Table Of ContentA STUDY OF CLOUD-TO-GROUND LIGHTNING PROCESSES WITH EMPHASIS ON
DATA ANALYSIS AND MODELING OF THE RETURN STROKE
By
RAJEEV THOTTAPPILLIL
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
1992
UtMVERSITY Or FLORIDA LIBRIKSS
ACKNOWLEDGEMENTS
Writing the acknowledgements is one ofthe most difficulttasks in a dissertationbecause
in a period ofa few years one intellectually interacts with colleagues and other researchers under
various circumstances, and it is often difficult to recollect which person or which conversation
has helped in formulating an idea reported in the dissertation. My case is no different from this
general rule, and my apologies are extended to anyone whose contribution might have gone
unacknowledged in this dissertation. I am certain that it was the inspiring leadership of Dr.
Martin A. Uman and the constant companionship of Dr. Vladimir A. Rakov and Dr. Marcos
Rubinstein that enabled me to complete the research successfully. I am indebted to Dr. Uman
for giving proper direction to the research and setting it on course whenever I tended to go
wayward. The dedication, scholarship, and thoroughness ofDr. Rakov was an example to me.
I consider the hilarious, at the same time intellectually stimulating, Friday lunches at Sonny’s
with Dr. Douglas M. Jordan as an integral part ofmy research work. Dr. Ewen M. Thomson’s
critical comments have helped me in improving this dissertation. It was Dr. Gerhard Diendorfer
who introduced me to return stroke modeling. I think it was Dr. Rakov who first suggested to
me the idea of comparing return stroke models using simultaneously measured current and
electric field data. I thank Dr. D. K. McLain for the help he has given in generalizing the
Diendorfer-Uman model and Mr. JamieStonefor enhancing my computer literacy. I am grateful
to Dr. J. C. Willettforprovidingthesimultaneoustriggered lightningreturn strokecurrent, field,
and speed data used in Chapters 5, 6, and 7, and to Mr. R. J. Fisher and Mr. G. H. Schnetzer
11
of Sandia National Laboratories and Mr. William Jafferis ofthe NASA Kennedy Space Center
for providing the triggered lightning data used in Chapter 4. My wife Ranjana and son Rohith
have showngreat understandingand patience during thepreparation ofthis manuscript, and I am
very thankful to them.
Ill
1
TABLE OF CONTENTS
sage
ACKNOWLEDGEMENTS
ii
LIST OF FIGURES vi
LIST OF TABLES xv
ABSTRACT xvi
INTRODUCTION
1 1
2 CRITICAL REVIEW OF LITERATURE 4
2.1 Natural Lightning 4
2.1.1 Current Measurements 7
2.1.2 Electric and Magnetic Field Measurements 9
2.1.3 Photographic Measurements 14
2.2 Triggered Lightning 16
2.2.1 Current Measurements 16
2.2.2 Field Measurements 18
2.2.3 Photographic Measurements 18
2.3 Comparison ofTriggered and Natural Lightning 19
2.4 Return Stroke Models 21
M
2.5 Modeling of Continuing Currents and Components 31
3 EXPERIMENTAL DATA USED 35
3.1 Natural Lightning Data 35
3.2 Triggered Lightning Data from the Sandia National Laboratories 37
3.3 Triggered Lightning Data of Willett et al. (1988, 1989) from the NASA
Kennedy Space Center 39
4 ANALYSIS OF EXPERIMENTAL DATA 45
4. Natural Lightning 45
IV
4.1.1 Subsequent-Stroke Peak Greater than the First-Stroke Peak 46
4.1.2 Spatial Separation ofthe Flash Ground Terminations 54
4.2 4.1.3 Discussion 56
Triggered Lightning 59
4.2.1 Return Stroke Current Parameters 59
M
4.2.2 Interstroke Intervals, Continuing Currents, and Components . . 60
4.2.3 Discussion 62
5 COMPARISON OF PREVIOUS RETURN-STROKE CURRENT MODELS 80
5.1 Comparison of Models Reviewed in Section 2.4 82
5.2 Discussion 92
6 GENERALIZATION OF THE DIENDORFER-UMAN MODEL 136
6.1 Mathematical Analysis for Single Channel Discharge Time Constant .... 137
6.2 Application 142
6.3 Comparison With Other Models for Triggered Lightning 145
6.4 Summary and Discussion 148
A NEW CHANNEL DISCHARGE MODEL WITH HEIGHT-VARIABLE TIME
7
CONSTANT 164
7.1 Mathematical Analysis 165
7.2 Application 170
8 MODELING OF CONTINUING CURRENTS AND M COMPONENTS 178
8.1 Theory 178
8.2 Application 181
8.3 Discussion 185
9 SUMMARY AND CONCLUSIONS 200
APPENDICES 205
A LIST OF JOURNAL AND CONFERENCE PAPERS DEVELOPED AS
PART OF THIS Ph.D. DISSERTATION WORK 206
B COMPUTER PROGRAM LISTINGS 207
REFERENCES 229
BIOGRAPHICAL SKETCH 237
V
LIST OF FIGURES
Figure 2-1. Geometry used in deriving the field equations given in equations (2-1) and
(2-2) 34
Figure 4-1. Histogram of subsequent-stroke initial electric field peak for 46 natural
lightning flashes recorded near Tampa, Florida 49
Figure 4-2. Histogram ofthe ratio of subsequent-stroke field peak to the first stroke
field peak 50
Figure 4-3. Histogram ofthe interstroke interval duration 51
Figure 4-4. Histogram ofsubsequent leader duration 52
Figure 4-5. Histogram of the distance between the multiple terminations of 22
individual ground flashes recorded near Tampa, Florida 55
Figure 4-6. Example of a triggered lightning return stroke current waveshape with
relativelyfast risetime recorded at Ft. McClellan, Alabama, a) Waveform
on a longer time scale; b) The front portion on an expanded time scale. 65
. .
Figure 4-7. Example of a triggered lightning return stroke current waveshape with
relatively slow rate-of-rise at the beginning and a fast rate-of-rise near the
peak recorded at Ft. McClellan, Alabama, a) Waveform on a longer time
scale; b) The front portion on an expanded time scale 66
Figure 4-8. Example of a triggered lightning return stroke current waveshape with a
slowly rising ramp at the beginning recorded at Ft. McClellan, Alabama,
a) Waveform on a longer time scale; b) The front portion on an expanded
time scale 67
Figure 4-9. Histogram of return-stroke peak current for triggered lightning 68
Figure 4-10. Histogram of return-stroke current rise time for triggered lightning 69
Figure 4-11. Scatter plot of return-stroke peak current vs. rise time for triggered
lightning 70
Figure 4-12. Example ofthe current record of a 10 stroke flash 71
VI
Figure 4-13. Portion ofthe flash between the arrows shown in Figure 4-12 72
Figure 4-14. Example of an M-current pulse waveshape 73
Figure 4-15. Histogram of interstroke interval for triggered lightning 74
Figure 4-16. Histogram of stroke duration including continuing current for triggered
lightning 75
Figure4-17. Histogramoftheportionofinterstroke interval at which currentflow is not
detected 76
Figure 4-18. Histogram of M-current rise time 77
Figure 4-19. Histogram of M-current duration 78
Figure 4-20. Histogram of M-current interval 79
Figure 5-1. Geometrical parameters used in the models 98
Figure 5-2. Current waveform for return stroke 8705_1 from triggered lightning at
KSC, 1987. a) Total available waveform; b) The wavefront on an
expanded scale 99
Figure 5-3. Current waveform for return stroke 8705_3. a) Total available waveform;
b) The wavefront on an expanded scale 99
Figure 5-4. Current waveform for return stroke 8705_5. a) Total available waveform;
b) The wavefront on an expanded scale 100
Figure 5-5. Current waveform for return stroke 8705 6. a) Total available waveform;
b) The wavefront on an expanded scale 100
Figure 5-6. Current waveform for return stroke 8715 2. a) Total available waveform;
b) The wavefront on an expanded scale 101
Figure 5-7. Current waveform for return stroke 8715 3. a) Total available waveform;
b) The wavefront on an expanded scale 101
Figure 5-8. Current waveform for return stroke 8715_4. a) Total available waveform;
b) The wavefront on an expanded scale 102
Figure 5-9. Current waveform for return stroke 8715_6. a) Total available waveform;
b) The wavefront on an expanded scale 102
Figure 5-10. Current waveform for return stroke 8715 7. a) Total available waveform;
b) The wavefront on an expanded scale 103
••
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Figure 5-11. Current waveform for return stroke 8715 8. a) Total available waveform;
b) The wavefront on an expanded scale 103
Figure 5-12. Current waveform for return stroke 8715 9. a) Total available waveform;
b) The wavefront on an expanded scale 104
Figure 5-13. Current waveform for return stroke 8715_10. a) Total available
waveform; b) The wavefront on an expanded scale 104
Figure 5-14. Current waveform for return stroke 8717_3. a) Total available waveform;
b) The wavefront on an expanded scale 105
Figure 5-15. Current waveform for returnstroke 8717_5. a) Total available waveform;
b) The wavefront on an expanded scale 105
Figure5-16. Current waveform for return stroke 8725 1. a) Total available waveform;
b) The wavefront on an expanded scale 106
Figure 5-17. Current waveform for return stroke 8725 2. a) Total available waveform;
b) The wavefront on an expanded scale 106
Figure5-18. Current waveform for return stroke 8725 3. a) Total available waveform;
b) The wavefront on an expanded scale 107
Figure 5-19. Current waveform for return stroke 8725 4. a) Total available waveform;
b) The wavefront on an expanded scale 107
Figure 5-20. Current waveform for return stroke 8725 5. a) Total available waveform;
b) The wavefront on an expanded scale 108
Figure 5-21 Current waveform for return stroke 8725 4. a) Total available waveform;
.
b) The wavefront on an expanded scale 108
Figure 5-22. Current waveform for return stroke 8726_2. a) Total available waveform;
b) The wavefront on an expanded scale 109
Figure 5-23. Current waveform for return stroke 8726 3. a) Total available waveform;
b) The wavefront on an expanded scale 109
Figure 5-24. Current waveform for return stroke 8726_4. a) Total available waveform;
b) The wavefront on an expanded scale 110
Figure 5-25. Current waveform for return stroke 8726_5. a) Total available waveform;
b) The wavefront on an expanded scale 110
Figure 5-26. Current waveform for return stroke 8728 10. a) Total available
waveform; b) The wavefront on an expanded scale Ill
Vlli
Figure 5-27. Current waveform for return stroke 8728_11. a) Total available
waveform; b) The wavefront on an expanded scale Ill
Figure 5-28. Current waveform for return stroke 8732_1 a) Total available waveform;
.
b) The wavefront on an expanded scale 112
Figure 5-29. Current waveform for return stroke 8732_2. a) Total available waveform;
b) The wavefront on an expanded scale 112
Figure 5-30. An example of comparison of electronically integrated and numerically
integrated return stroke electric field waveforms, a) Overall waveform; b)
The front portion on an expanded scale 113
Figure5-31 Comparison ofcalculated fieldsfrom thevarious models withthe measured
.
field at 5.16 km for the return stroke 8705_1. The measured current at
the channel base and the measured return stroke speed are given in Figure
5-2. a) TL model; b) MTL model; c) TCS model; d) DU model 114
Figure5-32. Comparisonofcalculated fields from the various models with themeasured
field at 5.16 km for the return stroke 8705_3. The measured current at
the channel base and the measured return stroke speed are given in Figure
5-3. a) TL model; b) MTL model; c) TCS model; d) DU model 115
Figure5-33. Comparison ofcalculated fields from thevarious models with the measured
field at 5.16 km for the return stroke 8705_5. The measured current at
the channel base and the measured return strokespeed are given in Figure
5-4. a) TL model; b) MTL model; c) TCS model; d) DU model 116
Figure5-34. Comparisonofcalculated fields from the various models withthe measured
field at 5.16 km for the return stroke 8705_6. The measured current at
the channel base and the measured return stroke speed are given in Figure
5-5. a) TL model; b) MTL model; c) TCS model; d) DU model 117
Figure5-35. Comparison ofcalculated fieldsfrom the various models with themeasured
field at 5.16 km for the return stroke 8715_9. The measured current at
the channel base and the measured return stroke speed are given in Figure
5-12. a) TL model; b) MTL model; c) TCS model; d) DU model 118
Figure5-36. Comparisonofcalculated fields from thevarious models withthe measured
field at 5.16 km for the return stroke 871510. The measured current at
the channel base and the measured return strokespeed are given in Figure
5-13. a) TL model; b) MTL model; c) TCS model; d) DU model 119
Figure5-37. Comparison ofcalculated fieldsfrom thevarious models with themeasured
field at 5.16 km for the return stroke 8725_1. The measured current at
the channel base and the measured return stroke speed are given in Figure
5-16. a) TL model; b) MTL model; c) TCS model; d) DU model 120
IX
Figure5-38. Comparison ofcalculated fieldsfrom thevarious models withthe measured
field at 5.16 km for the return stroke 8725_2. The measured current at
the channel base and the measured return stroke speed are given in Figure
5-17. a) TL model; b) MTL model; c) TCS model; d) DU model 121
Figure5-39. Comparisonofcalculated fields from thevariousmodels withthe measured
field at 5.16 km for the return stroke 8725_3. The measured current at
the channel base and the measured return stroke speed are given in Figure
5-18. a) TL model; b) MTL model; c) TCS model; d) DU model 122
Figure5-40. Comparison ofcalculated fields from thevarious models withthe measured
field at 5.16 km for the return stroke 8725_5. The measured current at
the channel base and the measured return stroke speed are given in Figure
5-20. a) TL model; b) MTL model; c) TCS model; d) DU model 123
Figure 5-41 Comparisonofcalculated fields from thevarious models withthe measured
.
field at 5.16 km for the return stroke 8726_1. The measured current at
the channel base and the measured return stroke speed are given in Figure
5-21. a) TL model; b) MTL model; c) TCS model; d) DU model 124
Figure5-42. Comparison ofcalculated fieldsfrom thevarious models withthemeasured
field at 5.16 km for the return stroke 8726_2. The measured current at
the channel base and the measured return stroke speed are given in Figure
5-22. a) TL model; b) MTL model; c) TCS model; d) DU model 125
Figure5-43. Comparison ofcalculated fields from thevarious models withthe measured
field at 5.16 km for the return stroke 8726_3. The measured current at
the channel base and the measured return stroke speed are given in Figure
5-23. a) TL model; b) MTL model; c) TCS model; d) DU model 126
Figure 5-44. Comparison ofcalculated fieldsfrom thevarious models with the measured
field at 5.16 km for the return stroke 8726_4. The measured current at
the channel base and the measured return stroke speed are given in Figure
5-24. a) TL model; b) MTL model; c) TCS model; d) DU model 127
Figure5-45. Comparisonofcalculated fieldsfrom thevarious models with the measured
field at 5.16 km for the return stroke 8728_10. The measured current at
the channel base and the measured return stroke speed are given in Figure
5-26. a) TL model; b) MTL model; c) TCS model; d) DU model 128
Figure5-46. Comparisonofcalculated fieldsfrom thevarious models with the measured
field at 5.16 km for the return stroke 8728_11. The measured current at
the channel base and the measured return stroke speed are given in Figure
5-27. a) TL model; b) MTL model; c) TCS model; d) DU model 129
Figure5-47. Comparison ofcalculated fields from the various models withthe measured
field at 5.16 km for the return stroke 8732 1. The measured current at
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