TRIGGERED-LIGHTNING PROPERTIES INFERRED FROM MEASURED...

TRIGGERED-LIGHTNING PROPERTIES INFERRED FROM MEASURED

CURRENTS AND VERY CLOSE MAGNETIC FIELDS

By

ASHWIN B. JHAVAR

A THESIS PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT

OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE

UNIVERSITY OF FLORIDA

2005

Copyright 2005

by

Ashwin B. Jhavar

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ACKNOWLEDGMENTS

I would like to thank Dr. Vladimir A. Rakov for his infinite patience, guidance, and

support throughout my graduate studies at the University of Florida. I would like to thank

Dr. Martin A. Uman and Dr. Douglas M. Jordan for their valuable suggestions during the

weekly lightning meetings. I sincerely thank Jens Schoene, Jason Jerauld, Rob Olsen,

Brian DeCarlo, and Vinod Jayakumar for helping me with the data and software, and for

other innumerable favors (without which I would not have been able to complete my

thesis). Research in my thesis was funded in part by National Science Foundation. The

data analyzed in the thesis were originally acquired with NSF and FAA funding.

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TABLE OF CONTENTS page

ACKNOWLEDGMENTS ................................................................................................. iii

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

LIST OF FIGURES .......................................................................................................... vii

ABSTRACT..................................................................................................................... xiii

CHAPTER

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

2 LITERATURE REVIEW .............................................................................................3

2.1 Cumulonimbus........................................................................................................3 2.2 Cloud Charge Distribution......................................................................................4 2.3 Mechanisms of Cloud Electrification .....................................................................6

2.3.1 Convection Mechanism. ...............................................................................7 2.3.2 Graupel-ice Mechanism................................................................................7

2.4 Downward Negative Lightning Discharges to Ground ........................................10 2.5 Artificial Initiation (Triggering) of Lightning Using the Rocket-and-Wire

Technique...............................................................................................................15 2.5.1 Classical Triggering....................................................................................16 2.5.2 Altitude Triggering.....................................................................................18

2.6 Previous Studies of Displacement Current Associated with Triggered Lightning................................................................................................................19

2.6.1 Theory.........................................................................................................19 2.6.2 Estimation of Displacement Current Contribution at 50 m........................21

3 CHARACTERIZATION OF EXPERIMENTAL DATA USED IN THIS STUDY .25

3.1 Magnetic Field Measuring Techniques ................................................................25 3.2 Experimental Setup...............................................................................................27

3.2.1 ICLRT Overview........................................................................................27 3.2.2 1997 Experiments .......................................................................................29 3.2.3 1999 Experiments .......................................................................................30

3.2.3.1 Instrumentation for Current Measurements .....................................32 3.2.3.2 Instrumentation for Electric Field Measurements ............................33

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3.2.3.3 Instrumentation for Electric Field Derivative Measurement............33 3.2.4 2000 Experiments .......................................................................................33 3.2.5 2001 Experiments .......................................................................................35

3.3 Data Presentation ..................................................................................................36 3.3.1 General Information ...................................................................................36 3.3.2 Channel-base current ..................................................................................40 3.3.3 Magnetic Field............................................................................................42 3.3.4 Electric field derivative (dE/dt) ..................................................................47

4 ESTIMATION OF LEADER AND RETURN-STROKE CURRENTS FROM MEASURED MAGNETIC FIELDS..........................................................................51

4.1 Introduction...........................................................................................................51 4.2 Estimation of Currents Using Ampere’s Law ......................................................51 4.3 Discussion and Summary .....................................................................................77

5 DISPLACEMENT CURRENT ASSOCIATED WITH LEADER/RETurN STROKE SEQUENCES IN TRIGGERED LIGHTNING.........................................80

5.1 Displacement Current Estimates from Measured Magnetic Fields and Channel-Base Currents ..........................................................................................80

5.2 Displacement Current Estimates from dE/dt Signatures at 15 and 30 m .............92 5.3 Discussion and Summary ...................................................................................106

6 SUMMARY..............................................................................................................108

7 RECOMMENDATIONS FOR FUTURE RESEARCH ..........................................112

APPENDIX DISPLACEMENT CURRENT GRAPHS.................................................113

LIST OF REFERENCES.................................................................................................144

BIOGRAPHICAL SKETCH ...........................................................................................147

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LIST OF TABLES

Table page 2-1 Displacement currents Id estimated from measured electric field data at times

prior to and at the onset of a 20 kA peak stroke current. .........................................22

3-1 Summary of mean, standard deviation, GM (geometric mean), and sample sizes of measured peak current, peak magnetic field and electric field derivative ...........37

5-1 Displacement currents estimated using eq. 5.4 (step-wise approximation of dE/dt distance dependence) and eq. 5.5 (linear approximations of dE/dt distance dependence)..............................................................................................................95

5-1 (Contd.) Displacement currents estimated using eq. 5.4 (step-wise approximation of dE/dt distance dependence) and eq. 5.5 (linear approximations of dE/dt distance dependence)..................................................................................96

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LIST OF FIGURES

Figure page 2-1 An isolated thundercloud in central New Mexico, with a rudimentary indication

of how electric charge is thought to be distributed inside and around the thundercloud, as inferred from the remote and in situ observations.. ........................5

2-2 Balloon measurements of corona current and the inferred vertical electric field E versus altitude and air temperature inside a small storm in New Mexico on 16 August 1981, which produced no lightning. ..............................................................6

2-3 Illustration of the convection mechanism of cloud electrification. ............................8

2-4 Charge transfer by collision in the graupel-ice mechanism of cloud electrification. It is assumed that the reversal temperature TR is -15 oC and that it occurs at a height of 6 km. ......................................................................................9

2-5 A vertical tripole representing the idealized gross charge structure of a thundercloud such as that shown in Figure 2-1; the negative screening layer charges at the cloud top and the positive corona space charge produced at ground are ignored here............................................................................................10

2-6 Various processes comprising a negative cloud-to-ground lightning flash. ............11

2-7 Sequence of events in classical triggered lightning. The upward positive leader and initial continuous current constitute the initial stage. ........................................16

2-8 Sequence of events in altitude-triggered lightning leading to the establishment of a relatively low-resistance connection between the upward-moving positive leader tip and the ground. The processes that follow the sequence shown, an initial continuous-current and possibly one or more downward-leader--upward-return-stroke sequences, are similar to their counterparts in classical triggered lightning. The rocket speed is of the order of 102 m s-1. ..........................................18

2-9 Qualitative illustration of the shape of the time derivative of the ground level vertical electric field of a nearby return stroke . Since displacement current density is simply related to the derivative of electric field by a constant, it has the same waveshape.. ...............................................................................................24

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2-10 From top to bottom, magnetic field measured at 50 m during stroke 5 of Flash 96-23, the corresponding field according to Ampere’s law for magnetostatics, as applied to the measured channel-base current, and the difference between the two.. ..........................................................................................................................24

3-1 Thevenin equivalent circuit of a loop antenna .........................................................25

3-2 Norton equivalent circuit for a loop antenna............................................................26

3-3 An overview of the ICLRT at Camp Blanding, Florida, 1999-2001. Not all test objects are shown. ....................................................................................................28

3-4 Photograph of lightning flash S0012 triggered from the underground launcher. ....28

3-5 Locations of different instrumentation stations for 1997 multiple station experiment. ...............................................................................................................30

3-6 Data acquisition system used in the 1997 multiple-station experiment. ..................31

3-7 Experimental setup (placement of electric and magnetic field antennas) used in SATTLIF for 2000.. .................................................................................................34

3-8 Setup of strike rod and ring mounted over launch tubes in 2000.............................35

3-9 Measured channel-base current, Flash S9901, Stroke 3...........................................37

3-10 Magnetic field at 15 m, Flash S9901, Stroke 3. .......................................................38


3-12 Electric field derivative (dE/dt) at 15 m, Flash S9901, Stroke 3. ............................39

3-13 Electric field derivative (dE/dt) at 30 m, Flash S9901, Stroke 3. ............................39

3-14 Return-stroke peak currents in (a) 1997, (b) 1999, (c) 2000, and (d) 2001. ............40

3-15 Return-stroke peak currents in 1997, 1999, 2000 and 2001.....................................41

3-16 Peak magnetic fields measured at (a) 5 m, (b) 10 m, (c) 20 m, and (d) 30 m in 1997. .........................................................................................................................42

3-17 Peak magnetic fields measured at (a) 15 m and (b) 30 m in 1999. ..........................43



3-20 Peak magnetic fields measured at (a) 15 m and (b) 30 m in 1997, 1999, 2000 and 2001. .........................................................................................................................46

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3-21 Peak dE/dt fields measured at (a) 15 m and (b) 30 m in 1999. ................................47



3-24 Peak dE/dt fields measured at (a) 15 m and (b) 30 m in 1999, 2000 and 2001. ......50

4-1 A straight current channel of infinite length and B at a distance r...........................51

4-2 A streaked-image diagram of a dart leader—return-stroke sequence in a rocket-triggered lightning flash ...........................................................................................52



4-5 Dart leader current inferred using Ampere’s Law for magnetostatics from measured magnetic fields at (a) 5 m, (b) 10 m, (c) 20 m, and (d) 30 m in 1997......55

4-6 Dart leader current inferred using Ampere’s Law for magnetostatics from measured magnetic fields at (a) 15 m and (b) 30 m in 1999. ...................................56



4-9 Dart leader current inferred using Ampere’s Law for magnetostatics from measured magnetic fields at 15 m in 1999, 2000, and 2001. ...................................59

4-10 Dart leader current inferred using Ampere’s Law for magnetostatics from measured magnetic fields at 30 m in 1997, 1999, 2000, and 2001. .........................60

4-11 Dart leader current inferred using Ampere’s Law for magnetostatics from measured magnetic fields measured at 30 m vs. that at 15 m in 1999, 2000, and 2001. .........................................................................................................................61

4-12 Dart leader current inferred using Ampere’s Law for magnetostatics from magnetic fields measured at 15 m vs. leader current inferred from dE/dt measurements in 1999, 2000, and 2001. ..................................................................62

4-13 Dart leader current inferred using Ampere’s Law for magnetostatics from magnetic fields measured at 30 m vs. leader current inferred from dE/dt measurements in 1999, 2000, and 2001. ..................................................................63

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4-14 Return-stroke peak currents inferred using Ampere’s Law for magnetostatics from measured magnetic fields at (a) 5 m, (b) 10 m, (c) 20 m, and (d) 30 m in 1997. .........................................................................................................................64

4-15 Return-stroke peak currents inferred using Ampere’s Law for magnetostatics from measured magnetic fields at (a) 15 m and (b) 30 m in 1999. ..........................65



4-18 Return-stroke peak currents inferred using Ampere’s Law for magnetostatics from measured magnetic fields at 15 m in 1999, 2000, and 2001. ..........................68

4-19 Return-stroke peak currents inferred using Ampere’s Law for magnetostatics from measured magnetic fields at 30 m in 1997, 1999, 2000, and 2001. ................69

4-20 Return-stroke peak current inferred using Ampere’s Law for magnetostatics from measured magnetic fields at 30 m vs. that inferred from measured magnetic fields at 15 m in 1999, 2000, and 2001. ...................................................70

4-21 Return-stroke peak current inferred using Ampere’s Law for magnetostatics from measured magnetic fields at 15 m vs. measured return-stroke peak current in 1999, 2000, and 2001. ..........................................................................................71

4-22 Return-stroke peak current inferred using Ampere’s Law for magnetostatics from measured magnetic fields at 30 m vs. measured return-stroke peak current in 1997, 1999, 2000, and 2001. ................................................................................72

4-23 Leader vs. return-stroke currents inferred using Ampere’s Law for magnetostatics from magnetic fields measured at 15 m in 1999, 2000, and 2001...73

4-24 Leader vs. return-stroke currents inferred using Ampere’s Law for magnetostatics from magnetic fields measured at 30 m in 1999, 2000, and 2001...74

4-25 Comparison of IRS from (BL+BRS)30m and IRS from (BL+BRS)15m for 1999, 2000, and 2001. ..................................................................................................................75

4-26 Comparison of IRS from (BL+BRS)15m inferred using Ampere’s Law for magnetostatics vs. IRS measured at channel base in 1999, 2000, and 2001. ............76

4-27 Comparison of IRS from (BL+BRS)30m inferred using Ampere’s Law for magnetostatics vs. IRS measured at channel base in 1997, 1999, 2000, and 2001. ..77

5-1 Superposition of measured magnetic field and channel-base current for Flash S9903, stroke 3. ........................................................................................................81

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5-2 Displacement current for S9903 RS3 as inferred, using Eq. 5.3, from Imeas and Hmeas at 30 m.............................................................................................................83

5-3 Return-stroke peak displacement current estimated, using Eq. 5.3, from Imeas and Hmeas at (a) 15 m and (b) 30 m in 1999. ...................................................................84

5-4 Return-stroke peak displacement current estimated, using Eq. 5.3, from Imeas and Hmeas at (a) 15 m and (b) 30 m in 2000. ...................................................................85

5-5 Return-stoke peak displacement current estimated, using Eq. 5.3, from Imeas and Hmeas at (a) 15 m and (b) 30 m in 2001. ...................................................................86

5-6 Return-stroke peak displacement current estimated, using Eq. 5.3, from Imeas and Hmeas at (a) 15 m and (b) 30 m in 1999, 2000, and 2001..........................................87

5-7 Leader peak displacement current estimated, using Eq. 5.3, from Imeas and Hmeas at (a) 15 m and (b) 30 m in 1999..............................................................................88



5-10 Leader peak displacement current estimated, using Eq. 5.3, from Imeas and Hmeas at (a) 15 m and (b) 30 m in 1999, 2000, and 2001. ..................................................91

5-11 Distance dependences of dE/dt used in evaluating displacement current within 30 m of the lightning channel based on measured dE/dt at 15 and 30 m.................92

5-12 Return-stroke displacement current within 30 m of the lightning channel at the time of dE/dt peak at 15 m estimated using step-wise approximation (with propagation delay taken into account) in (a) 1999 and (b) 2000. ............................97

5-13 Return-stroke displacement current within 30 m of the lightning channel at the time of dE/dt peak at 15 m estimated using step-wise approximation (with propagation delay taken into account) in (a) 2001 and (b) 1999, 2000, and 2001...98

5-14 Return-stroke displacement current within 30 m of the lightning channel estimated using peak values of dE/dt at both 15 and 30 m estimated using step-wise approximation (without propagation delay taken into account) in (a) 1999 and (b) 2000. ............................................................................................................99

5-15 Return-stroke displacement current within 30 m of the lightning channel estimated using peak values of dE/dt at both 15 and 30 m estimated using step-wise approximation (without taking propagation delay into account) in (a) 2001 and (b) 1999, 2000, and 2001.................................................................................100

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5-16 Return-stroke displacement current within 30 m of the lightning channel estimated using peak values of dE/dt at both 15 and 30 m estimated using linear approximation (without propagation delay taken into account) in (a) 1999 and (b) 2000. .................................................................................................................101

5-17 Return-stroke displacement current within 30 m of the lightning channel estimated using peak values of dE/dt at both 15 and 30 m estimated using linear approximation (without taking propagation delay into account) in (a) 2001 and (b) 1999, 2000, and 2001.................................................................................102

5-18 Scatter plot showing displacement current estimates from dE/dt measured at 15 and 30 m from the lightning channel (step-wise approximation) vs. those estimated from measured channel base current and associated magnetic field. In the former case, the estimate corresponds to the time of peak value of dE/dt at 15 m........................................................................................................................103

5-19 Scatter plot showing displacement current estimates from dE/dt measured at 15 and 30 m from the lightning channel (step-wise approximation) vs. those estimated from measured channel base current and associated magnetic field. In the former case, the estimate is obtained using peak values of dE/dt at both 15 and 30 m. ................................................................................................................104

5-20 Scatter plot showing displacement current from dE/dt measured at 15 and 30 m from the lightning channel (linear approximation) vs. those estimated from measured channel base current and associated magnetic field. In the former case, the estimate is obtained using peak values of dE/dt at both 15 and 30 m. .............105

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Abstract of Thesis Presented to the Graduate School

of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Master of Science

TRIGGERED-LIGHTNING PROPERTIES INFERRED FROM MEASURED CURRENTS AND VERY CLOSE MAGNETIC FIELDS

By

Ashwin B. Jhavar

December 2005

Chair: Vladimir A. Rakov Cochair: Martin A. Uman Major Department: Electrical and Computer Engineering

Very close magnetic fields produced by rocket-triggered lightning measured in

1997, 1999, 2000, and 2001 at Camp Blanding, Florida, are examined. The leader and

return stroke contributions to the total magnetic field are estimated and used to infer

leader and return-stroke currents. The statistical characteristics of these inferred currents

are examined. The return-stroke currents inferred from measured magnetic fields are

compared with directly measured ones. Leader currents inferred from measured magnetic

fields are compared with those estimated using dE/dt measurements. The statistics of the

ratio of leader to return stroke currents are compiled. Current estimates from measured

magnetic fields are in reasonable agreement with independent measurements and

theoretical predictions found in the literature. From the statistical analysis of 97 records

obtained in 1999, 2000, and 2001 the mean leader current inferred from magnetic field at

15 m is 1.87 kA and standard deviation is 1.01 kA. For magnetic fields at 30 m (103

records obtained in 1997, 1999, 2000, and 2001), the mean leader current is 2.58 kA and

xiv

the standard deviation is 1.57 kA. Typically leader currents are in the range of few

kiloamperes.

Displacement current associated with leader/return stroke sequences in triggered

lightning is estimated using (1) measured channel-base current and current inferred from

measured magnetic field and (2) dE/dt measurements at 15 and 30 m. The displacement

currents found using the above two approaches are compared. Return-stroke

displacement current within 30 m of the lightning channel at the time of peak dE/dt at 15

m, estimated using step-wise approximation of dE/dt variation with distance from the

lightning channel (after taking propagation delay into account) is characterized by a mean

value of 3.1 kA. The minimum value is 0.5 kA and maximum is 8.0 kA.

1

CHAPTER 1 INTRODUCTION

Lightning discharges are the cause of many deaths and injuries. Electromagnetic

fields generated by lightning can have deleterious effects on sensitive electronic devices.

A detailed knowledge of electromagnetic fields generated by close lightning is needed for

developing adequate lightning protection schemes.

A review of the lightning literature is presented in Chapter 2. Cloud electrical

structure and mechanisms of cloud electrification are discussed. Salient properties of both

natural and triggered lightning are given with focus on triggered lightning. Both classical

and altitude rocket-triggered lightning discharges are considered.

Chapter 3 presents the characteristics of measured current, magnetic field, and

electric field derivative (dE/dt) waveforms due to rocket-triggered lightning. It also

contains a description of the instrumentation used to measure these quantities in 1997,

1999, 2000 and 2001.

Leader and return-stroke currents inferred from measured magnetic fields are

presented in Chapter 4. These are compared with the directly measured return-stroke

currents and with the leader currents inferred from close electric field derivative (dE/dt)

measurements.

Chapter 5 deals with the displacement currents associated with leader/return stroke

sequences in triggered lightning. Displacement currents are estimated from measured

magnetic fields and current records using Maxwell’s equations. Also included is an

estimation of peak displacement currents from dE/dt signatures measured at 15 and 30 m.

2

Chapter 6 summarizes the data and analysis of the leader and return-stroke currents

and the displacement currents associated with triggered lightning.

Recommendations for future research are given in Chapter 7.

The Appendix has the waveforms of the displacement currents.

3

CHAPTER 2 LITERATURE REVIEW

2.1 Cumulonimbus

The primary source of lightning is the cloud type termed cumulonimbus or

thundercloud. A thundercloud develops from a small fair-weather cloud called a cumulus,

which is formed when parcels of warm, moist air rise and cool by adiabatic expansion,

that is, without the transfer of heat or mass across the boundaries of the air parcels. When

the relative humidity in a rising and cooling parcel exceeds saturation, moisture

condenses on airborne particulate matter within it to form the many small water particles

that constitute the visible cloud. The height of the condensation level, which determines

the height of the visible cloud base, increases with decreasing relative humidity at the

ground. This is why cloud bases in Florida are generally lower than in arid locations,

such as New Mexico or Arizona. Parcels of warm, moist air can only continue to rise to

form a cumulus and eventually a cumulonimbus if the atmospheric temperature lapse

rate, that is, the decrease in temperature with increasing height, is larger than the moist-

adiabatic lapse rate, about of 0.6 oC per 100 m.

The convection of buoyant moist air is usually confined to the troposphere, the

layer of the atmosphere that extends from the Earth’s surface to the tropopause. The

height of tropopause varies from approximately 18 km in the tropics in the summer to 8

km in high latitudes in the winter. The tropopause is a narrow layer that separates the

troposphere from the next layer of the atmosphere, the stratosphere, which extends from

tropopause to a height of 50 km. In the troposphere the temperature decreases with

4

increasing altitude, while in the stratosphere the temperature at first becomes roughly

independent of altitude and then increases with altitude. A zero or positive temperature

gradient in the stratosphere serves to suppress convection and, therefore, hampers the

penetration of cloud tops into the stratosphere.

Lightning is usually associated with convective cloud systems ranging from 3 to 20

km in vertical extent. The horizontal dimensions of active air-mass thunderstorms range

from about 3 km to >50 km.

2.2 Cloud Charge Distribution

The distribution and motion of thunderstorm electric charges, most resides on

hydrometeors but some of which is free ions, is complex and changes continuously as the

cloud evolves. Hydrometeors whose motion is predominantly influenced by gravity (with

fall speeds > 0.3 m s-1) are called precipitation particles. All other hydrometeors are

called cloud particles. The basic features of the cloud charge structure include a net

positive charge near the top, a net negative charge below it, and an additional positive

charge at the bottom of the cloud. These features are illustrated in Figure 2-1.

In-situ measurements of electric fields inside the cloud have been made using free

balloons carrying instruments to measure those fields. In situ measurements are superior

to remote measurements in that a relatively accurate charge height can be determined.

However, since the balloon can sense the field only along a more or less straight vertical

path and it samples different portions of that path at different times, the charge magnitude

can be estimated only if assumptions regarding the size and shape of individual charge

regions and the charge variation with time are made. The average volume charge density,

ρv, in the cloud is generally found by assuming that the charge (i) is horizontally uniform

and (ii) does not vary in time.

5

Figure 2-1. An isolated thundercloud in central New Mexico, with a rudimentary

indication of how electric charge is thought to be distributed inside and around the thundercloud, as inferred from the remote and in situ observations. Adapted from Krehbiel (1986).

Then according to Gauss’s law in point form ρv = εo(dEz/dz), that is, ρv is

proportional to the rate at which the vertical electric field Ez increases or decreases with

increasing altitude z as the balloon ascends. Figure 2-2 shows the results of a vertical

sounding of the electric field in a small New Mexico storm that produced no lightning.

This electric field profile was obtained up to a height of 10 km above mean sea level

using a balloon-borne instrument that measured the corona current from a 1-m-long

vertical wire. The corona current and the corresponding vertical electric field reversed

sign twice, between 6 and 7 km and above 9 km. The charge structure in Figure 2-2, a

negative charge between -5 and -15 oC with positive charges above and below it, appears

to be consistent with the “classical” tripolar charge structure.

6

Figure 2-2. Balloon measurements of corona current and the inferred vertical electric

field E versus altitude and air temperature inside a small storm in New Mexico on 16 August 1981, which produced no lightning. Adapted from Byrne et al. (1983)

2.3 Mechanisms of Cloud Electrification

Any cloud electrification mechanism involves (i) a small-scale process that

electrifies individual hydrometeros and (ii) a process that spatially separates these

charged hydrometeors by their polarity, the resultant distances between the charged cloud

regions being of the order of kilometers. Since most charges reside on hydrometeors of

relatively low mobility, the cloud is a relatively good electrical insulator and leakage

7

currents between the charged regions are thought to have a small effect on the charge

separation process.

2.3.1 Convection Mechanism.

In this mechanism the electric charges are supplied by external sources: fair-

weather space charge and corona near the ground and cosmic rays near the cloud top.

Organized convection provides large-scale separation. According to this mechanism,

illustrated in Figure 2-3, warm air currents (updrafts) carry positive fair-weather space

charge to the top of the growing cumulus. Negative charge, produced by cosmic rays

above the cloud, is attracted to the cloud’s boundary by the positive charges within it.

The negative charge attaches, within a second or so, to cloud particles to form a negative

screening layer. These charged cloud particles carry much more charge per unit volume

of cloudy air than is carried by precipitation particles. Downdrafts, caused by cooling and

convective circulation, assumed to carry the negative charge down the sides of the cloud

toward the cloud base, this negative charge serving to produce positive corona at the

Earth’s surface. Corona generates additional positive charge under the cloud and, hence,

provides a positive feedback to the process. The convective mechanism results in a

positive cloud-charge dipole, although it seems unlikely that the negative charge region

formed by this mechanism would lie in a similar temperature range for different types of

thunderstorms, as suggested by observations. Note that in convection model there is no

role for precipitation in forming the dipole charge structure.

2.3.2 Graupel-ice Mechanism.

In this mechanism the electric charges are produced by collisions between

precipitation particles (graupel) and cloud particles (small ice crystals). Precipitation

particles are generally larger than cloud particles, although there is no absolute

8

Figure 2-3. Illustration of the convection mechanism of cloud electrification. Adapted

from MacGorman and Rust (1998)

demarcation in size to distinguish precipitation particles, which are falling out of the

cloud, from cloud particles, which remain essentially suspended or move upward in

updrafts. The large-scale separation of charged particles is provided by the action of

gravity. In the graupel-ice mechanism, which appears to be capable of explaining the

“classical” tripolar cloud charge structure, the electrification of individual particles

involves collisions between graupel particles and ice crystals in the presence of water

droplets. The presence of water droplets is necessary for significant charge transfer, as

shown by the laboratory experiments. A simplified illustration of this mechanism is given

in Figure 2-4.

The heavy graupel particles (two of which are shown in Figure 2-4) fall through a

suspension of smaller ice crystals (hexagons) and supercooled water droplets (dots). The

droplets remain in a supercooled liquid state until they contact an ice surface, whereupon

they freeze and stick to the surface in a process called riming. Laboratory experiments

show that when the temperature is below a critical value called the reversal temperature,

TR, the falling graupel particles acquire a negative charge in collision with the ice

particles. At temperature above TR they acquire positive charge. The charge sign reversal

9

temperature TR is generally thought to be between -10 and -20 oC, the temperature range

characteristic of the main negative charge region found in thunderclouds.

Figure 2-4. Charge transfer by collision in the graupel-ice mechanism of cloud

electrification. It is assumed that the reversal temperature TR is -15 oC and that it occurs at a height of 6 km. Taken from Rakov and Uman (2003).

It is believed that the polarity of the charge that is separated in ice-graupel

collisions is determined by the rates at which the ice and graupel surfaces are growing.

The surface that is growing faster acquires a positive charge.

It is possible that the primary electrification mechanism changes once a storm

becomes strongly electrified. For example, collisions between ice crystals and graupel

10

could initiate the electrification, and then the larger convective energies of the storm

could continue it.

2.4 Downward Negative Lightning Discharges to Ground

The source of lightning is usually a cumulonimbus, whose idealized charge

structure is shown in the Figure 2-5 as three vertically stacked regions labeled P and LP

for the main positive and the lower positive charge regions and N for the main negative

charge region.

Figure 2-5. A vertical tripole representing the idealized gross charge structure of a

thundercloud such as that shown in Figure 2-1; the negative screening layer charges at the cloud top and the positive corona space charge produced at ground are ignored here.

Downward negative lightning discharges, that is, discharges that are initiated in the

cloud, initially develop in an overall downward direction, and transport negative charge

to ground, probably account for about 90 percent of all cloud-to-ground discharges. The

overall cloud-to-ground lightning discharge, termed a flash, is composed of a number of

processes, some of which involve channels that emerge from the cloud while others

involve channels that are confined to the cloud volume. Only processes occurring in the

channels outside the cloud render themselves to optical observations that can be used to

11

determine channel geometry, extension speed and other pertinent features of those

channels. The sequence of the processes involved in a typical negative downward

lightning flash is shown in Figure 2-6.

Figure 2-6. Various processes comprising a negative cloud-to-ground lightning flash.

Adapted from Uman (1987, 2001)

The stepped leader is preceded by an in-cloud process called the preliminary or

initial breakdown. There is no consensus on the mechanism of this process. It may be a

discharge bridging the main negative and the lower positive charge regions, as shown in

Figure 2-5. The initial breakdown may last from a few milliseconds to some tens of

milliseconds and serves to provide conditions for the formation of the stepped leader. The

latter is a negatively charged plasma channel extending toward the ground at an average

speed of 2 x 105 m s-1 in a series of discrete steps. From high-speed time resolved

CLOUD CHARGE DISTRIBUTION PRELIMINARY

BREAKDOWNSTEPPED LEADER

FIRST RETURN STROKE

K AND J PROCESSES DART

LEADER

SECOND RETURN STROKE

ATTACHMENT PROCESS

t = 0 1.10 ms1.00 ms 1.15 ms 1.20 ms

19 ms 20 ms 20.10 ms 20.15 ms 20.20 ms

40 ms 60 ms 61 ms 62 ms 62.05 ms

12

photographs, each step is typically 1 µs in duration and tens of meters in length, the time

interval between steps being 20 to 50 µs. The peak value of the current pulse associated

with an individual step has been inferred to be 1 kA or greater. The stepped leader serves

to form a conducting path or channel between the cloud charge source and ground.

Several coulombs of negative charge are distributed along this path, including downward

branches. Thus the leader may be viewed as a process removing negative charge from the

source and depositing this charge onto the downward extending channel. The stepped-

leader duration is typically some tens of milliseconds, and the average leader current is

some hundreds of amperes.

The electric potential difference between a downward-moving stepped-leader tip

and ground is probably some tens of megavolts which is comparable to or a considerable

fraction of that between the cloud charge source and ground. The magnitude of the

potential difference between two points, one at the cloud charge source and the other on

ground, is the line integral of the electric field intensity between those points.

The upper and lower limits for the potential difference between the lower boundary

of the main negative charge region and ground can be estimated by multiplying,

respectively, the typical observed electric field in the cloud, 105 V m-1, by the height of

the lower boundary of the negative charge center above ground, 5 km or so. The resultant

range is 50 to 500 MV. As the leader approaches ground, the electric field at the ground

surface, particularly at objects or relief features protruding above the surrounding terrain,

increases until it exceeds the critical value for the initiation of one or more upward-

connecting leaders. The initiation of an upward connecting leader from ground in

response to the descending stepped leader marks the beginning of the attachment process.

13

This process ends when contact is made between the downward and upward moving

leaders, probably some tens of meters above ground (more above a tall structure),

whereafter the first return stroke begins. The return stroke serves to neutralize the leader

charge, in other words, to transport the negative charges stored on the leader channel to

the ground. It is worth noting that the return-stroke process may not neutralize all the

leader charge or may deposit some excess positive charge onto the leader channel and

into the cloud charge source region. The final stage of the attachment process and the

initial stage of the return-stroke process are complex. The net result of those stages is a

fully formed return stroke, which is somewhat similar to the potential discontinuity that

would travel upward along a vertical, negatively charged transmission line if the lower

end of the line were connected to the ground. The first return-stroke current measured at

ground rises to an initial peak of about 30 kA in some microseconds and decays to half-

peak value in some tens of microseconds while exhibiting a number of subsidiary peaks,

probably associated with the branches. The return stroke effectively lowers to ground the

several coulombs of charge originally deposited on the stepped-leader channel, including

that on all the branches.

The high-current return-stroke wave rapidly heats the channel to a peak

temperature near or above 30 000 K and creates a channel pressure of 10 atm or more,

resulting in channel expansion, intense optical radiation, and an outward propagating

shock wave that eventually becomes the thunder (sound wave) we hear at a distance.

When the first return stroke, including any associated in-cloud discharge activity, ceases,

the flash may end. In this case, the lightning is called a single-stroke flash. However,

more often the residual first-stroke channel is traversed downwards by a leader that

14

appears to move continuously, a dart leader. During the time interval between the end of

the first return stroke and the initiation of a dart leader, J (for junction) and K processes

occur in the cloud. K-process can be viewed as transients occurring during the slower J-

process. The J-processes amount to a redistribution of cloud charge on a time scale of

tens of milliseconds, in response to the preceding return stroke. The J-process is often

viewed as a relatively slow positive leader extending from the flash origin into the

negative charge region, the K-process then being a relatively fast “recoil streamer” that

begins at the tip of the positive leader and propagates toward the flash origin. Both the J-

process and the K-process in cloud-to-ground flashes serve to transport additional

negative charge into and along the existing channel, although not all the way to the

ground. In this respect, K-process may be viewed as attempted dart leaders. The

processes that occur after the only stroke in single stroke flashes and after the last stroke

in multiple-stroke flashes are sometimes termed F (final) processes. These are similar, if

not identical, to J-processes.

The dart leader progresses downward at a typical speed of 107 m s-1, typically

ignores the first stroke branches and deposits along the channel a total charge of the order

of 1 C. The dart-leader current peak is about 1 kA. Some leaders exhibit stepping near

ground while propagating along the path traversed by the preceding return stroke, these

leaders being termed dart-stepped leaders. When a dart leader or dart-stepped leader

approaches the ground, an attachment process similar to that described for the first stroke

takes place, although it probably occurs over a shorter distance and consequently takes

less time, the upward connecting-leader length being of the order of some meters. Once

the bottom of the dart or the dart-stepped leader channel is connected to the ground, the

15

second return-stroke wave is launched upward and again serves to neutralize the leader

charge. The subsequent return-stroke current at ground typically rises to a peak value to

10 to 15 kA in less than a microsecond and decays to half-peak value in a few tens of

microseconds. The upward propagation speed of such a subsequent return stroke is

similar to that of the first return stroke, although due to the absence of branches the speed

variation along the channel does not exhibit abrupt drops.

The impulsive component of the current in a subsequent return stroke is often

followed by a continuing current that has a magnitude of tens to hundreds of amperes and

duration up to hundreds of milliseconds. Continuing currents with a duration in excess of

40 ms are traditionally termed long continuing currents. The source for the continuing

current is the cloud charge, as opposed to the charge distributed along the leader channel,

the latter charge contributing to at least the initial few hundred microseconds of the

return-stroke current observed at ground. The time interval between successive return

strokes in a flash is usually several tens of milliseconds, although it can be as large as

many hundreds of milliseconds if a long continuing current is involved and as small as

one millisecond or less. The total duration of a flash is typically some hundreds of

milliseconds, and the total charge lowered to ground is some tens of coulombs.

2.5 Artificial Initiation (Triggering) of Lightning Using the Rocket-and-Wire Technique

Two techniques for triggering lightning with a small rocket that extends a thin wire

in the gap between a thundercloud and the ground are “classical” triggering and

“altitude” triggering. These descriptions primarily apply to triggering negative lightning.

These two techniques are discussed in the next two sections. Figure 2.7 and Figure 2.8

show the sequence of events for these two techniques.

16

2.5.1 Classical Triggering

The most effective technique for triggering lightning involves the launching of a

small rocket trailing a thin grounded wire toward a charged cloud overhead. This

triggering method is usually called classical triggering and is illustrated in Figure 2-7.

Figure 2-7. Sequence of events in classical triggered lightning. The upward positive

leader and initial continuous current constitute the initial stage. Adapted from Rakov et al. (1998)

The triggering success rate is generally relatively low during very active periods of

thunderstorms, one reason being that during such periods the electric field is more likely

to be reduced by a natural lightning discharge before the rocket rises to a height sufficient

for triggering.

When the rocket, ascending at about 200 m s-1, is about 200 to 300 m high, the

enhanced field near the rocket tip results in a positively charged leader that propagates

upward toward the cloud. This upward positive leader (UPL) vaporizes the trailing wire,

bridges the gap between the cloud and ground, and establishes an initial continuous

current (ICC) with a duration of some hundreds of milliseconds that effectively transports

17

negative charge from the cloud charge source to the triggering facility. The ICC can be

viewed as a continuation of the UPL when the latter has reached the main negative

charge region in the cloud. At that time the upper extremity of the UPL is likely to

become heavily branched. The UPL and ICC constitute the initial stage (IS) of a classical

triggered-lightning discharge. After cessation of the initial continuous current, one or

more downward dart-leader--upward-return-stroke sequence may traverse the same path

to the triggering facility. The dart leaders and the following return strokes in triggered

lightning are similar to dart-leader – return-stroke sequences in natural lightning,

although the initial processes in natural downward and in classical triggered lightning are

distinctly different. In summer, the triggering success rate for positive lightning is

apparently lower than for the negative lightning.

There is contradictory information regarding whether the height H of the rocket at

the time of lightning triggering depends on the electric field intensity E at ground at the

time of launching the rocket. A strong correlation (with correlation coefficient – 0.82)

between H and E for triggered lightning in New Mexico was given by H = 3900E-1.33

where H is in meters and E in kV m-1.

In Florida it was found that lightning can be initiated with grounded triggering

wires approximately 400 m long when the ambient fields aloft are as small as 13 kV m-1.

When lightning occurred, ambient potentials with respect to earth at the triggering-rocket

altitude were 3.6 MV (negative with respect to earth). These potentials are referred to as

triggering potentials. The first measurable current pulses at the bottom of the triggering

wires were observed at similar fields aloft but at wire heights only about half as large, the

corresponding potential being 1.3 MV.

18

2.5.2 Altitude Triggering

A stepped leader followed by a first return stroke in natural downward lightning

can be reproduced to some degree by triggering lightning via a metallic wire not attached

to the ground. This ungrounded-wire technique is usually called altitude triggering. In

this type of lightning, illustrated in Figure 2-8, a bidirectional (positive charge up and

negative charge down) leader process is involved in initiating the first return stroke from

ground.

Figure 2-8. Sequence of events in altitude-triggered lightning leading to the establishment

of a relatively low-resistance connection between the upward-moving positive leader tip and the ground. The processes that follow the sequence shown, an initial continuous-current and possibly one or more downward-leader--upward-return-stroke sequences, are similar to their counterparts in classical triggered lightning. The rocket speed is of the order of 102 m s-1. Adapted from Rakov et al. (1998)

Note that the “gap”, in this case, the length of the insulating Kevlar cable, between

the bottom end of the upper (triggering) wire and the top end of the grounded

19

(intercepting) wire is some hundreds of meters. Altitude triggering can also be

accomplished without using an intercepting wire, whose only function is to increase the

probability of lightning attachment to instrumented rocket-launching facility.

2.6 Previous Studies of Displacement Current Associated with Triggered Lightning

Schnetzer et al. (1998) in a study reported only in a conference proceeding, carried

out a numerical evaluation of Maxwell’s integral equation relating azimuthal magnetic

field to its sources to investigate the relative contributions of conduction and

displacement currents to the total ground level azimuthal magnetic field at a distance of

50 m from the base of a triggered lightning stroke. The results revealed differences

between observed magnetic fields measured at 50 m from expectations based on

Ampere’s law for magnetostatics. It is concluded that Ampere’s law for magnetostatics,

which neglects displacement current contributions, provides an inadequate representation

of the total magnetic field due to a lightning ground stroke at distances beyond

approximately 30 m. The rest of this section contains an overview of Schnetzer et al.

(1998), which is the only publication, as of today, on the subject of displacement current

in triggered lightning.

2.6.1 Theory

The following simple expression based on Ampere’s law for magnetostatics is

often used to estimate the azimuthal magnetic field intensity at the ground due to nearby

lightning:

H(r,t)=I(t)/2πr (2.1)

where I(t) is the channel current, H(r,t) is the magnetic field intensity, and r is the radial

distance from the strike point on the earth. Schnetzer et al. (1998) observed that beyond

30 m, peak amplitudes of the measured magnetic fields are somewhat lower than their

20

counterparts predicted by equation (2.1) when measured currents are substituted in it. To

understand the sources of this observed behavior, a first-order numerical evaluation was

carried out using as a starting point Maxwell’s integral equation relating the azimuthal

magnetic field to its arbitrary, time-varying sources,

ol S S

EH dl J d S d St

ε ∂⋅ = ⋅ + ⋅

∂∫ ∫ ∫

oS

EI d St

ε ∂= + ⋅

∂∫ (2.2)

Here the first term on the right corresponds to I(t) in Eq. 2.1. The second term

constitutes the contribution to the azimuthal magnetic field due to displacement current

through the integration surface S bounded by l. When applied to a lightning stroke to

earth with S being defined as a flat, circular area of integration lying on the surface of the

ground and centered at the strike point, the first terms accounts for the effects of

conduction currents flowing normally through the designated surface. These would

include corona and upward leader currents prior to the attachment of the descending

leader, and the return-stroke current after that time. The second term accounts for the

effects of time variations of the vertical electric field associated with the changing charge

density distribution along the lightning channel during both the approach of the leader

and the resultant return stroke.

On the basis of circular symmetry considerations,

( ) 1 ( , )( )2 2

zo

S

I t E r tH t dStr r

επ π

∂= + ⋅

∂∫ (2.3)

To the degree that an average zEt

∂∂

can be treated as constant over the area of integration,

H can be approximated as

21

( ) ( )( )2 2

o zI t r dE tH tr dt

επ

= + = Hc + Hd (2.4)

where Hc and Hd are the contribution to the total magnetic field H from conduction and

displacement current, respectively. Alternately, average values of dEz/dt can be defined

for different ring-shaped parts of S, in which case the second term on the right side of Eq.

2.4 becomes the sum of all individual contributing subareas of S. The first term on the

right of Eq. 2.4 is recognized as corresponding to Ampere’s law for magnetostatics, and

therefore any effects due to the current variation with height and radiation field must be

accounted for by the second, displacement current term. Since the descending leader does

not penetrate the surface of integration, during the leader phase I(t) is approximately zero,

except for assumed-to-be-negligibly-small corona or upward leader currents emitted from

the prospective attachment point. During that time, therefore, the magnetic field intensity

is related solely to the displacement current. Commencing with the onset of the return

stroke, both terms contribute. However, close to the channel, where r → 0, the

displacement current contribution tends to zero, and the total field is dominated by the

contribution from the channel conduction current term.

2.6.2 Estimation of Displacement Current Contribution at 50 m

In order to investigate the distance at which the conduction current term alone

ceases to provide an adequate representation of the total magnetic field, Schnetzer et al

(1998) carried out a numerical evaluation of the relative contributions of both terms in

Eq. 2.4 for a typical 20-kA stroke using available recorded channel-base current and

associated magnetic field at 50 m and electric field data at two distances, 5 and 20 m,

from the strike point. The first step was to derive estimates of the displacement current

for r ranging from 0 to 10 m and from 10 to 50 m from electric fields measured at 5 and

22

20 m, respectively. Because electric fields were not recorded beyond 20 m, estimates of

the displacement current contributed by the annular area between 10 and 50 m were

obtained by assuming that the electric field over that area was, on average, the same as

the value measured at 20 m. Electric field waveforms were numerically differentiated to

obtain dEz/dt waveforms to be substituted in Eq. (2.4). The resulting estimated

amplitudes of displacement currents calculated at four time points prior to and at the

return-stroke onset are listed in Table 2.1.

Table 2-1. Displacement currents Id estimated from measured electric field data at times prior to and at the onset of a 20 kA peak stroke current. Taken from Schnetzer et al. (1998).

A qualitative representation of the electric field derivative is given in Figure 2-9.

According to Table 2-1, prior to the return stroke, while there is no appreciable

conduction current flowing through the integration surface at ground level, the

magnitudes of displacement currents out to 10 m at the various time steps are negligible

relative to the prospective returns stroke peak current of 20 kA. On the other hand, during

23

that same period the displacement current contribution from the area between 10 and 50

m becomes increasingly significant in comparison to 20 kA. Consistent with Figure 2-10,

the displacement current increases in amplitude with time and is negative in polarity up to

the point of onset of the return stroke. Upon initiation of the return stroke, the local

electric field abruptly changes sign and its derivative reaches its peak. The corresponding

magnitude of the total displacement current at that point becomes comparable to that of

the channel current, which then begun to flow but has not reached its peak.

Contribution of the displacement current in addition to the return-stoke channel

conduction current contribution clearly alters both the waveshape and amplitude of the

return-stroke portion of the total magnetic field compared to that predicted by Ampere’s

law for magnetostatics. This is demonstrated in Figure 2-10. Here, the magnetic field

measured at 50 m (labeled Measured) during stroke 5 of flash 96-23 is plotted along with

the magnetic field (labeled Ampere’s Law) that would be predicted by Eq. 2.1 when

applied to the recorded channel-base current of that stroke. Finally, the difference

between the two, which is qualitatively consistent with the results of Table 2-1 and

apparently represents the contribution due to the displacement current term of Eq. 2.4, is

also plotted. As can be seen in Figure 2-10, the shape of the difference curve corresponds

well to the anticipated shape of the electric field derivative, and hence of displacement

current density, illustrated in Figure 2-9. Prior to the return stroke, while no channel

current is flowing at ground level, the effect of the displacement current is apparent in the

initial ramp of the measured magnetic field. Further effects of the displacement current

component on the total field are the rounding and reduction in amplitude of the peak of

the magnetic field waveform.

24

Figure 2-9. Qualitative illustration of the shape of the time derivative of the ground level

vertical electric field of a nearby return stroke . Since displacement current density is simply related to the derivative of electric field by a constant, it has the same waveshape. Taken from Schnetzer et al. (1998).

Figure 2-10. From top to bottom, magnetic field measured at 50 m during stroke 5 of

Flash 96-23, the corresponding field according to Ampere’s law for magnetostatics, as applied to the measured channel-base current, and the difference between the two. Taken from Schnetzer et al. (1998).

25

CHAPTER 3 CHARACTERIZATION OF EXPERIMENTAL DATA USED IN THIS STUDY

3.1 Magnetic Field Measuring Techniques

To measure the magnetic field from lightning a loop of wire can be used as an

antenna. According to Faraday’s Law a changing magnetic field passing through an open

circuited loop of wire will induce a voltage at the terminals of the wire. The voltage at the

terminals of the wire is

dtdBAv n

out =

where A is the area of the antenna and B is the magnetic flux density passing through the

loop, perpendicular to the plane of the loop. Since the output voltage is proportional to

the time derivate of the magnetic field, this voltage will have to be integrated to obtain

the signal proportional to the field. The Thevenin equivalent circuit of a loop antenna is

the open circuit source voltage dBAdt

in series with the source impedance (primarily

inductive). The Thevenin equivalent is shown in Figure 3-1.

Figure 3-1. Thevenin equivalent circuit of a loop antenna

26

A Norton equivalent circuit model for the antenna can be derived from the

Thevenin equivalent with thV Aj B ABIj L j L L

ωω ω

= = = . The Norton equivalent circuit is

shown in Figure 3-2

Figure 3-2. Norton equivalent circuit for a loop antenna.

Since the loop antenna has an inductance L associated with it, the impedance of the

antenna will change with frequency. In the frequency domain that impedance is ωL

where ω is the angular frequency. This frequency-dependent impedance will cause

distortion in the derivative signal. To eliminate the distortion a resistor can be placed in

series with the antenna with the resistive impedance R much higher than the inductive

impedance ωL of the antenna at the highest frequency of interest. The decay time

constant of the overall circuit in Figure 3-1 and Figure 3-2 will be τ = RC as long as R is

much smaller then the input resistance of the recorder and C is much larger then the input

capacitance of the recorder, both conditions being usually met. In the frequency domain

the output voltage across the capacitor is

1( )( )

1out

A j Bj CV

R j Lj C

ωω

ωω

=+ +

27

If we choose R >> jωL and R >> 1j Cω

for the highest and lowest frequencies of

interest respectively, as discussed above, then outABVRC

= . In this way magnetic field from

lightning can be measured from a loop antenna. Using the output voltage, Vout, area of the

loop antenna A, and choosing appropriate resistance R the magnetic field B can be

estimated.

3.2 Experimental Setup

3.2.1 ICLRT Overview

In this section, an overview of International Center for Lightning Research and

Testing (ICLRT) is presented. The ICLRT is located at Camp Blanding, Florida, at

coordinates 29°56’ N, 82° 02’ W, 8 km east of Starke. It was constructed by Power

Technologies in 1993 to study the effect of lightning on power lines. It has been operated

by the University of Florida since 1994. The rocket-and-wire technique (e.g., Rakov et

al., 1998) was used to artificially initiate (trigger) lightning from natural thunderclouds.

An overview of the ICLRT during the 1999, 2000, and 2001 experiments is found in

Figure 3-3 and a photograph of Flash S0012, triggered in 2000, in Figure 3-4. Flash

S0012 was triggered using the underground launcher. The triggered-lightning

experiments are usually conducted from May through September. As can be seen from

Figure 3-3, the ICLRT includes a tower launcher 11 m in height. Other launchers placed

at different positions on the site were also used in different years. Apart from the

launchers, the ICLRT includes test overhead power lines, under-ground cables, four

instrumentation stations, a test house, test runway, other test objects and systems and

various office and storage trailers.

28

Figure 3-3. An overview of the ICLRT at Camp Blanding, Florida, 1999-2001. Not all

test objects are shown.

Figure 3-4. Photograph of lightning flash S0012 triggered from the underground launcher

(see Figure 3-3).

29

3.2.2 1997 Experiments

In this section, a brief discussion of instrumentation used in the 1997 multiple

station experiment is discussed. The multiple station experiment involved a 5 m rocket

launcher located at northeast corner of the ICLRT and grounded through three 8 foot

(2.43 m) galvanized steel rods driven into sandy soil. Seven field measuring stations were

located (see Figure 3-5) south of the rocket launcher with distances ranging from 5 to 500

m. Each station had electric field and magnetic field antennas. The lightning channel base

current was measured using 0.5 milliohm CVR (Current Viewing Resistor) located at the

launcher. Three digitizing systems (see Figure 3-6) were used in this experiment, two

were provided by the University of Florida and were located at SATTLIF trailer (see

Figure 3-5) and launch control, the third digitizing system was provided by Sandia and

was located at SATTLIF trailer. When the current measured by the CVR located at

SATTLIF launcher exceeded 4 kA a digital pulse was generated by a current threshold

triggering circuit, which triggered all three digitizing systems. The digitizing system at

SATTLIF trailer consisted of a single Nicolet Multipro 150 digitizer and five LeCroy

model RM9400 digital oscilloscopes. Nicolet Multipro consisted of 8 data acquisition

cards of 4 channels each, but for this experiment only two cards were used of which one

was faulty. Each channel had 12-bit resolution with a sampling rate of 10 MHz for a total

record length of 51.2 ms. The LeCroy oscilloscopes were segmented for multiple triggers

and provided 8-bit resolution with a sampling rate of 25 MHz for a total record length of

100 µs.

At launch control five Nicolet model pro90 digital oscilloscopes were used. Pro90

consists of 4 channels; channels 1 and 2 had 8-bit resolution and a sampling rate up to

200 MHz, and channels 3 and 4 had 12-bit resolution and a sampling rate up to10 MHz.

30

The first channel had a pretrigger delay of 2 ms and second channel had a 23.6 ms

pretrigger delay that allowed continuous recording of the same quantity for 51.2 ms.

Nicolet Isobe 3000 fiber optic links were used to transmit analog data from antennas to

digitizing systems. More detailed description of 1997 instrumentation can be found in

Chapter 4 of David E. Crawford’s thesis (Crawford 1998).

N

W E

S

SATTLIFLAUNCHER

UF LAUNCHCONTROL

TRAILER

100m

OFFICE ANDSTORAGE

UF TOWER LAUNCHER

SATTLIFTRAILER ANTENNA FIELD

TEST POWERLINE

Figure 3-5. Locations of different instrumentation stations for 1997 multiple station

experiment. Taken from Crawford (1998).


The rocket launcher consisted of six metallic tubes aligned vertically from which

rockets were launched. The rocket launcher was mounted on insulating fiberglass legs

and placed underground, with the top of the launcher flush with ground, in a 4 m × 4 m ×

4 m pit. The pit and the launcher were located in the center of a 70 m × 70 m buried

metallic grid (see Figure 3-3) intended to simulate a perfectly conducting ground. This

configuration eliminates ground surface arcing (e.g., Rakov et al., 1998) and minimizes

field propagation effects due to a finite ground conductivity. The low frequency, low

current grounding resistance of the buried grid was measured to be 6 Ω. A hollow metal

rod with an outside diameter of 3.8 cm and a wall thickness of 0.6 cm protruding 1 m

31

ANTENNAS

10 m

UF LAUNCH CONTROL

REC INNICOLET

DSOs10 Channels256 Ksamples/ch10 Msamples/sec12 bit res.

TRIG IN

ANALOG FIELD DATA

110 m

500 m

20 m

30 m

50 m

LEGEND:

ELECTRIC FIELDANTENNA (.155 m²)

MAGNETIC FIELDANTENNA (.27 m²)

DSO = Digital Storage Oscilloscope

SATTLIFLAUNCHER

5 m

TRIG IN10 Channels4 Ksamples/seg25 Msamples/sec8 bit res.

4 Channels512 Ksamples/ch10 Msamples/sec12 bit res.

REC IN

ANALOG FIELD DATAREC IN

NICOLETDIGITIZER

TRIG OUT

TRIG IN

ANALOGMAG TAPERECORDER

GEN. (±4 kA Thresh.)

CHANNEL BASE CURRENT SHUNT

REC IN

FIRE CONTROL

CONTROL

LECROYDSOs

TRIGGER

SATTLIF

LAUNCH

Figure 3-6. Data acquisition system used in the 1997 multiple-station experiment. Taken

from Crawford (1998).

above the ground surface was used as the strike object for flashes S9901–S9918 in 1999.

For the other flashes triggered in 1999 (flashes S9925 - S9935), a 2 m rod was used in

order to increase the probability of lightning attachment to the rod. During 1999, the

underground launcher was connected via four metal straps to the buried grid and the base

of the launcher was connected via two metal straps to a 16.5 m long vertical ground rod

whose low frequency, low current grounding resistance was measured to be 40 Ω.

The electric field, magnetic field, and their time derivatives produced by lightning

strokes were measured 15 and 30 m from the strike rod. A TTL-level digital pulse trigger

signal was generated when the magnetic field sensor located 15 m from the rocket

launcher detected a magnetic field that corresponded to a current of at least 5 kA (using

32

Ampere’s law of magnetostatics). The TTL signal was transmitted to the external trigger

input of the oscilloscopes located in the SATTLIF trailer (see Figure 3-3) to trigger the

digitizing system. The oscilloscopes for the field and current measurements had a pre-

trigger (stored data recorded prior to the trigger pulse) that ranged from 10% to 50% of

the total record length. Fiber optic transmitters (FOT) converted the analog output signals

from the antennas to optical signals and transmitted those signals via fiber optic cables to

fiber optic receivers (FOR). Meret and Nanofast fiber optic links (FOL) were used in the

experiment. The bandwidth of the Meret and Nanofast FOL was dc to 35 MHz and 5 Hz

to 175 MHz, respectively. The FOT were powered with 12 V dc lead-acid batteries. RG-

58 or RG-223 coaxial cables (both 50 Ω) connected the FOT to the antennas, which were

located in metal boxes near the antennas. The FORs in the SATTLIF trailer were

powered with 120 V ac uninterruptible power supplies (UPS). RG-58 or RG-223 coaxial

cables connected the FOR to the digitizing system. The optical fibers transmitting the

signal from the FOT to the FOR were 200 µm glass, Kevlar-reinforced, duplex cables.

3.2.3.1 Instrumentation for Current Measurements

Six P110A current transformers (CTs) with a lower frequency response of 1 Hz and

an upper frequency response of 20 MHz were used to measure the current at the lightning

channel base, two measured the current flow to the vertical ground rod, and four

measured the current flow to the buried grid. The current amplitude range of each sensor

is from a few amperes to approximately 20 kA. A passive combiner summed the two

signals from the ground rod CTs to obtain a total ground rod current, and another one

summed the four signals from the buried grid CTs to obtain a total grid current. The total

ground rod current signal and the total grid current signal were then each transmitted via

33

separate Meret FOL (35 MHz bandwidth) to the SATTLIF trailer. Both signals were

filtered with a 20 MHz, 3 dB anti-aliasing filters and then digitized at 50 MHz. The total

current at the lightning channel base was obtained by numerically summing the ground

rod current and the buried-grid current.

3.2.3.2 Instrumentation for Electric Field Measurements

Electric fields were measured using flat plate antennas with an area of 0.16 m2. The

output of each electric field antenna was connected to an integrating capacitor of value

105 nF at 15 m and 55 nF at 30 m. The input impedance of the fiber optic transmitter was

about 1 MΩ. Meret fiber optic links with a bandwidth of 35 MHz were used to transmit

the signal to the SATTLIF trailer where the 15-m electric field signals were filtered using

10 MHz, 3 dB anti-aliasing filters and digitized at 25 MHz, and the 30-m electric field

signals were filtered using 20 MHz, 3 dB anti-aliasing filters and digitized at 25 MHz.

3.2.3.3 Instrumentation for Electric Field Derivative Measurement

Electric field derivatives were measured using flat plate antennas with an area of

0.16 m2. The output of each electric field derivative antenna was terminated using 50 Ω,

and the input impedance of the fiber optic transmitter was about 1 MΩ. Meret fiber optic

links with a bandwidth of 35 MHz were used to transmit the 15-m signal, and a Nanofast

FOL was used to transmit the 30-m signal to SATTLIF trailer. Signals of dE/dt at 15 and

30 m were filtered using 20 MHz, 3 dB anti-aliasing filters and digitized at 250 MHz.


The strike object was a 2 m vertical rod surrounded by a 3 m diameter horizontal

ring elevated to 1.5 m height and electrically connected to the base of the rod (see Figure

3-8). Most of the 2000 instrumentation was the same as the 1999 instrumentation except

for the two major changes made in 2000 and listed below: (1) The triggering signal was

34

generated when the current measured at the strike rod base exceeded 3 kA. (2) Current at

the channel base was measured simultaneously by two different methods (a) the total

lightning current was measured using a single current viewing resistor installed just

below the strike object (new measurement), and (b) the current components flowing to

the vertical ground rod and to the buried grid were measured individually and added

numerically to obtain the total lightning current. The current to the ground rod was

measured as in 1999, while the currents to the buried grid were measured with two

current viewing resistors in the two connections rather than with the four current

transformers and four connections used in 1999. Electric field and electric field derivative

instrumentation in 2000 was the same as in 1999.

SATTLIF Pit & Launch Tubes

B(15)

B(30)

E(15)

E(30) dB(30)

dB(15)

dE(15)

dE(30)

M-E15

M-E30

M-B15

M-B30

sh(15)

E(5)

sh(30)

Camcorder

Camcorder

Video & 35-mm Cameras

Edge of Ground Screen

Pockel Cell sh(3)

30 o 30 o

o o 15 15

Figure 3-7 Experimental setup (placement of electric and magnetic field antennas) used

in SATTLIF for 2000 [Courtesy G. Schnetzer].

35

Figure 3-8 Setup of strike rod and ring mounted over launch tubes in 2000.


The experiment set-up was the same as in 2000, except for the strike ring and the

ground rod connection were removed. Additionally, the 2 m strike rod was replaced with

4.5 m section of gas pipeline for the experiments on August 18, 2001. The pipeline was

mounted directly onto the base of the incident current CVR (current viewing resistor) and

nylon fishing line was used to support the structure. The pipeline consisted of four

sections of different diameters, the sections being connected by three different insulating

joints. Current was measured in the same way as in 2000, but was digitized at 25 MHz

(instead of 50 MHz as in 1999 and 2000). The electric field and electric field derivative

instrumentation in 2001 was the same as in 1999 and 2000.

36

3.3 Data Presentation

3.3.1 General Information

In this section the statistical distributions of measured peak magnetic fields, return-

stroke peak currents and peak dE/dt fields are presented. Corresponding waveforms are

shown in Figures 3-9 to 3-13.

For measured return-stroke current which are not saturated the sample size is 88.

For 1997, 1999, 2000, and 2001 data combined, the mean value of peak current is 15.3

kA and standard deviation is 7.50 kA.

The magnetic fields are used in Chapter 4 to estimate the leader and return-stroke

currents. For measured peak magnetic fields which are not saturated at 15 m for 1999,

2000 and 2001 the mean value is 201 µWb/m2 and the standard deviation is 96.8

µWb/m2. At 30 m for 1997, 1999, 2000 and 2001 the mean value is 104 µW/m2 and the

standard deviation is 49.2 µW/m2. The sample size for 15 m data is 97, and for 30 m data

the sample size is 103. Histograms are shown in Figures 3.17-3.22.

For measured dE/dt waveforms which are not saturated the sample size is 50 for

both 15 and 30 m. At 15 m for 1999, 2000 and 2001 the mean value is 355 kV/m/µs and

the standard deviation is 154 kV/m/µs. At 30 m for those three years the mean value is

118 kV/m/µs and the standard deviation is 56 kV/m/µs.

Table 3-1 summarizes the mean, standard deviation, geometric mean and sample

sizes for 1999, 2000 and 2001 combined.

37

Table 3-1. Summary of mean, standard deviation, GM (Geometric Mean), and sample sizes of measured peak current, peak magnetic field and electric field derivative

Parameter Mean St. Dev. GM Sample size

Peak current, kA 15.3 7.5 13.4 88

Peak magnetic field at 15 m, µWb/m2

201 96.8 179 97

Peak magnetic field at 30 m, µWb/m2

104 49.2 92.9 103

Peak dE/dt field at 15 m, kV/m/µs

355 145 315 50

Peak dE/dt field at 30 m, kV/m/µs

118 56 103 50

Figure 3-9. Measured channel-base current, Flash S9901, Stroke 3.

38

Figure 3-10. Magnetic field at 15 m, Flash S9901, Stroke 3.


39

Figure 3-12. Electric field derivative (dE/dt) at 15 m, Flash S9901, Stroke 3.

Figure 3-13. Electric field derivative (dE/dt) at 30 m, Flash S9901, Stroke 3.

40

3.3.2 Channel-base Current

0 4 8 12 16 20 24 28 32 36 40

Num

ber

0

2

4

6

8

Return-Stroke Peak Current [kA]

0 4 8 12 16 20 24 28 32 36 40

Num

ber

0

2

4

6

8

10

12

Return-Stroke Peak Current [kA] 0 4 8 12 16 20 24 28 32 36 40

Num

ber

0

1

2

3

4


0 4 8 12 16 20 24 28 32 36 40

Num

ber

0

1

2

3

4


(a) (b)

(c) (d)

1997 1999

20012000

Mean 13.1 kASt. Dev. 5.60 kAMin 5.70 kAMax 23.0 kAGM 12.1 kASample Size 11




Figure 3-14. Return-stroke peak currents in (a) 1997, (b) 1999, (c) 2000, and (d) 2001.

41

0 4 8 12 16 20 24 28 32 36 40

Num

ber

0

2

4

6

8

10

12

14

16

18

20

1999 n = 24 Mean = 16.7 kA St. Dev. = 6.80 kA2000 n = 40 Mean = 13.2 kA St. Dev. = 6.90 kA2001 n = 13 Mean = 21.1 kA St. Dev. = 9.30 kA1997 n = 11 Mean = 13.1 kA St. Dev. = 5.60 kA


1997, 1999, 2000, & 2001


Figure 3-15. Return-stroke peak currents in 1997, 1999, 2000 and 2001.

42

3.3.3 Magnetic Field

0 200 400 600 800 1000

Num

ber

0

1

2

3

4

Peak Magnetic Field [µWb/m2]

Distance 5 m, 1997

Mean 511 µWb/m2

St. Dev. 274 µWb/m2

Min 176 µWb/m2

Max 916 µWb/m2

GM 443 µWb/m2

Sample Size 7

0 100 200 300 400 500

Num

ber

0

1

2

3

4

5


Distance 10 m, 1997

Mean 247 µWb/m2


Min 100 µWb/m2

Max 395 µWb/m2

GM 227 µWb/m2

Sample Size 9

0 50 100 150 200 250

Num

ber

0

1

2

3

4

5


Distance 20 m, 1997

Mean 111 µWb/m2

St. Dev. 47.3 µWb/m2

Min 51.3 µWb/m2

Max 183 µWb/m2

GM 103 µWb/m2

Sample Size 7

0 25 50 75 100 125 150

Num

ber

0

1

2

3

4Distance 30 m, 1997


Mean 79.8 µWb/m2


Min 37.8 µWb/m2

Max 118 µWb/m2

GM 73.4 µWb/m2

Sample Size 6

(a) (b)

(c) (d)

Figure 3-16. Peak magnetic fields measured at (a) 5 m, (b) 10 m, (c) 20 m, and (d) 30 m

in 1997.

43

0 50 100 150 200 250 300 350 400 450 500

Num

ber

0

2

4

6

8

10

12


Distance 15 m, 1999

Mean 223 µWb/m2


Min 74.1 µWb/m2

Max 434 µWb/m2

GM 202 µWb/m2

Sample Size 39

(a)

0 25 50 75 100 125 150 175 200 225 250

Num

ber

0

2

4

6

8

10



Mean 118 µWb/m2


Min 46.4 µWb/m2

Max 225 µWb/m2

GM 108 µWb/m2

Sample Size 39

(b)

Figure 3-17. Peak magnetic fields measured at (a) 15 m and (b) 30 m in 1999.

44

0 50 100 150 200 250 300 350 400 450 500

Num

ber

0

2

4

6

8

10

12

14


Distance 15 m, 2000

Mean 180 µWb/m2


Min 49.5 µWb/m2

Max 467 µWb/m2

GM 159 µWb/m2

Sample Size 47

(a)

0 25 50 75 100 125 150 175 200 225 250

Num

ber

0

2

4

6

8

10



Mean 93.1 µWb/m2


Min 25.4 µWb/m2

Max 235 µWb/m2

GM 82.5 µWb/m2

Sample Size 47

(b)


45

0 50 100 150 200 250 300 350 400 450 500

Num

ber

0

1

2

3

4

5


Distance 15 m, 2001

Mean 212 µWb/m2


Min 97.6 µWb/m2

Max 470 µWb/m2

GM 192 µWb/m2

Sample Size 11

(a)

0 25 50 75 100 125 150 175 200 225 250

Num

ber

0

1

2

3



Mean 113 µWb/m2


Min 48.8 µWb/m2

Max 248 µWb/m2

GM 102 µWb/m2

Sample Size 11

(b)


46

0 50 100 150 200 250 300 350 400 450 500

Num

ber

0

5

10

15

20

25

30

1999 n = 39 Mean = 223 µWb/m2 St. Dev. = 96.5 µWb/m2


2001 n = 11 Mean = 212 µWb/m2 St. Dev. = 107 µWb/m2


Distance 15 m (1999, 2000, & 2001)

Mean 201 µWb/m2


Min 49.5 µWb/m2

Max 470 µWb/m2

GM 179 µWb/m2

Sample Size 97

(a)

Distance 30 m (1997, 1999, 2000, and 2001)

0 25 50 75 100 125 150 175 200 225 250

Num

ber

0

5

10

15

20

25

30


2000 n = 47 Mean = 93.1 µWb/m2 St. Dev. = 47.2 µWb/m2


1997 n = 6 Mean = 79.8 µWb/m2 St. Dev. = 33.7 µWb/m2


Mean 104 µWb/m2


Min 25.4 µWb/m2

Max 248 µWb/m2

GM 92.9 µWb/m2

Sample Size 103

(b)

Figure 3-20. Peak magnetic fields measured at (a) 15 m and (b) 30 m in 1997, 1999, 2000 and 2001.

47

3.3.4 Electric Field Derivative (dE/dt)

0 100 200 300 400 500 600 700 800

Num

ber

0

1

2

3

4

5

Peak dE/dt [kV/m/µs]

Distance 15 m, 1999 Mean 304 kV/m/µsSt Dev 107 kV/m/µsMin 72.0 kV/m/µsMax 450 kV/m/µsGM 280 kV/m/µsSample Size 15

(a)

0 25 50 75 100 125 150 175 200 225 250

Num

ber

0

1

2

3

4

5

6



(b) Mean 92.6 kV/m/µsSt Dev 31.0 kV/m/µsMin 23.0 kV/m/µsMax 145 kV/m/µsGM 86.1 kV/m/µsSample Size 15

Figure 3-21. Peak dE/dt fields measured at (a) 15 m and (b) 30 m in 1999.

48

0 100 200 300 400 500 600 700 800

Num

ber

0

2

4

6

8

10


Distance 15 m, 2000

Mean 350 kV/m/µsSt Dev 156 kV/m/µsMin 50.0 kV/m/µsMax 673 kV/m/µsGM 308 kV/m/µsSample Size 31

(a)

0 25 50 75 100 125 150 175 200 225 250

Num

ber

0

2

4

6



Mean 178 kV/m/µsSt Dev 56.0 kV/m/µsMin 16.0 kV/m/µsMax 235 kV/m/µsGM 102 kV/m/µsSample Size 31

(b)

Figure 3-22. Peak dE/dt fields measured at (a) 15 m and (b) 30 m in 2000.

49

0 100 200 300 400 500 600 700 800

Num

ber

0

1

2

3

4


Distance 15 m, 2001

Mean 590 kV/m/µsSt Dev 61.0 kV/m/µsMin 519 kV/m/µsMax 644 kV/m/µsGM 579 kV/m/µsSample Size 4

(a)

0 25 50 75 100 125 150 175 200 225 250

Num

ber

0

1

2

3



Mean 210 kV/m/µsSt Dev 27.0 kV/m/µsMin 181 kV/m/µsMax 241 kV/m/µsGM 209 kV/m/µsSample Size 4

(b)

Figure 3-23 Peak dE/dt fields measured at (a) 15 m and (b) 30 m in 2001.

50

0 100 200 300 400 500 600 700 800

Num

ber

0

2

4

6

8

10

12

14

1999 n = 15 Mean = 304 kV/m/µs St. Dev. = 107 kV/m/µs 2000 n = 31 Mean = 350 kV/m/µs St.Dev. = 156 kV/m/µs2001 n = 4 Mean = 590 kV/m/µs St. Dev. = 61.0 kV/m/µs


Distance 15 m (1999, 2000, & 2001)

(a) Mean 355 kV/m/µsSt Dev 154 kV/m/µsMin 50.0 kV/m/µsMax 673 kV/m/µsGM 315 kV/m/µsSample Size 50

0 25 50 75 100 125 150 175 200 225 250

Num

ber

0

2

4

6

8

10

12

1999 n = 15 Mean = 92.6 kV/m/µs St. Dev. = 31.0 kV/m/µs2000 n = 31 Mean = 118 kV/m/µs St. Dev. = 56.0 kV/m/µs2001 n = 4 Mean = 211 kV/m/µs St. Dev. = 27.0 kV/m/µs

Distance 30 m (1999, 2000, & 2001)


(b) Mean 118 kV/m/µsSt Dev 56.0 kV/m/µsMin 16.0 kV/m/µsMax 241 kV/m/µsGM 103 kV/m/µsSample Size 50

Figure 3-24 Peak dE/dt fields measured at (a) 15 m and (b) 30 m in 1999, 2000 and 2001.

51

CHAPTER 4 ESTIMATION OF LEADER AND RETURN-STROKE CURRENTS FROM

MEASURED MAGNETIC FIELDS

4.1 Introduction

Magnetic fields measured at 15 and 30 m are available for 1999, 2000, and 2001.

In 1997, magnetic field records were measured at 5, 10, 20, and 30 m.

4.2 Estimation of Currents Using Ampere’s Law

According to Ampere’s law for magnetostatics, enc0Iµ=•∫ dlB , the line integral

of magnetic flux density, B, around a closed path is proportional to the enclosed current,

Ienc. The constant of proportionality µo is the permeability of free space. In SI units µo =

4π x 10-7 H/m.

For a straight wire of infinite length the magnetic flux density external to the wire

at a distance r from its axis is given by

r2IB o

πµ

=φ (4.1)

Figure 4-1. A straight current channel of infinite length and B at a distance r.

52

Here we have used the fact that the magnetic field is constant and tangential at any point

on the circular integration path. Equation (4.1) is essentially the same as equation (2.1).

If we assume that earth is a perfect conductor, and consider a very close

observation point (a distance 15 or 30 m compared to the lightning channel of some

kilometers) (4.1) will apply to a lightning channel above ground. Thus, knowing the

magnetic field at distance r, from the lightning channel and using (4.1) one can estimate

the current flowing in the channel if the magnetostatic approximation is valid.

Typical magnetic field waveforms with respect to time are shown in Figures 3.10

and 3.11. They usually exhibit a relatively slow initial front followed by a fast rise to

peak and then decay, as discussed below.

Figure 4-2. A streaked-image diagram of a dart leader—return-stroke sequence in a

rocket-triggered lightning flash

53

As the downward leader tip approaches ground surface the magnetic field on

ground associated with the leader current increases with time. When the leader attaches to

the ground, return stroke is initiated. Hence the current increases abruptly and there is a

fast rise in magnetic field.

The initial rising portion (up to the peak) of each magnetic field record can be

divided into two parts: a slow rise part corresponding to leader and steep rise part

corresponding to the return stroke. The division is illustrated in Figures 4-3 and 4-4,

where the magnitude of the leader part is labeled BL and that of the return stroke part BRS.

For each part the corresponding current was estimated using equation 4.1. It is important

to note that the leader current corresponds to the final stage of the dart-leader process,

when leader channel attaches to the ground, and the return-stroke current represents the

peak value based on the assumption that the leader current continues to flow in the

channel during the return-stroke process. Thus, the total peak current flowing in the

channel during the return-stroke stage is the sum of leader current inferred from BL and

return stroke current estimated from BRS.

Using this approach, leader and the return stroke currents for the years of 1997,

1999, 2000 and 2001 are evaluated. The histograms showing the statistics of leader and

return-stroke currents for 1997, 1999, 2000 and 2001 are shown in Figure 4-5 through

Figure 4-9.

The scatter plots (see Figures 4-13 and 4-14) show comparisons of leader currents

obtained from dE/dt (Kodali et al. 2005) vs. those obtained from magnetic fields (BL) and

of measured return stroke currents (see section 3.3) vs. those obtained from magnetic

fields (BRS).

54

Figure 4-3 Magnetic field at 15 m, Flash S9901, Stroke 3.


55

Distance 5 m, 1997

Leader Current [kA]0 1 2 3 4 5 6 7 8 9

Num

ber

0

1

2

3

4

5

6

Distance 10 m, 1997


Num

ber

0

1

2

3

4

5

6

Distance 20 m, 1997


Num

ber

0

1

2

3

4

5


Leader Current [kA]

0 1 2 3 4 5 6 7 8 9

Num

ber

0

1

2

3

4

5

6

(a) (b)

(c) (d)

Mean 1.80 kASt Dev 1.08 kAMin 0.94 kAMax 3.95 kAGM 1.58 kASample Size 7




Figure 4-5. Dart leader current inferred using Ampere’s Law for magnetostatics from

measured magnetic fields at (a) 5 m, (b) 10 m, (c) 20 m, and (d) 30 m in 1997.

56

Distance 15 m, 1999


Num

ber

0

2

4

6

8

10

12

14

16

18Mean 2.25 kASt. Dev. 1.02 kAMin 0.52 kAMax 4.29 kAGM 2.01 kASample Size 39

(a)

Distance 30 m, 1999


Num

ber

0

2

4

6

8

10

12

14


(b)


measured magnetic fields at (a) 15 m and (b) 30 m in 1999.

57

Distance 15 m, 2000


Num

ber

0

5

10

15

20


(a)

Distance 30 m, 2000


Num

ber

0

2

4

6

8

10

12

14


(b)



58

Distance 15 m, 2001


Num

ber

0

1

2

3

4


(a)

Distance 30 m, 2001


Num

ber

0

1

2

3

4


(b)



59

Distance 15 m, 1999,2000,&2001

Leader Current [kA]

0 1 2 3 4 5 6 7 8 9

Num

ber

0

10

20

30

40

50

1999 n = 39 Mean = 2.25 kA St. Dev. = 1.02 kA2000 n = 47 Mean = 1.53 kA St. Dev. = 0.82 kA2001 n = 11 Mean = 2.03 kA St. Dev. = 1.28 kA



measured magnetic fields at 15 m in 1999, 2000, and 2001.

60

Distance 30 m, 1997, 1999, 2000, and 2001

Leader Current [kA]

0 1 2 3 4 5 6 7 8 9

Num

ber

0

5

10

15

20

25

30

35




measured magnetic fields at 30 m in 1997, 1999, 2000, and 2001.

61

IL from B15 [kA]

0 2 4 6 8 10

I L fro

m B

30 [k

A]

0

2

4

6

8

10

199920002001

IL(30 m) = -0.10 + 1.44 IL(15 m) R2 = 0.83 Sample Size = 97


measured magnetic fields measured at 30 m vs. that at 15 m in 1999, 2000, and 2001.

62

IL from dE/dt [kA]

0 2 4 6 8 10 12

I L fro

m B

15 [k

A]

0

2

4

6

8

10

12

199920002001

IL(Ampere’s Law) = 1.23 + 0.32 IL(dE/dt)R2 = 0.51 Sample Size = 39

IL(dE/dt) [kA] IL(Amperes Law) [kA] Mean 3.51 2.36 StDev 2.39 1.07


magnetic fields measured at 15 m vs. leader current inferred from dE/dt measurements [Kodali et al. 2005] in 1999, 2000, and 2001.

63

IL from dE/dt [kA]

0 2 4 6 8 10

I L fro

m B

30 [k

A]

0

2

4

6

8

10

19992000 2001

IL(Ampere’s Law) = 3.6 + 0.44 IL(dE/dt) R2 = 0.56 Sample Size = 6

IL(dE/dt) [kA] IL(Amperes Law) [kA] Mean 4.98 5.86 StDev 2.90 1.71


magnetic fields measured at 30 m vs. leader current inferred from dE/dt measurements [Kodali et al. 2005] in 1999, 2000, and 2001.

64

Distance 5 m, 1997

Return-Stroke Peak Current [kA]0 4 8 12 16 20 24 28 32

Num

ber

0

1

2

3

4

Distance 10 m, 1997


0 4 8 12 16 20 24 28 32

Num

ber

0

1

2

3

4

Distance 20 m, 1997


Num

ber

0

1

2

3

4

5

Distance 30 m, 1997


Num

ber

0

1

2

3

4

5

(a) (b)

(c) (d)





Figure 4-14. Return-stroke peak currents inferred using Ampere’s Law for magnetostatics

from measured magnetic fields at (a) 5 m, (b) 10 m, (c) 20 m, and (d) 30 m in 1997.

65

Distance 15 m, 1999


Num

ber

0

2

4

6

8

10

12

14

(a) Mean 14.5 kASt Dev 6.40 kAMin 4.88 kAMax 28.7 kAGM 13.1 kASample Size 39

Distance 30 m, 1999


Num

ber

0

2

4

6

8

10

12

14(b) Mean 14.5 kA

St Dev 5.80 kAMin 5.70 kAMax 26.7 kAGM 13.4 kASample Size 39


from measured magnetic fields at (a) 15 m and (b) 30 m in 1999.

66

Distance 15 m, 2000


0 4 8 12 16 20 24 28 32

Num

ber

0

2

4

6

8

10

12

14


(a)

Distance 30 m, 2000


0 4 8 12 16 20 24 28 32

Num

ber

0

2

4

6

8

10

12

14


(b)



67

Distance 15 m, 2001


0 4 8 12 16 20 24 28 32

Num

ber

0

1

2

3

4


(a)

Distance 30 m, 2001


0 4 8 12 16 20 24 28 32

Num

ber

0

1

2

3

4


(b)



68

Distance 15 m, 1999, 2000, & 2001


0 4 8 12 16 20 24 28 32

Num

ber

0

5

10

15

20

25

30




from measured magnetic fields at 15 m in 1999, 2000, and 2001.

69

Distance 30 m, 1999, 2000, 2001 & 1997


0 4 8 12 16 20 24 28 32

Num

ber

0

5

10

15

20

25

30

35




from measured magnetic fields at 30 m in 1997, 1999, 2000, and 2001.

70

IRS from B15 [kA]

0 5 10 15 20 25 30 35

I RS

from

B30

[kA]

0

5

10

15

20

25

30

35

199920002001

IRS(30 m) = 0.99 + 0.93 IRS(15 m)R2 = 0.97 Sample Size = 97

Figure 4-20. Return-stroke peak current inferred using Ampere’s Law for magnetostatics

from measured magnetic fields at 30 m vs. that inferred from measured magnetic fields at 15 m in 1999, 2000, and 2001.

71

Measured IRS [kA]

0 5 10 15 20 25 30 35 40

I RS

from

B15

[kA]

0

5

10

15

20

25

30

35

40

199920002001

IRS(Ampere’s Law) = 0.08 + 0.83 IRS(Meas.) R2 = 0.86 Sample Size = 71

IRS(Meas.) [kA] IRS(Amperes Law) [kA] Mean 15.3 13.2 St. Dev. 6.70 6.10


from measured magnetic fields at 15 m vs. measured return-stroke peak current in 1999, 2000, and 2001.

72

Measured IRS [kA]

0 5 10 15 20 25 30 35 40

I RS

from

B30

[kA]

0

5

10

15

20

25

30

35

40

1999200020011997

IRS(Ampere’s Law) = 0.36 + 0.83 IRS(Meas.) R2 = 0.90 Sample Size = 76

IRS(Meas.) [kA] IRS(Ampere’s Law) [kA]Mean 15.4 13.1 St. Dev. 6.87 5.97


from measured magnetic fields at 30 m vs. measured return-stroke peak current in 1997, 1999, 2000, and 2001.

73

IRS from B15 [kA]

0 5 10 15 20 25 30 35

I L fro

m B

15 [k

A]

0

1

2

3

4

5

6

7

8

9

199920002001

IL(15 m) = 0.16 + 0.13 IRS(15 m) R2 = 0.68 Sample Size = 97

Figure 4-23. Leader vs. return-stroke currents inferred using Ampere’s Law for

magnetostatics from magnetic fields measured at 15 m in 1999, 2000, and 2001.

74

IRS from B30 [kA]

0 5 10 15 20 25 30 35

I L fro

m B

30 [k

A]

0

1

2

3

4

5

6

7

8

9

199920002001

IL(30 m) = -0.29 + 0.21 IRS(30 m) R2 = 0.72 Sample Size = 97

Figure 4-24. Leader vs. return-stroke currents inferred using Ampere’s Law for

magnetostatics from magnetic fields measured at 30 m in 1999, 2000, and 2001.

75

IRS from (BL+BRS)15m [kA]

0 5 10 15 20 25 30 35 40

I RS fr

om (B

L+B R

S) 30

m [k

A]

0

5

10

15

20

25

30

35

40

IRS from (BL+BRS)30m = 0.53 + 1.01 IRS from (BL+BRS)15m R2 = 0.98 Sample size = 97

Figure 4-25. Comparison of IRS from (BL+BRS)30m and IRS from (BL+BRS)15m for 1999,

2000, and 2001.

76

Measured IRS [kA]

0 10 20 30 40 50

I RS fr

om (B

L+B R

S) 15

m [k

A]

0

10

20

30

40

50

199920002001

IRS from (BL+BRS)15m = 0.07 + 0.95 IRS(Meas.) R2 = 0.87 Sample Size = 71

Figure 4-26. Comparison of IRS from (BL+BRS)15m inferred using Ampere’s Law for

magnetostatics vs. IRS measured at channel base in 1999, 2000, and 2001.

77

Measured IRS [kA]

0 10 20 30 40 50

I RS fr

om (B

L+B R

S) 30

m [k

A]

0

10

20

30

40

50

1999200020011997

IRS from (BL+BRS)30m = -0.02 + 1.01 IRS(Meas.) R2 = 0.89 Sample Size = 76

Figure 4-27. Comparison of IRS from (BL+BRS)30m inferred using Ampere’s Law for

magnetostatics vs. IRS measured at channel base in 1997, 1999, 2000, and 2001.

4.3 Discussion and Summary

From the statistical analysis of 97 records obtained in 1999, 2000, and 2001 the

mean dart-leader current (at the time of its attachment to ground) inferred from leader

magnetic fields measured at 15 m is 1.87 kA and standard deviation is 1.01 kA. The

minimum and maximum dart-leader currents are 0.38 and 5.40 kA, respectively. From

78

magnetic fields measured at 30 m (103 records obtained in 1997, 1999, 2000, and 2001),

the mean leader current is 2.58 kA and standard deviation is 1.57 kA. The minimum and

maximum dart-leader currents are 0.40 and 8.63 kA, respectively. Typically leader

currents are in the range of a few kiloamperes. Idone and Orville (1985) estimated dart-

leader peak currents for 22 leaders in two rocket-triggered flashes using the relation

between return-stroke peak current IR and return-stroke peak relative light intensity LR in

each of two flashes LR = 1.5 (IR)1.6 and LR = 6.4(IR)1.1 to the dart leader relative light

intensities in those flashes. The mean dart-leader current was 1.8 kA and the range was

0.1 to 6.0 kA. Results of this study are in reasonably good agreement with those of Idone

and Orville (1985).

Return-stroke peak currents estimated from magnetic fields (as the global magnetic

field peak minus the leader contribution) measured at 15 m in 1999, 2000, and 2001 have

a mean value of 13.2 kA and the standard deviation is 6.4 kA. For the individual years the

mean return-stroke current varies from 14.5 kA in 1999 to 12.0 kA in 2000 and 13.8 kA

in 2001. Return stroke peak currents estimated from magnetic fields measured at 30 m in

1997, 1999, 2000, and 2001 have a mean value of 13.0 kA and the standard deviation is

6.0 kA. For the individual years the mean return-stroke peak current varies from 9.9 kA

in 1997, to 14.9 kA in 1999, to 11.8 kA in 2000, and to 14.3 kA in 2001. These inferred

return-stroke peak currents are slightly lower than the directly measured return-stroke

peak currents whose mean is 15.3 kA and standard deviation is 7.5 kA. Depasse (1994)

reported an arithmetic mean of 14.3 kA (maximum value of 60 kA, standard deviation of

9 kA) for 305 peak current values directly measured at the Kennedy Space Center (KSC),

Florida and an arithmetic mean of 11 kA (maximum value 49.9 kA, and standard

79

deviation of 5.6 kA) for 54 values directly measured at Saint-Privat d’Allier, France.

Rakov et al. (1998), Crawford (1998), and Uman et al. (2000), reported an arithmetic

mean of 15.1 kA (sample size = 37, maximum = 44.4 kA, and st. dev. = 9 kA), 12. 8 kA

(sample size = 11, maximum = 22.6 kA, and st. dev. = 5.6 kA), and 14.8 kA (sample size

= 25, maximum = 33.2 kA, and st. dev. = 7 kA) from direct current measurements at

Camp Blanding in 1993, 1997, and 1998, respectively.

The return-stroke peak currents obtained using Ampere’s law for magnestotatics

and (BL+BRS), where BL and BRS are the leader and return-stroke contributions to the total

magnetic field (as done, for example, by Schoene et al. (2003)), measured at 15 m are

about 14 % higher than those obtained from BRS alone (excluding the leader

contribution). The return-stroke peak currents obtained using Ampere’s law for

magnestotatics and (BL+BRS) measured at 30 m are about 20 % higher than those

obtained from BRS alone.

Dart-leader current to return-stroke current ratio obtained from magnetic fields

measured at 15 m has a mean of 0.14 and the correlation coefficient between these

currents is 0.82. Leader to return-stroke current ratio obtained from magnetic fields at 30

m has a mean of 0.20 and the correlation coefficient is 0.85 (note that the determination

coefficient, R2, given in Figure 4-23 and Figure 4-24 is the square of the correlation

coefficient, R). Idone and Orville (1985) obtained the ratio of dart leader to return-stroke

current for 22 events having a mean of 0.17. Results of this study are consistent with

those of Idone and Orville (1985).

80

CHAPTER 5 DISPLACEMENT CURRENT ASSOCIATED WITH LEADER/RETURN STROKE

SEQUENCES IN TRIGGERED LIGHTNING

Maxwell’s integral equation relating azimuthal magnetic field to its sources has

been used to investigate the relative contributions of conduction and displacement

currents to the total ground level azimuthal magnetic field at 15 and 30 m from the base

of a triggered lightning stroke. The analysis is based on a comparison of channel base

current and corresponding magnetic fields measured at 15 and 30 m. It is concluded that

Ampere’s law for magnetostatics, which neglects the displacement current contribution,

is inadequate for presentation of the total magnetic field due to lightning strokes at

distances beyond approximately 30 m.

5.1 Displacement Current Estimates from Measured Magnetic Fields and Channel-Base Currents

The following simple expression (same as Eq. (2.1)) based on Ampere’s law for

magnetostatics is used here to estimate the azimuthal magnetic field intensity at the

ground due to nearby lightning:

( , ) ( ) / 2H r t I t rπ= (5.1)

where I(t) is the channel current, assumed to be the same in all contributing channel

sections, H(r,t) is the magnetic field intensity, and r is the radial distance from the

channel termination point on ground. This relationship has been found to describe

measured magnetic fields quite closely, in both magnitude and waveshape, at distances

up to 15 meters from the triggered-lightning channel base. Over the period from 1999 to

2001, magnetic field measurements have been made for nearly 70 return strokes in

81

Florida at a distance of 30 m from the triggered-lightning strike point. It is found that

amplitudes of the measured fields at both 15 and 30 m are somewhat lower then predicted

by Eq. 5.1, and the early portions of their waveforms exhibit slow fronts not seen in

measured current waveforms.

Figure 5-1. Superposition of measured magnetic field and channel-base current for Flash

S9903, stroke 3.

In order to examine the discrepancy, we consider as a starting point Maxwell’s

integral equation relating the azimuthal magnetic field to its arbitrary, time-varying

sources,

. . .ol S S

EH dl J d S d St

ε ∂= +

∂∫ ∫ ∫

.oS

EI d St

ε ∂= +

∂∫ = Ic + Id (5.2)

82

where Ic and Id are the channel-base conduction current and displacement current

respectively. As already described by Eq. 2.4 in section 2.6, the first term on the right

side of Eq. 5.2 corresponds to I(t) in Eq. 5.1. The second term is the displacement current

whose density is normal to the integration surface S bounded by the integration path l, on

the left-hand side of Eq. 5.2. When applied to a lightning stroke to earth with S being

defined as flat, circular area of integration lying on the surface of the ground and centered

at the strike point, the first term accounts for the effect of conduction current flowing

normally through the integration surface. The second term on right side of Eq. 5.2

accounts for the effects of time variation of the vertical electric field associated with the

changing charge density distribution along the lightning channel during both the

approach of the leader and the resultant return stroke.

Equivalently Eq. 5.2 can be written as

2d meas measI rH Iπ= − (5.3)

where Imeas and Hmeas are measured channel-base current and measured magnetic field at

distance r.

In order to investigate the peak displacement current, the following procedure was

used. As a first step, the measured magnetic field converted to current using Eq. 5.1. and

the measured conduction current, Imeas, at the channel base were superimposed. Then the

difference between the current obtained from magnetic field using Eq. 5.1 and directly

measured current was interpreted as the displacement current. The displacement current

appears to increase with time and has negative polarity up to the onset of the return

stroke. Upon initiation of the return stroke, the total displacement current at that point

changes polarity (becomes positive) and attains a peak of a few kA.

83

This is illustrated in Figure 5-2.

Figure 5-2. Displacement current for S9903 RS3 as inferred, using Eq. 5.3, from Imeas and

Hmeas at 30 m.

As seen in Fig. 5.2, the shape of the inferred displacement current waveform

resembles the shape of the electric field derivative (see Fig 3-13). Prior to the return-

stroke, while no conduction current is flowing at ground level, the effect of the

displacement current is apparent in the initial slow front of the measured magnetic field.

After the start of the return stroke, an abrupt increase in the slope of the magnetic field

takes place. Further effects of the displacement current component on the total magnetic

field are the reduction in amplitude of the peak of the magnetic field waveform.

Figures 5.3 – 5.6 show histograms of positive peak displacement currents (during

the return-stroke stage) for the years 1999, 2000, and 2001, estimated from waveforms

84

similar to that shown in Fig. 5-2. Similarly figures 5.7 – 5.10 show histograms of

negative peak displacement currents during the leader stage.

Distance 15 m, 1999

Return-Stroke Peak Displacement Current [kA]0 3 6 9 12 15

Num

ber

0

2

4

6

8

10

12

(a) Mean 6.09 kASt. Dev. 3.29 kAMin 1.10 kAMax 15.0 kAGM 5.25 kASample Size 23

Distance 30 m, 1999

Return-Stroke Peak Displacement current [kA]

0 3 6 9 12 15

Num

ber

0

2

4

6

8

10

(b) Mean 6.41 kASt. Dev. 3.11 kAMin 2.70 kAMax 15.0 kAGM 5.76 kASample Size 23

Figure 5-3. Return-stroke peak displacement current estimated, using Eq. 5.3, from Imeas and Hmeas at (a) 15 m and (b) 30 m in 1999.

85

Distance 15 m, 2000

Return-Stroke Peak Displacement Current [kA]

0 3 6 9 12 15

Num

ber

0

2

4

6

8

10

12

14

16(a)


Distance 30 m, 2000


0 3 6 9 12 15

Num

ber

0

2

4

6

8

10

12

14

16

18(b)


Figure 5-4. Return-stroke peak displacement current estimated, using Eq. 5.3, from Imeas

and Hmeas at (a) 15 m and (b) 30 m in 2000.

86

Distance 15 m, 2001


0 3 6 9 12 15

Num

ber

0

1

2

3

4

5

(a)Mean 4.07 kASt. Dev. 1.55 kAMin 2.30 kAMax 6.60 kAGM 3.82 kASample Size 8

Distance 30 m, 2001


0 3 6 9 12 15

Num

ber

0

1

2

3

4

5

6

(b)Mean 5.08 kASt. Dev. 1.86 kAMin 2.40 kAMax 7.70 kAGM 4.76 kASample Size 8

Figure 5-5. Return-stoke peak displacement current estimated, using Eq. 5.3, from Imeas

and Hmeas at (a) 15 m and (b) 30 m in 2001.

87

Distance 15 m


0 3 6 9 12 15

Num

ber

0

5

10

15

20

25

30

1999 n = 23 Mean = 6.09 kA St. Dev = 3.29 kA 2000 n = 31 Mean = 3.91 kA St. Dev = 2.15 kA2001 n = 8 Mean = 4.07 kA St. Dev = 1.55 kA


Distance 30 m


0 3 6 9 12 15

Num

ber

0

5

10

15

20

25

30

35



Figure 5-6. Return-stroke peak displacement current estimated, using Eq. 5.3, from Imeas

and Hmeas at (a) 15 m and (b) 30 m in 1999, 2000, and 2001.

88

Distance 15 m, 1999

Leader Peak Displacement Current [kA]

0 2 4 6 8 10

Num

ber

0

2

4

6

8

10

12

14(a)


Distance 30 m, 1999

Leader Peak Displacment Current [kA]

0 2 4 6 8 10

Num

ber

0

2

4

6

8

10

12(b) Mean 3.07 kA

St. Dev. 1.60 kAMin 0.50 kAMax 7.50 kAGM 2.66 kASample Size 23

Figure 5-7. Leader peak displacement current estimated, using Eq. 5.3, from Imeas and

Hmeas at (a) 15 m and (b) 30 m in 1999.

89

Distance 15 m, 2000


0 2 4 6 8 10

Num

ber

0

5

10

15

20(a)


Distance 30 m, 2000

Leader Peak Displamement Current [kA]

0 2 4 6 8 10

Num

ber

0

5

10

15

20

25(b)




90

Distance 15 m, 2001


0 2 4 6 8 10

Num

ber

0

1

2

3

4

5

6(a)


Distance 30 m, 2001


0 2 4 6 8 10

Num

ber

0

1

2

3

4

5(b)




91


Hmeas at (a) 15 m and (b) 30 m in 1999, 2000, and 2001.

92

5.2 Displacement Current Estimates from dE/dt Signatures at 15 and 30 m

Although variation of dE/dt as a function of radial distance from the lightning

channel is needed for estimating displacement current, a rough estimate of this current

can be obtained using dE/dt waveforms measured only at two distances, 15 and 30 m. In

the following, we will use two approximations to the expected distance dependence of

dE/dt, the latter being shown by a dashed line in Fig. 5-11.

In the first approximation, the dE/dt inside the circle of radius 15 m centered at the

channel attachment point is assumed to be constant and approximately equal to that at 15

m, and the dE/dt between 15 and 30 m is assumed to be constant and approximately equal

to that at 30 m. Clearly, this step-wise approximation of dE/dt distance dependence

(illustrated in Fig. 5-11) results in an underestimation of the displacement current.

Figure 5-11. Distance dependences of dE/dt used in evaluating displacement current within 30 m of the lightning channel based on measured dE/dt at 15 and 30 m.

The dE/dt waveform has a characteristic shape which is negative until the onset of

the return stroke. At the start of the return stroke, the polarity is reversed and its

Step-wise approximation

15 m 30 m

dEdt

Expected variation ofdEdt

Distance from the channel

Linear approximation

Measured at 30 mdEdt

Measured at 15 mdEdt

93

magnitude increases rapidly. This characteristic waveshape is seen both at 15 and 30 m.

At 30 m, the magnitude of dE/dt is smaller than at 15 m. Assuming that the dE/dt

waveform is similar at different distances ranging from 15 to 30 m from the lightning

channel, the next step was to determine the value of dE/dt at 30 m corresponding to dE/dt

peak at 15 m. Propagation over a distance of 15 m corresponds to 15/(3·108) = 5·10-8 s =

50 ns. dE/dt waveforms were digitized at 250 MHz. Since the sampling interval is 4 ns at

a rate of 250 MHz, the peak at 30 m will be observed after a delay of about 12 samples

after the occurrence of peak at 15 m. Thus, the dE/dt value at 30 m corresponding to the

peak at 15 m is 12 samples prior to the peak at 30 m. This gives us the dE/dt values at 15

and 30 m at the same instant on time but at different locations. The dE/dt values at 30 m

corresponding to dE/dt at 15 m along with peak dE/dt values at both 15 and 30 m are

given in Table 5-1.

Now, the displacement current based on the step-wise approximation of dE/dt distance

dependence can be estimated as

dI = .oS

E d St

ε ∂∂∫

15 30

0 15

(15 ) (30 )2 2o or r

E m E mrdr rdrt t

ε π ε π= =

∂ ∂= +

∂ ∂∫ ∫

2 2 2(15 ) (30 )2 (15 / 2) 2 (30 / 2 15 / 2)o oE m E m

t tε π ε π∂ ∂

= + −∂ ∂

(5.4)

Note that the displacement current estimated using Eq. 5.4 corresponds to the time of

peak dE/dt at 15 m. Displacement currents estimated in a manner described above are

summarized in Table 5-1, which also contains estimates obtained using peak values of

dE/dt at both 15 and 30 m (that is, without propagation delay taken into account).

The second approximation to the distance dependence of dE/dt, which has been used

here, is a linear approximation (also illustrated in Fig. 5-11),

94

dI = .oS

E d St

ε ∂∂∫

30

0

(15 ) ( 15) 2or

E m m r rdrt

ε π=

∂⎡ ⎤= + −⎢ ⎥∂⎣ ⎦∫

( ) ( )2 3 2(15 )2 (30 / 2) (30 / 3) (15).(30 / 2)oE m m m

tε π ⎡ ∂ ⎤⎛ ⎞= + −⎜ ⎟⎢ ⎥∂⎝ ⎠⎣ ⎦

i i i (5.5)

where

(15 ) (30 )

15 30

E m E mt tm

∂ ∂−

∂ ∂=−

is the slope of the slanted line shown in Fig. 5-11 for

linear approximation. Displacement current values calculated using Eq. 5.5 are given in

the last column of Table 5-1.

Figures 5.12 – 5.13 are the histograms of the displacement currents at the time of

dE/dt peak at 15 m, estimated using Eq. 5.4, for 1999, 2000 and 2001. Figures 5.14 –

5.15 are the histograms of the displacement currents, estimated using Eq. 5.4 and peak

values of dE/dt at both 15 and 30 m, that is, without accounting for propagation delay.

Figures 5.16 – 5.17 are histograms of the displacement currents, estimated using Eq. 5.5

and peak values of dE/dt at both 15 and 30 m.

95

Table 5-1 Displacement currents estimated using Eq. 5.4 (step-wise approximation of dE/dt distance dependence) and Eq. 5.5 (linear approximations of dE/dt distance dependence).

Flash and stroke ID

Peak dE/dt at

15m [kV/m/µs]

Peak dE/dt at

30m [kV/m/µs]

dE/dt at 30 m

corres-ponding

to peak at 15 m

[kV/m/µs]

Id at the time of

peak dE/dt at 15 m,

step-wise approx.

[kA]

Id using peak values of dE/dt at both 15 and

30 m, step-wise approx.

[kA]

Id using peak

values of dE/dt at both 15

and 30 m, linear

approx. [kA]

S9901 RS2 423 145 27 3.15 5.36 8.26S9901 RS3 172 55 14 1.34 2.11 3.33S9901 RS4 280 90 70 3.06 3.44 5.42S9915 RS4 198 74 34 1.88 2.63 3.92S9918 RS1 450 140 83 4.37 5.44 8.67S9918 RS2 235 80 15 1.75 2.97 4.59S9918 RS4 426 118 72 4.01 4.88 8.09S9918 RS6 362 96 47 3.15 4.06 6.84S9932 RS1 418 111 103 4.55 4.70 7.89S9932 RS2 307 80 32 2.52 3.42 5.79S9935 RS1 330 104 12 2.29 4.01 6.37S9935 RS3 300 92 10 2.06 3.60 5.77S9935 RS4 72 23 13 0.69 0.88 1.39S9935 RS5 250 77 3 1.62 3.01 4.81S9935 RS6 330 104 0 2.06 4.01 6.37S0006 RS1 182 73 70 2.45 2.51 3.64S0006 RS4 80 26 23 0.93 0.99 1.55S0006 RS5 50 16 12 0.54 0.61 0.97S0008 RS3 250 78 57 2.63 3.03 4.82S0008 RS4 495 166 82 4.63 6.21 9.64S0008 RS5 347 126 11 2.38 4.53 6.84S0008 RS6 258 82 8 1.76 3.15 4.99S0008 RS7 673 235 201 7.98 8.62 13.2S0012 RS1 545 200 76 4.83 7.16 10.8S0013 RS1 161 48 43 1.81 1.91 3.08S0013 RS3 336 105 54 3.11 4.07 6.48S0013 RS4 520 165 111 5.33 6.35 10.0S0013 RS5 345 107 41 2.93 4.16 6.64S0013 RS6 447 138 76 4.22 5.38 8.60

96

Table 5-1(Contd.) Displacement currents estimated using Eq. 5.4 (step-wise approximation of dE/dt distance dependence) and Eq. 5.5 (linear approximations of dE/dt distance dependence).

Flash and stroke ID

Peak dE/dt at

15m [kV/m/µs]

Peak dE/dt at

30m [kV/m/µs]

dE/dt at 30 m

corres-ponding

to peak at 15 m

[kV/m/µs]

Id at the time of

peak dE/dt at 15 m,

step-wise approx.

[kA]

Id using peak values of dE/dt at both 15 and

30 m, step-wise approx.

[kA]

Id using peak

values of dE/dt at both 15

and 30 m, linear

approx. [kA]

S0015 RS2 264 91 80.4 3.16 3.36 5.16S0015 RS4 456 166 31 3.43 5.96 8.99S0015 RS5 204 58 20 1.65 2.36 3.88S0015 RS6 349 113 76 3.61 4.30 6.76S0016 RS1 520 206 130 5.69 7.12 10.4S0016 RS5 227 95 18 1.76 3.20 4.58S0022 RS1 228 80 73 2.79 2.93 4.47S0022 RS2 406 130 33 3.16 4.98 7.85S0022 RS3 334 112 6 2.20 4.19 6.50S0023 RS1 339 111 11 2.33 4.20 6.58S0023 RS2 559 207 43 4.30 7.38 11.0S0023 RS3 656 216 88 5.75 8.15 12.7S0025 RS1 397 122 91 4.19 4.77 7.64S0025 RS3 229 67 25 1.90 2.69 4.38S0027 RS1 217 64 39 2.09 2.56 4.15S0027 RS2 355 120 23 2.65 4.47 6.92S0027 RS3 413 127 27 3.09 4.96 7.94S0105 RS5 644 241 5 4.12 8.55 12.7S0107 RS1 638 224 141 6.63 8.19 12.5S0123 RS2 560 181 7.5 3.64 6.90 10.8S0123 RS4 519 196 61 4.39 6.92 10.3

97

1999

Displacement Current [kA]

0 1 2 3 4 5 6 7 8

Num

ber

0

1

2

3

4

5(a) Mean 2.57 kA


2000


0 1 2 3 4 5 6 7 8

Num

ber

0

2

4

6

8

10(b) Mean 3.20 kA


Figure 5-12. Return-stroke displacement current within 30 m of the lightning channel at

the time of dE/dt peak at 15 m estimated using step-wise approximation (with propagation delay taken into account) in (a) 1999 and (b) 2000.

98

2001


0 1 2 3 4 5 6 7 8

Num

ber

0

1

2

3


1999, 2000, and 2001


0 1 2 3 4 5 6 7 8

Num

ber

0

2

4

6

8

10

12

14

1999 n = 15 Mean = 2.57 kA St. Dev = 1.13 kA2000 n = 31 Mean = 3.20 kA St. Dev = 1.59 kA2001 n = 4 Mean = 4.70 kA St. Dev = 1.33 kA


Figure 5-13. Return-stroke displacement current within 30 m of the lightning channel at

the time of dE/dt peak at 15 m estimated using step-wise approximation (with propagation delay taken into account) in (a) 2001 and (b) 1999, 2000, and 2001.

99

1999


0 1 2 3 4 5 6 7 8 9

Num

ber

0

1

2

3

4

5

6(a) Mean 3.63 kA


2000


0 1 2 3 4 5 6 7 8 9

Num

ber

0

2

4

6

8

10

12


Figure 5-14. Return-stroke displacement current within 30 m of the lightning channel

estimated using peak values of dE/dt at both 15 and 30 m estimated using step-wise approximation (without propagation delay taken into account) in (a) 1999 and (b) 2000.

100

2001


0 1 2 3 4 5 6 7 8 9

Num

ber

0

1

2

3

4

5(a) Mean 7.64 kA


1999, 2000, and 2001

Displacement Current [kA]0 1 2 3 4 5 6 7 8 9

Num

ber

0

2

4

6

8

10

12

14

16




estimated using peak values of dE/dt at both 15 and 30 m estimated using step-wise approximation (without taking propagation delay into account) in (a) 2001 and (b) 1999, 2000, and 2001.

101

1999


0 2 4 6 8 10 12 14

Num

ber

0

1

2

3

4

5

6(a) Mean 5.83 kA


2000


0 2 4 6 8 10 12 14

Num

ber

0

2

4

6

8

10

12(b) Mean 6.81 kA



estimated using peak values of dE/dt at both 15 and 30 m estimated using linear approximation (without propagation delay taken into account) in (a) 1999 and (b) 2000.

102

2001


0 2 4 6 8 10 12 14

Num

ber

0

1

2

3

4

5(a) Mean 11.6 kA


1999, 2000, and 2001

Displacement Current [kA]0 2 4 6 8 10 12 14

Num

ber

0

2

4

6

8

10

12

14

16




estimated using peak values of dE/dt at both 15 and 30 m estimated using linear approximation (without taking propagation delay into account) in (a) 2001 and (b) 1999, 2000, and 2001.

103

Figure 5-18 shows the scatter plot comparing displacement currents obtained using

Imeas and Hmeas (Eq. 5.3) vs. those obtained using dE/dt at 15 and 30 m at the time of peak

value of dE/dt at 15 m (step-wise approximation).

Displacement current from measured channel base current and associated magnetic field [kA]

0 2 4 6 8 10 12 14

Dis

plac

emen

t cur

rent

from

dE/

dt [k

A]

0

2

4

6

8

10

12

14

199920002001

Id(dE/dt) = 1.4 + 0.37 Id(Imeas and Hmeas) R2 = 0.43 Sample size = 21

Id(dE/dt) [kA] Id(Imeas and Hmeas) [kA] Mean 3.13 4.65 St. Dev. 1.52 2.50 Figure 5-18. Scatter plot showing displacement current estimates from dE/dt measured at

15 and 30 m from the lightning channel (step-wise approximation) vs. those estimated from measured channel base current and associated magnetic field. In the former case, the estimate corresponds to the time of peak value of dE/dt at 15 m.

104

Figure 5-19 is similar to Figure 5-18, but displacement currents on the vertical axis

are estimated using peak values of dE/dt at both 15 and 30 m (step-wise approximation),

that is, without taking into account propagation delay from 15 to 30 m.

Displacement current from measured channel base current and associated magnetic field [kA]

0 2 4 6 8 10 12 14

Dis

plac

emen

t cur

rent

from

dE

/dt [

kA]

0

2

4

6

8

10

12

14

199920002001


Id(dE/dt) [kA] Id(Imeas and Hmeas) [kA] Mean 4.43 4.65 St. Dev. 2.00 2.50 Figure 5-19. Scatter plot showing displacement current estimates from dE/dt measured at

15 and 30 m from the lightning channel (step-wise approximation) vs. those estimated from measured channel base current and associated magnetic field. In the former case, the estimate is obtained using peak values of dE/dt at both 15 and 30 m.

105

Figure 5-20 is similar to Figure 5-19, but displacement currents on the vertical axis

are estimated using linear approximation (see Fig. 5-11).

Displacement current from measured channel basecurrent and associated magnetic field [kA]

0 2 4 6 8 10 12 14

Dis

plac

emen

t cur

rent

from

dE

/dt [

kA]

0

2

4

6

8

10

12

14

199920002001


Id(dE/dt) [kA] Id(Imeas and Hmeas) [kA] Mean 6.90 4.65 St. Dev. 3.02 2.50 Figure 5-20. Scatter plot showing displacement current from dE/dt measured at 15 and 30

m from the lightning channel (linear approximation) vs. those estimated from measured channel base current and associated magnetic field. In the former case, the estimate is obtained using peak values of dE/dt at both 15 and 30 m.

106

5.3 Discussion and Summary

The displacement current waveform resembles the electric field derivative

waveform. The displacement current has negative polarity up to the onset of the return-

stroke. Upon initiation of the return-stroke, the total displacement current at that point

changes polarity (becomes positive) and attains a peak of a few kiloamperes.

The return-stroke peak displacement current inferred from channel-base currents,

Imeas, and associated magnetic fields, Hmeas, measured at 15 m in 1999, 2000, and 2001

has a mean value of 4.7 kA and standard deviation of 2.7 kA, while return-stroke peak

displacement current from Imeas and Hmeas at 30 m has a mean value of 5.5 kA and

standard deviation of 2.8 kA. The sample size for both 15 m and 30 m data is 62. The

leader peak displacement current from Imeas and Hmeas at 15 m has a mean of 2.2 kA and

standard deviation of 1.5 kA, whereas for 30-m measurements the mean is 2.4 kA and

standard deviation is 1.4 kA.

The return-stroke stage displacement current within 30 m of the lightning channel

at the time of dE/dt peak at 15 m estimated using step-wise approximation of dE/dt

variation with distance from the lightning channel (after taking propagation delay into

account) is characterized by a mean value of 3.1 kA. The minimum and maximum

values are 0.5 kA and 8.0 kA, respectively. The return-stroke displacement current within

30 m of the lightning channel estimated using peak values of dE/dt at both 15 and 30 m

(i.e. without taking propagation delay into account) and step-wise approximation of dE/dt

variation with distance from the lightning channel has a mean value of 4.4 kA. The

minimum value is 0.6 kA, and the maximum value is 8.6 kA. The return-stroke

displacement current within 30 m of the lightning channel estimated using peak values of

dE/dt at both 15 and 30 m and linear approximation of dE/dt variation with distance from

107

the lightning channel has a mean value of 6.9 kA. The minimum value is 1.0 kA, and the

maximum value is 13.2 kA. Note that the displacement current during the return-stroke

stage flows in the direction opposite to that of the conduction current in the lightning

channel.

Schnetzer et al. (1998) have obtained the displacement current for flash 96-23,

stroke 5, which had a return-stroke peak current directly measured at the channel base of

approximately 20 kA. The return-stroke peak displacement current was 13.5 kA within

50 m of the lightning channel and 0.7 kA within 10 m of the lightning channel. Our

results match reasonably well those obtained by Schnetzer et al. (1998).

The correlation coefficient of 0.66 is obtained between displacement current

estimates obtained from dE/dt measured at 15 and 30 m from the lightning channel (using

step-wise approximation and at the time of peak value of dE/dt at 15 m) and those

obtained from measured channel base currents and associated magnetic fields at 30 m.

108

CHAPTER 6 SUMMARY

From the statistical analysis of 97 records obtained in 1999, 2000, and 2001 the

mean dart-leader current (at the time of its attachment to ground) inferred from leader

magnetic fields measured at 15 m is 1.87 kA and standard deviation is 1.01 kA. The

minimum and maximum dart-leader currents are 0.38 and 5.40 kA, respectively. From

magnetic fields measured at 30 m (103 records obtained in 1997, 1999, 2000, and 2001),

the mean leader current is 2.58 kA and standard deviation is 1.57 kA. The minimum and

maximum dart-leader currents are 0.40 and 8.63 kA, respectively. Typically leader

currents are in the range of a few kiloamperes. Idone and Orville (1985) estimated dart-

leader peak currents for 22 leaders in two rocket-triggered flashes using the relation

between return-stroke peak current IR and return-stroke peak relative light intensity LR in

each of two flashes LR = 1.5 (IR)1.6 and LR = 6.4(IR)1.1 to the dart leader relative light

intensities in those flashes. The mean dart-leader current was 1.8 kA and the range was

0.1 to 6.0 kA. Results of this study are in reasonably good agreement with those of Idone

and Orville (1985).

Return-stroke peak currents estimated from magnetic fields (as the global magnetic

field peak minus the leader contribution) measured at 15 m in 1999, 2000, and 2001 have

a mean value of 13.2 kA and the standard deviation is 6.4 kA. For the individual years the

mean return-stroke current varies from 14.5 kA in 1999 to 12.0 kA in 2000 and 13.8 kA

in 2001. Return stroke peak currents estimated from magnetic fields measured at 30 m in

1997, 1999, 2000, and 2001 have a mean value of 13.0 kA and the standard deviation is

109

6.0 kA. For the individual years the mean return-stroke peak current varies from 9.9 kA

in 1997, to 14.9 kA in 1999, to 11.8 kA in 2000, and to 14.3 kA in 2001. These inferred

return-stroke peak currents are slightly lower than the directly measured return-stroke

peak currents whose mean is 15.3 kA and standard deviation is 7.5 kA. Depasse (1994)

reported an arithmetic mean of 14.3 kA (maximum value of 60 kA, standard deviation of

9 kA) for 305 peak current values directly measured at the Kennedy Space Center (KSC),

Florida and an arithmetic mean of 11 kA (maximum value 49.9 kA, and standard

deviation of 5.6 kA) for 54 values directly measured at Saint-Privat d’Allier, France.

Rakov et al. (1998), Crawford (1998), and Uman et al. (2000), reported an arithmetic

mean of 15.1 kA (sample size = 37, maximum = 44.4 kA, and st. dev. = 9 kA), 12. 8 kA

(sample size = 11, maximum = 22.6 kA, and st. dev. = 5.6 kA), and 14.8 kA (sample size

= 25, maximum = 33.2 kA, and st. dev. = 7 kA) from direct current measurements at

Camp Blanding in 1993, 1997, and 1998, respectively.

The return-stroke peak currents obtained using Ampere’s law for magnestotatics

and (BL+BRS), where BL and BRS are the leader and return-stroke contributions to the total

magnetic field (as done, for example, by Schoene et al. (2003)), measured at 15 m are

about 14 % higher than those obtained from BRS alone (excluding the leader

contribution). The return-stroke peak currents obtained using Ampere’s law for

magnestotatics and (BL+BRS) measured at 30 m are about 20 % higher than those

obtained from BRS alone.

Dart-leader current to return-stroke current ratio obtained from magnetic fields

measured at 15 m has a mean of 0.14 and the correlation coefficient between these

currents is 0.82. Leader to return-stroke current ratio obtained from magnetic fields at 30

110

m has a mean of 0.20 and the correlation coefficient is 0.85. Idone and Orville (1985)

obtained the ratio of dart leader to return-stroke current for 22 events having a mean of

0.17.

The displacement current waveform resembles the electric field derivative

waveform. The displacement current has negative polarity up to the onset of the return-

stroke. Upon initiation of the return-stroke, the total displacement current at that point

changes polarity (becomes positive) and attains a peak of a few kiloamperes.

The return-stroke peak displacement current inferred from channel-base currents,

Imeas, and associated magnetic fields, Hmeas, measured at 15 m in 1999, 2000, and 2001

has a mean value of 4.7 kA and standard deviation of 2.7 kA, while return-stroke peak

displacement current from Imeas and Hmeas at 30 m has a mean value of 5.5 kA and

standard deviation of 2.8 kA. The sample size for both 15 m and 30 m data is 62. The

leader peak displacement current from Imeas and Hmeas at 15 m has a mean of 2.2 kA and

standard deviation of 1.5 kA, whereas for 30-m measurements the mean is 2.4 kA and

standard deviation is 1.4 kA.

The return-stroke stage displacement current within 30 m of the lightning channel

at the time of dE/dt peak at 15 m estimated using step-wise approximation of dE/dt

variation with distance from the lightning channel (after taking propagation delay into

account) is characterized by a mean value of 3.1 kA. The minimum and maximum

values are 0.5 kA and 8.0 kA, respectively. The return-stroke displacement current within

30 m of the lightning channel estimated using peak values of dE/dt at both 15 and 30 m

(i.e. without taking propagation delay into account) and step-wise approximation of dE/dt

variation with distance from the lightning channel has a mean value of 4.4 kA. The

111

minimum value is 0.6 kA, and the maximum value is 8.6 kA. The return-stroke

displacement current within 30 m of the lightning channel estimated using peak values of

dE/dt at both 15 and 30 m and linear approximation of dE/dt variation with distance from

the lightning channel has a mean value of 6.9 kA. The minimum value is 1.0 kA, and the

maximum value is 13.2 kA. Note that the displacement current during the return-stroke

stage flows in the direction opposite to that of the conduction current in the lightning

channel.

Schnetzer et al. (1998) have obtained the displacement current for flash 96-23,

stroke 5, which had a return-stroke peak current directly measured at the channel base of

approximately 20 kA. The return-stroke peak displacement current was 13.5 kA within

50 m of the lightning channel and 0.7 kA within 10 m of the lightning channel. Our

results match reasonably well those obtained by Schnetzer et al. (1998).

The correlation coefficient of 0.66 is obtained between displacement current

estimates obtained from dE/dt measured at 15 and 30 m from the lightning channel (using

step-wise approximation and at the time of peak value of dE/dt at 15 m) and those

obtained from measured channel base currents and associated magnetic fields at 30 m.

112

CHAPTER 7 RECOMMENDATIONS FOR FUTURE RESEARCH

Additional data are needed to verify the findings presented here. In future

measurements, magnetic field records should be synchronized to better than 40-50 ns

with return stroke current records, so that the onset of return stroke current can be

accurately identified in the magnetic field waveform. This will allow one to better

distinguish the leader and return-stroke parts of the magnetic field waveform and hence

obtain more accurate estimates of the dart-leader current. Additional measurements of

dE/dt waveforms are needed and at more distances from the lightning channel. This will

give a better approximation of dE/dt variation with distance and, as a result, more

accurate estimates of the displacement current. Data collected during 1997, 1999, 2000,

and 2001 should be analyzed further to infer additional properties of rocket-triggered

lightning. For example, multiple-station electric and magnetic field measurements can be

used for estimating distributions of charge and current along the lightning channel.

113

APPENDIX DISPLACEMENT CURRENT GRAPHS

In this appendix, the displacement current waveforms inferred from measured

channel-base currents, Imeas, and associated magnetic fields, Hmeas, measured at 15 and 30

m for strokes in lightning flashes triggered in 1999 (23 strokes), 2000 (31 strokes), and

2001 (8 strokes) are shown. The displacement currents were estimated as

2d meas measI rH Iπ= − .

144

LIST OF REFERENCES

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Uman, M.A.; The Lightning Discharge; Academic Press, San Diego, California; 1987

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Uman, M.A., Schoene, J., Rakov, V.A., Rambo, K.J., and Schnetzer, G.H.; "Correlated Time Derivatives of Current, Electric Field Intensity, and Magnetic Flux Density for Triggered Lightning at 15 m," J. Geophys. Res., 107, D13, 4160, 10.1029/2000JD000249, 2002

Wang, D., Rakov, V.A., Uman, M.A., Fernandez, M.I., Rambo, K.J., Schnetzer, G.H., and Fisher, R.J.; "Characterization of the Initial Stage of Negative Rocket-Triggered Lightning," J. Geophys. Res., 104, 4213-4222, 1999

Wang, D., Rakov, V.A., Uman, M.A., Takagi, N., Watanabe, T., Crawford, D.E., Rambo, K.J., Schnetzer, G.H., Fisher, R.J., and Kawasaki, Z.I.; "Attachment Process in Rocket-Triggered Lightning Strokes," J. Geophys. Res., 104, 2141-2150, 1999

147

BIOGRAPHICAL SKETCH

Ashwin Jhavar was born in Akola, India, in 1979. He graduated with a bachelor’s

degree in electrical and electronics engineering from Birla Institute of Technology and

Science, India, in 2002. In 2003, he went to the USA to pursue graduate studies at the

University of Florida.

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