new regression equation was constrained to zero

in order to accommodate strokes with peak currents below 5 kA that were sometimes

locatable after the 1995 NLDN upgrade.

An adjustment to the NLDN propagation model was introduced in the NLDN on

July 1, 2004 [Cummins et al., 2006]. The adjustment was based on a comparison by

Jerauld et al. [2005] of directly measured (ground truth) return stroke peak currents in

rocket-triggered lightning with the corresponding peak currents reported by the NLDN.

Jerauld et al. [2005] found that the NLDN tended to somewhat underestimate the actual

peak current, and the new propagation model was introduced in order to correct this.

Tables 3-5 through 3-8 give the NLDN-reported parameters for flashes recorded

by the MSE network in 2002-2004. For each stroke of a given flash, the GPS time (if

available) is given, along with the corresponding relative time in the Yokogawa digitizer

(Scope 19) record (times are relative to the trigger point, which is time 0), and the

corresponding segment on the LeCroy digitizer (Scope 20) record. When calculating the

Yokogawa times of events within a flash, care was taken to properly distinguish return

strokes from other lightning processes, such as M-components, which are generally not

detectable by the NLDN. The NLDN data were provided by Vaisala, Inc., the operator

of the NLDN, and NLDN and MSE data were correlated by comparing the GPS times of

MSE strokes to stroke times in the NLDN database. When GPS times were not available,

precise inter-flash and inter-stroke intervals were used in conjunction with approximate

times obtained from oscilloscope and video records. Tables 3-5 through 3-8 include

NLDN-reported time, location, and peak current, as well as the semi-major axis length







143

of the 50% error ellipse, ellipse eccentricity (defined here as the ratio of the ellipse

semi-major and semi-minor axis lengths), and the X2 value.












144








Table 3-5. NLDN-reported parameters for natural flashes MSE0201 through MSE0208.











3 0 0 0 0 0 Cl 0 Q o o 0 0 0 0 0








v i Z 66 c c'i 6< Z 6 ( o Z Z 66 '5 Z Z 6 6 6 d


0 ~ o z00 z z z z ~ ~ O c o


Z Z Z Z o
0



z





~~~(N

f-


00

00
Cl
(N

Q Q Q Q I
Z Z Z


o ^

00
0-
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zzzzzzzz


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0
Cl
0


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0
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0 0
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0 0 0
0 0 0
o ro
O o O


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0
Cl
0


z






z
r~i











00
Cl






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r;i

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z z a-
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ci z z z r



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0


00
0
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(N

CICI
v-i


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o
d
0
zzz
0


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145









Table 3-6. NLDN-reported parameters for natural flashes MSE0209 through MSE0302.


Cfl 00 ND N-l N~ t~ l- fl 00i OO 'Dl 00 a> 0 'tl rfl 0 0 rn) N~ 0
666666ddd 66d6ddd Z 66 Z Z







ooo o ooooooooo Qooo QQoo
, ,, ^ ,, ( ,^ ,, ^^ z ^^ ^z. ^^





^ ^ '^ ~i 'i- '-- oo --- --- -- -i -i -i Q -I- -- -- -i -i -

o oo oo oo oo o Z oo ~d d Z. Z oo


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l~~ cc?9"~N~~1


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ci ci


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ci ci


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ND -
0 -

d d


ZZZZZZZZ


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0
a>






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Z


C,
0\


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C,



00
Zci



N



cc
a>

ci
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0
0
ci
00
ZNc

Z



ND
00\


Z~i

0\

0\

a>
ND
NII


ZZZZ-ZZZ-ZZZ


0:
0
0
0


00


Z Z Z Z-


ND
ci
N
NDd


ZZZ


C




























ao 0





00
C



o




P



0i













146









Table 3-7. NLDN-reported parameters for natural flashes MSE0303 through MSE0406.


'- 'Q ci ^ t 0^ Ci' r~i t-^ Ci r~i t-^ fCri'-' v ^ ^
Z 66 66 6 Z 66ddddddd6 Z 6







O coi a 0 0 0 0 0 0 0 0 0 o









6 Z dd66A 6666-6Z 6666666 Z 66


0 0 o 0 to C~ 0 C b ~ -


Ci 0 0 0 0
Ci Vi N t 0
Ci (^ ~ 'I

00 00 00 00 00


Z


r-0

Ci
o o


ZZ
0 0
0 N

N 3;



I'D C
C i

C, 00
(N \

Ci -D
Ci i
0 N
(N


0 0

Ci Ci


0
00
00
Ci
oo



0


g1 ^
ZIN


d
00
CN



a\
(N


Ci
Zo


- c Z Z


o Ci

(N
0 -
Ci t",
o", o'


0
0


ZZp




0
0


0



oo



Z
0
0





0\
0

0

0\
0

a 0

Q1 S
N


0 0



Ci C)




C Ci
(N (N




00
rCi '

rCi Ci
o o

Ci Ci
0\ 0
(N (N


0
IZo






0




0
&
0ri

g1 ^






IDi
a\
t<
o


g1 ,


ao













147









Table 3-8. NLDN-reported parameters for natural flashes MSE0407 through MSE0412.


ddddddddddd o o o o o o o o Z od







0 cl 0 C 0 0 0 0 0 0 0
Cl---- ------ AZ A




- 0 0 0 0 0 0 6 6 6


Cl ( c! n 'l 00 -n Q 'l (n
^ N C 0-Co l r '-
St CN l -- -


0 0 0 0 0



00 00 00 00 00


o o
00






00 0d
00 0
(N 0
eD e\
CN t~
00 CN
0\ o
d -

00 00
rm rm
t^ t


0 0
o o

Cl Cl
z z


r-i e-1i


t'-1, i 1
d d
(N eN
00 00



o o
cD cD

c^ c^
(N (N


ri ri
0 m


Ci 1
00 Cl
0 --


00 00
rm rm
t^ t


0



Z 00
Z



0
ZCl







00
00
00
oo



r~i
Vri

Qa 3
Z N


- Cl Z Z Z Z


o o
a\ i
CT) C)I
\o o
6 6
d d


CN
00
0
0\

vC
(N
rm
1t I 2
Z Z I


S00



d d
. g c
66


M
00



d
0

00
od~
i


Z .













Ct









3.3 Data Calibration and Processing

The analysis and modeling of recorded data requires the removal of time delays

and vertical offsets introduced by the fiber-optic links, as well as the application of

calibration scaling factors to convert the raw amplitude data (in units of volts) recorded

on the oscilloscopes to the proper physical units (such as kV m 1 for electric field). The

amplitude and vertical offset calibration is expressed analytically in Equation 3.2.


P = GnomGFOL scopee Voffset) (3.2)


The quantity P is the calibrated data in physical units (e.g., kV m1V 1 for electric

field). The quantity Vscope is the voltage recorded on a given oscilloscope channel. The

quantity Voffset is the vertical offset and is assumed to be artificial (that is, not physical)

and introduced by the fiber-optic link and/or other electronics. Offset is estimated by

averaging the first 1000 samples of the waveform and subtracting the average value

from each sample of the waveform. Gnom is the nominal calibration factor converting

the waveform from units of volts to the proper physical units. It is assumed here that

Gnom includes any gain or attenuation from amplifiers, active integrators, and/or the PIC

controllers. The nominal calibration factors for the electric and magnetic field (and their

associated derivative) measurements are discussed in Sections 2.6 and 2.7, respectively.

The quantity GFOL is an estimate of the low-frequency gain of the fiber-optic link (FOL)

and is obtained by measuring the amplitude of the 100 Hz square-wave calibration signals

recorded before the MSE network is armed and after it is disarmed. As discussed in

Section 2.3, each of the PIC controllers generates a 0.1 or 1 V peak-to-peak, 100 Hz,

square-wave calibration signal which is injected into the fiber-optic transmitter at a given

measurement station when the appropriate command is given by the control computer.

Typically, these waveforms are recorded both before the network is armed and after it is

disarmed, with the lightning data being recorded in between the two sets of calibration

waveforms. When both pre-storm and post-storm calibration waveforms are available, the









amplitudes are averaged and divided by the actual amplitude of the calibration waveform

(e.g., 1 V). The value of GFOL is then obtained by taking the reciprocal. This is expressed

analytically in Equation 3.3.


GFOL Vcalactual(3.3)
0.5 (Vcal-pre + Vcal post)

The quantities Vcal pre and Vcal-post are the peak-to-peak amplitudes of the

calibration waveforms recorded before and after the storm, respectively, and the quantity

Vcal-actual is the actual peak-to-peak amplitude of the waveform generated by the PIC

controller. If only a pre-storm or post-storm calibration waveform is available, then that

amplitude value is simply divided into Vcal-actual to obtain GFOL. Note that Equation

3.3 implies that the actual amplitude of the calibration waveform generated by the PIC

controller (Vcal-actual) is known, that is, it is very close to it's nominal value and does not

drift with time or environmental conditions. If this were not the case, then the measured

amplitudes Vcal-pre and Vcal-post would not provide any useful information. Fortunately,

the square wave generators of the PIC controllers were designed exactly for this

purpose and are very stable. In this study, the "effective" peak-to-peak amplitudes of the

calibration signals are estimated by separating all points of the square wave into values

above and below zero. For each group of points, the average is calculated, and all points

falling outside 10% of the average are thrown out. The averages are then recalculated,

yielding estimates of the positive and negative levels which are then subtracted to yield

the effective peak-to-peak value, which is reasonably immune to waveform noise and

overshoot, both of which can yield biased peak-to-peak values. It should be noted that

overshoot is typically not an issue with the Opticomm fiber-optic links used in this study.

An example calibration waveform showing the measure peak-to-peak value is given in

Figure 3-2. Amplitude calibration factors for all storm days are given in Appendix A.

In addition to amplitude calibration, the time delays introduced by the fiber-optic

links must be removed. The fiber delays measured in 2002 with an optical time-domain











0.6

0.4
0
> 0.2
N
:e 0.0

-0.2

-0.4


0.01 0.02 0.03 0.04
Time, s

Figure 3-2. Calibration signal acquired on a LeCroy oscilloscope. From top to bottom,
the three horizontal lines indicate the calculated positive level, offset (DC
level), and negative level, respectively.


reflectometer (OTDR) are given in Table 2-9. The delays due to the electronics

(fiber-optic transmitters, receivers, amplifiers, etc.) were not measured and are assumed

to be equal for a given type of measurement. For example, the four dE/dt measurements

were identically configured and are assumed to have the same electronic and cable delays.

This assumption and its implications are discussed further in Chapter 4.

The binary data files recorded on the LeCroy and Yokogawa digital storage

oscilloscopes are read by programs written by the author in the Interactive Data Language

(IDL). Additional programs were written to plot the waveforms, and it is during this

process in which the vertical offsets are removed, the amplitude calibration factors are

applied, and the fiber-optic time delays are removed. The actual binary files are never

altered, although the calibrated data may be exported in another format, such as the IDL

binary format or ASCII format.

As discussed in Section 2.8, data recorded with trigger configurations B and C result

in time offsets of-0.8 and 1 ms in the data recorded on Scopes 19 and 20, respectively.

This means that these data, when plotted, are shifted by -0.8 or 1 ms relative to time 0

(the trigger point of the oscilloscope). Thus, these time offsets, when present, are also


...1111111111111111111111111111111111 I I

-









.-,, ,, 1, I ,,,-
I I I I I I I I I I I I I I I I 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1







151

removed when the data are plotted or exported. As previously discussed, the trigger

configurations for each flash recorded by the MSE system are given in Tables 3-3 and

3-4.















CHAPTER 4
DETERMINING THE LOCATION OF LIGHTNING EVENTS

Proper analysis and modeling of the natural-lightning waveforms acquired by the

MSE network requires a knowledge of the location of the lightning channel relative to

each measurement station. Unfortunately, unlike rocket-triggered lightning, the lightning

location is not known a priori and must be estimated by some method. While video

records (when available) generally provide a rough indication of the lightning location,

the relative low image quality and lack of synchronization between individual cameras

in the MSE video system render a precise location estimate impossible. The location

accuracy required depends on the analysis to be performed. However, for the analysis and

modeling performed in this dissertation, an accuracy of 20 to 30 m is probably acceptable,

with an accuracy of 10 m or less considered ideal (the dimensions of the MSE network

are on the order of 1 km).

4.1 Methodology

The most promising method for locating natural lightning events observed with the

MSE network is two-dimensional (2-D) hyperbolic positioning, where a source location is

computed from the measured time difference of arrival (TOA) of a signal at three or more

measuring stations. Given a source s at Cartesian coordinates (xs,ys, 0) and a receiver

r at coordinates (x,,yr, 0), the propagation time, tprop, of a signal from s to r at speed

c 3 x 108 m s1 is given by


tprop (Xr- Xs)2 + (r -s)2 (4.1)
c/









Given two receiving stations, 1 and 2, the difference in propagation times, t12, is

given by

t12 =s)2 _I 2- + sx)2 2 + (y-s)2y (4.2)

Equation 4.2 defines a hyperbola in the x-y plane. If a third receiver is added, a second

hyperbola is defined by


t23 = V 2 x)2 2 -ys)2 (3 s)2 + 3 ys)2 (4.3)


If the locations of the three receivers are known, Equations 4.2 and 4.3 form a system

of two equations which can be solved (typically via numerical methods) for the two

unknowns (xs,ys). Depending on the geometry of the situation, one or two sets of

solutions will exist, the latter case corresponding to the hyperbolas intersecting at two

locations. A third equation, describing the time difference from receivers 1 and 3 (t13)

could be substituted for either Equation 4.2 or 4.3, but does not provide any additional

information not found in Equations 4.2 and 4.3, since t13 = tl2 + t23. Note that the 2-D

TOA technique does not require knowledge of the absolute arrival times of the signal at

each measurement station, only the difference in arrival time between individual stations.

The MSE dE/dt measurements, located at Stations 1, 4, 8, and 9, are best-suited

for the 2-D TOA technique due to their relatively high bandwidth (upper-frequency

limit of about 20 MHz) and high time resolution (5 ns for most flashes), compared with

other measurements in the MSE network. Station locations are estimated via GPS, as

discussed in Section 2.2, and are thought to be accurate to within a few meters. Note

that it is assumed that all stations lie in the same plane, i.e., elevation is ignored. Further,

accurate calculation of time differences requires knowledge of the propagation delay (due

to coaxial cables, electronics, and fiber-optics) between each measurement station and

the Launch Control trailer, where the waveforms are recorded. These system delays were

estimated by measuring the delays of the optical fibers with an Optical Time Domain

Reflectometer (OTDR), as discussed in Section 2.4, and assuming that the electronics and









cable delays are identical for each measurement, this assumption likely being reasonable

given the four dE/dt measurements were installed with identical equipment, the only

difference being the length of the fiber-optic cable.

Note that with four dE/dt stations it is generally possible to solve for a source

location in three dimensions (xs,,ys,z). Instead of the system of two equations and

two unknowns obtained with three stations the solution representing the intersection

point of two hyperbolas in the x-y plane one obtains a system of three equations and

three unknowns with the solution representing the intersection of three hyperboloids

in three-dimensional space. However, preliminary work by PhD student Joe Howard

suggests that altitude (z) component of the 3-D location solution is very sensitive to errors

in timing and receiver location, and it is believed the 2002-2004 experiment does not have

the necessary accuracy in station locations and system delay estimates to provide useful

3-D location. However, the examples given below suggest that adequate 2-D solutions,

which are all that are required in this work, can be obtained from the 2002-2004 data.

Since only three receiver stations are required for a 2-D solution, a four stations can be

used to form four combinations of three stations, that is, four sets of solutions can be

obtained and compared for each flash in which four-station dE/dt records are available.

These four sets of solutions can be used to rule out any incorrect solutions obtained

when any two hyperbolas intersect in two locations. Further, combining all independent

equations from the four dE/dt stations yields a single overdetermined system of six

equations and two variables, which can possibly be solved via an optimization technique,

though this technique would have to be applicable to non-linear equations of the form of

Equation 4.2.

When estimating locations with the 2-D TOA technique, the peaks of the dE/dt

waveforms were used as the feature for calculating the necessary time differences,

although sometimes the choice of the peak was somewhat subjective due to digitizer

noise (the dE/dt waveforms were recorded with an 8-bit LeCroy LT374 digital storage









oscilloscope). If deemed necessary, the waveform was smoothed with a moving-average

filter prior to choosing the peak. Using the measured time difference values and the

known locations of the dE/dt stations, solutions to the simultaneous equations were

computed numerically using the Mathematica software package. If four suitable (i.e.,

not saturated or very noisy) dE/dt waveforms were available for a given event, four

independent location solutions (from four sets of three stations) would be obtained.

The x andy coordinates for the four solutions were then each averaged to obtain a

single location estimate. When only three dE/dt waveforms were available for a given

event, either because one waveform was saturated or because one measurement was

non-operational, only one solution (from one combination of three stations) could be

determined, with that solution becoming the location estimate.

4.2 Results

Figure 4-1 shows the results obtained using the 2-D TOA technique for altitude

triggered1 flash FPL0205. The flash terminated on a building known as Instrumentation

Station 1 (IS1), located approximately 65 m north of the tower rocket launcher. Data from

three stations (1, 4, and 9) were available and the peaks of the dE/dt waveforms were

used in calculating the time differences. Note that for this event, the dE/dt waveforms

were sampled at a relatively low rate (50 MHz, compared with 200 MHz used for most

other events; see Tables 3-3 and 3-4). The error between the estimated location and the

ground-truth location (measured with GPS) is about 4 m, which is on the order of the

accuracy of the GPS location measurement.



1 Altitude triggering consists of launching a rocket trailing an ungrounded wire. A
downward negative stepped leader propagates from the bottom of the wire through virgin
air, similar to a stepped leader preceding first strokes in natural cloud-to-ground lightning.
This event was triggered unintentionally, the result of a breakage or partial vaporization of
a grounded wire used in classical-triggered lightning.










800
700

600

500

400

300
200

100


625 630 635
x, m


640 645 650


Figure 4-1. Location of the first stroke of altitude-triggered flash FPL0205, which
terminated on Instrumentation Station 1 (IS1), estimated using the 2-D
TOA technique. The peaks of the first-stroke dE/dt waveforms measured at
Stations 1, 4, and 9 were used in calculating the time differences. The top
image shows all four stations (colored boxes), the calculated solution (black
x), and the actual location (gray x). The bottom image is a zoom of the top
image around the intersection of the two hyperbolas.


FPL0205, dE/dt, Seg 1




IS1 St.4





St.9




200 400 600 800 1000 1200
x, m
FPL0205, dE/dt, Seg 1


540


535


530


E 525


520


515


-IS1----













FPL0213, dE/dt, Seg 1, Stations 1,4,8


800

700

600

500
E 400

300

200

100





467.5

465

462.5

S460

457.5

455

452.5


630 635 640 645
x, m


650


Figure 4-2. Location of classical-triggered flash FPL0213, which terminated on the tower
launcher (TL), estimated using the 2-D TOA technique. The peaks of the
dE/dt waveforms measured at Stations 1, 4, and 8 were used in calculating
the time differences. The top image shows all four dE/dt stations (colored
boxes), the calculated solution (black x), and the actual location (gray x).
The bottom image is a zoom of the top image around the intersection of the
two hyperbolas.


200 400 600 800 1000 1200
x, m
FPL0213, dE/dt, Seg 1, Stations 1,4,8









Table 4-1. Location results for the first stroke of classical-triggered flash FPL0213.
Results are given for each combination of three stations. The locations are
given in "Camp Blanding Coordinates" (CBC), which can be converted to
State Plane Coordinates (SPC) by adding 99750 and 621500 m to the east and
north values, respectively. The ground-truth location is (637, 459).

Station Location Estimate
Combination CBC East [m] CBC North [m] Error [m]
1,4,8 641 456 5
1,4,9 641 454 6
1,8,9 639 453 6
4,8,9 639 457 3
Mean 640 455 5


Table 4-1 shows the location results for classical-triggered flash FPL0213. Data

from all four dE/dt stations were available, thus four solutions were obtained (the

optimization technique has not yet been attempted). As before, peak dE/dt was used to

determine the time differences. The mean location error was approximately 5 m, similar

to that obtained for altitude-triggered flash FPL0205. Figure 4-2 shows a plot of the

solution obtained using Stations 1, 4, and 8.

The previous two examples suggest that the 2-D TOA technique works well, and that

the following assumptions are reasonably valid, at least for triggered-lightning strokes

located well within the perimeter defined by the four dE/dt stations.

The delays associated with the electronics and coaxial cables for the four dE/dt
measurements, which are not accounted for, are approximately equal and the OTDR
fiber-delay measurements provide an adequate estimate of the relative system
delays.

The relative elevations of the four dE/dt sensors are small enough to be ignored,
that is, all four sensors can be assumed to lie in the same horizontal plane.

The peak of the dE/dt waveform is an adequate point for calculating the time
differences of arrival. This implies that the source of the dE/dt peak, which is
likely not a single point at ground-level but rather an elevated source distributed
along some section of the channel, is close enough to the ground that the additional
propagation time introduced by the elevated source (relative to a source on ground)
does not introduce significant errors when calculating the location using the 2-D
TOA technique.









The two examples presented above were from rocket-triggered lightning, and hence it is

not clear how well the technique works for first strokes in natural lightning, although first

strokes in altitude-triggered lightning (e.g., FPL0205) are somewhat similar to those in

natural lightning.

Location estimates have been determined for 19 natural first return strokes, and are

summarized in Table 4-2. As mentioned above, if four suitable (i.e., not saturated or

very noisy) dE/dt waveforms were available for a given event, four independent location

solutions (from four sets of three stations) would be obtained. In these cases, the x and

y coordinates for the four solutions were averaged to obtain a single location estimate.

If the resulting solutions were within or close to the perimeter defined by the four dE/dt

stations, then generally the four solutions would be very similar, differing by only a

few meters (e.g, flashes MSE0201, MSE0205, and MSE0303). For example, Table 4-3

gives the location results for the first stroke of natural negative flash MSE0303, using

four combinations of three dE/dt stations. The maximum difference between individual

solutions is on the order of 10 m, with the average location being approximately 100 m

from the tower rocket launcher, which is well within the perimeter defined by the

four dE/dt stations. Plots showing the individual solutions (intersection of hyperbolas

determined by the station locations and measured time differences) are given in Figure

4-3. The location estimate obtained via hyperbolic positioning is consistent with the

general channel location indicated by video records.

When the ground strike location was likely well outside of the perimeter defined

by the four stations, the four solutions sometimes differed considerably (e.g., flashes

MSE0209 and MSE0210), and/or solutions could not be found for some sets of stations

(e.g., flashes MSE0403 and MSE0407). In such cases, the different solutions were

typically distributed along a line, separated from each other by some tens or hundreds

of meters. An example of such a case, flash MSE0210, is presented in Table 4-4 and

Figure 4-4. For this event, the east-west spread in the location solutions was only 19 m,









160




Table 4-2. Location estimates (ground strike points) for natural first return strokes

recorded by the MSE network, obtained with the 2-D TOA technique, using

the time difference of arrival of features (typically the peak) of the measured

dE/dt waveforms. In cases where four dE/dt stations were available, typically

the four individual location solutions (from four sets of three stations)

were averaged to obtain the estimated location. The locations are given in

"Camp Blanding Coordinates" (CBC), which can be converted to State Plane

Coordinates (SPC) by adding 99750 and 621500 m to the east and north

values, respectively.


e .e


88~





8) 8 -
33 S


0 ,- ,- 0
3 1- 00C



c^ Cg -g^^
o ~ ~ o o o\
is o ^ g g g



oa a a) 0
(U ~ (ua
0 0
~- ~-
* c0 0 0 0
o oyo o o o

a a a aa-
mo mo g m m m ^H M H ^H ^
0 *


I






~~ OC OC Z~~0
z ZZ C OCOCOC C O ~ C C 0Z t \
~m~ -~ -~3 3


OC

OC



OC OC O


oC
OC C
hh


OC

OC



00
OCO O








161


Table 4-3. Location results for the first stroke of natural negative flash MSE0303,
estimated using the 2-D TOA technique. Results are given for each
combination of three stations. The locations are given in "Camp Blanding
Coordinates" (CBC), which can be converted to State Plane Coordinates
(SPC) by adding 99750 and 621500 m to the east and north values,
respectively.


Station
Combination
1,4,8
1,4,9
1,8,9
4,8,9
Mean


800
700
600
500
E 400
300
200
100



800
700
600
500
E 400
300
200
100


Location Estimate
CBC East [m] CBC North [m]
638 353
638 365
644 365
646 354
641 359


MSEO303, dE/dt, Seg 1, Stations 1,4,8



U



St.9



200 400 600 800 1000 12
x, m
MSEO303, dE/dt, Seg 1, Stations 1,8,9




/ m


St.9


, ,^ ^,, ^^^ ,


800
700
600
500
E 400
300
200
100



800
700
600
500
E 400
300
200
100


0 08 1000 1 200


MSEO303, dE/dt, Seg 1, Stations 1,4,9



E St.4
TL



St.9



200 400 600 800 1000 12(
x, m
MSEO303, dE/dt, Seg 1, Stations 4,8,9



TL
I


St.9



200 400 600 800 1000 12(
x, m


Figure 4-3. Location results for the first stroke of natural negative flash MSE0303,
estimated using the 2-D TOA technique. The peaks of the dE/dt waveforms
measured at Stations 1, 4, 8, and 9 (locations indicated by the colored
boxes) were used in calculating the time differences. Each of the four plots
(each corresponding to one combination of three stations) shows the two
hyperbolas defined by the station locations and measured time differences,
the intersection of which (each indicated by a black x) represents the
individual location solution. The coordinates of each location estimate are
given in Table 4-3. The gray box indicates the location of the tower rocket
launcher (TL).


200 400


^^







162

Table 4-4. Location results for the first stroke of natural negative flash MSE0210,
estimated using the 2-D TOA technique. Results are given for each
combination of three stations. The locations are given in "Camp Blanding
Coordinates" (CBC), which can be converted to State Plane Coordinates
(SPC) by adding 99750 and 621500 m to the east and north values,
respectively.

Station Location Estimate
Combination CBC East [m] CBC North [m]
1,4,8 694 1103
1,4,9 687 1054
1,8,9 675 1029
4,8,9 685 1147
Mean 685 1083


while the north-south spread was 118 m. These location estimates, obtained by averaging

multiple solutions having relatively poor agreement, are considered less accurate than

the case of good agreement between solutions. For two events, MSE0202 and MSE0412,

the former being a positive first stroke (see Chapter 7), very good agreement was found

between the four individual solutions, despite the fact that the two sets of location

solutions were each some hundreds of meters from the perimeter defined by the four

dE/dt stations. In over half the cases (11 out of 19), only three dE/dt waveforms were

available, either because one waveform was saturated (e.g., flashes MSE0203, MSE0207,

MSE0409, MSE0410, and MSE0411) or because one measurement was non-operational

(e.g., flashes MSE0211, MSE0301, MSE0401, MSE0402, and MSE0404). In these

cases, only one solution (from one combination of three stations) could be determined,

with that solution becoming the location estimate. As with the multiple-solution case,

relatively-close solutions (that is, within or near the perimeter defined by the three

operational dE/dt stations) are likely to be more accurate than those for flashes that are

relatively far away.


















MSEO210, dE/dt, Seg 1, Stations 1,4,8
1200 --


1000


800


600 .1 T
TL S--
400

St.9
2nn __


200 400 600 800 1000
x, m

MSE0210, dE/dt, Seg 1, Stations 1,8,9


1000


800


600 St.
TL *

400 -t

St.9
200 --


1200


800 1000 1200


MSE0210, dE/dt, Seg 1, Stations 1,4,9
1200


1000


800


600 .1 t
TL

400 TL

St.9
200St. 9



200 400 600 800 1000 1200
x, m

MSE0210, dE/dt, Seg 1, Stations 4,8,9
1200 -'


1000 ..


800


600 -.1
TL

400

St.9
200 -


200 400


800 1000 1200


Figure 4-4. Location results for the first stroke of natural negative flash MSE0210,

estimated using the 2-D TOA technique. The peaks of the dE/dt waveforms
measured at Stations 1, 4, 8, and 9 (locations indicated by the colored

boxes) were used in calculating the time differences. Each of the four plots
(each corresponding to one combination of three stations) shows the two
hyperbolas defined by the station locations and measured time differences,
the intersection of which (each indicated by a black x) represents the
individual location solution. The coordinates of each location estimate are

given in Table 4-4. The gray box indicates the location of the tower rocket
launcher (TL).















CHAPTER 5
ANALYSIS OF MEASURED WAVEFORMS

5.1 Comparison of Measured Electric Field and Numerically-Integrated dE/dt
Waveforms

As discussed in Chapter 2, both the electric field (E) its time derivative (dE/dt)

were measured at Stations 4 and 9. It is thus of considerable interest to compare

the directly-measured E waveforms with the corresponding numerically-integrated

dE/dt waveforms at these two stations. Ideally, integrated dE/dt should be identical to

directly-measured E. One could also compare measured dE/dt with numerically-differentiated

E, although differentiation enhances noise and the E waveforms do not have sufficient

high-frequency response and time resolution to adequately reproduce the dE/dt

waveforms, making that comparison less justified.

Numerical integration of the dE/dt waveforms was achieved by the rectangular

approximation method, where the area under the curve is approximated by a finite

number of rectangles. Other methods, such as those using a trapezoidal approximation,

are more accurate, but little difference was found in the numerically-integrated dE/dt

waveforms integrated using the rectangular and trapezoidal methods. The amplitude and

shape of the integrated waveforms are very sensitive to the vertical offset in the dE/dt

waveforms. Care was taken to remove these offsets prior to integration.

It was found that the waveshapes of the numerically-integrated dE/dt waveforms

matched the directly-measured E waveforms well. However, the amplitudes of the

integrated dE/dt waveforms were always smaller than those of the E waveforms. The

amplitude difference was a multiplicative scaling factor and not a function of time,

indicating the discrepancy is not due to offsets in the dE/dt waveforms (offsets in the

dE/dt waveforms would yield increasing discrepancies with increasing time, since









integrating a constant offset results in a ramp function). The scaling factor was typically

different at each of the two stations, and different at a given station on different days.

However, at a given station, the amplitude difference was apparently the same for all

strokes (including those in different flashes, terminating on ground at different points

within the network) measured on a given storm day. Hence, the amplitude difference

is apparently neither a function of distance to the lightning channel nor a function of

the relative azimuth angle between the channel and the antenna. Figure 5-1 shows

an example of integrated dE/dt compared with the corresponding directly-measured

E. Figure 5-2 shows the same data, but with the integrated dE/dt waveforms (red

curves) scaled in order to match the amplitude of the E waveforms. Figures 5-3, 5-4,

5-5 illustrate the observation that the scaling factors are the same for natural-first,

natural-subsequent, and triggered-lightning strokes, respectively, that were recorded on

the same day. Table 5-1 gives the relative amplitude differences between the integrated

dE/dt and the directly-measured E waveforms at Stations 4 and 9, for each day on which

data were obtained. The amplitude differences are expressed in terms of a scaling factor

applied to the integrated dE/dt waveforms. Note that the scaling factors observed at

Stations 4 and 9 both exhibit general decreasing trends with increasing time, with a

notable exception at Station 4 on 6/14/2004.

The observation that the amplitude difference was always a multiplicative scaling

factor, along with the observation that the scaling factor was apparently neither a function

of distance nor azimuth angle, seems to indicate calibrations error in either the E or dE/dt

measurements or both measurements. However, the observation that the scaling factor

tends neither to be the same for Stations 4 and 9, nor to be the same for different days,

seems to indicate that the problem is not a simple calibration error, but is more complex.

The problem is most-likely not due to errors in attenuation settings or terminations for the

following reasons.









Each of the PIC controllers (which provide attenuation for the measurements, as
discussed in Section 2.3) was tested prior to each summer, as well as occasionally
tested in the field. It is unlikely that attenuation errors would go unnoticed for
such a long period of time. The amplifiers associated with the electric field
measurements were also tested.

The calibration signals generated by the PIC controllers have a peak-to-peak
amplitude of 1 V into a 50 Q load and 2 V into a high-impedance load. If the
termination resistance at a given measurement differed significantly from 50 Q,
then the amplitudes of the measured calibration signals (recorded before and after
each storm) would differ significantly from 1 V. Although some difference was
observed due to variation in the gain of the fiber-optic links (and accounted for,
as discussed in Section 3.3), the discrepancy is not enough to account for the
amplitude variations between measured E and integrated dE/dt observed here.

It is impossible to know for certain whether the E, dE/dt, or both measurements were

in error. Unfortunately, there were only two stations in which E and dE/dt were

simultaneously recorded, and thus it is impossible to estimate the accuracy of the

amplitudes of the E and dE/dt waveforms measured at other stations. However, there is

some evidence to suggest that the directly-measured electric field amplitudes are correct

(within 15 percent or so because of possible local enhancement due to different terrain at

each station) and the dE/dt amplitudes are incorrect (at least at the two stations for which

a comparison was made) This supposition comes from the fact that, for a given stroke, if

the stepped-leader electric field change is plotted versus distance, the result is reasonable

(some inverse power-law dependence with distance), while plots of dE/dt peak versus

distance often yield unreasonable results, such as increasing peak with distance. This is

why the values given in Table 5-1 are presented as amplitude scaling factors for dE/dt,

with the amplitudes of the electric field waveforms being assumed to be correct.

The issue may be related to the fact that the grounding electrodes of the E and dE/dt

antennas were not connected together. Since each antenna and its surrounding metal

screen is grounded via a single 3-m copper rod driven in sandy soil, the housing of each

antenna (and associated ground rod) in some sense "floats" above true ground, resulting

in some field enhancement. One would expect different enhancement factors if the soil









under the antennas were different somehow, perhaps due to the presence of rain water,

and the grounding electrodes were not electrically connected. In an experiment being

performed during summer 2007, a 10 m x 10 m wire screen has been placed beneath and

connected to both the E and dE/dt antennas at one station. These new data should verify

or disprove the hypothesis given above.

Further, it has been suggested that the ground rods themselves may contribute

to enhancement of the field in poorly conducting soil (George Schnetzer, personal

communication). Vertical ground rods in poorly conducting soil can short out the electric

field in the ground, creating an enhancement for the E-field or dE/dt antenna connected

to it. Thus, a large ground screen under both the electric field and dE/dt antennas, with a

single ground rod at the center, would be preferable to small screens with separate vertical

ground rods.

It is important to note that the explanations discussed above do not explain why the

electric field measurements appear to be more accurate than the dE/dt measurements. If

the amplitude discrepancy is indeed due to grounding, there is no obvious reason why it

would affect the dE/dt measurements more than the electric field measurements. Clearly,

a more detailed investigation is necessary.











MSE0201, Station 4


0 10 20
Time, Ys
MSE0201, Station 9


0 10 20
Time, us


Figure 5-1. Comparison of directly-measured E (blue curves) and integrated dE/dt (red
curves) at Station 4 (A) and Station 9 (B), for the first stroke of natural flash
MSE0201. No scaling has been applied to the integrated dE/dt waveforms.


2
-10
-10


E


-10










A MSE0201, Station 4, dE/dt Scale Factor = 1.70

12
10

E 8


S4 --E
-integrated dE/dt
2
0 -

-10 0 10 20 30
Time, Ps
B MSE0201, Station 9, dE/dt Scale Factor = 2.20

50

40

E 30

J 20E
Integrated dE/dt
10


-10 0 10 20 30
Time, /ts
Figure 5-2. Comparison of directly-measured E (blue curves) and integrated dE/dt (red
curves) at Station 4 (A) and Station 9 (B), for the first stroke of natural flash
MSE0201. The waveforms are the same as those shown in Figure 5-1, except
that the red curves were each scaled by the indicated scale factor in order to
match the corresponding blue curves.










dE/dt Scale Factor = 1.26


0 20 40 60
Time, ps
MSE0303, Station 9, dE/dt Scale Factor = 1.50


0 20 40 60
Time, ps


Figure 5-3. Comparison of directly-measured E (blue curves) and integrated dE/dt (red
curves) at Station 4 (A) and Station 9 (B), for the first stroke of natural flash
MSE0303. The red curves were each scaled by the indicated scale factor in
order to match the corresponding blue curves.


E
LU


E

LU










Station 4, dE/dt Scale Factor = 1.26


-5 0 5 10


MSE0303, Station


Time, ps
9, dE/dt Scale Factor = 1.50


-5 0 5 10 15
Time, ps


Figure 5-4. Comparison of directly-measured E (blue curves) and integrated dE/dt (red
curves) at Station 4 (A) and Station 9 (B), for the fifth stroke of natural flash
MSE0303. The red curves were each scaled by the indicated scale factor in
order to match the corresponding blue curves.


E

uJ











FPL0321, Station 4, dE/dt Scale Factor = 1.26


0 10 20
Time, Ps
FPL0321, Station 9, dE/dt Scale Factor = 1.50


0 10 20
Time, ys


Figure 5-5.


Comparison of directly-measured E (blue curves) and integrated dE/dt (red
curves) at Station 4 (A) and Station 9 (B), for the first stroke of triggered
flash FPL0321. The red curves were each scaled by the indicated scale factor
in order to match the corresponding blue curves.


E

ur
Ll























Table 5-1. Amplitude scaling factors for the electric field derivatives (dE/dt) measured
at Stations 4 and 9, estimated by comparing measured electric field (E) with
numerically-integrated dE/dt. Scaling factors were estimated for each of the
storm days in which both E and dE/dt were available.


dE/dt scaling factor
Station 4 Station 9
1.70 2.20
1.45 2.00
1.55 1.90
1.55 1.75
1.22 1.55
1.29 No data
1.40 No data
1.26 1.50
1.26 1.50
3.50 No data
1.17 No data
1.15 1.55
1.20 1.53
1.60 1.65
1.25 1.65
1.25 1.55


Date
07/20/2002
08/02/2002
08/04/2002
08/30/2002
11/10/2002
12/24/2002
06/18/2003
07/18/2003
07/22/2003
06/14/2004
06/23/2004
06/30/2004
07/11/2004
07/15/2004
07/24/2004
08/24/2004









5.2 Relative Azimuth Angles Between the Lightning Channel and the Loop Sensor

As stated in Chapter 2, only the east-west components of the horizontal magnetic

fields and field derivatives at ground were measured at Stations 4 and 9. Each of these

measurements consisted on a single coaxial cable loop antenna oriented north-south. At

Station 1, there were two dB/dt measurements situated in a crossed-loop configuration,

so that both components of the field derivative could be measured. In the case of the

single-loop measurements, some assumptions must be made in order to estimate the

total field at a given location (that is, both north-south and east-west components). If the

location of both the antenna and the lightning channel are known, one can easily calculate

the relative azimuth angle, 4.

= 90 -tan y (5.1)
Ax

As shown in Figure 5-6, 0 is defined to be relative to the plane of the loop antenna.

If the lightning channel is assumed to be straight and vertical, then the total horizontal

field, Btot, can be estimated from the east-west component, BEW.


B, = B, ii (0) (5.2)


The quantity sec(4) in Equation 5.2 is the secant of 0 and is equal to the reciprocal

of the cosine of 4. The secant function is plotted in Figure 5-7. The secant function

asymptotically approaches infinity as 0 approaches 90 degrees. 0 being equal to 90

degrees corresponds to the situation where location of the lightning channel is exactly

normal to the plane of the loop antenna. Assuming a straight and vertical channel, no field

should be sensed by the antenna in this configuration. Note that the nature of the secant

function implies that, beyond 80 degrees or so, small changes in 0, result in relatively

large changes in sec(4). Since there is likely some error in any given lightning location

estimate, which results in some error in the calculated value of 0, it is reasonable to

conclude that the estimated values ofBto are likely less reliable for measurements where

0 exceeds roughly 80 degrees. Further, the assumption of a straight and vertical channel









Lightning
channel


N


Ay

& -- -- -- -- -- -- ----------- --- --- -I
Ax

Loop
sensor

Figure 5-6. Plan-view diagram illustrating the relative azimuth angle between a lightning
channel and a north-south oriented loop sensor.

is dubious, especially for natural first strokes, which are often tortuous and contain
branches. Nevertheless, even with these limitations, these estimates should provide a
rough indication of the total field.
Table 5-2 gives the values of 4 and sec(4) at Stations 1, 4, and 9, for 19 natural first
strokes recorded by the MSE system. Note that while both components of dB/dt were
measured at Station 1, it is possible that a sensor may be offline for any given event. If
only the east-west component of the field is available at Station 1, the values given in
Table 5-2 can be used to estimate the total field. If only the north-south component
is available, then the amplitude should be scaled by sec(90 4), where 0 is still
measured relative to the north-south oriented sensor (which measures the east-west
component). Table 5-3 gives the values of 0 and sec(4) for all of the rocket launchers
used in rocket-triggered lightning experiments.











Table 5-2. Relative azimuth angles, 4, between the location of the lightning channel and
the locations of the north-south oriented loop sensors at Stations 1, 4, and 9,
for each of the natural first strokes recorded by the MSE system. Also given
is the secant of each angle, which is an amplitude scaling factor that can be
applied to B and dB/dt waveforms measured that station.

Station 1 Station 4 Station 9
Flash ID 0 [deg.] Sec(O) 0 [deg.] Sec(4) 0 [deg.] Sec(O)
MSE0201 43.0 1.47 44.9 1.41 70.6 3.01
MSE0202 2.9 1.00 44.1 1.39 25.9 1.11
MSE0203 72.2 3.27 84.6 10.7 4.1 1.00
MSE0205 76.2 4.19 64.2 2.29 48.7 1.52
MSE0207 32.3 1.18 78.1 4.85 5.8 1.01
MSE0209 38.5 1.28 62.3 2.15 71.6 3.17
MSE0210 33.3 1.20 19.3 1.06 16.0 1.04
MSE0211 29.3 1.14 63.4 2.23 15.2 1.04
MSE0301 32.5 1.19 65.1 2.38 84.4 10.3
MSE0303 57.7 1.87 54.4 1.72 52.2 1.63
MSE0401 53.7 1.69 9.2 1.01 32.9 1.19
MSE0402 65.6 2.42 71.6 3.18 34.3 1.21
MSE0403 86.5 16.3 75.5 3.99 60.9 2.05
MSE0404 10.5 1.02 64.3 2.30 26.4 1.12
MSE0407 12.9 1.03 20.0 1.06 11.5 1.02
MSE0409 44.8 1.41 79.0 5.21 3.5 1.00
MSE0410 73.3 3.48 84.3 10.1 32.0 1.18
MSE0411 24.7 1.10 86.6 17.1 13.2 1.03
MSE0412 74.6 3.78 84.4 10.2 65.9 2.44




Table 5-3. Relative azimuth angles, 4, between the locations of the ICLRT rocket
launchers and the locations of the north-south oriented loop sensors at Stations
1, 4, and 9. Also given is the secant of each angle, which is an amplitude
scaling factor that can be applied to B and dB/dt waveforms measured that
station.

Station 1 Station 4 Station 9
Launcher Locationa 0 [deg.] Sec(4) 0 [deg.] Sec(4) 0 [deg.] Sec(4)
Tower 72.8 3.39 73.8 3.57 38.1 1.27
Mobile 2002b 69.7 2.88 76.4 4.26 30.7 1.16
Mobile 2003a-b 27.8 1.13 78.3 4.92 7.6 1.01
Mobile 2003c 79.7 5.60 59.8 1.99 70.8 3.04
a) See Table 2-6.











50- -
5 -
40- 4
-- D

30 -- -
a> 2
C) 20
0 20 40 60 80
10 Degrees

0-

0 20 40 60 80
4, Degrees

Figure 5-7. Plot of the secant function versus angle in degrees. The inset shows the same
plot ranging from 0 to 80 degrees.

5.3 Description of Close Negative First Stroke Field and Field Derivative
Waveforms

The purpose of this section is to provide qualitative descriptions of the close

first-stroke field and field derivative waveforms recorded by the MSE network. These

descriptions will be useful when discussing the waveform parameters (quantitative

descriptions) presented in the following sections. The description of waveform features

will also be useful when discussing the modeling of return stroke processes in Chapter 6.

Figure 5-8 shows a plot of a typical first-stroke electric field waveform, which

was measured at a distance of 260 m, displayed on a 20 ms time scale. The vertical

offset and fiber-optic time delay have been removed using the procedure described in

Section 3.3. The waveform exhibits an asymmetrical V-shape indicative of lightning

leader/return-stroke sequences, with transition from leader to return stroke occurring near

the bottom of the V. Figure 5-9 shows all of the electric field waveforms for this event

overlayed and displayed on a 5 ms time scale. For this event, there is a clear relationship









MSE0410, RS1, Station 6
10



S-10
E
2-20
ui Leader Return
-30 --
-0 Stroke
-40

-50 I I I
-10 -5 0
Time, ms

Figure 5-8. Example first-stroke electric field waveform for natural flash MSE0410,
displayed on a 20 ms time scale. The waveform was measured at Station 6,
which was about 260 m from the channel.

between the distance and the magnitude of the leader electric field which occurs at the

bottom of the V. Also, while perhaps not as obvious, there is a relationship between the

distance and width of the V-shaped waveforms at half the maximum amplitude. The

relationship between distance and electric field waveform parameters is discussed in

detail in the following sections.

As discussed in Section 1.3.2, the stepped leader process typically occurs on a time

scale of tens to hundreds of milliseconds, while the return stroke process occurs on a

time scale of tens of microseconds. Therefore, fine structure of the electric field from

the return stroke process is not discernible in Figure 5-8; only the overall field change

is seen. Figures 5-10 and 5-11 show the same waveform as Figure 5-8, but on 200 uts

and 50 uis time scales, respectively. On these time scales, fine features of the leader and

return stroke portions of the waveforms can be resolved. In Figure 5-10, small pulses

associated with the stepping process of the initial downward negative leader are observed

to be superimposed on the overall leader field. In Figure 5-11, features observed are the

slow front, the fast transition, and the static ramp that follows the fast transition.











MSE0410, RS1, E-Field


-4 -3 -2 -1 0
Time, ms


Figure 5-9.


-20

-30

-40


-150


Overlayed first-stroke electric field waveforms for natural flash MSE0410,
displayed on a 5 ms time scale.





MSE0410, RS1, Station 6


-100 -50 0
Time, ps


Figure 5-10. Example first-stroke electric field waveform for natural flash MSE0410,
displayed on a 200 uts time scale. The waveform was measured at Station 6,
which was about 260 m from the channel. Some features of the waveform
are labeled.









MSE0410, RS1, Station 6


-10


E -20
S/ --- Ramp -
uj -30 -

SF ast Transition
-40
Slow Front

-50 -40 -30 -20 -10
Time, us

Figure 5-11. Example first-stroke electric field waveform for natural flash MSE0410,
displayed on a 50 uts time scale. The waveform was measured at Station 6,
which was about 260 m from the channel. Some features of the waveform
are labeled.

The so-called "slow-front/fast-transition" combination has been observed both in the

measured channel-base currents [Berger et al., 1975] and in measured distant (radiation)

electric and magnetic fields [Weidman andKrider, 1978; Cooray andLundquist, 1982]

of positive and negative lightning first return strokes (see Figures 1-4, 1-6, and 1-7 for

examples of such waveforms). Weidman andKrider [1978] describe the initial rising

portion of distant negative first-stroke field waveforms propagating over seawater as

having an "initial slow front," rising for 2 8 uts (mean of 4 uts) to about half the field

peak, followed by an abrupt "fast transition," rising to peak with a 10-90% rise time of

0.2 uis or less. The origin of the slow front in measured first-stroke currents and fields

has long been a matter of discussion, and has often been attributed to the presence of an

upward connecting leader (this attribution is discussed and disputed in Chapter 6).

The electric field waveform shown in Figure 5-11 exhibits this slow-front /

fast-transition combination, as do the waveforms shown in Figure 5-12 (which gives

all of the electric field waveforms for this event on the same time scale as Figure 5-11).









For this event, the slow front has an apparent duration of about 4 his, although the exact

demarcation between the end of the downward leader and the beginning of the slow front

is not clear. Further, neither the beginning of the fast transition nor its peak is distinct in

these waveforms, presumably due to the contribution of the electrostatic field component

that masks the radiation field component of the fast transition at such close distances.

However, the electric field fast transition peak is reasonably discernible in the Station 10

waveform of Figure 5-12, which was measured at a distance of about 800 m, the farthest

measurement from the channel. This is not surprising, since at farther distances one

would expect the contribution of the radiation field of the fast transition, relative to the

contribution of the electrostatic field, to be larger than what would be observed at closer

distances.

All of the waveforms in Figure 5-12 exhibit similar features, although it is difficult

to compare the relative amplitudes from Figure 5-12 alone. Figure 5-13 shows the same

electric field data presented in Figure 5-12, but with the waveforms overlayed on a single

plot. Each waveform in Figure 5-13 was vertically shifted by its value at -50 ts, so

that each waveform begins at zero amplitude, and thus the waveform amplitudes can

be directly compared. Further, each waveform was also shifted in time so that the fast

transition occurs at time zero. Thus, one is able to directly compare the features on the

waveforms at a specific time. In the waveforms of Figure 5-13, the demarcation between

the slow front and the fast transition (occurring at time zero) becomes more discernible as

distance increases.

Figure 5-14 shows electric field waveforms from eight different natural first strokes,

all measured between 100 and 200 m of the channel, and displayed on a 200 uts time

scale. Figures 5-15 and 5-16 show the same waveforms displayed on 100 uts and 25 uts

time scales, respectively. As was done with Figure 5-13, all of the waveforms have been

time shifted so that the fast transition occurs at time zero. These plots give an indication

of the variation in waveshapes observed in close first-stroke electric field waveforms.













MSE0410, Station 2


-40 -30 -20 -10
Time, us
MSE0410, Station 5


Time, us
MSE0410, Station 9


-40 -30 -20 -10
Time, us


-10

E -20

U- -30

-40






-6

E -8

'- -10
UJ

-12


-40 -30 -20 -10
Time, is
MSE0410, Station 6








r = 260 m


-40 -30 -20 -10
Time, us
MSE0410, Station 10


-40 -30 -20
Time, us


Figure 5-12. Electric field waveforms, measured at six stations, for the first stroke of
natural flash MSE0410. Each waveform is displayed on a 50 ps time scale.
The estimated distance to the channel is given on each plot.


MSE0410, Station 4










MSE0410, RS1, E-Field

40 -
40 Station 6,260 m -
Station 5, 404 m
Station 2, 447 m
30 Station 9,475 m
-- Station 4, 703 m
: -- Station 10, 794 m

20 -


10-


0

-10 0 10 20 30
Time, us


Figure 5-13. Overlayed first-stroke electric field waveforms for natural flash MSE0410,
displayed on a 50 uts time scale. Each waveform was vertically shifted so
that it would begin with zero amplitude and horizontally shifted so that the
fast transition occurs at time zero.


While some of the waveforms are similar to Figure 5-11 (e.g., MSE0203, MSE0211,

MSE0303, and MSE0409), others are somewhat different (e.g., MSE0404). All of the

waveforms exhibit one or more "humps" in the electric field at times ranging from a few

to several tens of microseconds after the fast transition. These "humps" are also observed

in the waveforms measured at a distance of about 1 km that are presented by Lin et al.

[1979].

Figures 5-17, 5-18, and 5-19 give a selection of first stroke electric field waveforms

measured at distance ranges of 200-300, 300-400, and 400 500 m, respectively.

Figure 5-20 shows the electric and magnetic field waveforms, measured at

Station 9 (about 265 m from the channel), from the first stroke of flash MSE0303.

The slow-front/fast-transition combination is similar in both waveforms, although the

fast transition and peak are better resolved in the magnetic field waveform. This is not

surprising, since the magnetic field has only induction and radiation components, unlike













MSE0404, Station 9, 106 m


MSE0411, Station 6, 147 m


-10
S-20
E
> -30
LL -40
-50






-10
E -20

L -30

-40





0

E -10

L -20

-30


MSE0201, Station 9, 188 m


-50 0
Time, us


50 100


MSE0303, Station 5, 177 m


-50 0 50
Time, Ms
MSE0205, Station 2, 187 m


MSE0409, Station 5, 197 m


-50 0
Time, /s


50 100


Figure 5-14. Electric field waveforms from eight first return strokes, all measured
between 100 and 200 m of the channel. Each waveform is displayed on
a 200 pts time scale, with time zero corresponding the the fast transition of
the waveform. The waveforms are sorted by distance, which is given on
each plot.


-50 0 50
Time, pls
MSE0203, Station 5, 179 m


MSE0211, Station 9, 130 m













MSE0404, Station 9, 106 m


MSE0411, Station 6, 147 m


-10
S-20
E
> -30
L -40
-50





-10
E -20

-30

-40





0

E -10

L -20

-30


E -20

u -30

-40


MSE0201, Station 9, 188 m


0 20 40
Time, us


60 80


MSE0303, Station 5, 177 m









0 20 40 60 80
Time, Ms
MSE0205, Station 2, 187 m


MSE0409, Station 5, 197 m


0 20 40 60 80
Time, /s


Figure 5-15.


Electric field waveforms from eight different first return strokes, all
measured between 100 and 200 m of the channel. Each waveform is
displayed on a 100 uts time scale, with time zero corresponding the the
fast transition of the waveform. The waveforms are sorted by distance,
which is given on each plot.


0 20 40 60
Time, ps
MSE0203, Station 5, 179 m


MSE0211, Station 9, 130 m








186




MSE0404, Station 9, 106 m MSE0211, Station 9, 130 m
-10
-20 -20
E E
> -30 > -30

L -40 -40
-50
-.. . -50
-10 -5 0 5 10 -10 -5 0 5 10
Time, ps Time, /s
MSE0411, Station 6, 147 m MSE0303, Station 5, 177 m

-10 -10

E -20 E
-20
-30 -
L -30
-40
. .. .. ..- -40 -
-10 -5 0 5 10 -10 -5 0 5 10
Time, us Time, Ms
MSE0203, Station 5, 179 m MSE0205, Station 2, 187 m

0 -10

E -10 E -20

-20 -30

-30 -40
....I ....I. ..I ... .. ... .... I.... I.... I
-10 -5 0 5 10 -10 -5 0 5 10
Time, us Time, us
MSE0201, Station 9, 188 m MSE0409, Station 5, 197 m
-20
-15
-30
E E
S-40 -- -20
W W -25
-50 -

-30 ....
-10 -5 0 5 10 -10 -5 0 5 10
Time, Ms Time, /s


Figure 5-16. Electric field waveforms from eight different first return strokes, all
measured between 100 and 200 m of the channel. Each waveform is
displayed on a 25 uts time scale, with time zero corresponding the fast
transition of the waveform. The waveforms are sorted by distance, which is
given on each plot.













MSE0409, Station 2, 222 m


-5
-10
E
S-15
-20
-25
-30








-30
LU -40
-50





0

E -10

-20

-30





-10

-20
E
- -30
-40
-40


MSE0301, Station 6, 291 m


0 20 40 60 80
Time, us


MSE0203, Station 6, 234 m








-- ,, I I I I I
0 20 40 60 80
Time, /s
MSE0410, Station 6, 260 m


MSE0403, Station 4, 294 m


0 20 40 60 80
Time, /s


Figure 5-17. Electric field waveforms from eight different first return strokes, all
measured between 200 and 300 m of the channel. Each waveform is
displayed on a 100 ts time scale, with time zero corresponding the fast
transition of the waveform. The waveforms are sorted by distance, which is
given on each plot.


MSE0211, Station 5, 230 m








-, I . I . I . I . I -
0 20 40 60 80
Time, ls
MSE0303, Station 2, 255 m


MSE0411, Station 5, 217 m













MSE0404, Station 5, 301 m


MSE0201, Station 6, 331 m
. II....I ..I, .I-







, I I I . I . I -
0 20 40 60 80
Time, pls
MSE0301, Station 9, 345 m


MSE0203, Station 9, 378 m


0 20 40
Time, us


60 80


MSE0211, Station 2, 333 m
l- I . I I . I .I I








0 20 40 60 80
Time, /s
MSE0303, Station 6, 345 m


MSE0205, Station 9, 394 m


0 20 40 60 80
Time, /s


Figure 5-18. Electric field waveforms from eight different first return strokes, all
measured between 300 and 400 m of the channel. Each waveform is
displayed on a 100 pts time scale, with time zero corresponding the fast
transition of the waveform. The waveforms are sorted by distance, which is
given on each plot.


MSE0411, Station 9, 311 m













MSE0404, Station 2, 403 m


MSE0211, Station 10, 430 m
. |.I . I . I .I L



I-




0 20 40 60 80
Time, pls
MSE0403, Station 10, 445 m


0

E -10
. -20

-30


MSE0203, Station 4, 477 m


0 20 40
Time, us


60 80


MSE0205, Station 6, 441 m
- I . I . I .I .








0 20 40 60 80
Time, /s
MSE0410, Station 2, 447 m


MSE0401, Station 4, 484 m








., I . I . I . I


0 20 40
Time, /s


60 80


Figure 5-19. Electric field waveforms from eight different first return strokes, all
measured between 400 and 500 m of the channel. Each waveform is
displayed on a 100 pts time scale, with time zero corresponding the fast
transition of the waveform. The waveforms are sorted by distance, which is
given on each plot.


MSE0409, Station 9, 427 m










A MSE0303, RS1, Station 9 B MSE0303, RS1, Station 9
-5
15
1Fast
-10 Peak Transition
E -15 -Transition \
Pulse
5 -
-20

-25 Slow Front 0- Slow Front
-10 -5 0 5 -10 -5 0 5
Time, ps Time, ys

Figure 5-20. First-stroke electric field (A) and magnetic field (B) waveforms for natural
flash MSE0303, displayed on a 20 uts time scale. The waveforms were both
measured at Station 9, which was about 265 m from the channel. Only the
east-west component of the azimuthal magnetic field was measured. The
waveforms were shifted in time so that the fast transition occurs at time
zero.


the electric field which also has an electrostatic component that dominates at close

distances.

Figures 5-21 and 5-22 give a selection of first stroke magnetic field waveforms

measured at distance ranges of 100-300, and 300 400 m, respectively, all displayed on

a 100 ts. The waveforms share similar characteristics, such as multiple humps after the

peak, but there are significant variations in the structure of the waveforms.

Figure 5-23 shows shows the dE/dt waveform measured at Station 8 (126 m from

the channel), from the first stroke of flash MSE0303. The dE/dt waveform exhibits a

slow-front/fast-transition combination similar to that seen in the corresponding E and B

waveforms (Figure 5-20), but exhibits much more fine structure. Specifically, multiple

pulses are superimposed on the slow front portion of the dE/dt waveform. Further, a burst

of pulses is observed immediately prior to the start of the slow front, which apparently

corresponds to a single unipolar pulse observed at the same time in the corresponding

B-field waveform. It is unclear if the burst of pulses is in fact the signature of the last

downward leader step, or the result of a different process. Interestingly, the close first

stroke dE/dt waveform presented here is very similar to the distant first stroke dE/dt











MSE0404, Station 9,106 m
-l .l .







0 20 40 60 80
Time. us
MSE0205, Station 4,168 m

- . I . .






0 20 40 60 80
Time, ps
MSE0303, Station 9,266 m


0 20 40
Time, us


60 80


40

30

ZL 20

10

0


15

S10

5

0


MSE0211, Station 9, 130 m


MSE0201, Station 9,188 m








0 20 40 60 80
Time, ps
MSE0403, Station 4, 294 m








0 20 40 60 80
Time, ps


Figure 5-21. Magnetic field waveforms (east-west component only) from eight
different first return strokes, all measured between 100 and 300 m of the
channel. Each waveform is displayed on a 00 ts time scale, with time zero
corresponding the fast transition of the waveform. The waveforms are sorted
by distance, which is given on each plot.


waveforms (propagated over seawater) that are presented by Murray et al. [2005]. Murray

et al. [2005] observed pulses both immediately prior to and during the slow front, with

the slow front pulses appearing similar to the "dominant" dE/dt pulse (presumably due to

the return stroke), which possibly suggests a common or related generation mechanism.

Further, Murray et al. [2005] noted, as done here, that the exact demarcation between

the slow front and the fast transition is not always apparent in the measured waveforms.

Figures 5-24 and 5-25 give a selection of first-stroke dE/dt waveforms measured at

distance ranges of 70 300 m, displayed on 100 ts and 25 ts time scales, respectively.


20
15
I-
- 10
5
0













MSE0411, Station 9, 311 m


MSE0201, Station 4, 382 m


0 20 40 60
Time, pls
MSE0409, Station 9, 427 m


MSE0205, Station 9, 394 m


6

- 4

2

0




6


MSE0410, Station 9, 475 m


0 20 40
Time, us


60 80


0 20 40 60
Time, /s
MSE0211, Station 4, 463 m


MSE0401, Station 4, 484 m


0 20 40 60 80
Time, /s


Figure 5-22. Magnetic field waveforms (east-west component only) from eight different
first return strokes, all measured between 300 and 400 m of the channel.
Each waveform is displayed on a 100 uts time scale, with time zero
corresponding the fast transition of the waveform. The waveforms are
sorted by distance, which is given on each plot.


6

-4

2

0


MSE0203, Station 9, 378 m









A MSE0303, RS1, Station 8 B MSE0303, RS1, Station 8
25 Peak 25
S25 Fast
S20 Slow Front 20 Transition Peak
E 15 Pulses E to Peak (Saturated)
1 Pulse \ 15 Slow Front
105_ /Burst \ V 10--

0 Slow Front
-10 -5 0 5 -3 -2 -1 0 1
Time, ps Time, /s

Figure 5-23. dE/dt waveform from the first stroke of natural flash MSE0303, displayed
on a 20 uts (A) and a 5 uts (B) time scale. The waveforms were measured
at Station 8, which was about 126 m from the channel. The waveform was
shifted in time so that the peak occurs at time zero. Some features of the
waveforms are labeled.

In addition to the features described above, the dE/dt waveforms also typically

exhibit one or more secondary pulses, occurring a from one to several microseconds

after the dominant pulse. These secondary pulses are smaller in amplitude and longer

in duration than the dominant pulse. Also, bursts of small pulses are often observed

superimposed on or some microseconds after the secondary pulses. Unlike the stepped

leader and slow front pulses (which occur before the dominant pulse), which are

always positive, these pulses are observed to be both positive and negative. An example

illustrating these waveform features is shown in Figure 5-26.

Figure 5-27 shows the north-south and east-west components of dB/dt, measured

at Station 1, at a distance of about 72 m from the first stroke channel of flash MSE0207,

displayed on a 25 uts time scale. Figure 5-28 shows the same waveforms, but displayed

on a 25 ts. Figures 5-29 and 5-30 show Station 1 dB/dt data for flash MSE0207,

measured about 96 m. Overall, the dB/dt waveforms are similar to the dE/dt waveforms

shown in Figures 5-23 through 5-25, including features such as the slow front, fast

transition, secondary peaks after the dominant peak, and small pulses superimposed on

the waveforms both before and after the fast transition pulse.














MSE0203, Station 1, 72 m


0 20 40 60
Time, ,s
MSE0303, Station 8, 126 m


0 20 40 60
Time, us
MSE0410, Station 1, 163 m


a.15

E 10

S5

0 0


MSE0211, Station 1,264 m


0 20 40
Time, ,s


60 80


0 20 40 60
Time, ys
MSE0205, Station 8, 134 m


0 20 40 60
Time, Ms
MSE0201, Station 8, 168 m


MSE0402, Station 8, 283 m


0 20 40
Time, ys


60 80


Figure 5-24.


dE/dt waveforms from eight different first return strokes, all measured
between 70 and 300 m of the channel. Each waveform is displayed on a
100 uts time scale, with time zero corresponding the peak of the waveform.
The waveforms are sorted by distance, which is given on each plot.


(I,
20
E
_ 10

w0


MSE0409, Station 1, 98 m














MSE0203, Station 1, 72 m


(I,
20
E
_ 10

w0


-10 -5 0 5 10
Time, ,s
MSE0303, Station 8, 126 m

25 -
20
15
10
5
0

-10 -5 0 5 10
Time, us
MSE0410, Station 1, 163 m


MSE0211, Station 1,264 m


-10 -5 0 5
Time, ,s


Figure 5-25.


-10 -5 0 5 10
Time, ys
MSE0205, Station 8, 134 m


C 15

E 10

S5
- 0


-10 -5 0 5 10
Time, Ms
MSE0201, Station 8, 168 m


MSE0402, Station 8, 283 m


-10 -5 0 5
Time, ys


dE/dt waveforms from eight different first return strokes, all measured
between 70 and 300 m of the channel. Each waveform is displayed on a
25 uis time scale, with time zero corresponding the peak of the waveform.
The waveforms are sorted by distance, which is given on each plot.


MSE0409, Station 1, 98 m












MSE0303, RS1, Station 8


-2 0 2 4 6 8 10
Time, ps


Figure 5-26.


dE/dt waveform from the first stroke of natural flash MSE0303, displayed
on a 15 ts time scale. The waveforms were measured at Station 8, which
was about 126 m from the channel. The waveform was shifted in time
so that the peak occurs at time zero. The secondary pulse and following
negative pulses are labeled. Note that this is the same dE/dt waveform as
shown in Figure 5-23.


A MSE0203, dB/dt, Station 1, N-S Component B


100 -
80
L 60
40
6 20

-20
-10 -5 0 5 10
Time, ps


OV
- 60
40
m 20


-20
-1


MSE0203, dB/dt, Station 1, E-W Component
100 -


0


-5 0 5 10
Time, ps


Figure 5-27. North-south (A) and east-west (B) components of dB/dt, measured at
Station 1, at a distance of about 72 m from the first stroke channel of flash
MSE0203. Each waveform is displayed on a 25 ts time scale, with time
zero corresponding the peak of the waveform. Note that both waveforms are
slightly saturated.


25

w 20

E 15

S10
-Dt
0O
i 5


0


~c~urc~x


o,,


i
















A MSE0203, Station 1, N-S N .. ....-. B

100
80


S60
40
20
D


120
100


MSE0203, .!L .. S tion 1, EW -i--


80
60
S40
S20
0


-4 -2 0 2 4
Time, as


-4 -2 0 2
Time, fs


Figure 5-28. North-south (A) and east-west (B) components of dB/dt, measured at
Station 1, at a distance of about 72 m from the first stroke channel of flash
MSE0203. Each waveform is displayed on a 10 ts time scale, with time
zero corresponding the peak of the waveform. Note that both waveforms are
slightly saturated.


A r'-Lt' IL -i r ri1 ri .. .,- B


100
80
60
40
20

0 "' ",,. ''
-20


-10 -5 0 5 10
'h, fus


- .J


MSEO2O7, dB/dt, Station 1, E W ~


S60
- 40
, 20


-20
-10 -5 0 5


Figure 5-29. North-south (A) and east-west (B) components of dB/dt, measured at
Station 1, at a distance of about 96 m from the first stroke channel of flash
MSE0207. Each waveform is displayed on a 25 uts time scale, with time
zero corresponding the peak of the waveform. Note that both waveforms are
slightly saturated.



































A M.'Er'"rv' IL. _: i'tiin 1 M Q rn-nnfn~n- B


80
3 60
ib-
^ 40
20
"0


4 -2 0 2 4
Time, us


-4 -2 0 2
Time, fs


Figure 5-30. North-south (A) and east-west (B) components of dB/dt, measured at
Station 1, at a distance of about 96 m from the first stroke channel of flash
MSE0207. Each waveform is displayed on a 10 us time scale, with time
zero corresponding the peak of the waveform. Note that both waveforms are
slightly saturated.









5.4 Measurement of Waveform Parameters

This section describes how waveform parameters were measured from the electric

and magnetic field and field-derivative waveforms obtained by the MSE network. All

waveform parameters were obtained by computer programs which were written by the

author. The programs were interactive, which allowed the user to observe the waveforms

as the parameters were being measured, and the measured parameters were checked

against the displayed waveforms to make sure they were reasonable values. In addition,

a subset of values were compared with values obtained via manual measurement. In

certain cases, the shape of a particular waveform prevented the measurement of a given

parameter.

5.4.1 Electric field waveforms

An illustration of the measured leader electric field change and half-peak width

values is given in Figure 5-31. For each stepped-leader/first-return-stroke sequence

recorded by the MSE network, the asymmetric "V-shaped" electric field waveforms

measured at each station were windowed, with the choice of the beginning of the window

picked so that the field would remain "flat" for a few hundred microseconds or more

(preferably some milliseconds for first strokes) before deflecting from this baseline value.

Typically, the windowed waveforms were then filtered with a moving average filter

having a width of 2 uts in order to minimize noise introduced by the fiber-optic links (note

this smoothing typically removes the fine features of the waveforms, as well as reduces

noise, but preserves the overall leader wave shape). The first 5 uts of each windowed

and filtered waveform were then averaged to obtain the initial value of the field. The

final value of each leader field was obtained by finding the apparent field minimum and

averaging 1 pts of data around that minimum value. The leader field change, AEL, for

each waveform was then calculated by subtracting the initial leader field value, ELinitial,

from the final value field value, EL final.


AEL = ELfinal ELinitial


(5.3)









The half-peak value for each waveform was obtained by dividing AEL by two. The

time indices of all of the data values falling below the half value were then obtained, and

the half-peak width, denoted THPW, was calculated by subtracting the minimum time

index from the maximum time index. This method of estimating the half-peak width

was found to be sensitive to the relative noise level of the waveform, so that applying a

moving average filter to the data beforehand typically results in better half-peak width

estimates. Note that the "peak" in half-peak width is defined here in terms of the leader

field change, not the following return stroke field change, which is discussed below.

The definition of the return-stroke field change, AER, is more ambiguous than the

leader field change when determined from the close field records, since it is difficult

or impossible to differentiate, solely from field records, the field change due to the

return stroke process itself and that due to following flow of continuing current in the

return stroke channel. Further, it is difficult or impossible to discern the exact point

in which the leader ends and the return stroke begins, although the error in this latter

determination is relatively small. Also, it is generally unknown how branches of the

stepped-leader channel affect the overall return stroke field wave shape. Close first stroke

field waveforms are noticeably more complex than those of subsequent strokes, the latter

generally being devoid of branches.

The initial value of the return-stroke field change, ERinitial, is calculated in the same

manner as the final value of the leader field and hence the two quantities are equal.


ER-initial =EL final (5.4)


Since, as noted above, it is difficult to determine the precise end of the return stroke

process from close field records alone, several "final" return-stroke field values are

calculated via the following algorithm (implemented in a computer program). First,

the field value is measured 100 uts after the minimum value of the leader portion of the

waveform and the resulting field change, denoted AE~oo0, is calculated. Next, the point







201





MSE0410, RS1, E-Field, Station 5












0.5 AE

,E _L-final


-10


-5
Time, ms


MSE0410, RS1, E-Field, Station 5


-20


-30

-2.0
-2.0


-1.5 -1.0 -0.5 0.0
Time, ms


Figure 5-31. Example first-stroke electric field waveform illustrating the measured leader
field change parameters. A) Overall electric field waveform on a 20 ms time
scale. B) Expansion of the waveform shown in (A), on a 2.5 ms time scale.


-10









on the waveform equal to 5% of this field change is determined, which typically occurs

at the beginning of the rising portion of the return stroke waveform, within a few to ten

microseconds of the leader's minimum value. Three "final" return-stroke field values are

then measured 20, 100, and 1000 pts from this new point. The corresponding field change

values, AER 20, AER 100, and AER 1000, are then calculated by subtracting ER initial from

the respective final field values. An illustration of the measured return-stroke field change

parameters is given in Figure 5-32. It should be noted that the waveform shown in Figure

5-32B (bottom plot) is similar in shape to the electric field waveforms observed at a

distance of about 1 km by Lin et al. [1979], this being discussed in more detail in Section

5.3.


AER-20 = ER20 -ER initial

ER-100 = ER-100 -ER initial

ER-1000 = ER-1000 -ERinitial (5.5)


5.4.2 dE/dt and dB/dt waveforms

For each of the recorded dE/dt and dB/dt waveforms, the artificial vertical offset

introduced by the fiber-optic links was removed by averaging the first 1000 data points

of the waveform and subtracting this value from the entire waveform. In order to obtain

more precise time estimates, typically the waveforms were interpolated by a factor of

five prior to analysis. If the waveforms were very noisy, a moving average filter was

also applied, with care being taken to preserve the salient characteristics (particularly

the various peak values and rise times) of the waveform. The primary peak value of

each waveform (denoted dEpeak in the case of a dE/dt waveform) was then estimated

by averaging a few samples around the maximum value of the waveform. The inclusion

of digitizer and fiber-optic noise in the waveforms results in an overestimation of the

peak value (with larger percentage overestimation for waveforms having relatively poor

signal-to-noise ratios), thus averaging is performed to minimize the effects of this noise.











MSE0410, RS1, E-Field, Station 5


-0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0
Time, ms


MSE0410, RS1, E-Field, Station 5


-20


-30.1

-0.10


-0.05 0.00 0.05
Time, ms


Figure 5-32. Example first-stroke electric field waveform illustrating the measured return
stroke field change parameters. The top plot (A) shows the three measured
return-stroke field changes and the bottom plot (B) shows in detail the
measurement of the parameter AER 100. The quantity ER 100 is the value of
the electric field at 100 uts from the 5% value of AE 10oo.


-10









After the peak value is calculated, the times corresponding to the 30, 50, and 90 percent

values on the rising-edge of the waveform are calculated, as shown in Figure 5-33 for an

example first stroke dE/dt waveform. Using these values, the half-peak width, THPW, and

30-90% rise time, T30-90, are calculated. The more traditional 10-90 and 20-80 percent

rise times were not calculated, since the inclusion of electronics and digitizer noise, as

well as fine structure (due to lightning processes) superimposed on the waveforms made

estimation of the 10 and 20 percent values difficult.

5.4.3 Magnetic field waveforms

For each of the recorded magnetic field waveforms, the artificial vertical offset

introduced by the fiber-optic links was removed by averaging the first 1000 data points

of the waveform and subtracting this value from the entire waveform. If the waveforms

were very noisy, a moving average filter was also applied, with care being taken to

preserve the salient characteristics (particularly the various peak values and rise times)

of the waveform. The primary peak value of each waveform (denoted BEW,max) was then

estimated by averaging a few samples around the maximum value of the waveform. The

inclusion of digitizer and fiber-optic noise in the waveforms results in an overestimation

of the peak value (with larger percentage overestimation for waveforms having relatively

poor signal-to-noise ratios), thus averaging is performed to minimize the effects of this

noise. The subscript EW in BEW,max indicates that only the east-west component of

the magnetic field was measured, as discussed in Section 2.7. After the peak value is

calculated, the corresponding half-peak width of the waveform, THPW is calculated. An

example illustrating these waveform parameters is given in Figure 5-34A. For some

events, the complex structure of the waveforms did not allow the half-peak widths to be

uniquely identified, as shown in Figure 5-35. In these cases, the waveform parameters

were not measured.

In addition, in cases where the the initial field peak (discussed in more detail in

Section 5.3) could be clearly identified, the amplitude (denoted BEW,i) was measured







205



A MSE0402, RS1, dE/dt, Station 8


15 -- dEpeak
=------n---\3v --


10 0.9dEpeak
E 10

4- ^4-j
S0.5dEPeak
V 5
0.3dEpeak
o ----- -----


-8.0 -7.5 -7.0 -6.5
Time, tps

B MSE0402, RS1, dE/dt, Station 8

PdEpak
15
0.9dEpeak


E 10-
> -0.5dEpeak
.-'




0
-6.6 -6.5 -6.4 -6.3
Time, ps

Figure 5-33. Example first-stroke dE/dt waveform illustrating the measured waveform
parameters. The top plot (A) shows the measured peak value along with the
corresponding 30, 50, and 90 percent values. The bottom plot (B) shows the
measured half-peak width (THPW) and 30-90 percent rise time (730-90).











MSE0303, FS1, B-field. E-W Component, Station 9
1~ : : i


B EWmax


5 J !


0 B .--..'-" -.. -' :

-100 -bO 0 50 100
Time, ,s


MSE0303. RS1, B-field, E-W Component, Slation 9


0 9B1 F ,..


T


0 3 B .,, ,


5F.P: ,
5




0


-10
Time, uS


Figure 5-34. Example first-stroke magnetic field waveform (east-west component only)
illustrating the measured waveform parameters. The top plot (A) shows the
measured maximum peak value (BEW,max) along with the corresponding 50
percent value and the measured half-peak width (THPW) The bottom plot
(B) shows the measured initial peak value (BEW,i) and corresponding 30-90
percent rise time (7i,30-90).


I-

B1











B


;J
z










MSEO411, RS1, B-field, E-W Component, Station 4

2.0 -

1.5 BEW.ma
I--
S1.0

0.5 0 5 BWa,

0.0 .

-20 -10 0 10 20
Time, ps


Figure 5-35. Example first-stroke magnetic field waveform (east-west component
only) illustrating a case where the measured half-peak width (THpw) is
not uniquely identified.


along with the corresponding 30-90% rise time (T30-90). An example illustrating these

waveform parameters is given in Figure 5-34B.

It should be noted that the contribution of the descending leader to the magnetic

field (which occurs prior to the beginning of the slow front) is also included in the

measurement ofBEW,max and BEW,i. However, it has been verified that this contribution

(to the extent that the leader process can be clearly distinguished from the start of the

slow front) is always small compared to the measured values of BEW,max and BEW,i. For

example, the waveform of Figure 5-34B does exhibit a non-zero field prior to the start

of the slow front (assumed to occur at about 11 is), which is presumably due to the

descending leader, but whose amplitude is relatively small compared to the peak value.

Finally, as discussed in Section 5.8, the values BEW,max and BEW,i can be scaled by

the appropriate values in Table 5-2, in order to estimate the total magnetic field (that is,

both the east-west and north-south components).

5.5 Electric Field Waveform Parameters Versus Distance

For each event recorded by the MSE system, the measured waveform parameters

were plotted versus distance and regression analysis was performed on the data. Figures









5-36 and 5-37 give plots of the initial stepped leader electric field change versus distance

for 14 negative first strokes recorded by the MSE system, along with the corresponding

best-fit power-law equations of the form AEL (r) = Arb and coefficients of determination

(R2). Table 5-4 gives the parameters of the stepped leader electric field change power-law

equations, along with the distance ranges over which the equations are strictly valid.

Power-law equations were also obtained for 23 subsequent strokes in 5 natural

flashes. Table 5-5 gives the parameters of the best-fit power-law equations, for both the

first and the subsequent strokes, along with the distance ranges over which the regressions

were calculated, for all of the strokes in the six natural flashes in which both first and

subsequent strokes were recorded. Interesting, the mean value of the exponent for both

first and subsequent strokes is almost exactly -1, a value consistent with a straight and

uniform channel having uniform line charge density. Crawford et al. [2001] showed

that the dart leader electric field change for strokes in rocket-triggered lightning (which

are thought to be similar to natural subsequent strokes) tend to have an r 1 distance

dependence.

Tables 5-6 and 5-7 give the parameters of the power-law equations for 48 strokes in

18 rocket-triggered lightning flashes. The average exponent value is -1.2, which is close

to the value of -1 reported by Crawford et al. [2001] for triggered-lightning strokes, as

well as the average value of-1 reported here for natural first and subsequent strokes.

Figures 5-38 and 5-39 give plots of the stepped-leader/first-return-stroke electric

field half-peak width versus distance for 14 negative first strokes recorded by the MSE

system, along with the corresponding best-fit linear equations of the form THPW(r) =Ar+

b and coefficients of determination (R2). Tables 5-8 through 5-11 give the parameters of

the linear equations for first, subsequent, rocket-triggered strokes, along with the distance

ranges over which the equations are strictly valid. For a single channel descending

downward at a constant velocity, one expects a positive linear correlation with distance.

Indeed, for natural first and subsequent strokes, as well as for strokes in rocket-triggered









Table 5-4. Parameters of the best-fit power-law equations (of the form |AEL(r) = Arb)
for the measured leader electric field change versus distance for 14 natural
negative first strokes. R2 is the coefficient of determination. The equations
were obtained for AEL in kV m 1 and r in meters..


Min. distance
[m]
188
179
166
511
130
291
177
484
294
106
585
197
260
148


Max distance
[m]
382
587
441
1087
463
872
345
966
899
549
993
615
794
588


lightning, this linear dependence with distance is generally observed, although the


equation intercepts often significantly differ from zero.


Flash ID
MSE0201
MSE0203
MSE0205
MSE0209
MSE0211
MSE0301
MSE0303
MSE0401
MSE0403
MSE0404
MSE0407
MSE0409
MSE0410
MSE0411


A
2.33 x 105
4.53 x 104
5.61 x 104
1.27 x 104
5.41 x 102
2.52 x 102
1.36 x 103
9.10 x 104
1.04 x 103
9.43 x 102
2.66 x 105
3.98 x 103
1.59 x 104
1.15x 104


b
-1.60
-1.40
-1.40
-1.00
-0.47
-0.34
-0.68
-1.25
-0.56
-0.69
-1.44
-0.89
-1.05
-1.11


R2
0.72
0.95
0.90
0.86
0.72
0.55
0.54
0.91
0.43
0.78
0.79
0.89
0.86
0.93














Table 5-5. Parameters of the best-fit power-law equations (of the form |AEL(r) = Arb)
for the measured leader electric field change versus distance for 29 strokes
(first and subsequent) in 6 natural negative flashes. R2 is the coefficient of
determination. The equations were obtained for AEL in kV m 1 and r in
meters.


Flash ID
MSE0201


Min.
distance [m]
188


Max
distance [m]
382


MSE0205 166




MSE0211 130


MSE0301 291

MSE0303 177














MSE0401 484


Stroke
order
1
2
3
4
5
1
2
3
4
1
2
3
1
2
1
2
3
4
5
6
7
8
9
10
11
12
1
2
3


2.33 x
1.64 x
9.71 x
5.20 x
1.10 x
5.61 x
3.43 x
8.78 x
5.81 x
5.41 x
1.79 x
4.31 x
2.52 x
2.55 x
1.36x
2.58 x
1.69 x
1.56 x
4.57 x
1.34 x
7.14 x
1.06 x
8.44 x
6.89 x
1.50 x
8.31 x
9.10x
2.64 x
1.68 x


b
-1.60
-1.10
-1.10
-1.20
-1.10
-1.40
-1.60
-1.69
-1.61
-0.47
-0.49
-0.38
-0.34
-0.41
-0.68
-0.80
-0.98
-0.99
-1.06
-0.96
-0.93
-0.98
-0.93
-0.95
-0.96
-0.98
-1.25
-1.25
-1.29


R2
0.72
0.81
0.86
0.90
0.88
0.90
0.91
0.92
0.92
0.72
0.89
0.85
0.55
0.38
0.54
0.78
0.89
0.89
0.91
0.86
0.90
0.89
0.85
0.92
0.87
0.85
0.91
0.94
0.95











Table 5-6. Parameters of the best-fit power-law equations (of the form |AEL(r) = Arb)
for the measured leader electric field change versus distance for 32 strokes in
triggered-lightning flashes FPL0208 through FPL0331 (8 flashes total). R2 is
the coefficient of determination. The equations were obtained for AEL in kV
m 1 and r in meters.


Flash ID
FPL0208


Min.
distance [m]
155


Max.
distance [m]
353


FPL0213 155


FPL0219 155

FPL0221 155














FPL0228 89





FPL0315 155

FPL0321 124




FPL0331 124


Stroke
order
1
2
3
1
2
3
2
3
1
2
3
4
5b
6
7
8
9
10
11
12
1
2
3
4
5
1
2
1
2
3
4
1


A
1.42 x 104
2.46 x 104
1.15x 104
6.53 x 103
5.59 x 103
8.62 x 103
7.53 x 103
3.11 x 103
2.64 x 103
6.20 x 103
2.83 x 103
4.46 x 103
6.38 x 101
1.75 x 103
4.56 x 103
3.53 x 103
5.71 x 103
4.50 x 103
2.00 x 102
4.87 x 103
4.22 x 103
1.60 x 103
1.39 x 103
5.18 x 103
5.49 x 103
5.95 x 102
6.59 x 102
7.56 x 103
3.08 x 104
1.78 x 104
8.72 x 103
3.97 x 103


a) All strokes in triggered-lightning flashes are of subsequent type. b) Possibly
an M-component.


b
-1.42
-1.40
-1.40
-1.20
-1.21
-1.23
-1.24
-1.08
-1.21
-1.27
-1.17
-1.25
-0.70
-1.13
-1.18
-1.19
-1.19
-1.20
-0.84
-1.21
-1.13
-1.06
-1.08
-1.17
-1.13
-0.88
-0.89
-1.39
-1.52
-1.42
-1.35
-1.22


R2
0.97
0.97
0.98
0.75
0.75
0.75
0.96
0.93
0.89
0.90
0.88
0.90
0.66
0.91
0.89
0.92
0.91
0.91
0.80
0.92
0.99
0.99
0.99
0.99
0.99
0.99
0.99
0.98
0.98
0.98
0.98
0.98





















Table 5-7. Parameters of the best-fit power-law equations (of the form IAEL(r) = Arb)
for the measured leader electric field change versus distance for 16 strokes in
triggered-lightning flashes FPL0336 through FPL0403 (5 flashes total). R2 is
the coefficient of determination. The equations were obtained for AEL in kV
m1 and r in meters.

Min. Max. Stroke
Flash ID distance [m] distance [m] order A b R2
FPL0336 120 522 1 1.25 x 104 -1.31 0.98
2 9.88 x 103 -1.34 0.98
3 2.60 x 103 -1.24 0.98
4 8.66 x 103 -1.38 0.98
5 1.36 x 104 -1.38 0.98
6 1.22 x 104 -1.36 0.98
7 9.30 x 103 -1.38 0.98
FPL0350 220 676 1 5.95 x 102 -0.92 0.85
LSA0401 89 353 1 4.52 x 103 -1.21 0.93
2 4.03 x 103 -1.19 0.92
3 3.86 x 103 -1.21 0.93
4 2.57 x 103 -1.16 0.92
LSA0403 89 353 1 5.13 x 102 -0.84 0.98
2 4.39 x 102 -0.91 0.99
FPL0403 89 353 1 6.43 x 102 -0.85 0.98
2 2.82 x 102 -0.81 0.98
a) All strokes in triggered-lightning flashes are of subsequent type.
















MSE0201 Stroke 1


so -. ,, f' -

40 R6 072

30 ....

20
10 -


100 200 300 400
r, m

MSEO205, Stroke 1
70

60 x ... 5.61x10" r4
50 I- \ 2 090 -
40

30 x
20
10


r, m

MhSE0211, Stroke 1


50 -
50 R2 = 0.72

40


30


100 200 300 400
r, m

MSE0303, Stroike 1
60

50




30 -

20


150 200 250 300 350
r, ri


E 40

230

20

10





40


30


> 40
--30

20


MSE0203, Stroke 1


-\~k = It = 4.53x10 r'i"

\ R O = 0.95








00 200 300 400 500 600


MSEO209 Stroke 1


.. = 1.27x10 r

\- R2 = 0O86








00 600 800 1000
r, ri

MSEO301 Stroke 1


S252x100 r-
x R = 0.55








00 400 600 800
r, m

MSE0401, Stroke 1


9.10x104'r'


R2 =0.91


-


400 500 600 700 800 9?00 1000
r, rn


Figure 5-36. Leader electric field change plotted versus distance for the first strokes of

flashes MSE0201, MSE0203, MSE0205, MSE0209, MSE0211, MSE0301,

MSE0303, and MSE0401. Included on each plot is the best-fit power-law

equation of the form |AEL(r)| =Arb along with the corresponding

coefficient of determination (R2).
























60

50


M5E043 Strke I SEWO4O4 Stroke I


H2


0.43


200 400 600 800
r, m

MSE0407 Stroke 1

35 = 610 r" 4 I'




20 -
15
10 -

500 600 700 800 900 1000
r, m

MSE0410, Stroke 1
'60Et I 1 I i',i I


H=0.86


200 300 400


500 600 700 800


60

50

'E 40

130

20

10


100


._--. I -- __ _/_-
200 300 400 500 600
r, m


MSE0409, Stroke 1


0 .8.. I
- -

x


00 200 300 400 500 600
r, m

MSE411, Stroke 1


\ ,.i = -1.15x10' r' -
S= 0.93
4


100 200 300 400
r, m


500 600


Figure 5-37. Leader electric field change plotted versus distance for the first strokes of
flashes MSE0403, MSE0404, MSE0407, MSE0409, MSE0410, MSE0411.
Included on each plot is the best-fit power-law equation of the form |AEL(r)
= Arb along with the corresponding coefficient of determination (R2).


""''''"'""""""""""" '"'"'"''"'"""""


"' I I I "' I -


VMSE0403. StroIke


i


`e


3















MSE0201, Stroke 1


4000 _r--

3000 -

2000

1000 -

0 -


100


'I'









200 300 400
r, ro


MSEO021 1 Stroke 31


r 3114r-1 +1
0.83


00 200 300 400
r, mi

MSE0303, Stroke I













200 250 300 350
r, m


MSE0203 S Itroke
-11
2500


to I

1000-















200 40
500
100 200 300 400 500 600
r, m

MSE021, Stroke 1
1200
1100 T


900 -

800 E-
--
700

600

400 0 600 7 800 1800 1000
r, m

MSE0301, Stroke 1

16


, 1400-


I- 1200


1000

: .... I ............ I ....
200 400 600 800
r, mi

MSE040I1, Stroke 1
2000 .

T- (r) =1.99r -2,

15 P, = 0.86 .



I 1000 -



500-
400 500 600 700 800 900 1000
r, mr


Figure 5-38. Stepped-leader/first-return-stroke electric field half-peak width plotted

versus distance for the first strokes of flashes MSE0201, MSE0203,

MSE0205, MSE0209, MSE0211, MSE0301, MSE0303, and MSE0401.

Included on each plot is the best-fit power-law equation of the form

THPw(r) = Ar+b along with the corresponding coefficient of determination

(R2).


200 300 400
r, m

MSEO205, Stroke I


4000 i

3000




0l
I-
1000 -


0 -

100


1500 -



1000


500

1!


20301


1500


1000
I-

500

























MSE0403,Stroke 1


2000 TH,
T F

S1500

I0




200


1400 :

1200 _

S1000-

r- 800-

600 -

400
500


4000 P-r-


,(r) = 1.84 r + 300
=0.68








400 00 800


MSE407, Stroke 1


600 700 800 900 1000


MSE0410, Stroke 1


2000 -


1000

... ........l.... I .... J ........
200 300 400 500 600 700 800
r, m


1000
4000 m
MSE048, Stroke 1





5000 I
400 ,
3000

2000 -

1000 : -


100 200 300 400 500 600
r, m

MSE040, Stroke 1

5000


4000
I -
-1 3000-

2000 -

",> I .. I I .i . .
100 200 300 400 500 600
r, m

MSE0411, Stroke 1
nno,


4000


in1 30a00



1000 -


100 200 300 400 500 600
r, fT


Figure 5-39. Stepped-leader/first-return-stroke electric field half-peak width plotted

versus distance for the first strokes of flashes MSE0403, MSE0404,

MSE0407, MSE0409, MSE0410, MSE0411. Included on each plot is

the best-fit power-law equation of the form THpw(r) = Ar+b along with the

corresponding coefficient of determination (R2).





-r


I























Table 5-8. Parameters of the best-fit linear equations (of the form THpw(r) = Ar+b) for
the measured stepped-leader/first-return-stroke electric field half-peak width
versus distance for 14 natural negative first strokes. R2 is the coefficient of
determination. The equations were obtained for THPW in uts and r in meters.

Min. distance Min. distance
Flash ID A b R2 [m] [m]
MSE0201 12.4 -2100 0.87 188 382
MSE0203 3.12 -93 0.88 179 587
MSE0205 10.9 -1300 0.99 166 441
MSE0209 0.741 280 0.96 511 1087
MSE0211 3.14 110 0.83 130 463
MSE0301 0.822 850 0.84 291 872
MSE0303 6.39 -700 0.81 177 345
MSE0401 1.99 -280 0.86 484 966
MSE0403 1.84 300 0.68 294 899
MSE0404 7.61 409 0.82 106 549
MSE0407 1.75 -500 0.82 585 993
MSE0409 7.08 640 0.98 197 615
MSE0410 4.73 -530 0.97 260 794
MSE0411 9.30 -1000 0.95 148 588















Table 5-9. Parameters of the best-fit linear equations (of the form THpw(r) = Ar+b) for
the measured leader/return-stroke electric field half-peak width versus distance
for 29 strokes (first and subsequent) in 6 natural negative flashes. R2 is the
coefficient of determination. The equations were obtained for THPW in uts and
r in meters.


Flash ID
MSE0201


Min.
distance [m]
188


Max
distance [m]
382


MSE0205 166




MSE0211 130


MSE0301 291

MSE0303 177













MSE0401 484


Stroke
order
1
2
3
4
5
1
2
3
4
1
2
3
1
2
1
2
3
4
5
6
7
8
9
10
11
12
1
2
3


A
12.4
3.1
0.14
0.41
0.45
10.9
0.63
0.58
0.25
3.14
0.63
-0.31
0.82
2.7
6.39
0.52
0.09
0.11
0.01
0.13
0.17
0.08
0.09
0.17
0.09
0.45
1.99
0.22
0.06


b
-2100
-63
-11
2.7
-54
-1300
-30
-38
-16
110
79
290
850
870
-700
-15
-0.12
0.96
3.5
2.0
0.04
0.30
-2.8
-6.5
-2.1
-24
-280
-12
-3.8


R2
0.87
0.94
0.87
0.95
0.85
0.99
0.96
1.00
1.00
0.83
0.89
0.35
0.84
0.71
0.81
0.98
0.82
0.90
0.90
0.92
0.90
0.84
0.94
0.88
0.91
0.98
0.86
0.92
0.94











Table 5-10.


Parameters of the best-fit linear equations (of the form THpw(r) = Ar+b)
for the measured leader/return-stroke electric field half-peak width versus
distance for 32 strokes in triggered-lightning flashes FPL0208 through
FPL0331 (8 flashes total). R2 is the coefficient of determination. The
equations were obtained for THPW in uts and r in meters.


Flash ID
FPL0208


Min. distance
[m]
155


Max. distance
[m]
353


FPL0213 155


FPL0219 155

FPL0221 155















FPL0228 89





FPL0315 155

FPL0321 124




FPL0331 124


Stroke
order
1
2
3
1
2
3
2
3
1
2
3
4
5b
6
7
8
9
10
11
12
13
1
2
3
4
5
1
2
1
2
3
4
1


A
0.56
0.11
0.14
0.11
0.17
0.17
0.28
1.0
0.19
0.086
0.15
0.073
0.074
0.28
0.048
0.11
0.098
0.073
0.48
0.27
0.45
0.063
0.19
0.57
0.16
0.085
0.19
0.21
0.27
0.094
0.24
0.26
0.29


b
-8.7
-2.1
-5.4
-7.0
-11.9
-11.0
-14.7
-43.2
0.16
1.4
-0.18
4.6
54.5
22.2
1.3
3.1
2.0
2.5
21.5
0.90
37.7
-1.6
-8.9
-28.7
-3.9
-2.3
9.1
-3.1
-7.1
-7.2
-16.8
-21.6
-28.5


R2
0.90
0.88
0.85
0.87
0.79
0.88
0.98
0.99
0.86
0.94
0.91
0.80
0.33
0.78
0.89
0.91
0.94
0.89
0.85
0.90
0.77
1.0
1.0
0.99
1.0
1.0
0.94
0.87
1.0
0.97
0.99
0.99
0.99


a) All strokes in triggered-lightning flashes are of subsequent type. b) Possibly
an M-component.






















Table 5-11.


Parameters of the best-fit linear equations (of the form THpw(r) = Ar+b)
for the measured leader/return-stroke electric field half-peak width versus
distance for 16 strokes in triggered-lightning flashes FPL0336 through
FPL0403 (5 flashes total). R2 is the coefficient of determination. The
equations were found for THPW in uts and r in meters.


Flash ID
FPL0336







FPL0350
LSA0401


Min. distance
[m]
120


220
89


LSA0403 89

FPL0403 89


Min. distance
[m]
522


676
353




353

353


a) All strokes in triggered-lightning flashes are of subsequent type.


Stroke
order
1
2
3
4
5
6
7


A
0.097
0.52
1.0
0.28
0.28
0.39
0.65
1.6
0.16
0.24
0.21
0.31
0.16
0.32
0.097
0.40


b
-7.9
-48.3
-89.9
-32.3
-25.8
-39.8
-62.2
-125.3
-11.4
-16.5
-15.4
-19.5
-8.2
-19.6
-2.0
-7.0


R2
0.98
0.98
0.99
0.96
0.98
0.98
0.98
0.90
0.93
0.92
0.92
0.94
0.90
0.88
0.84
0.81









5.6 Statistics on Measured Stepped Leader and First Return Stroke Electric Field
Waveform Parameters

For a given electric field waveform parameter, the measured values were grouped

into 100 m bins based on distance. For example, all leader electric field change values

obtained from waveforms measured at distances ranging from 100 to 200 m were

grouped into a single bin. Table 5-12 gives information on the distances at which

stepped-leader/first-stroke electric fields were measured. The last bin ranges from

900 1000 m since it contains one value between 1000 and 1100 m. Note that data were

obtained from each stroke at multiple stations. Thus some bins may contain multiple

values from a single stroke.

Statistical characteristics of each of the waveform parameters were calculated for

the data within each bin. Table 5-13 gives statistics on AEL for each distance range.

Tables 5-14, 5-15, and 5-16 give the corresponding statistics on AER 20, AER-100, and

AER 1000, respectively. No electric field data were obtained at distances less than 100 m,

but there were 11 stepped-leader/first-stroke electric field waveforms measured between

106 and 197 m. The closest electric field was measured at a distance of 106 m, with a

corresponding stepped leader electric field change of -53 kV m 1 (the NLDN reported a

return stroke peak current of -13.5 kA). The largest stepped-leader electric field change

was -56 kV m 1 (the leader waveform was slightly saturated), measured at a distance of

168 m from the lightning channel (the NLDN reported a peak current of -14.7 kA).

The mean leader field change in the 100 200 m bin was found to be -41.4 kV m 1

The corresponding return stroke field changes at 20, 100, and 1000 uts were found to be

34.4, 38.8, and 39.5 kV m-1. For the 200-300 and 300 400 m bins, the mean leader

field change decreased to -32.7 and -20.2 kV m-1, respectively, with similar trends

observed for the corresponding return stroke field changes. Interestingly, beyond 400 m,

both the mean leader and the mean return stroke field changes remain relatively steady,

mostly in the range of 15 to 20 kV m-1. The mean values of the leader and return stroke










Table 5-12.






Distance
100 -200
200- 300
300- 400
400 500
500 600
600 700
700 800
800 -900


Statistics on the distances at which stepped-leader/first-stroke electric fields
were measured. The data were sorted by distance into 100 m bins, beginning
with 100 200 m, except for the last bin, which contains one value measured
at a distance greater than 1000 m. All units are meters.


Sample
size
11
16
10
12
11
3
6
4


m
m
m
m
m
m
m
m


900 1100m 8


Geom. St.


Mean
160
261
348
449
548
612
743
850
969


Median
168
267
345
451
543
615
737
849


mean
157
260
346
448
547
612
742
850


965 967


dev.
31
27
30
29
34
5
44
43


Min.
106
217
301
403
506
607
702
804


Max.
197
294
394
484
593
615
794
899


59 901 1087


Table 5-13.







Distance
100 -200n
200 -300n
300 -400n
400 -500n
500 600n
600 -700n
700 800n
800 900n
900 1100


Statistics on the first-stroke stepped leader electric field change, AEL. The
data were sorted by distance into 100 m bins, beginning with 100 200 m,
except for the last bin, which contains one value measured at a distance
greater than 1000 m.


AEL [kVm 1]


n
n
n
n
n
n
n
n
m


Sample
size
11
16
10
12
11
3
6
4
8


Mean
distance [m]
160
261
348
449
548
612
743
850
969


Mean
-41.4
-32.7
-20.2
-22.6
-22.3
-21.9
-20.1
-22.2
-14.3


Median
-42.8
-32.0
-16.3
-20.8
-21.5
-26.2
-18.8
-22.5
-13.8


Geom.
mean
-40.1
-31.3
-18.7
-21.2
-18.7
-20.4
-19.4
-21.6
-14.0


Min.
-26.2
-14.2
-12.1
-11.2
-6.4
-11.8
-12.9
-15.1
-10.7


Max.
-56.2
-49.9
-41.2
-36.7
-43.3
-27.6
-30.3
-28.6
-19.2


electric field changes for each distance range are summarized in Table 5-17, along

with the corresponding mean values of the stepped-leader/first-stroke half-peak width

(discussed below).

Figure 5-40 shows the magnitude of the mean leader field change in each bin

plotted versus the mean distance in each bin. Also given in Figure 5-40 is the best-fit

power law equation of the form EL(r) = Arb, which was found to have an exponent













Table 5-14.


Statistics on the first return stroke electric field change at 20 hts, AER 20. The
data were sorted by distance into 100 m bins, beginning with 100 200 m,
except for the last bin, which contains one value measured at a distance
greater than 1000 m.


AER20 [kVm 1]


Distance
100 -200m
200 -300m
300 -400m
400 500m
500 600m
600 700m
700 800m
800 900m
900 1100m








Table 5-15. St
TI
1(
at




Distance
100 -200m
200 -300m
300 -400m
400 500m
500 600m
600 700m
700 800m
800 900m
900 1100m


Sample
size
11
16
10
12
11
3
6
4
8


Mean
distance [m]
160
261
348
449
548
612
743
850
969


Mean
34.4
25.5
14.9
14.5
16.9
12.7
13.0
7.6
11.7


Median
34.4
25.1
13.2
13.8
15.4
9.1
11.3
7.0
11.9


Geom.
mean
33.0
24.2
13.7
12.7
13.4
9.7
11.4
7.4
11.5


St.
dev.
9.4
8.3
7.1
8.0
12.1
11.0
7.2
2.3
2.3


Min.
17.0
13.1
6.6
6.3
4.7
4.0
5.2
5.8
8.4


Max.
46.4
42.6
32.1
33.6
40.7
25.0
24.4
10.7
14.4


atistics on the first return stroke electric field change at 100 pis, AER 100.
he data were sorted by distance into 100 m bins, beginning with
)0 200 m, except for the last bin, which contains one value measured
a distance greater than 1000 m.

AER100 [kVm 1]


Sample
size
11
16
10
12
11
3
6
4
8


Mean
distance [m]
160
261
348
449
548
612
743
850
969


Mean
38.8
30.8
19.0
22.5
26.5
18.2
20.4
16.4
20.2


Median
39.5
29.2
15.5
22.6
30.6
14.1
20.9
16.3
18.9


Geom.
mean
37.6
29.4
17.6
19.9
20.9
14.6
19.7
15.6
19.9


St.
dev.
9.8
9.7
8.4
11.2
15.9
14.4
5.9
5.8
3.6


Min.
21.6
17.4
9.6
9.4
6.4
6.4
13.5
11.2
16.5


Max.
51.8
47.9
38.6
43.2
51.0
34.2
29.0
21.7
25.2










Table 5-16.


Statistics on the first return stroke electric field change at 1000 pis,
AER-1000. The data were sorted by distance into 100 m bins, beginning
with 100 200 m, except for the last bin, which contains one value measured
at a distance greater than 1000 m.


AERooo1000 [kVm 1]


Distance
100 -200m
200 -300m
300 -400m
400 500m
500 600m
600 700m
700 800m
800 900m
900 1100


Sample
size
11
16
10
12
11
3
6
4
8


Mean
distance [m]
160
261
348
449
548
612
743
850
969


Mean
39.5
33.2
20.7
23.9
25.3
21.5
24.8
21.5
22.6


Median
41.8
31.5
19.4
24.9
30.2
20.6
24.8
21.9
22.0


Geom.
mean
37.9
31.7
19.2
21.2
19.5
17.9
24.4
21.3
22.3


St.
dev.
11.2
10.2
8.8
12.1
17.0
14.4
4.8
2.4
3.7


Min.
21.3
20.0
10.6
10.7
6.9
7.6
17.4
18.3
17.8


Max.
55.5
51.9
40.3
46.0
54.1
36.4
32.1
23.7
28.0


Table 5-17. Summary of the mean values of AEL, AER, and THPW. The data were sorted
by distance into 100 m bins, beginning with 100 200 m, except for the last
bin, which contains one value measured at a distance greater than 1000 m.


Distance
100 -200m
200 -300m
300 -400m
400 500m
500 600m
600 700m
700 800m
800 900m
900 1100m


Sample
size
11
16
10
12
11
3
6
4
8


Mean
AEL AER 100 AER 100 AER 1000 THPW


[kVm-1]
-41.4
-32.7
-20.2
-22.6
-22.3
-21.9
-20.1
-22.2
-14.3


[kVm-1]
34.4
25.5
14.9
14.5
16.9
12.7
13.0
7.6
11.7


[kVm-1]
38.8
30.8
19.0
22.5
26.5
18.2
20.4
16.4
20.2


[kVm-1]
39.5
33.2
20.7
23.9
25.3
21.5
24.8
21.5
22.6


[ms]
0.767
1.15
1.98
2.19
2.14
2.42
1.74
1.48
1.20


of b = -0.45. This is significantly different from the exponent value of-1, which is

indicative of a straight and vertical leader channel having a uniform line charge density

distribution. Crawford et al. [2001] showed that dart leader electric field change for

strokes in rocket-triggered lightning (which are thought to be similar to natural negative

subsequent strokes) tend to have a r 1 distance dependence. However, the stepped leader

channels preceding first return strokes are not likely to be straight and vertical, but rather









First Stroke Leader Field Change
70

60.45
S 60 AE,(r)I =371 r45

S50 R = 0.76
40

S-30

& 20

10

0 200 400 600 800 1000
Mean distance, m

Figure 5-40. Mean leader electric field change plotted versus mean distance within
each 100 m bin. The vertical bars indicate the range of values within each
bin. Also given is the best-fit power law equation and the corresponding
coefficient of determination (R2).

are tortuous with branches. Further, if the branches are located higher up the channel,

the charge distribution will likely be skewed upward relative to a uniformly-charged

channel. This situation is consistent with an exponent smaller in magnitude than -1. As
discussed in Section 5.5, for individual first strokes, the best-fit power-law equations were

found to have exponents ranging from -0.34 to -1.6, with a mean value of-1 (see Table
5-4). Interestingly, lower values of the exponent tend to correspond to lower values of

R2 (the coefficient of determination). If relatively-low equation exponents are a result

of the presence of branches, then this correlation might be expected, since the presence
of branches may also introduce scatter in the leader field change vs. distance plots, thus

lowering the value of R2. It can not be ruled out, however, that the low values of the

exponent and R2 are due to errors in channel location. On the other hand, for at least one
event, flash MSE0303, which has an exponent of -0.68, there is high confidence in the







226

Table 5-18. Statistics on the distances at which stepped-leader/first-stroke electric fields
were measured. The data were sorted by distance into bins of increasing size,
beginning with 100 200 m. All units are meters.

Sample Geom. St.
Distance size Mean Median Mean dev. Min. Max.
100 200m 11 160 168 157 31 106 197
200 400 m 26 294 290 290 51 217 394
400- 800 m 32 554 529 543 112 403 794
800 1100 m 12 929 921 926 78 804 1087


channel location (obtained via a 2-D TOA technique) and distinct channel branches are

observed in video records.

It should be noted that some of the sample sizes in the 100 m bins are very small

(e.g., the 600 700 m bin, having a sample size of 3), with a non-uniform distribution

of distances within those bins. Thus, the statistics within those bins are not likely to be

reliable. In view of this situation, larger, non-uniform, bin sizes were chosen in order

to increase the sample size per bin. The bin sizes were 100 200 m, 200 400 m,

400 800 m, and 800 1100 m. Statistics on the distances within each range are given in

Table 5-18. The leader and return stroke field change statistics for the non-uniform bin

sizes are given in Tables 5-19 through 5-22 and Figures 5-41 and 5-42.

For the non-uniform bin sizes, the best-fit power-law equation on the mean leader

field change has an exponent of -0.50, which is similar to the value of -0.45 found for the

100 m bin size. However, the R2 value of the former (0.99) is larger than that of the latter

(0.76). For the return stroke field changes at 20, 100, and 1000 ts, the equation exponents

are -0.69, -0.40, and -0.32, respectively. It is interesting to note that the value of exponent

is apparently related to the time at which the return stroke field change is measured, with

the magnitude of the exponent decreasing as a function of increasing time.

Table 5-23 gives statistics on the stepped-leader/first-stroke field waveform

half-peak width, THPW, for the 100 m bin size. Interestingly, there is no clear dependence

with distance. In fact, the mean half-peak width increases quasi-linearly from the










Table 5-19.


Statistics on the first-stroke stepped leader electric field change, AEL. The
data were sorted by distance into bins of increasing size, beginning with
100 200 m.


Distance
100 -200m
200 -400m
400 800m
800 1100m


Sample
size
11
26
32
12


Mean
distance [m] Mean
160 -41.4
294 -27.9
554 -22.0
929 -16.9


AEL [kVm 1]
Geom. St.
Median mean dev.
-42.8 -40.1 10.7
-28.3 -25.7 11.1
-20.4 -19.9 9.5
-16.0 -16.2 5.5


Table 5-20. Statistics on the first return stroke electric field change at 20 is, AER 20.
The data were sorted by distance into bins of increasing size, beginning with
100 200 m.


Distance
100 -200m
200 -400m
400 800m
800 1100m


Table 5-21.


Distance
100 -200m
200 -400m
400 800m
800 1100


Table 5-22.


Distance
100 -200m
200 -400m
400 800m
800 1100m


Sample
size
11
26
32
12


Mean
distance [m]
160
294
554
929


Mean
34.4
21.7
14.7
10.4


AER20 [kV m1]
Geom. St.
Median mean dev.
34.4 33.0 9.4
19.8 19.7 9.3
13.7 12.3 9.2
11.1 9.9 3.0


Min.
17.0
6.6
4.0
5.8


Max.
46.4
42.6
40.7
14.4


Statistics on the first return stroke electric field change at 100 pis, AER 100.
The data were sorted by distance into bins of increasing size, beginning with
100 200 m.


Sample
size
11
26
32
12


Mean
distance [m]
160
294
554
929


Mean
38.8
26.6
22.9
18.9


AERoo [kVm 1]
Geom. St.
Median mean dev.
39.5 37.6 9.8
24.8 24.5 10.8
22.6 19.5 12.1
18.9 18.3 4.6


Min.
21.6
9.6
6.4
11.2


Max.
51.8
47.9
51.0
25.2


Statistics on the first return stroke electric field change at 1000 his, AERlooo.
The data were sorted by distance into bins of increasing size, beginning with
100 200 m.


Sample
size
11
26
32
12


Mean
distance [m]
160
294
554
929


Mean
39.5
28.4
24.3
22.2


AER oo [kVm 1]
Geom. St.
Median mean dev.
41.8 37.9 11.2
26.1 26.2 11.3
24.9 20.8 12.8
22.0 22.0 3.3


Min.
21.3
10.6
6.9
17.8


Max.
55.5
51.9
54.1
28.0


Min.
-26.2
-12.1
-6.4
-10.7


Max.
-56.2
-49.9
-43.3
-28.6












First Stroke Leader Field Change


.\EL(r) 494r

R = 0.99


0 200


Figure 5-41








Table 5-23.







Distance
100 -200n
200 -300n
300 -400n
400 -500n
500 600n
600 -700n
700 800n
800 900n
900 1100


400 600 800
Mean distance, rn


1000


SMean leader electric field change plotted versus mean distance within each
non-uniform bin. The vertical and horizontal bars indicate the range of
values within each bin. Also given is the best-fit power law equation and the
corresponding coefficient of determination (R2).




Statistics on the electric field stepped-leader/first-stroke field waveform
half-peak width, THPW. The data were sorted by distance into 100 m bins,
beginning with 100 200 m, except for the last bin, which contains one
value measured at a distance greater than 1000 m.


THPW [ms]


n
n
n
n
n
n
n
n
m


Sample
size
11
16
10
12
11
3
6
4
8


Mean
distance [m]
160
261
348
449
548
612
743
850
969


Mean
0.767
1.15
1.98
2.19
2.14
2.42
1.74
1.48
1.20


Median
0.570
0.980
1.56
1.61
1.18
1.39
1.51
1.51
1.16


Geom.
mean
0.680
1.04
1.77
1.92
1.54
1.82
1.50
1.41
1.18


St.
dev.
0.476
0.589
0.992
1.18
1.70
2.25
1.01
0.476
0.229


Min.
0.393
0.587
0.984
0.715
0.522
0.873
0.668
0.866
0.910


Max.
2.03
2.68
3.67
3.93
4.55
5.00
3.26
2.03
1.57


70

60

50

40


-'1 LI-


















~I-;~ III ~-~'~: :F~i. I.! i '1


0 200 400 600 800 1000
Mean ir r- m



5 0 _


I-, II''-


400 600 800 1000
Sean1 i ,. r- m

i l ioJrr Fi, 1, ,



I0 0I '1Ow









200 400 600 800 1000
Mean. 1,-.i ; : r m


Figure 5-42. Mean return stroke electric field change plotted versus mean distance within
each non-uniform bin. The three plots (A, B, and C) correspond to the
return stroke field changes measured at 20, 100, and 1000 us, respectively.
The vertical and horizontal bars on each plot indicate the range of values
within each bin. Also given is the best-fit power-law equations and the
corresponding coefficients of determination (R2).


E
40

30


50
E
, 40


30
,L
20
10







230

Table 5-24. Statistics on the distances at which first stroke dE/dt waveforms were
measured. The data were sorted by distance into 100 m bins, beginning
with 0 100 m, except for the last bin, which contains one value measured at
a distance greater than 1000 m. All units are meters.

Sample Geom. St.
Distance size Mean Median mean dev. Min. Max.
0- 100 m 4 81 84 79 19 58 98
100 200 m 7 150 163 148 29 106 188
200 300 m 7 271 283 269 34 201 297
300 400 m 7 358 378 356 37 301 394
400 500m 16 454 462 453 28 400 487
500 600 m 7 552 549 551 33 502 587
600 700m 4 662 659 662 27 636 694
700 800 m 5 735 735 735 30 703 769
800 900 m 5 861 867 860 28 829 899
900 1100m 5 982 965 980 63 922 1087


100 200 m bin to a maximum in the 600 700 m bin, then is found to decrease. For a

single channel extending downward at a constant velocity, one expects a positive linear

correlation with distance. Indeed, for individual first strokes, as shown in Section 5.5,

this linear dependence with distance is generally observed, although the best-fit equation

intercepts are all non-zero. It is not clear why an overall positive-linear trend is not

observed in Table 5-23.

5.7 Statistics on Measured First Return Stroke dE/dt Waveform Parameters

For a given dE/dt waveform parameter, the measured values were grouped

into 100 m bins based on distance. For example, all leader electric field change

values obtained from waveforms measured at distances from 100 to 200 m were

grouped into a single bin. Table 5-24 gives information on the distances at which

stepped-leader/first-stroke electric fields were measured. The last bin ranges from

900 1100 m since it contains one value between 1000 and 1100 m. Note that since data

were obtained from each stroke at multiple stations, some bins may contain multiple

values from a single stroke.







231

Table 5-25. Statistics on the first return stroke dE/dt peak. The data were sorted by
distance into 100 m bins, beginning with 0 100 m, except for the last bin,
which contains one value measured at a distance greater than 1000 m. No
scaling factors were applied to the data.

dE/dt peak [kV m 1 ps 1]
Sample Mean Geom. St.
Distance size distance [m] Mean Median mean dev. Min. Max.
0- 100ma 4 81 23.7 26.6 23.1 6.2 16.6 28.0
100 200mb 7 150 14.9 16.6 13.3 7.0 6.3 26.1
200 300m 7 271 10.5 9.3 10.1 3.3 7.2 15.9
300 400m 7 358 4.0 4.3 3.4 2.5 1.2 8.4
400 500m 16 454 4.7 4.4 4.5 1.2 3.1 7.6
500 600m 7 552 3.7 3.1 3.1 1.8 0.7 5.6
600 700m 4 662 4.0 4.1 3.7 1.8 1.8 6.1
700 800 m 5 735 5.4 5.9 5.2 1.5 2.8 6.8
800 900m 5 861 2.0 2.1 1.9 0.8 1.2 3.1
900 1100 m 5 982 2.9 2.3 2.7 1.2 1.7 4.6
a) All dE/dt peaks are saturated. b) Contains two saturated peak values.


Statistical characteristics of each of the waveform parameters were calculated

for the data within each bin. Table 5-25 gives statistics on the measured return stroke

dE/dt peaks, using 100 m bin sizes, as before. Four dE/dt waveforms were measured

between 50 and 100 m, although all of their peak values are saturated, and therefore the

value given for the 0 100 m bin in Table 5-25 should be considered an underestimate.

The closest measured dE/dt waveform was measured at a distance of 58 m, with a

return-stroke peak saturated at 26.6 kV m 1 ts-1. The largest measured return-stroke

dE/dt peak value was saturated at 28 kV m1 ts-1, which was measured at a distance of

72 m.

Unfortunately, as discussed in Section 5.1, there is considerable uncertainty in the

peak values of the dE/dt waveforms. It was observed that, at the two stations (4 and 9) at

which both E and dE/dt were simultaneously recorded, numerically-integrated dE/dt was

always less in amplitude than directly-measured E, with evidence to suggest the problem

is more complex than a simple calibration error. It is impossible to know for certain

whether the E, dE/dt, or both measurements were in error. Unfortunately, there were only







232

Table 5-26. Statistics on the first return stroke dE/dt peak, based only on scaled data
obtained at Stations 4 and 9. The data were sorted by distance into 100 m
bins, beginning with 100 200 m, except for the last bin, which contains one
value measured at a distance greater than 1000 m.

dE/dt peak [kV m 1 s 1]
Sample Mean Geom. St.
Distance size distance [m] Mean Median mean dev. Min. Max.
100 200 m 3 154 14.9 13.9 14.3 5.2 10.2 20.5
200 300m 3 284 10.2 10.3 10.1 1.6 8.4 11.7
300 400m 5 353 7.1 7.9 6.7 2.3 3.2 9.1
400 500 m 7 464 7.3 6.8 6.9 2.6 4.2 10.9
500 600 m 7 552 5.2 4.8 4.3 2.6 0.8 8.6
600 -700m ND ND ND ND ND ND ND ND
700 800 m 2 736 5.2 5.2 5.1 1.0 4.5 5.9
800 900m 2 855 1.8 1.8 1.8 0.1 1.7 1.9
900 1100m 4 989 3.1 3.1 3.0 1.0 2.1 4.3
ND = No data.


two stations at which E and dE/dt were simultaneously recorded, and thus it is impossible

to estimate the accuracy of the amplitudes of the E and dE/dt waveforms measured at

other stations. However, there is some evidence to suggest that the directly-measured

electric field amplitude is correct (within 15 percent or so because of possible local

enhancement due to different terrain at each station) and the dE/dt amplitude is incorrect

(at least at the two stations for which a comparison was made). This supposition comes

from the fact that, for a given stroke, if the stepped-leader electric field change is plotted

versus distance, the result is reasonable (some inverse power-law dependence with

distance), while plots of dE/dt peak versus distance often yield unreasonable results, such

as increasing peak with distance.

Due to the uncertainty in the dE/dt waveform amplitudes, a second set of statistics

was compiled for the return stroke dE/dt peaks, which is given in Table 5-26. While the

first set of statistics was compiled for all of the return stroke dE/dt peak data, obtained

at all four dE/dt stations, with no amplitude scaling, the second set was compiled using

only the data obtained at Stations 4 and 9, with the amplitudes scaled to so that the

integrated dE/dt waveforms match the corresponding E waveforms (see Table 5-1 for a







233

Table 5-27. Statistics on the first return stroke dE/dt half-peak width, THPW. The data
were sorted by distance into 100 m bins, beginning with 100 200 m, except
for the last bin, which contains one value measured at a distance greater than
1000 m. Note that THPW was not calculated for waveforms with saturated
peaks.

THPW [Ls]
Sample Mean Geom. St.
Distance size distance [m] Mean Median mean dev. Min. Max.
100 200m 5 152 0.145 0.130 0.140 0.041 0.095 0.200
200 300m 7 271 0.161 0.153 0.157 0.041 0.116 0.239
300-400m 7 358 0.159 0.137 0.152 0.055 0.103 0.250
400 500m 16 454 0.174 0.170 0.169 0.044 0.124 0.300
500 600m 7 552 0.243 0.244 0.221 0.109 0.118 0.381
600 -700m 4 662 0.270 0.231 0.255 0.113 0.189 0.430
700 800 m 5 735 0.279 0.270 0.273 0.072 0.204 0.397
800 900m 5 861 0.296 0.299 0.285 0.089 0.187 0.420
900 1100 m 5 982 0.323 0.361 0.307 0.102 0.170 0.413


list of scaling factors). Although interpretation of the differences between Tables 5-25

(all data, unsealed) and 5-26 (scaled data only) is not straightforward, due to the smaller

sample size of the latter, it can be seen that the mean dE/dt peak values within each bin

are similar at most distances for the two data sets.

As discussed in Section 6.3, the presence of a finitely conducting ground will

influence the measured dE/dt waveform parameters, including the peak value. Specifically,

the peak value observed over a finitely conducting ground will be less than that observed

for the same field propagating over a perfectly conducting ground. The calculations of

Cooray andMing [1994] indicate that propagation over 1 km of land having conductivity

of 0.001 S m 1 would decrease the peak field derivative by about 70%. Rakov et al.

[1998] report a measured value of 2.5 x 10-4 S m 1 for the soil at the ICLRT, where this

experiment was conducted.

Despite these limitations, it is of interest to compare the dE/dt peak values measured

here with those obtained for first stroke waveforms propagating over tens of kilometers

of seawater by Krider et al. [1996]. Given the relatively high conductivity of seawater ( a

few S m 1), the mean value of about 39 kV m 1 s-1 (all peaks were range-normalized







234

Table 5-28. Statistics on the first return stroke dE/dt 30-90% rise time, T30-90. The data
were sorted by distance into 100 m bins, beginning with 100 200 m, except
for the last bin, which contains one value measured at a distance greater than
1000 m. Note that T30-90 was not calculated for waveforms with saturated
peaks.

T30-90 [LS]
Sample Mean Geom. St.
Distance size distance [m] Mean Median mean dev. Min. Max.
100 200m 5 152 0.244 0.200 0.190 0.187 0.065 0.540
200 300m 7 271 0.142 0.160 0.134 0.045 0.061 0.180
300-400m 7 358 0.171 0.101 0.131 0.138 0.058 0.370
400 500m 16 454 0.229 0.132 0.148 0.287 0.041 1.152
500 600m 7 552 0.605 0.403 0.369 0.562 0.055 1.440
600 -700m 4 662 0.621 0.357 0.318 0.752 0.059 1.710
700 800m 5 735 0.415 0.400 0.387 0.150 0.182 0.553
800 900m 5 861 0.657 0.328 0.375 0.674 0.100 1.600
900 1100 m 5 982 0.807 0.400 0.645 0.617 0.372 1.740


to 100 km assuming a r 1 distance dependence) obtained by Krider et al. [1996]

should be a reasonable representation of first stroke dE/dt radiation fields in the

absence of propagation losses. Using the mean dE/dt peak value in the 100 200 m

bin, 14.9 kV m-1 ts 1, which is the same for both the scaled and unsealed data, and

the mean distance of about 150 m, the peak value range-normalized to 100 km is

22.4 V m-1 ts 1, which is about half the mean value observed by Krider et al. [1996].

However, considering that (1) the sample size of the data presented here is relatively

small, (2) some of the dE/dt waveforms presented here are saturated, and (3) the dE/dt

waveforms presented here were likely attenuated by propagation effects, and (4) the

measurement trigger threshold in these two studies was likely different, there is quite

good agreement between the mean peak value presented here and that given by Krider

etal. [1996].

Tables 5-25 and 5-28 give statistics on the dE/dt half-peak width, THPW, and

30-90% rise time, T30-90, respectively. For the mean half-peak width values, there is

a clear trend of increasing with distance. This result is likely due to the influence of

propagation effects. Return stroke modelling, assuming propagation over a perfectly









conducting ground, predicts an initial decrease in dE/dt width with increasing distance.

This is because, at very close distances (within a few hundred meters), the electrostatic

component of dE/dt is significant relative to the radiation component. As distance

increases, the contribution of the electrostatic component relative to the radiation

component decreases, resulting in a decrease in the width. Observed is an overall trend

of increasing rise time with increasing distance, although there is considerable scatter.

This scatter is possibly due to the presence of the slow front in the dE/dt waveforms (see

Section 5.3). The slow front typically has a duration of a 4 or 5 uts and will influence

the measured dE/dt 30-90% rise times if its amplitude is larger than 30% of the peak

dE/dt value. The slow front in dE/dt is generally more pronounced in closer waveforms,

which may explain why the 100 200 m bin has a larger mean 30-90% rise time than the

following three bins.

Interestingly, for individual first strokes, we often observe little or no discernible

trend in the dE/dt half-peak width and 30-90% rise time versus distance. This may be

because both of these quantities are likely influenced by (1) propagation effects, (2) the

electrostatic component of the field derivative at close distances, and (3) the presence of

the slow front in the dE/dt waveforms. Further, how these factors combine to influence

the return stroke dE/dt waveform parameters is currently not well understood, but return

stroke modelling may yield some insight, as discussed in Chapter 6.

5.8 First Return Stroke Magnetic Field Waveform Parameters

Section 5.4.3 discusses the measurement of the parameters of the magnetic field

waveforms recorded by the MSE system. Table 5-29 lists the measured initial peak

(BEW,i) and maximum peak (BEW,max) values for each of the recorded waveforms, along

with the corresponding estimated distance to the lightning channel. As discussed in

Section 5.4.3, the subscript EW refers to the fact that only the east-west component

of the magnetic field was measured at each station (because only one loop sensor

was used, with the plane of the loop oriented north-south). Section 5.2 discusses the








236

Table 5-29. Initial peak, BEW,i, and maximum peak, BEW,max values of the return stroke
magnetic field waveforms (east-west component only) measured at Stations 4
and 9, for 14 negative first strokes recorded by the MSE system.

Flash ID Station Dist. [m] BEW,I [ptT] BEW,max [ptT]
MSE0201 4 382 5.1 7.9
9 188 6.0 16.9
MSE0203 4 477 2.0
9 378 7.1 13.0
MSE0205 4 168 19.6
9 394 3.9 6.4
MSE0209 4 1087 5.7 10.3
9 543 7.7 16.0
MSE0211 4 463 3.7 6.0
9 130 23.2 36.3
MSE0301 4 872 1.4 3.7
9 345 2.1 5.3
MSEi i- 4 292 10.3 12.7
9 266 11.6 17.5
MISEli4l 4 484 17.7 39.3
9 966 5.7 13.4
MlSEl4 l 4 294 2.7 14.2
9 838 1.3 4.2
MISEi4114 4 549 4.5
9 106 14.2
MI\SE"i47 4 965 12.1 16.4
9 585 24.8 34.5
MlISE"14" 4 483 0.6 1.9
9 427 5.0 6.8
MSE0410 4 703 -
9 475 16.4 21.4
MSE0411 4 520 1.1 2.0
9 311 9.9 12.7


method for estimating the total magnetic field (that is, both the north-south and east-west

components) from a single component, based upon the estimated relative azimuth angle

between the lightning channel and the plane of the loop sensor. The resulting scaling

factors used to estimate the total field from the east-west component are given in Table

5-2.

Table 5-30 gives the magnetic field amplitude values listed in Table 5-29 scaled

by the appropriate factor given in Table 5-2. Also given in Table 5-30 are the measured










Table 5-30.


Parameters of the return stroke magnetic field waveforms measured at
Stations 4 and 9, for 14 negative first strokes recorded by the MSE system.
The quantities Bi and Bmax are the values BEW,i and BEw,max, respectively,
given in Table 5-29, scaled by the appropriate values given in Table 5-2 (in
order to account for the relative orientation between the lightning channel
and the magnetic field loop sensor).


Flash ID Station
MSE0201 4
9
MSE0203 4
9
MSE0205 4
9
MSE0209 4
9
MSE0211 4
9
MSE0301 4
9
M\SEi"il- 4
9
MISEi"4" 4
9
ISE" 4i"i 4
9
MISE"i414 4
9
ISE"i4" 7 4
9
MISE''4'" 4
9
MSE0410 4
9
MSE0411 4
9


Dist. [m]
382
188
477
378
168
394
1087
543
463
130
872
345
292
266
484
966
294
838
549
106
965
585
483
427
703
475
520
311


B, [TT]
7.2
18.1


29.1


5.9
12.3
24.4
8.3
24.1
3.3
21.6
17.7
18.9
17.9
6.8
10.8
2.7


12.8
25.3
3.1
5.0


19.4
18.8
10.2


T,30-90 [ts] Bmax [tT]
0.5 11.1
0.2 50.9
21.4
0.9 53.3
44.9
1.6 9.7
1.8 22.1
1.7 50.7
0.9 13.4
0.8 37.8
8.8
54.6
1.7 21.8
1.8 28.5
0.8 39.7
0.7 15.9
1.5 56.7
1.7 8.6
10.4
-15.9
1.9 17.4
1.9 35.2
2.3 9.9
0.8 6.8


25.3
34.2
13.1


146 0.77
0.55
56 0.78


values of the 30-90% rise time (T7,30-90) and half-peak width (THPW), along with the ratio

of Bi/Bmax.

Although the sample size of the data presented in Table 5-30 is small, it is

nevertheless of interest to tabulate statistics at different distance ranges, as done for the

measured electric field and dE/dt waveform parameters (see Sections 5.6 and 5.7). These


THPW [pIS]
88
24


19
31
72
118
112
46
33
73
6
65
57
67
67
15
21
51
15
129
107
40
55


Bi/Bmax
0.65
0.36


0.55


0.61
0.56
0.48
0.62
0.64
0.38
0.40
0.81
0.66
0.45
0.43
0.19
0.31



0.74
0.72
0.31
0.74







238

Table 5-31. Statistics on the measured parameters of the first return stroke magnetic field
waveforms recorded by the MSE system. The data were sorted by distance
into bins of increasing size, beginning with 100 200 m.

Distance range 100 200 m 200 400 m 400 800 m 800 1100 m
Sample size 4 8 10 5
Geom. Geom. Geom. Geom.
Parameter Mean mean Mean mean Mean mean Mean mean
Dist. [m] 144 148 333 330 501 499 946 942
B, [pT] 21.1 20.9 15.2 13.3 15.3 12.3 7.6 6.3
,30-90 [p-s] 0.5 0.4 1.3 1.2 1.6 1.4 1.5 1.4
Bmax [-T] 37.4 34.2 31.1 24.8 24.7 20.4 14.6 13.6
THPW [ps] 26 25 47 35 78 70 82 69
B,/Bmax 0.50 0.48 0.58 0.54 0.58 0.56 0.48 0.46


statistics are given in Table 5-31. As done for the electric field waveform parameters,

non-uniform bin sizes of 100 200 m, 200 400 m, 400 800 m, and 800 1100 m

were used. Despite the very small sample size per bin, there is apparently some trend with

distance for each of the waveform parameters, with the exception of the ratio of Bi/Bmax,

which appears to be roughly constant at about 0.5. However, few conclusions should be

drawn from such a small data set, and clearly more data are required in order to tabulate

more meaningful statistics.










Charge source



Leader
Channel
PL= const

Hm R(Hm)



R (zt)

Zt V
P


r

Figure 5-43. Illustration of the geometry involved in calculating the electric and magnetic
fields at horizontal distance r from a descending leader (speed v) using the
electrostatic and magnetostatic approximations, respectively. The ground is
assumed to be perfectly conducting.

5.9 Lightning Channel Properties Inferred from Measured Electric Field
Waveforms

5.9.1 Leader model

For the case of a descending leader, the so called "electrostatic" and "magnetostatic"

approximations are valid when the significant wavelengths of the electric and magnetic

fields are much larger than the dimensions of the overall system of the lightning and the

observer. In other words, the maximum difference in propagation time from any source

on the channel to the observer is much less than the time required for significant variation

of the sources. The leader process is often modeled as a spherically-symmetrical cloud

charge source at height Hm that is "drained" by a straight and vertical leader channel

extending at constant speed v and having uniform line charge density PL, as shown in

Figure 5-43. The height zt of the descending leader at time t is Hm vt, and the time T









required for the leader to propagate between cloud and ground is Hm/v. Using this simple

model, the resulting vertical electric field and azimuthal magnetic field on the surface of a

perfectly-conducting ground at distance r from the channel are given by

E(rt) PL 1 1 (Hm- zt)Hm 6)
E (r, t)=(5.6)
2z nr ( l+z?/r2)1/2 ( + H 2)1/2 r2 + H/r2) 3/2


B(r, t) po Hm zt
B (r (r2t+ H=)1/2 (r2 + z,)1/2 i(t) (5.7)

The quantity iL(t) is the current in the leader channel and is assumed to be slowly

varying and the same at all heights along the vertical lightning channel [Uman, 1987]. For
a fully-developed leader touching ground (zt = 0), Equations 5.6 and 5.7 simplify to

z(r L 1 1 (Hm)2 (5.8)
) 2nir (1 +H /r2)1/2 r2(1 +Hm/r2) 3/2



B (r, t) = iL(t) (5.9)

Equations 5.8 and 5.9 can be used to estimate the leader charge density and current

from the measured electric and magnetic fields. The leader line charge density was

estimated in this way by Rubinstein et al. [1995], using electric fields measured at 30
and 500 m and an assumed channel height of 7.5 km (a reasonable value for lightning in

Florida).

For a very close observation point (r < Hm), Equations 5.8 and 5.9 can be further

simplified to

Ez(r) L (5.10)
27 or


PoiL(t)
B (r,t) u (5.11)
27cr









If the leader current is assumed to be a step function (that is, iL(t) = ILU(t), where IL

is a constant), then the leader charge density and velocity are related to the current by


IL = PLV (5.12)

Equation 5.12 gives a simple relationship between leader current, line charge density,

and velocity, provided that all of the above assumptions are valid. Thus, if one is able

to estimate two of the quantities in 5.12, then the third quantity can be readily obtained.

While this technique is admittedly crude, it is useful in providing rough estimates of

leader parameters, as shown by Jerauld et al. [2004] and Kodali et al. [2005] for dart

leaders preceding strokes in rocket-triggered lightning.

5.9.2 Leader charge density, speed, and current inferred from measured electric
field waveforms

In this section, the simple leader model described in Section 5.9.1 is used to

estimate leader line charge densities, speeds, and currents from electric field waveforms

recorded by the MSE system. While this simple model seems to produce reasonable

leader parameters for dart leaders preceding return strokes in rocket-triggered lightning,

indicating that the necessary assumptions are at least somewhat valid, it is not clear how

well it works for stepped leaders preceding first return strokes in natural lightning. The

necessary assumptions are likely to be less valid for initial stepped leaders than dart

leaders, since first stroke channels tend to be more tortuous and contain branches.

For a given electric field waveform, the line charge density was estimated by

using Equation 5.8 and the measured leader electric field change. The channel height

was assumed to be 7.5 km (a reasonable value for lightning in Florida), although the

chosen height did not significantly affect the results obtained from close (on the order of

hundreds of meters) electric field data. As discussed in Chapter 4, the location of each

of the natural lightning channels (and by extension the distance) was estimated using a

2-D time-of-arrival technique. It should be noted that any errors in the location estimates









will result in errors in the calculated leader parameters. For strokes in rocket-triggered

lightning, the distances are known to within a few meters. For a given stroke, the

individual charge density values estimated from the waveforms at different stations

were averaged to obtain a single line charge density estimate for that stroke. For strokes

having a leader field change distance dependence of about r-1, less variation will be

observed between the individual calculated charge density values. This is because the

uniformly-charged leader model predicts a r 1 dependence.

For a given electric field waveform, the leader speed was estimated by using

Equation 5.6 (again assuming a channel height of 7.5 km) and finding a velocity which is

consistent with the measured leader/return-stroke half-peak width. For a given stroke, the

individual speed values estimated from the waveforms at different stations were averaged

to obtain a single leader speed estimate for that stroke.

Finally, for each stroke, Equation 5.12 was used to calculate the leader current

from the estimated leader charge density and speed. The resulting stepped-leader charge

density, speed, and current estimates for 14 natural first strokes are given in Table 5-32.

As shown in Table 5-32, the mean stepped leader line charge density was found to

be -0.69 mC m-1. This is generally consistent with the values reported by others. The

value reported here is on the low end of the range of values (-0.7 to -32 x 10 3 C m 1)

reported by Thomson [1985] for 10 stepped leaders in Florida, although it is in good

agreement with the mean of 1 mC m 1 reported by Proctor [1997] for stepped leaders

in so-called lower-origin flashes (beginning at 1 to 7.4 km above mean sea level), for both

cloud and cloud-to-ground discharges. In calculating the line charge density, it is assumed

that the channel is uniformly charged and has a height of 7.5 km. Using the mean value

of -0.69 mC m 1 reported here and the assumed height of 7.5 km, the average total

channel charge is about -5 C. This value is in reasonable agreement with values reported

by Brook et al. [1962], Krehbiel et al. [1979], and Proctor et al. [1988], as well as being

in very good agreement with the typical value given by Rakov and Uman [2003].









Table 5-32.


243

Stepped-leader charge density (p), speed (v), and current (I = pv) estimates
for 14 natural negative first strokes. For both p and v, the values given are
the means of the values calculated at each station, along with the standard
deviation.


Flash ID p mCm 1] v


MSE0201
MSE0203
MSE0205
MSE0209
MSE0211
MSE0301
MSE0303
MSE0401
MSE0403
MSE0404
MSE0407
MSE0409
MSE0410
MSE0411
Mean
Geom. mean


-0.40 0.13
-0.34 0.07
-0.38 0.10
-0.89 0.14
-0.69 0.19
-1.2 0.44
-0.48 0.08
-1.2 0.15
-1.1 0.36
-0.35 0.13
-1.0 0.16
-0.47 0.07
-0.76 0.13
-0.39 0.06
-0.69 0.33
-0.61


xl105m s-
3.8 2.3
5.6 0.8
3.6 1.7
12.4 0.9
4.6 1.2
6.2 1.4
4.5 0.9
9.5 2.1
6.2 1.3
1.7 1.0
12.7 2.8
1.7 0.1
4.4 1.3
2.9 0.9
5.73.5
4.8


I [kA]
-0.15
-0.19
-0.14
-1.1
-0.31
-0.74
-0.21
-1.1
-0.68
-0.06
-1.3
-0.08
-0.33
-0.11
-0.46
-0.29


The mean speed of 5.7 x 105 m s 1 reported here is somewhat higher than the

typical value of 2 x 105 m s-1, averaged over a few kilometers of channel, but is still

in reasonable agreement, especially considering the very simple model employed here

[Rakov and Uman, 2003]. It should be noted that since the speed estimates presented

here were obtained from relatively close (1 km or less) electric field measurements, they

probably represent the average speed along the bottom kilometer or so of the channel,

as opposed to the average speed along several kilometers of channel. If this is true,

then it might be expected that the average speed reported here be somewhat higher

than the typical value of, 2.5 x 105 m s 1, as there is evidence to suggest that stepped

leaders accelerate as they approach ground [Schonland, 1938; Schonland et al., 1938a,b;

Schonland, 1956; Nagai et al., 1982].

The mean leader current of -0.46 kA reported here is somewhat less than the mean

value of -1.3 kA reported by Krehbiel [1981], obtained via multiple-station electric field








244


A 1.4 B
15
1.2 x x
1.0 x
X 7I 1.
E 0.8 x
E 0,6 0 ,
0.6
0 x -
0.4 X x p = 0.0045 INLDN + 0.54 x = 0.082 1NLN + 2.76
0.2 R' = 0.22 x R2 = 0.67
0.0 0
0 20 40 60 80 100 120 140 2 4 6 8 10 120 1
NLDN Peak Current, kA NLDN Peak Current, kA
C D 1.4 i-

1.5 1.2 X X
Sx 1.0 x
x
1.0 -C- 0.8

0.6
w 0.5 x
x I. 0.00941 +0.12 X p= 0.062 V + 0.34
00R2 = 0.55 0.2 R = 0.42
0.0
I I I, I, I ,I , I , I ,,I, I I 0 .0 I 1 2 1 1 1 4 1 1 1 I6 1 1 1 0 1 1 1 2 1
0 20 40 60 80 100 120 140 2 4 6 8 10 12
NLDN Peak Current, kA v, x105 m s"


Figure 5-44. Estimated leader (A) charge density, (B) velocity, and (C) current, each
plotted versus the NLDN-reported return stroke peak current, for 13
negative first strokes. NLDN current was not available for one event
(MSE0404). (D) is a scatter plot of estimated charge density versus velocity.
Also given on each plot is the best-fit linear equation and corresponding
coefficient of determination (R2). Note that for simplicity the charge density
and current values are presented as positive values.


measurements in Florida, but is in reasonable agreement with typical value of -100 to

-200 A given by [Rakov and Uman, 2003].

Figure 5-44 gives plots of the estimated parameters versus NLDN-reported return

stroke peak current, as well as a plot of the estimated charge density versus estimated

speed. The best-fit linear equation is included on each plot. Both the estimated leader

velocity and current are moderately correlated with NLDN peak current (R2 values of

0.67 and 0.55, respectively). Somewhat surprisingly, the correlation between estimated

charge density and NLDN peak current is relatively poor, having an R2 value of 0.22.

If a single data point corresponding to an NLDN peak current of about 140 kA is

removed, the correlation improves somewhat (R2 increases to 0.38). However, there is no







245

Table 5-33. Subsequent-leader c