1

4b Properties of negative downward lightning discharge to ground - II

Cloud Charge

DistributionPreliminaryBreakdown

SteppedLeader

AttachmentProcess

First ReturnStroke

DartLeader

K and J

Process

t = 0 100 ms 110 ms 120 ms

1900 ms 2000 ms 2010 ms 2020 ms

4000 ms 6000 ms 6100 ms 6205 ms

A drawing illustrating various processes comprising a negative cloud-to-ground lightning flash Adapted from Uman

(1987 2001)

Second ReturnStroke

Downward Negative Lightning Discharges to Ground

2

(a)

Streak‐camera photograph of a lightning discharge to a tower on Monte San

Salvatore Switzerland showing evidence of an upward connecting

leader

(b)

Still photograph of the same flash and another flash that attached to the tower

below its top

Adapted from Berger and Vogelsanger

(1966)

(a)

Streak‐camera photograph of a lightning discharge to a tower on Monte San

Salvatore Switzerland showing evidence of an upward connecting

leader

(b)

Still photograph of the same flash and another flash that attached to the tower

below its top

Adapted from Berger and Vogelsanger

(1966)

Adapted from Howard (2009)5

Lightning Attachment Process

6

Optical Images of Leader and Attachment Process ndash Triggered Lightning

Dart-stepped leader and attachement

process in rocket-triggered lightning (Sept 17 2008) at Camp Blanding Florida Photron

FASTCAM SA11 50000 fps (20 micros per frame)

Biagi

et al (2009 GRL)2 frames before return stroke 8 1 frame before return stroke 8

56 m

16 m

25 m

7

Optical Images of Leader and Attachment Process ndash Laboratory Sparks

Single-frame K008 images of four negative discharges (-22 MV1307500 μs) in a 45 m rod-rod gap Frame duration in a b and c is 2 micros and in d it is 05 micros L in b is the length of last step Adapted from Lebedev et al (2007)

-4

5 m

8

Optical Images of Attachment Process

55

m

HV rod

JP

Single-frame image-converter-camera K008 images of negative discharges in a 55-m rod-rod gap with frame exposure of 02 μs JP is the junction point between downward negative and upward connecting positive leaders Adapted from

Shcherbakov

et al (2006)

A photograph of a lightning strike to a chimney pot showing a split in the channel interpreted as evidence of an upward connecting leader Adapted from Golde

(1967)

JP

9

Illustration of capture surfaces of two towers and earthrsquos surface in the electrogeometrical

model (EGM) rs

is the striking distance defined as the distance from the tip of the descending leader to the object to be struck at the instant when an upward connecting leader is initiated from this object

Vertical arrows represent descending leaders assumed to be uniformly distributed (Ng=const) above the capture surfaces Adapted from Bazelyan

and Raizer

(2000)

Electrogeometrical Model (EGM)

rs

rsrs

Capture surfaces

Ng=const

10

Electrogeometrical Model (EGM)

rs

= 10 I065 m where I

is in kA

4

3

12

Striking distance rs

versus return-stroke peak current I

[curve 1 Golde

(1945) curve 2 Wagner (1963) curve 3 Love (1973) curve 4 Ruhling

(1972) x theory of Davis (1962) estimates from two-

dimensional photographs by Eriksson (1978) estimates from three-dimensional photography by Eriksson (1978) Adapted from Golde

(1977) and Eriksson (1978)

I kA rs m

10 45

30 91

170 282

11

Scatter plot of impulse charge Q versus return-stroke peak current

I Note that both vertical and horizontal scales are logarithmic The best fit to data I

= 106 Q07 where Q is in coulombs and I

is in kiloamperes was used in deriving rs

= 10 I065

Adapted from Berger (1972)

Electrogeometrical Model (EGM)

Finding rs = f(I)

bull

Assume critical average electric field between the leader tip and the strike object at the time of initiation of upward connecting leader from the object (200-600 kVm)

bull

Use an empirical relation between Q and I

to find rs

= f(I)

bull

Find rs

= f(Q)

bull

Assume leader geometry total leader charge Q and distribution of this charge along the channel

Q

10-1

100

101

102

100 101 102I

I

peak Q impulseneg first strokes n=89

I

= 106 Q07

For Q = 5 CI

= 33 kA

12

Electrogeometrical Model (EGM)

Illustration of the rolling-sphere method (RSM) The shaded area is that area into which it is postulated lightning cannot enter Adapted from Szczerbinski

(2000)

rs

rsrs

rs = 45 m (150 ft) (NFPA 780 2004) corresponds to I

= 10 kA (95 of currents exceed this value)

Rolling-Sphere Method

Return‐Stroke Fields Variation with Distance

Typical vertical electric field intensity (left column) and azimuthal

magnetic flux density (right column) waveforms for first (solid line) and subsequent (dashed line) return strokes at distances of 1 2 and 5 km Adapted from Lin et al (1979)

Electric Field Intensity Magnetic Flux Density

Return‐Stroke Fields Variation with Distance

Electric Field IntensityMagnetic Flux Density

Typical vertical electric field intensity (left column) and azimuthal

magnetic flux density (right column) waveforms for first (solid line) and subsequent (dashed line) return strokes at distances of 10 15 50 and 200 km Adapted from Lin et al (1979)

Return-Stroke Current Waveshapes

ndash

Switzerland (Berger et al 1975)

15

Average negative first and subsequent-stroke current waveshapes

each shown on two time scales A

and B The lower time scales (A) correspond to the solid curves while the upper time scales (B) correspond to the broken curves The vertical (amplitude) scale is in relative units the peak values being equal to negative unity Adapted from Berger et al (1975)

Lightning Parameters Derived from Direct Current Measurements

Parameters Units Sample Size

Percent Exceeding Tabulated Value

95 50 5

Peak current

(minimum 2 kA)First strokesSubsequent strokes

kA 101135

1446

3012

8030

Charge

(total charge)First strokesSubsequent strokesComplete flash

C 9312294

110213

521475

241140

Impulse charge

(excluding continuing current)

First strokesSubsequent strokes

C90

11711

02245

09520

4Front duration

(2 kA to peak)First strokesSubsequent strokes

μs 89118

18022

5511

1845

Maximum dIdtFirst strokesSubsequent strokes

kA μs-1 92122

5512

1240

32120

Stroke duration

(2 kA to half peak value on the tail)

First strokesSubsequent strokes

μs90

1153065

7532

200140

Action integral (intI2dt)First strokesSubsequent strokes

A2s 9188

60 x 103

55 x 10255 x 104

60 x 10355 x 105

52 x 104

17

Cumulative statistical distributions of lightning peak currents

giving percent of cases exceeding abscissa value from direct measurements in Switzerland (Berger 1972 Berger et al 1975) The distributions are assumed to be lognormal and given for (1) negative first strokes (2) positive first strokes (3) negative and positive first strokes and (4) negative subsequent strokes Adapted from Bazelyan

et al (1978)

Lightning peak currents for first strokes vary by a factor of 50 or more from about 5 to 250 kA

The probability of occurrence of a given value rapidly increases up to 25 kA

or so and then slowly decreasesStatistical distributions of this type are often assumed to be lognormal

Lightning Peak Current ndash

Bergerrsquos Distributions

18

Cumulative statistical distributions of peak currents (percent values on the vertical axis should be subtracted from 100 to obtain the probability to exceed the peak current value on the horizontal axis) for negative first strokes adopted by IEEE

and CIGRE Taken from CIGRE Document 63 (1991)

For the CIGRE

distribution 98 of peak currents exceed 4 kA 80 exceed 20 kA and 5 exceed 90 kA

For the IEEE

distribution the ldquoprobability to exceedrdquo

values are given by the following equation

where PI

is in per unit and I is in kA This equation applies to values of I up to 200 kA The median (50) peak current value is equal to 31 kA

Peak current I kA(IEEE

distribution) 5 10 20 40 60 80 100 200

Percentage exceeding tabulated value PI

10099 95 76 34 15 78 45 08

( ) 62

311

1I

PI+

=

Lightning Peak Current ndash

IEEE and CIGRE Distributions

dIdt

in Rocket-Triggered Lightning ( ~100 kAμs)

19

Relation between the peak rate of current rise dIdt and the peak current I from triggered-lightning experiments conducted at the NASA Kennedy Space Center Florida in 19851987 and 1988 and in France in 1986 The regression line for each year is shown the sample size N and the regression equation are given in table Adapted from Leteinturier

et al (1991)

Morro Do Cachimbo

Tower (60 m) Belo Horizonte Brazil

20

Courtesy Prof Dr Silverio Visacro Filho Lightning Research Center (UFMG-CEMIG)

Lightning Parameters Derived from Direct Current Measurements ndash

Brazil

21

First Stroke

Subsequent Strokes

404

52

163

099

Optical Measurements of Return-Stroke Speed

22

Optical intensity (in millivolts

at the input of the oscilloscope) vs time waveforms at four different heights 7 63 117 and 170 m

above the lightning termination point for stroke 1 in flash F0336 Adapted from Olsen et al (2004)

23

Reference St Dev ms Comments

Natural Lightning

Boyle and Orville (1976)

20 x 107 12 x 108 071 x 108 26 x 107 12 Streak camera 2-D speed

Idone and Orville (1982)

29 x 107 24 x 108 11 x 108 47 x 107 63 Streak camera2-D speed

Mach and Rust (1989a Fig 7)

20 x 107

80 x 10726 x 108

gt28 x 1085 x 107

7 x 1075443

Long channelShort channel (Photoelectric 2-D)

Triggered Lightning

Hubert and Mouget (1981)

45 x 107 17 x 108 99 x 107 41 x 107 13 Photoelectric3-D speed

Idone et al (1984) 67 x 107 17 x 108 12 x 108 27 x 107 56 Streak camera 3-D speed

Willett et al (1988)

10 x 108 15 x 108 12 x 108 16 x 107 9 Streak camera 2-D speed

Willett et al (1989a)

12 x 108 19 x 108 15 x 108 17 x 107 18 Streak camera 2-D speed

Mach and Rust (1989a Fig 8)

60 x 107

60 x 10716 x 108

20 x 1082 x 107

4 x 1074039

Long channelShort channel(Photoelectric 2-D)

Min ms Max ms Mean ms Sample

Size

13 plusmn03 x 108

19 plusmn07 x 108

12 plusmn03 x 108

14 plusmn04 x 108

Summary of measured return stroke speeds averaged over the visible part of the channel in natural and triggered negative lightning Adapted from Rakov

et al (1992b)

Return-Stroke Speed Near Ground

24

Height Above Ground

7-63 m

63-117 m

117-170

m

12

16

15

12121213

18

16

16

17

18 18

1512

Return-stroke speed profiles estimated tracking the 20 point on the light-pulse front for triggered lightning flash F0336 (Olsen et al 2004)

Return-Stroke Speed vs Return-Stroke Peak Current

25

Return-stroke speed vs peak current for 29 triggered-lightning strokes observed at the Kennedy Space Center (KSC) Florida in 1986 and reported by Mach and Rust (1989a) and 18 triggered-lightning strokes from the 1987 KSC experiments reported by Willett et al

(1989a) Peak curent shown in the scatter plot as 38 kA may be an underestimate Note that the linear correlation coefficients (r) for both data sets are low and negative not in support of the often assumed relationship between these two lightning parameters

00

05

10

15

20

25

0 5 10 15 20 25 30 35 40 45

Return-Stroke Peak Current kA

Ret

urn-

Stro

ke S

peed

108 m

s

Mach and Rust (1989a) r = -008

Willett el al (1998a) r = -027

First Return Stroke

Electric field waveforms of a first return stroke The waveform is shown on two time scales 5 μsdiv

and 10 μsdiv The fields are normalized to a distance of 100 km L denotes individual leader pulses F slow front and R fast transition Also marked are the small secondary peak or shoulder α

and the larger subsidiary peaks a b and c Adapted from Weidman and Krider

(1978)

-20 -15 -10 -5 0 5 10 15 20

5

microsdiv

10

microsdiv

-60 -40 -20 0 20 40 60 80

26

Subsequent Return Strokes

-20 -15 -10 -5 0 5 10 15 20

5 microsdiv

5 microsdiv

10 microsdiv

10 microsdiv

-60 -40 -20 0 20 40 60 80

Electric field waveforms of (b) a subsequent return stroke initiated by a dart-stepped leader and (c) a subsequent return stroke initiated by a dart leader showing the fine structure both before and after the initial field peak Each waveform is shown on two time scales 5 μsdiv

and 10 μsdiv The fields are normalized to a distance of 100 km L denotes individual leader pulses F slow front and R fast transition Also marked are the small secondary peak or shoulder α

and the larger subsidiary peaks a b and c Adapted from Weidman and Krider

(1978)

27

First Return Stroke Electric Field Derivative

Examples of (top) the time derivative of the electric field intensity dEdt

and (bottom)

the electric field intensity E produced by a first return stroke at a distance of about 36 km over the Atlantic Ocean The propagation path was almost entirely over salt water The vertical arrow under the E record shows the time of the dEdt

trigger Adapted from Krider

et al (1996)

28

Return Strokes Measured Parameters

Parameters of microsecond-scale electric field waveforms produced by negative return strokes

Parameter Location First strokes Subsequent strokes

Sample size Mean SD Sample size Mean SD

Initial peak (V m‐1) (normalized to 100 km)Rakov

and Uman

(1990b)

Cooray

and Lundquist (1982)Lin et al (1979)

Florida

SwedenKSCOcala

76

5535129

59 (GM)

536758

273825

232a

38b

8359

27(GM)41(GM)

5043

2215

Zero‐crossing time (μs)Cooray

and Lundquist (1985)

Lin et al (1979)

SwedenSri LankaFlorida

1029146c

498954

123018

9414377c

394236

81417

Zero‐to‐peak rise time (μs)Master et al (1984)Cooray

and Lundquist (1982)Lin et al (1979)

FloridaSwedenKSCOcala

1051405129

44702427

18201213

220

8359

28

1519

15

0807

10‐90 percent rise time (μs)Master et al (1984) Florida 105 26 12 220 15 09

Slow front duration

(μs)Master et al (1984)Cooray

and Lundquist (1982)Weidman and Krider

(1978)

FloridaSwedenFlorida

105826290

29504041

13201716

44 120 34d

060921

020509

29

Return Strokes Measured ParametersParameters of microsecond-scale electric field waveforms produced by negative return strokes (contrsquod)

Parameter Locatio

nFirst strokes Subsequent strokes

Sample size

Mean SD Sample size Mean SD

Slow front amplitude as percentage of peakMaster et al (1984)Cooray

and Lundquist (1982)Weidman and Krider

(1978)

FloridaSwedenFlorida

105836290

28415040

15112020

4412034d

202540

101020

Fast

transition 10-90 percent risetime

(ns)Master et al (1984)Weidman and Krider

(1978)

Weidman and Krider

(1980a 1984)

Weidman (1982)

FloridaFlorida

Florida

1023815125

97020020090

68010010040

2178034

610200150

27040100

Peak time derivative (normalized to100 km ) (V m-1

μs-1)Krider

et al (1996) Florida 63 39 11

Time derivative pulse width at half-peak value (ns)

Krider

et al (1996) Florida 61 100 20

If not specicied

otherwise multiple lines for a given source for the same location correspond to different thunderstorms GM = geometric mean value a better characteristic of the distribution of initial field peaks since this distribution is approximately log-normala

Strokes following previously formed channelb

Strokes creating new termination on groundcBoth

electric and magnetic fieldsd

Subsequent strokes initiated by dart-stepped leaders Other subsequent strokes studied by Weidman and

Krider

(1978) were initiated by dart leaders

30

• Slide Number 1
• Slide Number 2
• Slide Number 3
• Slide Number 4
• Slide Number 5
• Slide Number 6
• Slide Number 7
• Slide Number 8
• Slide Number 9
• Slide Number 10
• Slide Number 11
• Slide Number 12
• Return-Stroke Fields Variation with Distance
• Return-Stroke Fields Variation with Distance
• Slide Number 15
• Slide Number 16
• Slide Number 17
• Slide Number 18
• Slide Number 19
• Slide Number 20
• Slide Number 21
• Slide Number 22
• Slide Number 23
• Slide Number 24
• Slide Number 25
• First Return Stroke
• Subsequent Return Strokes
• First Return Stroke Electric Field Derivative
• Return Strokes Measured Parameters
• Return Strokes Measured Parameters

Cloud Charge

DistributionPreliminaryBreakdown

SteppedLeader

AttachmentProcess

First ReturnStroke

DartLeader

K and J

Process

t = 0 100 ms 110 ms 120 ms

1900 ms 2000 ms 2010 ms 2020 ms

4000 ms 6000 ms 6100 ms 6205 ms

A drawing illustrating various processes comprising a negative cloud-to-ground lightning flash Adapted from Uman

(1987 2001)

Second ReturnStroke

Downward Negative Lightning Discharges to Ground

2

(a)

Streak‐camera photograph of a lightning discharge to a tower on Monte San

Salvatore Switzerland showing evidence of an upward connecting

leader

(b)

Still photograph of the same flash and another flash that attached to the tower

below its top

Adapted from Berger and Vogelsanger

(1966)

(a)

Streak‐camera photograph of a lightning discharge to a tower on Monte San

Salvatore Switzerland showing evidence of an upward connecting

leader

(b)

Still photograph of the same flash and another flash that attached to the tower

below its top

Adapted from Berger and Vogelsanger

(1966)

Adapted from Howard (2009)5

Lightning Attachment Process

6

Optical Images of Leader and Attachment Process ndash Triggered Lightning

Dart-stepped leader and attachement

process in rocket-triggered lightning (Sept 17 2008) at Camp Blanding Florida Photron

FASTCAM SA11 50000 fps (20 micros per frame)

Biagi

et al (2009 GRL)2 frames before return stroke 8 1 frame before return stroke 8

56 m

16 m

25 m

7

Optical Images of Leader and Attachment Process ndash Laboratory Sparks

Single-frame K008 images of four negative discharges (-22 MV1307500 μs) in a 45 m rod-rod gap Frame duration in a b and c is 2 micros and in d it is 05 micros L in b is the length of last step Adapted from Lebedev et al (2007)

-4

5 m

8

Optical Images of Attachment Process

55

m

HV rod

JP

Single-frame image-converter-camera K008 images of negative discharges in a 55-m rod-rod gap with frame exposure of 02 μs JP is the junction point between downward negative and upward connecting positive leaders Adapted from

Shcherbakov

et al (2006)

A photograph of a lightning strike to a chimney pot showing a split in the channel interpreted as evidence of an upward connecting leader Adapted from Golde

(1967)

JP

9

Illustration of capture surfaces of two towers and earthrsquos surface in the electrogeometrical

model (EGM) rs

is the striking distance defined as the distance from the tip of the descending leader to the object to be struck at the instant when an upward connecting leader is initiated from this object

Vertical arrows represent descending leaders assumed to be uniformly distributed (Ng=const) above the capture surfaces Adapted from Bazelyan

and Raizer

(2000)

Electrogeometrical Model (EGM)

rs

rsrs

Capture surfaces

Ng=const

10

Electrogeometrical Model (EGM)

rs

= 10 I065 m where I

is in kA

4

3

12

Striking distance rs

versus return-stroke peak current I

[curve 1 Golde

(1945) curve 2 Wagner (1963) curve 3 Love (1973) curve 4 Ruhling

(1972) x theory of Davis (1962) estimates from two-

dimensional photographs by Eriksson (1978) estimates from three-dimensional photography by Eriksson (1978) Adapted from Golde

(1977) and Eriksson (1978)

I kA rs m

10 45

30 91

170 282

11

Scatter plot of impulse charge Q versus return-stroke peak current

I Note that both vertical and horizontal scales are logarithmic The best fit to data I

= 106 Q07 where Q is in coulombs and I

is in kiloamperes was used in deriving rs

= 10 I065

Adapted from Berger (1972)

Electrogeometrical Model (EGM)

Finding rs = f(I)

bull

Assume critical average electric field between the leader tip and the strike object at the time of initiation of upward connecting leader from the object (200-600 kVm)

bull

Use an empirical relation between Q and I

to find rs

= f(I)

bull

Find rs

= f(Q)

bull

Assume leader geometry total leader charge Q and distribution of this charge along the channel

Q

10-1

100

101

102

100 101 102I

I

peak Q impulseneg first strokes n=89

I

= 106 Q07

For Q = 5 CI

= 33 kA

12

Electrogeometrical Model (EGM)

Illustration of the rolling-sphere method (RSM) The shaded area is that area into which it is postulated lightning cannot enter Adapted from Szczerbinski

(2000)

rs

rsrs

rs = 45 m (150 ft) (NFPA 780 2004) corresponds to I

= 10 kA (95 of currents exceed this value)

Rolling-Sphere Method

Return‐Stroke Fields Variation with Distance

Typical vertical electric field intensity (left column) and azimuthal

magnetic flux density (right column) waveforms for first (solid line) and subsequent (dashed line) return strokes at distances of 1 2 and 5 km Adapted from Lin et al (1979)

Electric Field Intensity Magnetic Flux Density

Return‐Stroke Fields Variation with Distance

Electric Field IntensityMagnetic Flux Density

Typical vertical electric field intensity (left column) and azimuthal

magnetic flux density (right column) waveforms for first (solid line) and subsequent (dashed line) return strokes at distances of 10 15 50 and 200 km Adapted from Lin et al (1979)

Return-Stroke Current Waveshapes

ndash

Switzerland (Berger et al 1975)

15

Average negative first and subsequent-stroke current waveshapes

each shown on two time scales A

and B The lower time scales (A) correspond to the solid curves while the upper time scales (B) correspond to the broken curves The vertical (amplitude) scale is in relative units the peak values being equal to negative unity Adapted from Berger et al (1975)

Lightning Parameters Derived from Direct Current Measurements

Parameters Units Sample Size

Percent Exceeding Tabulated Value

95 50 5

Peak current

(minimum 2 kA)First strokesSubsequent strokes

kA 101135

1446

3012

8030

Charge

(total charge)First strokesSubsequent strokesComplete flash

C 9312294

110213

521475

241140

Impulse charge

(excluding continuing current)

First strokesSubsequent strokes

C90

11711

02245

09520

4Front duration

(2 kA to peak)First strokesSubsequent strokes

μs 89118

18022

5511

1845

Maximum dIdtFirst strokesSubsequent strokes

kA μs-1 92122

5512

1240

32120

Stroke duration

(2 kA to half peak value on the tail)

First strokesSubsequent strokes

μs90

1153065

7532

200140

Action integral (intI2dt)First strokesSubsequent strokes

A2s 9188

60 x 103

55 x 10255 x 104

60 x 10355 x 105

52 x 104

17

Cumulative statistical distributions of lightning peak currents

giving percent of cases exceeding abscissa value from direct measurements in Switzerland (Berger 1972 Berger et al 1975) The distributions are assumed to be lognormal and given for (1) negative first strokes (2) positive first strokes (3) negative and positive first strokes and (4) negative subsequent strokes Adapted from Bazelyan

et al (1978)

Lightning peak currents for first strokes vary by a factor of 50 or more from about 5 to 250 kA

The probability of occurrence of a given value rapidly increases up to 25 kA

or so and then slowly decreasesStatistical distributions of this type are often assumed to be lognormal

Lightning Peak Current ndash

Bergerrsquos Distributions

18

Cumulative statistical distributions of peak currents (percent values on the vertical axis should be subtracted from 100 to obtain the probability to exceed the peak current value on the horizontal axis) for negative first strokes adopted by IEEE

and CIGRE Taken from CIGRE Document 63 (1991)

For the CIGRE

distribution 98 of peak currents exceed 4 kA 80 exceed 20 kA and 5 exceed 90 kA

For the IEEE

distribution the ldquoprobability to exceedrdquo

values are given by the following equation

where PI

is in per unit and I is in kA This equation applies to values of I up to 200 kA The median (50) peak current value is equal to 31 kA

Peak current I kA(IEEE

distribution) 5 10 20 40 60 80 100 200

Percentage exceeding tabulated value PI

10099 95 76 34 15 78 45 08

( ) 62

311

1I

PI+

=

Lightning Peak Current ndash

IEEE and CIGRE Distributions

dIdt

in Rocket-Triggered Lightning ( ~100 kAμs)

19

Relation between the peak rate of current rise dIdt and the peak current I from triggered-lightning experiments conducted at the NASA Kennedy Space Center Florida in 19851987 and 1988 and in France in 1986 The regression line for each year is shown the sample size N and the regression equation are given in table Adapted from Leteinturier

et al (1991)

Morro Do Cachimbo

Tower (60 m) Belo Horizonte Brazil

20

Courtesy Prof Dr Silverio Visacro Filho Lightning Research Center (UFMG-CEMIG)

Lightning Parameters Derived from Direct Current Measurements ndash

Brazil

21

First Stroke

Subsequent Strokes

404

52

163

099

Optical Measurements of Return-Stroke Speed

22

Optical intensity (in millivolts

at the input of the oscilloscope) vs time waveforms at four different heights 7 63 117 and 170 m

above the lightning termination point for stroke 1 in flash F0336 Adapted from Olsen et al (2004)

23

Reference St Dev ms Comments

Natural Lightning

Boyle and Orville (1976)

20 x 107 12 x 108 071 x 108 26 x 107 12 Streak camera 2-D speed

Idone and Orville (1982)

29 x 107 24 x 108 11 x 108 47 x 107 63 Streak camera2-D speed

Mach and Rust (1989a Fig 7)

20 x 107

80 x 10726 x 108

gt28 x 1085 x 107

7 x 1075443

Long channelShort channel (Photoelectric 2-D)

Triggered Lightning

Hubert and Mouget (1981)

45 x 107 17 x 108 99 x 107 41 x 107 13 Photoelectric3-D speed

Idone et al (1984) 67 x 107 17 x 108 12 x 108 27 x 107 56 Streak camera 3-D speed

Willett et al (1988)

10 x 108 15 x 108 12 x 108 16 x 107 9 Streak camera 2-D speed

Willett et al (1989a)

12 x 108 19 x 108 15 x 108 17 x 107 18 Streak camera 2-D speed

Mach and Rust (1989a Fig 8)

60 x 107

60 x 10716 x 108

20 x 1082 x 107

4 x 1074039

Long channelShort channel(Photoelectric 2-D)

Min ms Max ms Mean ms Sample

Size

13 plusmn03 x 108

19 plusmn07 x 108

12 plusmn03 x 108

14 plusmn04 x 108

Summary of measured return stroke speeds averaged over the visible part of the channel in natural and triggered negative lightning Adapted from Rakov

et al (1992b)

Return-Stroke Speed Near Ground

24

Height Above Ground

7-63 m

63-117 m

117-170

m

12

16

15

12121213

18

16

16

17

18 18

1512

Return-stroke speed profiles estimated tracking the 20 point on the light-pulse front for triggered lightning flash F0336 (Olsen et al 2004)

Return-Stroke Speed vs Return-Stroke Peak Current

25

Return-stroke speed vs peak current for 29 triggered-lightning strokes observed at the Kennedy Space Center (KSC) Florida in 1986 and reported by Mach and Rust (1989a) and 18 triggered-lightning strokes from the 1987 KSC experiments reported by Willett et al

(1989a) Peak curent shown in the scatter plot as 38 kA may be an underestimate Note that the linear correlation coefficients (r) for both data sets are low and negative not in support of the often assumed relationship between these two lightning parameters

00

05

10

15

20

25

0 5 10 15 20 25 30 35 40 45

Return-Stroke Peak Current kA

Ret

urn-

Stro

ke S

peed

108 m

s

Mach and Rust (1989a) r = -008

Willett el al (1998a) r = -027

First Return Stroke

Electric field waveforms of a first return stroke The waveform is shown on two time scales 5 μsdiv

and 10 μsdiv The fields are normalized to a distance of 100 km L denotes individual leader pulses F slow front and R fast transition Also marked are the small secondary peak or shoulder α

and the larger subsidiary peaks a b and c Adapted from Weidman and Krider

(1978)

-20 -15 -10 -5 0 5 10 15 20

5

microsdiv

10

microsdiv

-60 -40 -20 0 20 40 60 80

26

Subsequent Return Strokes

-20 -15 -10 -5 0 5 10 15 20

5 microsdiv

5 microsdiv

10 microsdiv

10 microsdiv

-60 -40 -20 0 20 40 60 80

Electric field waveforms of (b) a subsequent return stroke initiated by a dart-stepped leader and (c) a subsequent return stroke initiated by a dart leader showing the fine structure both before and after the initial field peak Each waveform is shown on two time scales 5 μsdiv

and 10 μsdiv The fields are normalized to a distance of 100 km L denotes individual leader pulses F slow front and R fast transition Also marked are the small secondary peak or shoulder α

and the larger subsidiary peaks a b and c Adapted from Weidman and Krider

(1978)

27

First Return Stroke Electric Field Derivative

Examples of (top) the time derivative of the electric field intensity dEdt

and (bottom)

the electric field intensity E produced by a first return stroke at a distance of about 36 km over the Atlantic Ocean The propagation path was almost entirely over salt water The vertical arrow under the E record shows the time of the dEdt

trigger Adapted from Krider

et al (1996)

28

Return Strokes Measured Parameters

Parameters of microsecond-scale electric field waveforms produced by negative return strokes

Parameter Location First strokes Subsequent strokes

Sample size Mean SD Sample size Mean SD

Initial peak (V m‐1) (normalized to 100 km)Rakov

and Uman

(1990b)

Cooray

and Lundquist (1982)Lin et al (1979)

Florida

SwedenKSCOcala

76

5535129

59 (GM)

536758

273825

232a

38b

8359

27(GM)41(GM)

5043

2215

Zero‐crossing time (μs)Cooray

and Lundquist (1985)

Lin et al (1979)

SwedenSri LankaFlorida

1029146c

498954

123018

9414377c

394236

81417

Zero‐to‐peak rise time (μs)Master et al (1984)Cooray

and Lundquist (1982)Lin et al (1979)

FloridaSwedenKSCOcala

1051405129

44702427

18201213

220

8359

28

1519

15

0807

10‐90 percent rise time (μs)Master et al (1984) Florida 105 26 12 220 15 09

Slow front duration

(μs)Master et al (1984)Cooray

and Lundquist (1982)Weidman and Krider

(1978)

FloridaSwedenFlorida

105826290

29504041

13201716

44 120 34d

060921

020509

29

Return Strokes Measured ParametersParameters of microsecond-scale electric field waveforms produced by negative return strokes (contrsquod)

Parameter Locatio

nFirst strokes Subsequent strokes

Sample size

Mean SD Sample size Mean SD

Slow front amplitude as percentage of peakMaster et al (1984)Cooray

and Lundquist (1982)Weidman and Krider

(1978)

FloridaSwedenFlorida

105836290

28415040

15112020

4412034d

202540

101020

Fast

transition 10-90 percent risetime

(ns)Master et al (1984)Weidman and Krider

(1978)

Weidman and Krider

(1980a 1984)

Weidman (1982)

FloridaFlorida

Florida

1023815125

97020020090

68010010040

2178034

610200150

27040100

Peak time derivative (normalized to100 km ) (V m-1

μs-1)Krider

et al (1996) Florida 63 39 11

Time derivative pulse width at half-peak value (ns)

Krider

et al (1996) Florida 61 100 20

If not specicied

otherwise multiple lines for a given source for the same location correspond to different thunderstorms GM = geometric mean value a better characteristic of the distribution of initial field peaks since this distribution is approximately log-normala

Strokes following previously formed channelb

Strokes creating new termination on groundcBoth

electric and magnetic fieldsd

Subsequent strokes initiated by dart-stepped leaders Other subsequent strokes studied by Weidman and

Krider

(1978) were initiated by dart leaders

30

• Slide Number 1
• Slide Number 2
• Slide Number 3
• Slide Number 4
• Slide Number 5
• Slide Number 6
• Slide Number 7
• Slide Number 8
• Slide Number 9
• Slide Number 10
• Slide Number 11
• Slide Number 12
• Return-Stroke Fields Variation with Distance
• Return-Stroke Fields Variation with Distance
• Slide Number 15
• Slide Number 16
• Slide Number 17
• Slide Number 18
• Slide Number 19
• Slide Number 20
• Slide Number 21
• Slide Number 22
• Slide Number 23
• Slide Number 24
• Slide Number 25
• First Return Stroke
• Subsequent Return Strokes
• First Return Stroke Electric Field Derivative
• Return Strokes Measured Parameters
• Return Strokes Measured Parameters

(a)

Streak‐camera photograph of a lightning discharge to a tower on Monte San

Salvatore Switzerland showing evidence of an upward connecting

leader

(b)

Still photograph of the same flash and another flash that attached to the tower

below its top

Adapted from Berger and Vogelsanger

(1966)

(a)

Streak‐camera photograph of a lightning discharge to a tower on Monte San

Salvatore Switzerland showing evidence of an upward connecting

leader

(b)

Still photograph of the same flash and another flash that attached to the tower

below its top

Adapted from Berger and Vogelsanger

(1966)

Adapted from Howard (2009)5

Lightning Attachment Process

6

Optical Images of Leader and Attachment Process ndash Triggered Lightning

Dart-stepped leader and attachement

process in rocket-triggered lightning (Sept 17 2008) at Camp Blanding Florida Photron

FASTCAM SA11 50000 fps (20 micros per frame)

Biagi

et al (2009 GRL)2 frames before return stroke 8 1 frame before return stroke 8

56 m

16 m

25 m

7

Optical Images of Leader and Attachment Process ndash Laboratory Sparks

Single-frame K008 images of four negative discharges (-22 MV1307500 μs) in a 45 m rod-rod gap Frame duration in a b and c is 2 micros and in d it is 05 micros L in b is the length of last step Adapted from Lebedev et al (2007)

-4

5 m

8

Optical Images of Attachment Process

55

m

HV rod

JP

Single-frame image-converter-camera K008 images of negative discharges in a 55-m rod-rod gap with frame exposure of 02 μs JP is the junction point between downward negative and upward connecting positive leaders Adapted from

Shcherbakov

et al (2006)

A photograph of a lightning strike to a chimney pot showing a split in the channel interpreted as evidence of an upward connecting leader Adapted from Golde

(1967)

JP

9

Illustration of capture surfaces of two towers and earthrsquos surface in the electrogeometrical

model (EGM) rs

is the striking distance defined as the distance from the tip of the descending leader to the object to be struck at the instant when an upward connecting leader is initiated from this object

Vertical arrows represent descending leaders assumed to be uniformly distributed (Ng=const) above the capture surfaces Adapted from Bazelyan

and Raizer

(2000)

Electrogeometrical Model (EGM)

rs

rsrs

Capture surfaces

Ng=const

10

Electrogeometrical Model (EGM)

rs

= 10 I065 m where I

is in kA

4

3

12

Striking distance rs

versus return-stroke peak current I

[curve 1 Golde

(1945) curve 2 Wagner (1963) curve 3 Love (1973) curve 4 Ruhling

(1972) x theory of Davis (1962) estimates from two-

dimensional photographs by Eriksson (1978) estimates from three-dimensional photography by Eriksson (1978) Adapted from Golde

(1977) and Eriksson (1978)

I kA rs m

10 45

30 91

170 282

11

Scatter plot of impulse charge Q versus return-stroke peak current

I Note that both vertical and horizontal scales are logarithmic The best fit to data I

= 106 Q07 where Q is in coulombs and I

is in kiloamperes was used in deriving rs

= 10 I065

Adapted from Berger (1972)

Electrogeometrical Model (EGM)

Finding rs = f(I)

bull

Assume critical average electric field between the leader tip and the strike object at the time of initiation of upward connecting leader from the object (200-600 kVm)

bull

Use an empirical relation between Q and I

to find rs

= f(I)

bull

Find rs

= f(Q)

bull

Assume leader geometry total leader charge Q and distribution of this charge along the channel

Q

10-1

100

101

102

100 101 102I

I

peak Q impulseneg first strokes n=89

I

= 106 Q07

For Q = 5 CI

= 33 kA

12

Electrogeometrical Model (EGM)

Illustration of the rolling-sphere method (RSM) The shaded area is that area into which it is postulated lightning cannot enter Adapted from Szczerbinski

(2000)

rs

rsrs

rs = 45 m (150 ft) (NFPA 780 2004) corresponds to I

= 10 kA (95 of currents exceed this value)

Rolling-Sphere Method

Return‐Stroke Fields Variation with Distance

Typical vertical electric field intensity (left column) and azimuthal

magnetic flux density (right column) waveforms for first (solid line) and subsequent (dashed line) return strokes at distances of 1 2 and 5 km Adapted from Lin et al (1979)

Electric Field Intensity Magnetic Flux Density

Return‐Stroke Fields Variation with Distance

Electric Field IntensityMagnetic Flux Density

Typical vertical electric field intensity (left column) and azimuthal

magnetic flux density (right column) waveforms for first (solid line) and subsequent (dashed line) return strokes at distances of 10 15 50 and 200 km Adapted from Lin et al (1979)

Return-Stroke Current Waveshapes

ndash

Switzerland (Berger et al 1975)

15

Average negative first and subsequent-stroke current waveshapes

each shown on two time scales A

and B The lower time scales (A) correspond to the solid curves while the upper time scales (B) correspond to the broken curves The vertical (amplitude) scale is in relative units the peak values being equal to negative unity Adapted from Berger et al (1975)

Lightning Parameters Derived from Direct Current Measurements

Parameters Units Sample Size

Percent Exceeding Tabulated Value

95 50 5

Peak current

(minimum 2 kA)First strokesSubsequent strokes

kA 101135

1446

3012

8030

Charge

(total charge)First strokesSubsequent strokesComplete flash

C 9312294

110213

521475

241140

Impulse charge

(excluding continuing current)

First strokesSubsequent strokes

C90

11711

02245

09520

4Front duration

(2 kA to peak)First strokesSubsequent strokes

μs 89118

18022

5511

1845

Maximum dIdtFirst strokesSubsequent strokes

kA μs-1 92122

5512

1240

32120

Stroke duration

(2 kA to half peak value on the tail)

First strokesSubsequent strokes

μs90

1153065

7532

200140

Action integral (intI2dt)First strokesSubsequent strokes

A2s 9188

60 x 103

55 x 10255 x 104

60 x 10355 x 105

52 x 104

17

Cumulative statistical distributions of lightning peak currents

giving percent of cases exceeding abscissa value from direct measurements in Switzerland (Berger 1972 Berger et al 1975) The distributions are assumed to be lognormal and given for (1) negative first strokes (2) positive first strokes (3) negative and positive first strokes and (4) negative subsequent strokes Adapted from Bazelyan

et al (1978)

Lightning peak currents for first strokes vary by a factor of 50 or more from about 5 to 250 kA

The probability of occurrence of a given value rapidly increases up to 25 kA

or so and then slowly decreasesStatistical distributions of this type are often assumed to be lognormal

Lightning Peak Current ndash

Bergerrsquos Distributions

18

Cumulative statistical distributions of peak currents (percent values on the vertical axis should be subtracted from 100 to obtain the probability to exceed the peak current value on the horizontal axis) for negative first strokes adopted by IEEE

and CIGRE Taken from CIGRE Document 63 (1991)

For the CIGRE

distribution 98 of peak currents exceed 4 kA 80 exceed 20 kA and 5 exceed 90 kA

For the IEEE

distribution the ldquoprobability to exceedrdquo

values are given by the following equation

where PI

is in per unit and I is in kA This equation applies to values of I up to 200 kA The median (50) peak current value is equal to 31 kA

Peak current I kA(IEEE

distribution) 5 10 20 40 60 80 100 200

Percentage exceeding tabulated value PI

10099 95 76 34 15 78 45 08

( ) 62

311

1I

PI+

=

Lightning Peak Current ndash

IEEE and CIGRE Distributions

dIdt

in Rocket-Triggered Lightning ( ~100 kAμs)

19

Relation between the peak rate of current rise dIdt and the peak current I from triggered-lightning experiments conducted at the NASA Kennedy Space Center Florida in 19851987 and 1988 and in France in 1986 The regression line for each year is shown the sample size N and the regression equation are given in table Adapted from Leteinturier

et al (1991)

Morro Do Cachimbo

Tower (60 m) Belo Horizonte Brazil

20

Courtesy Prof Dr Silverio Visacro Filho Lightning Research Center (UFMG-CEMIG)

Lightning Parameters Derived from Direct Current Measurements ndash

Brazil

21

First Stroke

Subsequent Strokes

404

52

163

099

Optical Measurements of Return-Stroke Speed

22

Optical intensity (in millivolts

at the input of the oscilloscope) vs time waveforms at four different heights 7 63 117 and 170 m

above the lightning termination point for stroke 1 in flash F0336 Adapted from Olsen et al (2004)

23

Reference St Dev ms Comments

Natural Lightning

Boyle and Orville (1976)

20 x 107 12 x 108 071 x 108 26 x 107 12 Streak camera 2-D speed

Idone and Orville (1982)

29 x 107 24 x 108 11 x 108 47 x 107 63 Streak camera2-D speed

Mach and Rust (1989a Fig 7)

20 x 107

80 x 10726 x 108

gt28 x 1085 x 107

7 x 1075443

Long channelShort channel (Photoelectric 2-D)

Triggered Lightning

Hubert and Mouget (1981)

45 x 107 17 x 108 99 x 107 41 x 107 13 Photoelectric3-D speed

Idone et al (1984) 67 x 107 17 x 108 12 x 108 27 x 107 56 Streak camera 3-D speed

Willett et al (1988)

10 x 108 15 x 108 12 x 108 16 x 107 9 Streak camera 2-D speed

Willett et al (1989a)

12 x 108 19 x 108 15 x 108 17 x 107 18 Streak camera 2-D speed

Mach and Rust (1989a Fig 8)

60 x 107

60 x 10716 x 108

20 x 1082 x 107

4 x 1074039

Long channelShort channel(Photoelectric 2-D)

Min ms Max ms Mean ms Sample

Size

13 plusmn03 x 108

19 plusmn07 x 108

12 plusmn03 x 108

14 plusmn04 x 108

Summary of measured return stroke speeds averaged over the visible part of the channel in natural and triggered negative lightning Adapted from Rakov

et al (1992b)

Return-Stroke Speed Near Ground

24

Height Above Ground

7-63 m

63-117 m

117-170

m

12

16

15

12121213

18

16

16

17

18 18

1512

Return-stroke speed profiles estimated tracking the 20 point on the light-pulse front for triggered lightning flash F0336 (Olsen et al 2004)

Return-Stroke Speed vs Return-Stroke Peak Current

25

Return-stroke speed vs peak current for 29 triggered-lightning strokes observed at the Kennedy Space Center (KSC) Florida in 1986 and reported by Mach and Rust (1989a) and 18 triggered-lightning strokes from the 1987 KSC experiments reported by Willett et al

(1989a) Peak curent shown in the scatter plot as 38 kA may be an underestimate Note that the linear correlation coefficients (r) for both data sets are low and negative not in support of the often assumed relationship between these two lightning parameters

00

05

10

15

20

25

0 5 10 15 20 25 30 35 40 45

Return-Stroke Peak Current kA

Ret

urn-

Stro

ke S

peed

108 m

s

Mach and Rust (1989a) r = -008

Willett el al (1998a) r = -027

First Return Stroke

Electric field waveforms of a first return stroke The waveform is shown on two time scales 5 μsdiv

and 10 μsdiv The fields are normalized to a distance of 100 km L denotes individual leader pulses F slow front and R fast transition Also marked are the small secondary peak or shoulder α

and the larger subsidiary peaks a b and c Adapted from Weidman and Krider

(1978)

-20 -15 -10 -5 0 5 10 15 20

5

microsdiv

10

microsdiv

-60 -40 -20 0 20 40 60 80

26

Subsequent Return Strokes

-20 -15 -10 -5 0 5 10 15 20

5 microsdiv

5 microsdiv

10 microsdiv

10 microsdiv

-60 -40 -20 0 20 40 60 80

Electric field waveforms of (b) a subsequent return stroke initiated by a dart-stepped leader and (c) a subsequent return stroke initiated by a dart leader showing the fine structure both before and after the initial field peak Each waveform is shown on two time scales 5 μsdiv

and 10 μsdiv The fields are normalized to a distance of 100 km L denotes individual leader pulses F slow front and R fast transition Also marked are the small secondary peak or shoulder α

and the larger subsidiary peaks a b and c Adapted from Weidman and Krider

(1978)

27

First Return Stroke Electric Field Derivative

Examples of (top) the time derivative of the electric field intensity dEdt

and (bottom)

the electric field intensity E produced by a first return stroke at a distance of about 36 km over the Atlantic Ocean The propagation path was almost entirely over salt water The vertical arrow under the E record shows the time of the dEdt

trigger Adapted from Krider

et al (1996)

28

Return Strokes Measured Parameters

Parameters of microsecond-scale electric field waveforms produced by negative return strokes

Parameter Location First strokes Subsequent strokes

Sample size Mean SD Sample size Mean SD

Initial peak (V m‐1) (normalized to 100 km)Rakov

and Uman

(1990b)

Cooray

and Lundquist (1982)Lin et al (1979)

Florida

SwedenKSCOcala

76

5535129

59 (GM)

536758

273825

232a

38b

8359

27(GM)41(GM)

5043

2215

Zero‐crossing time (μs)Cooray

and Lundquist (1985)

Lin et al (1979)

SwedenSri LankaFlorida

1029146c

498954

123018

9414377c

394236

81417

Zero‐to‐peak rise time (μs)Master et al (1984)Cooray

and Lundquist (1982)Lin et al (1979)

FloridaSwedenKSCOcala

1051405129

44702427

18201213

220

8359

28

1519

15

0807

10‐90 percent rise time (μs)Master et al (1984) Florida 105 26 12 220 15 09

Slow front duration

(μs)Master et al (1984)Cooray

and Lundquist (1982)Weidman and Krider

(1978)

FloridaSwedenFlorida

105826290

29504041

13201716

44 120 34d

060921

020509

29

Return Strokes Measured ParametersParameters of microsecond-scale electric field waveforms produced by negative return strokes (contrsquod)

Parameter Locatio

nFirst strokes Subsequent strokes

Sample size

Mean SD Sample size Mean SD

Slow front amplitude as percentage of peakMaster et al (1984)Cooray

and Lundquist (1982)Weidman and Krider

(1978)

FloridaSwedenFlorida

105836290

28415040

15112020

4412034d

202540

101020

Fast

transition 10-90 percent risetime

(ns)Master et al (1984)Weidman and Krider

(1978)

Weidman and Krider

(1980a 1984)

Weidman (1982)

FloridaFlorida

Florida

1023815125

97020020090

68010010040

2178034

610200150

27040100

Peak time derivative (normalized to100 km ) (V m-1

μs-1)Krider

et al (1996) Florida 63 39 11

Time derivative pulse width at half-peak value (ns)

Krider

et al (1996) Florida 61 100 20

If not specicied

otherwise multiple lines for a given source for the same location correspond to different thunderstorms GM = geometric mean value a better characteristic of the distribution of initial field peaks since this distribution is approximately log-normala

Strokes following previously formed channelb

Strokes creating new termination on groundcBoth

electric and magnetic fieldsd

Subsequent strokes initiated by dart-stepped leaders Other subsequent strokes studied by Weidman and

Krider

(1978) were initiated by dart leaders

30

• Slide Number 1
• Slide Number 2
• Slide Number 3
• Slide Number 4
• Slide Number 5
• Slide Number 6
• Slide Number 7
• Slide Number 8
• Slide Number 9
• Slide Number 10
• Slide Number 11
• Slide Number 12
• Return-Stroke Fields Variation with Distance
• Return-Stroke Fields Variation with Distance
• Slide Number 15
• Slide Number 16
• Slide Number 17
• Slide Number 18
• Slide Number 19
• Slide Number 20
• Slide Number 21
• Slide Number 22
• Slide Number 23
• Slide Number 24
• Slide Number 25
• First Return Stroke
• Subsequent Return Strokes
• First Return Stroke Electric Field Derivative
• Return Strokes Measured Parameters
• Return Strokes Measured Parameters

(a)

Streak‐camera photograph of a lightning discharge to a tower on Monte San

Salvatore Switzerland showing evidence of an upward connecting

leader

(b)

Still photograph of the same flash and another flash that attached to the tower

below its top

Adapted from Berger and Vogelsanger

(1966)

Adapted from Howard (2009)5

Lightning Attachment Process

6

Optical Images of Leader and Attachment Process ndash Triggered Lightning

Dart-stepped leader and attachement

process in rocket-triggered lightning (Sept 17 2008) at Camp Blanding Florida Photron

FASTCAM SA11 50000 fps (20 micros per frame)

Biagi

et al (2009 GRL)2 frames before return stroke 8 1 frame before return stroke 8

56 m

16 m

25 m

7

Optical Images of Leader and Attachment Process ndash Laboratory Sparks

Single-frame K008 images of four negative discharges (-22 MV1307500 μs) in a 45 m rod-rod gap Frame duration in a b and c is 2 micros and in d it is 05 micros L in b is the length of last step Adapted from Lebedev et al (2007)

-4

5 m

8

Optical Images of Attachment Process

55

m

HV rod

JP

Single-frame image-converter-camera K008 images of negative discharges in a 55-m rod-rod gap with frame exposure of 02 μs JP is the junction point between downward negative and upward connecting positive leaders Adapted from

Shcherbakov

et al (2006)

A photograph of a lightning strike to a chimney pot showing a split in the channel interpreted as evidence of an upward connecting leader Adapted from Golde

(1967)

JP

9

Illustration of capture surfaces of two towers and earthrsquos surface in the electrogeometrical

model (EGM) rs

is the striking distance defined as the distance from the tip of the descending leader to the object to be struck at the instant when an upward connecting leader is initiated from this object

Vertical arrows represent descending leaders assumed to be uniformly distributed (Ng=const) above the capture surfaces Adapted from Bazelyan

and Raizer

(2000)

Electrogeometrical Model (EGM)

rs

rsrs

Capture surfaces

Ng=const

10

Electrogeometrical Model (EGM)

rs

= 10 I065 m where I

is in kA

4

3

12

Striking distance rs

versus return-stroke peak current I

[curve 1 Golde

(1945) curve 2 Wagner (1963) curve 3 Love (1973) curve 4 Ruhling

(1972) x theory of Davis (1962) estimates from two-

dimensional photographs by Eriksson (1978) estimates from three-dimensional photography by Eriksson (1978) Adapted from Golde

(1977) and Eriksson (1978)

I kA rs m

10 45

30 91

170 282

11

Scatter plot of impulse charge Q versus return-stroke peak current

I Note that both vertical and horizontal scales are logarithmic The best fit to data I

= 106 Q07 where Q is in coulombs and I

is in kiloamperes was used in deriving rs

= 10 I065

Adapted from Berger (1972)

Electrogeometrical Model (EGM)

Finding rs = f(I)

bull

Assume critical average electric field between the leader tip and the strike object at the time of initiation of upward connecting leader from the object (200-600 kVm)

bull

Use an empirical relation between Q and I

to find rs

= f(I)

bull

Find rs

= f(Q)

bull

Assume leader geometry total leader charge Q and distribution of this charge along the channel

Q

10-1

100

101

102

100 101 102I

I

peak Q impulseneg first strokes n=89

I

= 106 Q07

For Q = 5 CI

= 33 kA

12

Electrogeometrical Model (EGM)

Illustration of the rolling-sphere method (RSM) The shaded area is that area into which it is postulated lightning cannot enter Adapted from Szczerbinski

(2000)

rs

rsrs

rs = 45 m (150 ft) (NFPA 780 2004) corresponds to I

= 10 kA (95 of currents exceed this value)

Rolling-Sphere Method

Return‐Stroke Fields Variation with Distance

Typical vertical electric field intensity (left column) and azimuthal

magnetic flux density (right column) waveforms for first (solid line) and subsequent (dashed line) return strokes at distances of 1 2 and 5 km Adapted from Lin et al (1979)

Electric Field Intensity Magnetic Flux Density

Return‐Stroke Fields Variation with Distance

Electric Field IntensityMagnetic Flux Density

Typical vertical electric field intensity (left column) and azimuthal

magnetic flux density (right column) waveforms for first (solid line) and subsequent (dashed line) return strokes at distances of 10 15 50 and 200 km Adapted from Lin et al (1979)

Return-Stroke Current Waveshapes

ndash

Switzerland (Berger et al 1975)

15

Average negative first and subsequent-stroke current waveshapes

each shown on two time scales A

and B The lower time scales (A) correspond to the solid curves while the upper time scales (B) correspond to the broken curves The vertical (amplitude) scale is in relative units the peak values being equal to negative unity Adapted from Berger et al (1975)

Lightning Parameters Derived from Direct Current Measurements

Parameters Units Sample Size

Percent Exceeding Tabulated Value

95 50 5

Peak current

(minimum 2 kA)First strokesSubsequent strokes

kA 101135

1446

3012

8030

Charge

(total charge)First strokesSubsequent strokesComplete flash

C 9312294

110213

521475

241140

Impulse charge

(excluding continuing current)

First strokesSubsequent strokes

C90

11711

02245

09520

4Front duration

(2 kA to peak)First strokesSubsequent strokes

μs 89118

18022

5511

1845

Maximum dIdtFirst strokesSubsequent strokes

kA μs-1 92122

5512

1240

32120

Stroke duration

(2 kA to half peak value on the tail)

First strokesSubsequent strokes

μs90

1153065

7532

200140

Action integral (intI2dt)First strokesSubsequent strokes

A2s 9188

60 x 103

55 x 10255 x 104

60 x 10355 x 105

52 x 104

17

Cumulative statistical distributions of lightning peak currents

giving percent of cases exceeding abscissa value from direct measurements in Switzerland (Berger 1972 Berger et al 1975) The distributions are assumed to be lognormal and given for (1) negative first strokes (2) positive first strokes (3) negative and positive first strokes and (4) negative subsequent strokes Adapted from Bazelyan

et al (1978)

Lightning peak currents for first strokes vary by a factor of 50 or more from about 5 to 250 kA

The probability of occurrence of a given value rapidly increases up to 25 kA

or so and then slowly decreasesStatistical distributions of this type are often assumed to be lognormal

Lightning Peak Current ndash

Bergerrsquos Distributions

18

Cumulative statistical distributions of peak currents (percent values on the vertical axis should be subtracted from 100 to obtain the probability to exceed the peak current value on the horizontal axis) for negative first strokes adopted by IEEE

and CIGRE Taken from CIGRE Document 63 (1991)

For the CIGRE

distribution 98 of peak currents exceed 4 kA 80 exceed 20 kA and 5 exceed 90 kA

For the IEEE

distribution the ldquoprobability to exceedrdquo

values are given by the following equation

where PI

is in per unit and I is in kA This equation applies to values of I up to 200 kA The median (50) peak current value is equal to 31 kA

Peak current I kA(IEEE

distribution) 5 10 20 40 60 80 100 200

Percentage exceeding tabulated value PI

10099 95 76 34 15 78 45 08

( ) 62

311

1I

PI+

=

Lightning Peak Current ndash

IEEE and CIGRE Distributions

dIdt

in Rocket-Triggered Lightning ( ~100 kAμs)

19

Relation between the peak rate of current rise dIdt and the peak current I from triggered-lightning experiments conducted at the NASA Kennedy Space Center Florida in 19851987 and 1988 and in France in 1986 The regression line for each year is shown the sample size N and the regression equation are given in table Adapted from Leteinturier

et al (1991)

Morro Do Cachimbo

Tower (60 m) Belo Horizonte Brazil

20

Courtesy Prof Dr Silverio Visacro Filho Lightning Research Center (UFMG-CEMIG)

Lightning Parameters Derived from Direct Current Measurements ndash

Brazil

21

First Stroke

Subsequent Strokes

404

52

163

099

Optical Measurements of Return-Stroke Speed

22

Optical intensity (in millivolts

at the input of the oscilloscope) vs time waveforms at four different heights 7 63 117 and 170 m

above the lightning termination point for stroke 1 in flash F0336 Adapted from Olsen et al (2004)

23

Reference St Dev ms Comments

Natural Lightning

Boyle and Orville (1976)

20 x 107 12 x 108 071 x 108 26 x 107 12 Streak camera 2-D speed

Idone and Orville (1982)

29 x 107 24 x 108 11 x 108 47 x 107 63 Streak camera2-D speed

Mach and Rust (1989a Fig 7)

20 x 107

80 x 10726 x 108

gt28 x 1085 x 107

7 x 1075443

Long channelShort channel (Photoelectric 2-D)

Triggered Lightning

Hubert and Mouget (1981)

45 x 107 17 x 108 99 x 107 41 x 107 13 Photoelectric3-D speed

Idone et al (1984) 67 x 107 17 x 108 12 x 108 27 x 107 56 Streak camera 3-D speed

Willett et al (1988)

10 x 108 15 x 108 12 x 108 16 x 107 9 Streak camera 2-D speed

Willett et al (1989a)

12 x 108 19 x 108 15 x 108 17 x 107 18 Streak camera 2-D speed

Mach and Rust (1989a Fig 8)

60 x 107

60 x 10716 x 108

20 x 1082 x 107

4 x 1074039

Long channelShort channel(Photoelectric 2-D)

Min ms Max ms Mean ms Sample

Size

13 plusmn03 x 108

19 plusmn07 x 108

12 plusmn03 x 108

14 plusmn04 x 108

Summary of measured return stroke speeds averaged over the visible part of the channel in natural and triggered negative lightning Adapted from Rakov

et al (1992b)

Return-Stroke Speed Near Ground

24

Height Above Ground

7-63 m

63-117 m

117-170

m

12

16

15

12121213

18

16

16

17

18 18

1512

Return-stroke speed profiles estimated tracking the 20 point on the light-pulse front for triggered lightning flash F0336 (Olsen et al 2004)

Return-Stroke Speed vs Return-Stroke Peak Current

25

Return-stroke speed vs peak current for 29 triggered-lightning strokes observed at the Kennedy Space Center (KSC) Florida in 1986 and reported by Mach and Rust (1989a) and 18 triggered-lightning strokes from the 1987 KSC experiments reported by Willett et al

(1989a) Peak curent shown in the scatter plot as 38 kA may be an underestimate Note that the linear correlation coefficients (r) for both data sets are low and negative not in support of the often assumed relationship between these two lightning parameters

00

05

10

15

20

25

0 5 10 15 20 25 30 35 40 45

Return-Stroke Peak Current kA

Ret

urn-

Stro

ke S

peed

108 m

s

Mach and Rust (1989a) r = -008

Willett el al (1998a) r = -027

First Return Stroke

Electric field waveforms of a first return stroke The waveform is shown on two time scales 5 μsdiv

and 10 μsdiv The fields are normalized to a distance of 100 km L denotes individual leader pulses F slow front and R fast transition Also marked are the small secondary peak or shoulder α

and the larger subsidiary peaks a b and c Adapted from Weidman and Krider

(1978)

-20 -15 -10 -5 0 5 10 15 20

5

microsdiv

10

microsdiv

-60 -40 -20 0 20 40 60 80

26

Subsequent Return Strokes

-20 -15 -10 -5 0 5 10 15 20

5 microsdiv

5 microsdiv

10 microsdiv

10 microsdiv

-60 -40 -20 0 20 40 60 80

Electric field waveforms of (b) a subsequent return stroke initiated by a dart-stepped leader and (c) a subsequent return stroke initiated by a dart leader showing the fine structure both before and after the initial field peak Each waveform is shown on two time scales 5 μsdiv

and 10 μsdiv The fields are normalized to a distance of 100 km L denotes individual leader pulses F slow front and R fast transition Also marked are the small secondary peak or shoulder α

and the larger subsidiary peaks a b and c Adapted from Weidman and Krider

(1978)

27

First Return Stroke Electric Field Derivative

Examples of (top) the time derivative of the electric field intensity dEdt

and (bottom)

the electric field intensity E produced by a first return stroke at a distance of about 36 km over the Atlantic Ocean The propagation path was almost entirely over salt water The vertical arrow under the E record shows the time of the dEdt

trigger Adapted from Krider

et al (1996)

28

Return Strokes Measured Parameters

Parameters of microsecond-scale electric field waveforms produced by negative return strokes

Parameter Location First strokes Subsequent strokes

Sample size Mean SD Sample size Mean SD

Initial peak (V m‐1) (normalized to 100 km)Rakov

and Uman

(1990b)

Cooray

and Lundquist (1982)Lin et al (1979)

Florida

SwedenKSCOcala

76

5535129

59 (GM)

536758

273825

232a

38b

8359

27(GM)41(GM)

5043

2215

Zero‐crossing time (μs)Cooray

and Lundquist (1985)

Lin et al (1979)

SwedenSri LankaFlorida

1029146c

498954

123018

9414377c

394236

81417

Zero‐to‐peak rise time (μs)Master et al (1984)Cooray

and Lundquist (1982)Lin et al (1979)

FloridaSwedenKSCOcala

1051405129

44702427

18201213

220

8359

28

1519

15

0807

10‐90 percent rise time (μs)Master et al (1984) Florida 105 26 12 220 15 09

Slow front duration

(μs)Master et al (1984)Cooray

and Lundquist (1982)Weidman and Krider

(1978)

FloridaSwedenFlorida

105826290

29504041

13201716

44 120 34d

060921

020509

29

Return Strokes Measured ParametersParameters of microsecond-scale electric field waveforms produced by negative return strokes (contrsquod)

Parameter Locatio

nFirst strokes Subsequent strokes

Sample size

Mean SD Sample size Mean SD

Slow front amplitude as percentage of peakMaster et al (1984)Cooray

and Lundquist (1982)Weidman and Krider

(1978)

FloridaSwedenFlorida

105836290

28415040

15112020

4412034d

202540

101020

Fast

transition 10-90 percent risetime

(ns)Master et al (1984)Weidman and Krider

(1978)

Weidman and Krider

(1980a 1984)

Weidman (1982)

FloridaFlorida

Florida

1023815125

97020020090

68010010040

2178034

610200150

27040100

Peak time derivative (normalized to100 km ) (V m-1

μs-1)Krider

et al (1996) Florida 63 39 11

Time derivative pulse width at half-peak value (ns)

Krider

et al (1996) Florida 61 100 20

If not specicied

otherwise multiple lines for a given source for the same location correspond to different thunderstorms GM = geometric mean value a better characteristic of the distribution of initial field peaks since this distribution is approximately log-normala

Strokes following previously formed channelb

Strokes creating new termination on groundcBoth

electric and magnetic fieldsd

Subsequent strokes initiated by dart-stepped leaders Other subsequent strokes studied by Weidman and

Krider

(1978) were initiated by dart leaders

30

• Slide Number 1
• Slide Number 2
• Slide Number 3
• Slide Number 4
• Slide Number 5
• Slide Number 6
• Slide Number 7
• Slide Number 8
• Slide Number 9
• Slide Number 10
• Slide Number 11
• Slide Number 12
• Return-Stroke Fields Variation with Distance
• Return-Stroke Fields Variation with Distance
• Slide Number 15
• Slide Number 16
• Slide Number 17
• Slide Number 18
• Slide Number 19
• Slide Number 20
• Slide Number 21
• Slide Number 22
• Slide Number 23
• Slide Number 24
• Slide Number 25
• First Return Stroke
• Subsequent Return Strokes
• First Return Stroke Electric Field Derivative
• Return Strokes Measured Parameters
• Return Strokes Measured Parameters

Adapted from Howard (2009)5

Lightning Attachment Process

6

Optical Images of Leader and Attachment Process ndash Triggered Lightning

Dart-stepped leader and attachement

process in rocket-triggered lightning (Sept 17 2008) at Camp Blanding Florida Photron

FASTCAM SA11 50000 fps (20 micros per frame)

Biagi

et al (2009 GRL)2 frames before return stroke 8 1 frame before return stroke 8

56 m

16 m

25 m

7

Optical Images of Leader and Attachment Process ndash Laboratory Sparks

Single-frame K008 images of four negative discharges (-22 MV1307500 μs) in a 45 m rod-rod gap Frame duration in a b and c is 2 micros and in d it is 05 micros L in b is the length of last step Adapted from Lebedev et al (2007)

-4

5 m

8

Optical Images of Attachment Process

55

m

HV rod

JP

Single-frame image-converter-camera K008 images of negative discharges in a 55-m rod-rod gap with frame exposure of 02 μs JP is the junction point between downward negative and upward connecting positive leaders Adapted from

Shcherbakov

et al (2006)

A photograph of a lightning strike to a chimney pot showing a split in the channel interpreted as evidence of an upward connecting leader Adapted from Golde

(1967)

JP

9

Illustration of capture surfaces of two towers and earthrsquos surface in the electrogeometrical

model (EGM) rs

is the striking distance defined as the distance from the tip of the descending leader to the object to be struck at the instant when an upward connecting leader is initiated from this object

Vertical arrows represent descending leaders assumed to be uniformly distributed (Ng=const) above the capture surfaces Adapted from Bazelyan

and Raizer

(2000)

Electrogeometrical Model (EGM)

rs

rsrs

Capture surfaces

Ng=const

10

Electrogeometrical Model (EGM)

rs

= 10 I065 m where I

is in kA

4

3

12

Striking distance rs

versus return-stroke peak current I

[curve 1 Golde

(1945) curve 2 Wagner (1963) curve 3 Love (1973) curve 4 Ruhling

(1972) x theory of Davis (1962) estimates from two-

dimensional photographs by Eriksson (1978) estimates from three-dimensional photography by Eriksson (1978) Adapted from Golde

(1977) and Eriksson (1978)

I kA rs m

10 45

30 91

170 282

11

Scatter plot of impulse charge Q versus return-stroke peak current

I Note that both vertical and horizontal scales are logarithmic The best fit to data I

= 106 Q07 where Q is in coulombs and I

is in kiloamperes was used in deriving rs

= 10 I065

Adapted from Berger (1972)

Electrogeometrical Model (EGM)

Finding rs = f(I)

bull

Assume critical average electric field between the leader tip and the strike object at the time of initiation of upward connecting leader from the object (200-600 kVm)

bull

Use an empirical relation between Q and I

to find rs

= f(I)

bull

Find rs

= f(Q)

bull

Assume leader geometry total leader charge Q and distribution of this charge along the channel

Q

10-1

100

101

102

100 101 102I

I

peak Q impulseneg first strokes n=89

I

= 106 Q07

For Q = 5 CI

= 33 kA

12

Electrogeometrical Model (EGM)

Illustration of the rolling-sphere method (RSM) The shaded area is that area into which it is postulated lightning cannot enter Adapted from Szczerbinski

(2000)

rs

rsrs

rs = 45 m (150 ft) (NFPA 780 2004) corresponds to I

= 10 kA (95 of currents exceed this value)

Rolling-Sphere Method

Return‐Stroke Fields Variation with Distance

Typical vertical electric field intensity (left column) and azimuthal

magnetic flux density (right column) waveforms for first (solid line) and subsequent (dashed line) return strokes at distances of 1 2 and 5 km Adapted from Lin et al (1979)

Electric Field Intensity Magnetic Flux Density

Return‐Stroke Fields Variation with Distance

Electric Field IntensityMagnetic Flux Density

Typical vertical electric field intensity (left column) and azimuthal

magnetic flux density (right column) waveforms for first (solid line) and subsequent (dashed line) return strokes at distances of 10 15 50 and 200 km Adapted from Lin et al (1979)

Return-Stroke Current Waveshapes

ndash

Switzerland (Berger et al 1975)

15

Average negative first and subsequent-stroke current waveshapes

each shown on two time scales A

and B The lower time scales (A) correspond to the solid curves while the upper time scales (B) correspond to the broken curves The vertical (amplitude) scale is in relative units the peak values being equal to negative unity Adapted from Berger et al (1975)

Lightning Parameters Derived from Direct Current Measurements

Parameters Units Sample Size

Percent Exceeding Tabulated Value

95 50 5

Peak current

(minimum 2 kA)First strokesSubsequent strokes

kA 101135

1446

3012

8030

Charge

(total charge)First strokesSubsequent strokesComplete flash

C 9312294

110213

521475

241140

Impulse charge

(excluding continuing current)

First strokesSubsequent strokes

C90

11711

02245

09520

4Front duration

(2 kA to peak)First strokesSubsequent strokes

μs 89118

18022

5511

1845

Maximum dIdtFirst strokesSubsequent strokes

kA μs-1 92122

5512

1240

32120

Stroke duration

(2 kA to half peak value on the tail)

First strokesSubsequent strokes

μs90

1153065

7532

200140

Action integral (intI2dt)First strokesSubsequent strokes

A2s 9188

60 x 103

55 x 10255 x 104

60 x 10355 x 105

52 x 104

17

Cumulative statistical distributions of lightning peak currents

giving percent of cases exceeding abscissa value from direct measurements in Switzerland (Berger 1972 Berger et al 1975) The distributions are assumed to be lognormal and given for (1) negative first strokes (2) positive first strokes (3) negative and positive first strokes and (4) negative subsequent strokes Adapted from Bazelyan

et al (1978)

Lightning peak currents for first strokes vary by a factor of 50 or more from about 5 to 250 kA

The probability of occurrence of a given value rapidly increases up to 25 kA

or so and then slowly decreasesStatistical distributions of this type are often assumed to be lognormal

Lightning Peak Current ndash

Bergerrsquos Distributions

18

Cumulative statistical distributions of peak currents (percent values on the vertical axis should be subtracted from 100 to obtain the probability to exceed the peak current value on the horizontal axis) for negative first strokes adopted by IEEE

and CIGRE Taken from CIGRE Document 63 (1991)

For the CIGRE

distribution 98 of peak currents exceed 4 kA 80 exceed 20 kA and 5 exceed 90 kA

For the IEEE

distribution the ldquoprobability to exceedrdquo

values are given by the following equation

where PI

is in per unit and I is in kA This equation applies to values of I up to 200 kA The median (50) peak current value is equal to 31 kA

Peak current I kA(IEEE

distribution) 5 10 20 40 60 80 100 200

Percentage exceeding tabulated value PI

10099 95 76 34 15 78 45 08

( ) 62

311

1I

PI+

=

Lightning Peak Current ndash

IEEE and CIGRE Distributions

dIdt

in Rocket-Triggered Lightning ( ~100 kAμs)

19

Relation between the peak rate of current rise dIdt and the peak current I from triggered-lightning experiments conducted at the NASA Kennedy Space Center Florida in 19851987 and 1988 and in France in 1986 The regression line for each year is shown the sample size N and the regression equation are given in table Adapted from Leteinturier

et al (1991)

Morro Do Cachimbo

Tower (60 m) Belo Horizonte Brazil

20

Courtesy Prof Dr Silverio Visacro Filho Lightning Research Center (UFMG-CEMIG)

Lightning Parameters Derived from Direct Current Measurements ndash

Brazil

21

First Stroke

Subsequent Strokes

404

52

163

099

Optical Measurements of Return-Stroke Speed

22

Optical intensity (in millivolts

at the input of the oscilloscope) vs time waveforms at four different heights 7 63 117 and 170 m

above the lightning termination point for stroke 1 in flash F0336 Adapted from Olsen et al (2004)

23

Reference St Dev ms Comments

Natural Lightning

Boyle and Orville (1976)

20 x 107 12 x 108 071 x 108 26 x 107 12 Streak camera 2-D speed

Idone and Orville (1982)

29 x 107 24 x 108 11 x 108 47 x 107 63 Streak camera2-D speed

Mach and Rust (1989a Fig 7)

20 x 107

80 x 10726 x 108

gt28 x 1085 x 107

7 x 1075443

Long channelShort channel (Photoelectric 2-D)

Triggered Lightning

Hubert and Mouget (1981)

45 x 107 17 x 108 99 x 107 41 x 107 13 Photoelectric3-D speed

Idone et al (1984) 67 x 107 17 x 108 12 x 108 27 x 107 56 Streak camera 3-D speed

Willett et al (1988)

10 x 108 15 x 108 12 x 108 16 x 107 9 Streak camera 2-D speed

Willett et al (1989a)

12 x 108 19 x 108 15 x 108 17 x 107 18 Streak camera 2-D speed

Mach and Rust (1989a Fig 8)

60 x 107

60 x 10716 x 108

20 x 1082 x 107

4 x 1074039

Long channelShort channel(Photoelectric 2-D)

Min ms Max ms Mean ms Sample

Size

13 plusmn03 x 108

19 plusmn07 x 108

12 plusmn03 x 108

14 plusmn04 x 108

Summary of measured return stroke speeds averaged over the visible part of the channel in natural and triggered negative lightning Adapted from Rakov

et al (1992b)

Return-Stroke Speed Near Ground

24

Height Above Ground

7-63 m

63-117 m

117-170

m

12

16

15

12121213

18

16

16

17

18 18

1512

Return-stroke speed profiles estimated tracking the 20 point on the light-pulse front for triggered lightning flash F0336 (Olsen et al 2004)

Return-Stroke Speed vs Return-Stroke Peak Current

25

Return-stroke speed vs peak current for 29 triggered-lightning strokes observed at the Kennedy Space Center (KSC) Florida in 1986 and reported by Mach and Rust (1989a) and 18 triggered-lightning strokes from the 1987 KSC experiments reported by Willett et al

(1989a) Peak curent shown in the scatter plot as 38 kA may be an underestimate Note that the linear correlation coefficients (r) for both data sets are low and negative not in support of the often assumed relationship between these two lightning parameters

00

05

10

15

20

25

0 5 10 15 20 25 30 35 40 45

Return-Stroke Peak Current kA

Ret

urn-

Stro

ke S

peed

108 m

s

Mach and Rust (1989a) r = -008

Willett el al (1998a) r = -027

First Return Stroke

Electric field waveforms of a first return stroke The waveform is shown on two time scales 5 μsdiv

and 10 μsdiv The fields are normalized to a distance of 100 km L denotes individual leader pulses F slow front and R fast transition Also marked are the small secondary peak or shoulder α

and the larger subsidiary peaks a b and c Adapted from Weidman and Krider

(1978)

-20 -15 -10 -5 0 5 10 15 20

5

microsdiv

10

microsdiv

-60 -40 -20 0 20 40 60 80

26

Subsequent Return Strokes

-20 -15 -10 -5 0 5 10 15 20

5 microsdiv

5 microsdiv

10 microsdiv

10 microsdiv

-60 -40 -20 0 20 40 60 80

Electric field waveforms of (b) a subsequent return stroke initiated by a dart-stepped leader and (c) a subsequent return stroke initiated by a dart leader showing the fine structure both before and after the initial field peak Each waveform is shown on two time scales 5 μsdiv

and 10 μsdiv The fields are normalized to a distance of 100 km L denotes individual leader pulses F slow front and R fast transition Also marked are the small secondary peak or shoulder α

and the larger subsidiary peaks a b and c Adapted from Weidman and Krider

(1978)

27

First Return Stroke Electric Field Derivative

Examples of (top) the time derivative of the electric field intensity dEdt

and (bottom)

the electric field intensity E produced by a first return stroke at a distance of about 36 km over the Atlantic Ocean The propagation path was almost entirely over salt water The vertical arrow under the E record shows the time of the dEdt

trigger Adapted from Krider

et al (1996)

28

Return Strokes Measured Parameters

Parameters of microsecond-scale electric field waveforms produced by negative return strokes

Parameter Location First strokes Subsequent strokes

Sample size Mean SD Sample size Mean SD

Initial peak (V m‐1) (normalized to 100 km)Rakov

and Uman

(1990b)

Cooray

and Lundquist (1982)Lin et al (1979)

Florida

SwedenKSCOcala

76

5535129

59 (GM)

536758

273825

232a

38b

8359

27(GM)41(GM)

5043

2215

Zero‐crossing time (μs)Cooray

and Lundquist (1985)

Lin et al (1979)

SwedenSri LankaFlorida

1029146c

498954

123018

9414377c

394236

81417

Zero‐to‐peak rise time (μs)Master et al (1984)Cooray

and Lundquist (1982)Lin et al (1979)

FloridaSwedenKSCOcala

1051405129

44702427

18201213

220

8359

28

1519

15

0807

10‐90 percent rise time (μs)Master et al (1984) Florida 105 26 12 220 15 09

Slow front duration

(μs)Master et al (1984)Cooray

and Lundquist (1982)Weidman and Krider

(1978)

FloridaSwedenFlorida

105826290

29504041

13201716

44 120 34d

060921

020509

29

Return Strokes Measured ParametersParameters of microsecond-scale electric field waveforms produced by negative return strokes (contrsquod)

Parameter Locatio

nFirst strokes Subsequent strokes

Sample size

Mean SD Sample size Mean SD

Slow front amplitude as percentage of peakMaster et al (1984)Cooray

and Lundquist (1982)Weidman and Krider

(1978)

FloridaSwedenFlorida

105836290

28415040

15112020

4412034d

202540

101020

Fast

transition 10-90 percent risetime

(ns)Master et al (1984)Weidman and Krider

(1978)

Weidman and Krider

(1980a 1984)

Weidman (1982)

FloridaFlorida

Florida

1023815125

97020020090

68010010040

2178034

610200150

27040100

Peak time derivative (normalized to100 km ) (V m-1

μs-1)Krider

et al (1996) Florida 63 39 11

Time derivative pulse width at half-peak value (ns)

Krider

et al (1996) Florida 61 100 20

If not specicied

otherwise multiple lines for a given source for the same location correspond to different thunderstorms GM = geometric mean value a better characteristic of the distribution of initial field peaks since this distribution is approximately log-normala

Strokes following previously formed channelb

Strokes creating new termination on groundcBoth

electric and magnetic fieldsd

Subsequent strokes initiated by dart-stepped leaders Other subsequent strokes studied by Weidman and

Krider

(1978) were initiated by dart leaders

30

• Slide Number 1
• Slide Number 2
• Slide Number 3
• Slide Number 4
• Slide Number 5
• Slide Number 6
• Slide Number 7
• Slide Number 8
• Slide Number 9
• Slide Number 10
• Slide Number 11
• Slide Number 12
• Return-Stroke Fields Variation with Distance
• Return-Stroke Fields Variation with Distance
• Slide Number 15
• Slide Number 16
• Slide Number 17
• Slide Number 18
• Slide Number 19
• Slide Number 20
• Slide Number 21
• Slide Number 22
• Slide Number 23
• Slide Number 24
• Slide Number 25
• First Return Stroke
• Subsequent Return Strokes
• First Return Stroke Electric Field Derivative
• Return Strokes Measured Parameters
• Return Strokes Measured Parameters

6

Optical Images of Leader and Attachment Process ndash Triggered Lightning

Dart-stepped leader and attachement

process in rocket-triggered lightning (Sept 17 2008) at Camp Blanding Florida Photron

FASTCAM SA11 50000 fps (20 micros per frame)

Biagi

et al (2009 GRL)2 frames before return stroke 8 1 frame before return stroke 8

56 m

16 m

25 m

7

Optical Images of Leader and Attachment Process ndash Laboratory Sparks

Single-frame K008 images of four negative discharges (-22 MV1307500 μs) in a 45 m rod-rod gap Frame duration in a b and c is 2 micros and in d it is 05 micros L in b is the length of last step Adapted from Lebedev et al (2007)

-4

5 m

8

Optical Images of Attachment Process

55

m

HV rod

JP

Single-frame image-converter-camera K008 images of negative discharges in a 55-m rod-rod gap with frame exposure of 02 μs JP is the junction point between downward negative and upward connecting positive leaders Adapted from

Shcherbakov

et al (2006)

A photograph of a lightning strike to a chimney pot showing a split in the channel interpreted as evidence of an upward connecting leader Adapted from Golde

(1967)

JP

9

Illustration of capture surfaces of two towers and earthrsquos surface in the electrogeometrical

model (EGM) rs

is the striking distance defined as the distance from the tip of the descending leader to the object to be struck at the instant when an upward connecting leader is initiated from this object

Vertical arrows represent descending leaders assumed to be uniformly distributed (Ng=const) above the capture surfaces Adapted from Bazelyan

and Raizer

(2000)

Electrogeometrical Model (EGM)

rs

rsrs

Capture surfaces

Ng=const

10

Electrogeometrical Model (EGM)

rs

= 10 I065 m where I

is in kA

4

3

12

Striking distance rs

versus return-stroke peak current I

[curve 1 Golde

(1945) curve 2 Wagner (1963) curve 3 Love (1973) curve 4 Ruhling

(1972) x theory of Davis (1962) estimates from two-

dimensional photographs by Eriksson (1978) estimates from three-dimensional photography by Eriksson (1978) Adapted from Golde

(1977) and Eriksson (1978)

I kA rs m

10 45

30 91

170 282

11

Scatter plot of impulse charge Q versus return-stroke peak current

I Note that both vertical and horizontal scales are logarithmic The best fit to data I

= 106 Q07 where Q is in coulombs and I

is in kiloamperes was used in deriving rs

= 10 I065

Adapted from Berger (1972)

Electrogeometrical Model (EGM)

Finding rs = f(I)

bull

Assume critical average electric field between the leader tip and the strike object at the time of initiation of upward connecting leader from the object (200-600 kVm)

bull

Use an empirical relation between Q and I

to find rs

= f(I)

bull

Find rs

= f(Q)

bull

Assume leader geometry total leader charge Q and distribution of this charge along the channel

Q

10-1

100

101

102

100 101 102I

I

peak Q impulseneg first strokes n=89

I

= 106 Q07

For Q = 5 CI

= 33 kA

12

Electrogeometrical Model (EGM)

Illustration of the rolling-sphere method (RSM) The shaded area is that area into which it is postulated lightning cannot enter Adapted from Szczerbinski

(2000)

rs

rsrs

rs = 45 m (150 ft) (NFPA 780 2004) corresponds to I

= 10 kA (95 of currents exceed this value)

Rolling-Sphere Method

Return‐Stroke Fields Variation with Distance

Typical vertical electric field intensity (left column) and azimuthal

magnetic flux density (right column) waveforms for first (solid line) and subsequent (dashed line) return strokes at distances of 1 2 and 5 km Adapted from Lin et al (1979)

Electric Field Intensity Magnetic Flux Density

Return‐Stroke Fields Variation with Distance

Electric Field IntensityMagnetic Flux Density

Typical vertical electric field intensity (left column) and azimuthal

magnetic flux density (right column) waveforms for first (solid line) and subsequent (dashed line) return strokes at distances of 10 15 50 and 200 km Adapted from Lin et al (1979)

Return-Stroke Current Waveshapes

ndash

Switzerland (Berger et al 1975)

15

Average negative first and subsequent-stroke current waveshapes

each shown on two time scales A

and B The lower time scales (A) correspond to the solid curves while the upper time scales (B) correspond to the broken curves The vertical (amplitude) scale is in relative units the peak values being equal to negative unity Adapted from Berger et al (1975)

Lightning Parameters Derived from Direct Current Measurements

Parameters Units Sample Size

Percent Exceeding Tabulated Value

95 50 5

Peak current

(minimum 2 kA)First strokesSubsequent strokes

kA 101135

1446

3012

8030

Charge

(total charge)First strokesSubsequent strokesComplete flash

C 9312294

110213

521475

241140

Impulse charge

(excluding continuing current)

First strokesSubsequent strokes

C90

11711

02245

09520

4Front duration

(2 kA to peak)First strokesSubsequent strokes

μs 89118

18022

5511

1845

Maximum dIdtFirst strokesSubsequent strokes

kA μs-1 92122

5512

1240

32120

Stroke duration

(2 kA to half peak value on the tail)

First strokesSubsequent strokes

μs90

1153065

7532

200140

Action integral (intI2dt)First strokesSubsequent strokes

A2s 9188

60 x 103

55 x 10255 x 104

60 x 10355 x 105

52 x 104

17

Cumulative statistical distributions of lightning peak currents

giving percent of cases exceeding abscissa value from direct measurements in Switzerland (Berger 1972 Berger et al 1975) The distributions are assumed to be lognormal and given for (1) negative first strokes (2) positive first strokes (3) negative and positive first strokes and (4) negative subsequent strokes Adapted from Bazelyan

et al (1978)

Lightning peak currents for first strokes vary by a factor of 50 or more from about 5 to 250 kA

The probability of occurrence of a given value rapidly increases up to 25 kA

or so and then slowly decreasesStatistical distributions of this type are often assumed to be lognormal

Lightning Peak Current ndash

Bergerrsquos Distributions

18

Cumulative statistical distributions of peak currents (percent values on the vertical axis should be subtracted from 100 to obtain the probability to exceed the peak current value on the horizontal axis) for negative first strokes adopted by IEEE

and CIGRE Taken from CIGRE Document 63 (1991)

For the CIGRE

distribution 98 of peak currents exceed 4 kA 80 exceed 20 kA and 5 exceed 90 kA

For the IEEE

distribution the ldquoprobability to exceedrdquo

values are given by the following equation

where PI

is in per unit and I is in kA This equation applies to values of I up to 200 kA The median (50) peak current value is equal to 31 kA

Peak current I kA(IEEE

distribution) 5 10 20 40 60 80 100 200

Percentage exceeding tabulated value PI

10099 95 76 34 15 78 45 08

( ) 62

311

1I

PI+

=

Lightning Peak Current ndash

IEEE and CIGRE Distributions

dIdt

in Rocket-Triggered Lightning ( ~100 kAμs)

19

Relation between the peak rate of current rise dIdt and the peak current I from triggered-lightning experiments conducted at the NASA Kennedy Space Center Florida in 19851987 and 1988 and in France in 1986 The regression line for each year is shown the sample size N and the regression equation are given in table Adapted from Leteinturier

et al (1991)

Morro Do Cachimbo

Tower (60 m) Belo Horizonte Brazil

20

Courtesy Prof Dr Silverio Visacro Filho Lightning Research Center (UFMG-CEMIG)

Lightning Parameters Derived from Direct Current Measurements ndash

Brazil

21

First Stroke

Subsequent Strokes

404

52

163

099

Optical Measurements of Return-Stroke Speed

22

Optical intensity (in millivolts

at the input of the oscilloscope) vs time waveforms at four different heights 7 63 117 and 170 m

above the lightning termination point for stroke 1 in flash F0336 Adapted from Olsen et al (2004)

23

Reference St Dev ms Comments

Natural Lightning

Boyle and Orville (1976)

20 x 107 12 x 108 071 x 108 26 x 107 12 Streak camera 2-D speed

Idone and Orville (1982)

29 x 107 24 x 108 11 x 108 47 x 107 63 Streak camera2-D speed

Mach and Rust (1989a Fig 7)

20 x 107

80 x 10726 x 108

gt28 x 1085 x 107

7 x 1075443

Long channelShort channel (Photoelectric 2-D)

Triggered Lightning

Hubert and Mouget (1981)

45 x 107 17 x 108 99 x 107 41 x 107 13 Photoelectric3-D speed

Idone et al (1984) 67 x 107 17 x 108 12 x 108 27 x 107 56 Streak camera 3-D speed

Willett et al (1988)

10 x 108 15 x 108 12 x 108 16 x 107 9 Streak camera 2-D speed

Willett et al (1989a)

12 x 108 19 x 108 15 x 108 17 x 107 18 Streak camera 2-D speed

Mach and Rust (1989a Fig 8)

60 x 107

60 x 10716 x 108

20 x 1082 x 107

4 x 1074039

Long channelShort channel(Photoelectric 2-D)

Min ms Max ms Mean ms Sample

Size

13 plusmn03 x 108

19 plusmn07 x 108

12 plusmn03 x 108

14 plusmn04 x 108

Summary of measured return stroke speeds averaged over the visible part of the channel in natural and triggered negative lightning Adapted from Rakov

et al (1992b)

Return-Stroke Speed Near Ground

24

Height Above Ground

7-63 m

63-117 m

117-170

m

12

16

15

12121213

18

16

16

17

18 18

1512

Return-stroke speed profiles estimated tracking the 20 point on the light-pulse front for triggered lightning flash F0336 (Olsen et al 2004)

Return-Stroke Speed vs Return-Stroke Peak Current

25

Return-stroke speed vs peak current for 29 triggered-lightning strokes observed at the Kennedy Space Center (KSC) Florida in 1986 and reported by Mach and Rust (1989a) and 18 triggered-lightning strokes from the 1987 KSC experiments reported by Willett et al

(1989a) Peak curent shown in the scatter plot as 38 kA may be an underestimate Note that the linear correlation coefficients (r) for both data sets are low and negative not in support of the often assumed relationship between these two lightning parameters

00

05

10

15

20

25

0 5 10 15 20 25 30 35 40 45

Return-Stroke Peak Current kA

Ret

urn-

Stro

ke S

peed

108 m

s

Mach and Rust (1989a) r = -008

Willett el al (1998a) r = -027

First Return Stroke

Electric field waveforms of a first return stroke The waveform is shown on two time scales 5 μsdiv

and 10 μsdiv The fields are normalized to a distance of 100 km L denotes individual leader pulses F slow front and R fast transition Also marked are the small secondary peak or shoulder α

and the larger subsidiary peaks a b and c Adapted from Weidman and Krider

(1978)

-20 -15 -10 -5 0 5 10 15 20

5

microsdiv

10

microsdiv

-60 -40 -20 0 20 40 60 80

26

Subsequent Return Strokes

-20 -15 -10 -5 0 5 10 15 20

5 microsdiv

5 microsdiv

10 microsdiv

10 microsdiv

-60 -40 -20 0 20 40 60 80

Electric field waveforms of (b) a subsequent return stroke initiated by a dart-stepped leader and (c) a subsequent return stroke initiated by a dart leader showing the fine structure both before and after the initial field peak Each waveform is shown on two time scales 5 μsdiv

and 10 μsdiv The fields are normalized to a distance of 100 km L denotes individual leader pulses F slow front and R fast transition Also marked are the small secondary peak or shoulder α

and the larger subsidiary peaks a b and c Adapted from Weidman and Krider

(1978)

27

First Return Stroke Electric Field Derivative

Examples of (top) the time derivative of the electric field intensity dEdt

and (bottom)

the electric field intensity E produced by a first return stroke at a distance of about 36 km over the Atlantic Ocean The propagation path was almost entirely over salt water The vertical arrow under the E record shows the time of the dEdt

trigger Adapted from Krider

et al (1996)

28

Return Strokes Measured Parameters

Parameters of microsecond-scale electric field waveforms produced by negative return strokes

Parameter Location First strokes Subsequent strokes

Sample size Mean SD Sample size Mean SD

Initial peak (V m‐1) (normalized to 100 km)Rakov

and Uman

(1990b)

Cooray

and Lundquist (1982)Lin et al (1979)

Florida

SwedenKSCOcala

76

5535129

59 (GM)

536758

273825

232a

38b

8359

27(GM)41(GM)

5043

2215

Zero‐crossing time (μs)Cooray

and Lundquist (1985)

Lin et al (1979)

SwedenSri LankaFlorida

1029146c

498954

123018

9414377c

394236

81417

Zero‐to‐peak rise time (μs)Master et al (1984)Cooray

and Lundquist (1982)Lin et al (1979)

FloridaSwedenKSCOcala

1051405129

44702427

18201213

220

8359

28

1519

15

0807

10‐90 percent rise time (μs)Master et al (1984) Florida 105 26 12 220 15 09

Slow front duration

(μs)Master et al (1984)Cooray

and Lundquist (1982)Weidman and Krider

(1978)

FloridaSwedenFlorida

105826290

29504041

13201716

44 120 34d

060921

020509

29

Return Strokes Measured ParametersParameters of microsecond-scale electric field waveforms produced by negative return strokes (contrsquod)

Parameter Locatio

nFirst strokes Subsequent strokes

Sample size

Mean SD Sample size Mean SD

Slow front amplitude as percentage of peakMaster et al (1984)Cooray

and Lundquist (1982)Weidman and Krider

(1978)

FloridaSwedenFlorida

105836290

28415040

15112020

4412034d

202540

101020

Fast

transition 10-90 percent risetime

(ns)Master et al (1984)Weidman and Krider

(1978)

Weidman and Krider

(1980a 1984)

Weidman (1982)

FloridaFlorida

Florida

1023815125

97020020090

68010010040

2178034

610200150

27040100

Peak time derivative (normalized to100 km ) (V m-1

μs-1)Krider

et al (1996) Florida 63 39 11

Time derivative pulse width at half-peak value (ns)

Krider

et al (1996) Florida 61 100 20

If not specicied

otherwise multiple lines for a given source for the same location correspond to different thunderstorms GM = geometric mean value a better characteristic of the distribution of initial field peaks since this distribution is approximately log-normala

Strokes following previously formed channelb

Strokes creating new termination on groundcBoth

electric and magnetic fieldsd

Subsequent strokes initiated by dart-stepped leaders Other subsequent strokes studied by Weidman and

Krider

(1978) were initiated by dart leaders

30

• Slide Number 1
• Slide Number 2
• Slide Number 3
• Slide Number 4
• Slide Number 5
• Slide Number 6
• Slide Number 7
• Slide Number 8
• Slide Number 9
• Slide Number 10
• Slide Number 11
• Slide Number 12
• Return-Stroke Fields Variation with Distance
• Return-Stroke Fields Variation with Distance
• Slide Number 15
• Slide Number 16
• Slide Number 17
• Slide Number 18
• Slide Number 19
• Slide Number 20
• Slide Number 21
• Slide Number 22
• Slide Number 23
• Slide Number 24
• Slide Number 25
• First Return Stroke
• Subsequent Return Strokes
• First Return Stroke Electric Field Derivative
• Return Strokes Measured Parameters
• Return Strokes Measured Parameters

7

Optical Images of Leader and Attachment Process ndash Laboratory Sparks

Single-frame K008 images of four negative discharges (-22 MV1307500 μs) in a 45 m rod-rod gap Frame duration in a b and c is 2 micros and in d it is 05 micros L in b is the length of last step Adapted from Lebedev et al (2007)

-4

5 m

8

Optical Images of Attachment Process

55

m

HV rod

JP

Single-frame image-converter-camera K008 images of negative discharges in a 55-m rod-rod gap with frame exposure of 02 μs JP is the junction point between downward negative and upward connecting positive leaders Adapted from

Shcherbakov

et al (2006)

A photograph of a lightning strike to a chimney pot showing a split in the channel interpreted as evidence of an upward connecting leader Adapted from Golde

(1967)

JP

9

Illustration of capture surfaces of two towers and earthrsquos surface in the electrogeometrical

model (EGM) rs

is the striking distance defined as the distance from the tip of the descending leader to the object to be struck at the instant when an upward connecting leader is initiated from this object

Vertical arrows represent descending leaders assumed to be uniformly distributed (Ng=const) above the capture surfaces Adapted from Bazelyan

and Raizer

(2000)

Electrogeometrical Model (EGM)

rs

rsrs

Capture surfaces

Ng=const

10

Electrogeometrical Model (EGM)

rs

= 10 I065 m where I

is in kA

4

3

12

Striking distance rs

versus return-stroke peak current I

[curve 1 Golde

(1945) curve 2 Wagner (1963) curve 3 Love (1973) curve 4 Ruhling

(1972) x theory of Davis (1962) estimates from two-

dimensional photographs by Eriksson (1978) estimates from three-dimensional photography by Eriksson (1978) Adapted from Golde

(1977) and Eriksson (1978)

I kA rs m

10 45

30 91

170 282

11

Scatter plot of impulse charge Q versus return-stroke peak current

I Note that both vertical and horizontal scales are logarithmic The best fit to data I

= 106 Q07 where Q is in coulombs and I

is in kiloamperes was used in deriving rs

= 10 I065

Adapted from Berger (1972)

Electrogeometrical Model (EGM)

Finding rs = f(I)

bull

Assume critical average electric field between the leader tip and the strike object at the time of initiation of upward connecting leader from the object (200-600 kVm)

bull

Use an empirical relation between Q and I

to find rs

= f(I)

bull

Find rs

= f(Q)

bull

Assume leader geometry total leader charge Q and distribution of this charge along the channel

Q

10-1

100

101

102

100 101 102I

I

peak Q impulseneg first strokes n=89

I

= 106 Q07

For Q = 5 CI

= 33 kA

12

Electrogeometrical Model (EGM)

Illustration of the rolling-sphere method (RSM) The shaded area is that area into which it is postulated lightning cannot enter Adapted from Szczerbinski

(2000)

rs

rsrs

rs = 45 m (150 ft) (NFPA 780 2004) corresponds to I

= 10 kA (95 of currents exceed this value)

Rolling-Sphere Method

Return‐Stroke Fields Variation with Distance

Typical vertical electric field intensity (left column) and azimuthal

magnetic flux density (right column) waveforms for first (solid line) and subsequent (dashed line) return strokes at distances of 1 2 and 5 km Adapted from Lin et al (1979)

Electric Field Intensity Magnetic Flux Density

Return‐Stroke Fields Variation with Distance

Electric Field IntensityMagnetic Flux Density

Typical vertical electric field intensity (left column) and azimuthal

magnetic flux density (right column) waveforms for first (solid line) and subsequent (dashed line) return strokes at distances of 10 15 50 and 200 km Adapted from Lin et al (1979)

Return-Stroke Current Waveshapes

ndash

Switzerland (Berger et al 1975)

15

Average negative first and subsequent-stroke current waveshapes

each shown on two time scales A

and B The lower time scales (A) correspond to the solid curves while the upper time scales (B) correspond to the broken curves The vertical (amplitude) scale is in relative units the peak values being equal to negative unity Adapted from Berger et al (1975)

Lightning Parameters Derived from Direct Current Measurements

Parameters Units Sample Size

Percent Exceeding Tabulated Value

95 50 5

Peak current

(minimum 2 kA)First strokesSubsequent strokes

kA 101135

1446

3012

8030

Charge

(total charge)First strokesSubsequent strokesComplete flash

C 9312294

110213

521475

241140

Impulse charge

(excluding continuing current)

First strokesSubsequent strokes

C90

11711

02245

09520

4Front duration

(2 kA to peak)First strokesSubsequent strokes

μs 89118

18022

5511

1845

Maximum dIdtFirst strokesSubsequent strokes

kA μs-1 92122

5512

1240

32120

Stroke duration

(2 kA to half peak value on the tail)

First strokesSubsequent strokes

μs90

1153065

7532

200140

Action integral (intI2dt)First strokesSubsequent strokes

A2s 9188

60 x 103

55 x 10255 x 104

60 x 10355 x 105

52 x 104

17

Cumulative statistical distributions of lightning peak currents

giving percent of cases exceeding abscissa value from direct measurements in Switzerland (Berger 1972 Berger et al 1975) The distributions are assumed to be lognormal and given for (1) negative first strokes (2) positive first strokes (3) negative and positive first strokes and (4) negative subsequent strokes Adapted from Bazelyan

et al (1978)

Lightning peak currents for first strokes vary by a factor of 50 or more from about 5 to 250 kA

The probability of occurrence of a given value rapidly increases up to 25 kA

or so and then slowly decreasesStatistical distributions of this type are often assumed to be lognormal

Lightning Peak Current ndash

Bergerrsquos Distributions

18

Cumulative statistical distributions of peak currents (percent values on the vertical axis should be subtracted from 100 to obtain the probability to exceed the peak current value on the horizontal axis) for negative first strokes adopted by IEEE

and CIGRE Taken from CIGRE Document 63 (1991)

For the CIGRE

distribution 98 of peak currents exceed 4 kA 80 exceed 20 kA and 5 exceed 90 kA

For the IEEE

distribution the ldquoprobability to exceedrdquo

values are given by the following equation

where PI

is in per unit and I is in kA This equation applies to values of I up to 200 kA The median (50) peak current value is equal to 31 kA

Peak current I kA(IEEE

distribution) 5 10 20 40 60 80 100 200

Percentage exceeding tabulated value PI

10099 95 76 34 15 78 45 08

( ) 62

311

1I

PI+

=

Lightning Peak Current ndash

IEEE and CIGRE Distributions

dIdt

in Rocket-Triggered Lightning ( ~100 kAμs)

19

Relation between the peak rate of current rise dIdt and the peak current I from triggered-lightning experiments conducted at the NASA Kennedy Space Center Florida in 19851987 and 1988 and in France in 1986 The regression line for each year is shown the sample size N and the regression equation are given in table Adapted from Leteinturier

et al (1991)

Morro Do Cachimbo

Tower (60 m) Belo Horizonte Brazil

20

Courtesy Prof Dr Silverio Visacro Filho Lightning Research Center (UFMG-CEMIG)

Lightning Parameters Derived from Direct Current Measurements ndash

Brazil

21

First Stroke

Subsequent Strokes

404

52

163

099

Optical Measurements of Return-Stroke Speed

22

Optical intensity (in millivolts

at the input of the oscilloscope) vs time waveforms at four different heights 7 63 117 and 170 m

above the lightning termination point for stroke 1 in flash F0336 Adapted from Olsen et al (2004)

23

Reference St Dev ms Comments

Natural Lightning

Boyle and Orville (1976)

20 x 107 12 x 108 071 x 108 26 x 107 12 Streak camera 2-D speed

Idone and Orville (1982)

29 x 107 24 x 108 11 x 108 47 x 107 63 Streak camera2-D speed

Mach and Rust (1989a Fig 7)

20 x 107

80 x 10726 x 108

gt28 x 1085 x 107

7 x 1075443

Long channelShort channel (Photoelectric 2-D)

Triggered Lightning

Hubert and Mouget (1981)

45 x 107 17 x 108 99 x 107 41 x 107 13 Photoelectric3-D speed

Idone et al (1984) 67 x 107 17 x 108 12 x 108 27 x 107 56 Streak camera 3-D speed

Willett et al (1988)

10 x 108 15 x 108 12 x 108 16 x 107 9 Streak camera 2-D speed

Willett et al (1989a)

12 x 108 19 x 108 15 x 108 17 x 107 18 Streak camera 2-D speed

Mach and Rust (1989a Fig 8)

60 x 107

60 x 10716 x 108

20 x 1082 x 107

4 x 1074039

Long channelShort channel(Photoelectric 2-D)

Min ms Max ms Mean ms Sample

Size

13 plusmn03 x 108

19 plusmn07 x 108

12 plusmn03 x 108

14 plusmn04 x 108

Summary of measured return stroke speeds averaged over the visible part of the channel in natural and triggered negative lightning Adapted from Rakov

et al (1992b)

Return-Stroke Speed Near Ground

24

Height Above Ground

7-63 m

63-117 m

117-170

m

12

16

15

12121213

18

16

16

17

18 18

1512

Return-stroke speed profiles estimated tracking the 20 point on the light-pulse front for triggered lightning flash F0336 (Olsen et al 2004)

Return-Stroke Speed vs Return-Stroke Peak Current

25

Return-stroke speed vs peak current for 29 triggered-lightning strokes observed at the Kennedy Space Center (KSC) Florida in 1986 and reported by Mach and Rust (1989a) and 18 triggered-lightning strokes from the 1987 KSC experiments reported by Willett et al

(1989a) Peak curent shown in the scatter plot as 38 kA may be an underestimate Note that the linear correlation coefficients (r) for both data sets are low and negative not in support of the often assumed relationship between these two lightning parameters

00

05

10

15

20

25

0 5 10 15 20 25 30 35 40 45

Return-Stroke Peak Current kA

Ret

urn-

Stro

ke S

peed

108 m

s

Mach and Rust (1989a) r = -008

Willett el al (1998a) r = -027

First Return Stroke

Electric field waveforms of a first return stroke The waveform is shown on two time scales 5 μsdiv

and 10 μsdiv The fields are normalized to a distance of 100 km L denotes individual leader pulses F slow front and R fast transition Also marked are the small secondary peak or shoulder α

and the larger subsidiary peaks a b and c Adapted from Weidman and Krider

(1978)

-20 -15 -10 -5 0 5 10 15 20

5

microsdiv

10

microsdiv

-60 -40 -20 0 20 40 60 80

26

Subsequent Return Strokes

-20 -15 -10 -5 0 5 10 15 20

5 microsdiv

5 microsdiv

10 microsdiv

10 microsdiv

-60 -40 -20 0 20 40 60 80

Electric field waveforms of (b) a subsequent return stroke initiated by a dart-stepped leader and (c) a subsequent return stroke initiated by a dart leader showing the fine structure both before and after the initial field peak Each waveform is shown on two time scales 5 μsdiv

and 10 μsdiv The fields are normalized to a distance of 100 km L denotes individual leader pulses F slow front and R fast transition Also marked are the small secondary peak or shoulder α

and the larger subsidiary peaks a b and c Adapted from Weidman and Krider

(1978)

27

First Return Stroke Electric Field Derivative

Examples of (top) the time derivative of the electric field intensity dEdt

and (bottom)

the electric field intensity E produced by a first return stroke at a distance of about 36 km over the Atlantic Ocean The propagation path was almost entirely over salt water The vertical arrow under the E record shows the time of the dEdt

trigger Adapted from Krider

et al (1996)

28

Return Strokes Measured Parameters

Parameters of microsecond-scale electric field waveforms produced by negative return strokes

Parameter Location First strokes Subsequent strokes

Sample size Mean SD Sample size Mean SD

Initial peak (V m‐1) (normalized to 100 km)Rakov

and Uman

(1990b)

Cooray

and Lundquist (1982)Lin et al (1979)

Florida

SwedenKSCOcala

76

5535129

59 (GM)

536758

273825

232a

38b

8359

27(GM)41(GM)

5043

2215

Zero‐crossing time (μs)Cooray

and Lundquist (1985)

Lin et al (1979)

SwedenSri LankaFlorida

1029146c

498954

123018

9414377c

394236

81417

Zero‐to‐peak rise time (μs)Master et al (1984)Cooray

and Lundquist (1982)Lin et al (1979)

FloridaSwedenKSCOcala

1051405129

44702427

18201213

220

8359

28

1519

15

0807

10‐90 percent rise time (μs)Master et al (1984) Florida 105 26 12 220 15 09

Slow front duration

(μs)Master et al (1984)Cooray

and Lundquist (1982)Weidman and Krider

(1978)

FloridaSwedenFlorida

105826290

29504041

13201716

44 120 34d

060921

020509

29

Return Strokes Measured ParametersParameters of microsecond-scale electric field waveforms produced by negative return strokes (contrsquod)

Parameter Locatio

nFirst strokes Subsequent strokes

Sample size

Mean SD Sample size Mean SD

Slow front amplitude as percentage of peakMaster et al (1984)Cooray

and Lundquist (1982)Weidman and Krider

(1978)

FloridaSwedenFlorida

105836290

28415040

15112020

4412034d

202540

101020

Fast

transition 10-90 percent risetime

(ns)Master et al (1984)Weidman and Krider

(1978)

Weidman and Krider

(1980a 1984)

Weidman (1982)

FloridaFlorida

Florida

1023815125

97020020090

68010010040

2178034

610200150

27040100

Peak time derivative (normalized to100 km ) (V m-1

μs-1)Krider

et al (1996) Florida 63 39 11

Time derivative pulse width at half-peak value (ns)

Krider

et al (1996) Florida 61 100 20

If not specicied

otherwise multiple lines for a given source for the same location correspond to different thunderstorms GM = geometric mean value a better characteristic of the distribution of initial field peaks since this distribution is approximately log-normala

Strokes following previously formed channelb

Strokes creating new termination on groundcBoth

electric and magnetic fieldsd

Subsequent strokes initiated by dart-stepped leaders Other subsequent strokes studied by Weidman and

Krider

(1978) were initiated by dart leaders

30

• Slide Number 1
• Slide Number 2
• Slide Number 3
• Slide Number 4
• Slide Number 5
• Slide Number 6
• Slide Number 7
• Slide Number 8
• Slide Number 9
• Slide Number 10
• Slide Number 11
• Slide Number 12
• Return-Stroke Fields Variation with Distance
• Return-Stroke Fields Variation with Distance
• Slide Number 15
• Slide Number 16
• Slide Number 17
• Slide Number 18
• Slide Number 19
• Slide Number 20
• Slide Number 21
• Slide Number 22
• Slide Number 23
• Slide Number 24
• Slide Number 25
• First Return Stroke
• Subsequent Return Strokes
• First Return Stroke Electric Field Derivative
• Return Strokes Measured Parameters
• Return Strokes Measured Parameters

8

Optical Images of Attachment Process

55

m

HV rod

JP

Single-frame image-converter-camera K008 images of negative discharges in a 55-m rod-rod gap with frame exposure of 02 μs JP is the junction point between downward negative and upward connecting positive leaders Adapted from

Shcherbakov

et al (2006)

A photograph of a lightning strike to a chimney pot showing a split in the channel interpreted as evidence of an upward connecting leader Adapted from Golde

(1967)

JP

9

Illustration of capture surfaces of two towers and earthrsquos surface in the electrogeometrical

model (EGM) rs

is the striking distance defined as the distance from the tip of the descending leader to the object to be struck at the instant when an upward connecting leader is initiated from this object

Vertical arrows represent descending leaders assumed to be uniformly distributed (Ng=const) above the capture surfaces Adapted from Bazelyan

and Raizer

(2000)

Electrogeometrical Model (EGM)

rs

rsrs

Capture surfaces

Ng=const

10

Electrogeometrical Model (EGM)

rs

= 10 I065 m where I

is in kA

4

3

12

Striking distance rs

versus return-stroke peak current I

[curve 1 Golde

(1945) curve 2 Wagner (1963) curve 3 Love (1973) curve 4 Ruhling

(1972) x theory of Davis (1962) estimates from two-

dimensional photographs by Eriksson (1978) estimates from three-dimensional photography by Eriksson (1978) Adapted from Golde

(1977) and Eriksson (1978)

I kA rs m

10 45

30 91

170 282

11

Scatter plot of impulse charge Q versus return-stroke peak current

I Note that both vertical and horizontal scales are logarithmic The best fit to data I

= 106 Q07 where Q is in coulombs and I

is in kiloamperes was used in deriving rs

= 10 I065

Adapted from Berger (1972)

Electrogeometrical Model (EGM)

Finding rs = f(I)

bull

Assume critical average electric field between the leader tip and the strike object at the time of initiation of upward connecting leader from the object (200-600 kVm)

bull

Use an empirical relation between Q and I

to find rs

= f(I)

bull

Find rs

= f(Q)

bull

Assume leader geometry total leader charge Q and distribution of this charge along the channel

Q

10-1

100

101

102

100 101 102I

I

peak Q impulseneg first strokes n=89

I

= 106 Q07

For Q = 5 CI

= 33 kA

12

Electrogeometrical Model (EGM)

Illustration of the rolling-sphere method (RSM) The shaded area is that area into which it is postulated lightning cannot enter Adapted from Szczerbinski

(2000)

rs

rsrs

rs = 45 m (150 ft) (NFPA 780 2004) corresponds to I

= 10 kA (95 of currents exceed this value)

Rolling-Sphere Method

Return‐Stroke Fields Variation with Distance

Typical vertical electric field intensity (left column) and azimuthal

magnetic flux density (right column) waveforms for first (solid line) and subsequent (dashed line) return strokes at distances of 1 2 and 5 km Adapted from Lin et al (1979)

Electric Field Intensity Magnetic Flux Density

Return‐Stroke Fields Variation with Distance

Electric Field IntensityMagnetic Flux Density

Typical vertical electric field intensity (left column) and azimuthal

magnetic flux density (right column) waveforms for first (solid line) and subsequent (dashed line) return strokes at distances of 10 15 50 and 200 km Adapted from Lin et al (1979)

Return-Stroke Current Waveshapes

ndash

Switzerland (Berger et al 1975)

15

Average negative first and subsequent-stroke current waveshapes

each shown on two time scales A

and B The lower time scales (A) correspond to the solid curves while the upper time scales (B) correspond to the broken curves The vertical (amplitude) scale is in relative units the peak values being equal to negative unity Adapted from Berger et al (1975)

Lightning Parameters Derived from Direct Current Measurements

Parameters Units Sample Size

Percent Exceeding Tabulated Value

95 50 5

Peak current

(minimum 2 kA)First strokesSubsequent strokes

kA 101135

1446

3012

8030

Charge

(total charge)First strokesSubsequent strokesComplete flash

C 9312294

110213

521475

241140

Impulse charge

(excluding continuing current)

First strokesSubsequent strokes

C90

11711

02245

09520

4Front duration

(2 kA to peak)First strokesSubsequent strokes

μs 89118

18022

5511

1845

Maximum dIdtFirst strokesSubsequent strokes

kA μs-1 92122

5512

1240

32120

Stroke duration

(2 kA to half peak value on the tail)

First strokesSubsequent strokes

μs90

1153065

7532

200140

Action integral (intI2dt)First strokesSubsequent strokes

A2s 9188

60 x 103

55 x 10255 x 104

60 x 10355 x 105

52 x 104

17

Cumulative statistical distributions of lightning peak currents

giving percent of cases exceeding abscissa value from direct measurements in Switzerland (Berger 1972 Berger et al 1975) The distributions are assumed to be lognormal and given for (1) negative first strokes (2) positive first strokes (3) negative and positive first strokes and (4) negative subsequent strokes Adapted from Bazelyan

et al (1978)

Lightning peak currents for first strokes vary by a factor of 50 or more from about 5 to 250 kA

The probability of occurrence of a given value rapidly increases up to 25 kA

or so and then slowly decreasesStatistical distributions of this type are often assumed to be lognormal

Lightning Peak Current ndash

Bergerrsquos Distributions

18

Cumulative statistical distributions of peak currents (percent values on the vertical axis should be subtracted from 100 to obtain the probability to exceed the peak current value on the horizontal axis) for negative first strokes adopted by IEEE

and CIGRE Taken from CIGRE Document 63 (1991)

For the CIGRE

distribution 98 of peak currents exceed 4 kA 80 exceed 20 kA and 5 exceed 90 kA

For the IEEE

distribution the ldquoprobability to exceedrdquo

values are given by the following equation

where PI

is in per unit and I is in kA This equation applies to values of I up to 200 kA The median (50) peak current value is equal to 31 kA

Peak current I kA(IEEE

distribution) 5 10 20 40 60 80 100 200

Percentage exceeding tabulated value PI

10099 95 76 34 15 78 45 08

( ) 62

311

1I

PI+

=

Lightning Peak Current ndash

IEEE and CIGRE Distributions

dIdt

in Rocket-Triggered Lightning ( ~100 kAμs)

19

Relation between the peak rate of current rise dIdt and the peak current I from triggered-lightning experiments conducted at the NASA Kennedy Space Center Florida in 19851987 and 1988 and in France in 1986 The regression line for each year is shown the sample size N and the regression equation are given in table Adapted from Leteinturier

et al (1991)

Morro Do Cachimbo

Tower (60 m) Belo Horizonte Brazil

20

Courtesy Prof Dr Silverio Visacro Filho Lightning Research Center (UFMG-CEMIG)

Lightning Parameters Derived from Direct Current Measurements ndash

Brazil

21

First Stroke

Subsequent Strokes

404

52

163

099

Optical Measurements of Return-Stroke Speed

22

Optical intensity (in millivolts

at the input of the oscilloscope) vs time waveforms at four different heights 7 63 117 and 170 m

above the lightning termination point for stroke 1 in flash F0336 Adapted from Olsen et al (2004)

23

Reference St Dev ms Comments

Natural Lightning

Boyle and Orville (1976)

20 x 107 12 x 108 071 x 108 26 x 107 12 Streak camera 2-D speed

Idone and Orville (1982)

29 x 107 24 x 108 11 x 108 47 x 107 63 Streak camera2-D speed

Mach and Rust (1989a Fig 7)

20 x 107

80 x 10726 x 108

gt28 x 1085 x 107

7 x 1075443

Long channelShort channel (Photoelectric 2-D)

Triggered Lightning

Hubert and Mouget (1981)

45 x 107 17 x 108 99 x 107 41 x 107 13 Photoelectric3-D speed

Idone et al (1984) 67 x 107 17 x 108 12 x 108 27 x 107 56 Streak camera 3-D speed

Willett et al (1988)

10 x 108 15 x 108 12 x 108 16 x 107 9 Streak camera 2-D speed

Willett et al (1989a)

12 x 108 19 x 108 15 x 108 17 x 107 18 Streak camera 2-D speed

Mach and Rust (1989a Fig 8)

60 x 107

60 x 10716 x 108

20 x 1082 x 107

4 x 1074039

Long channelShort channel(Photoelectric 2-D)

Min ms Max ms Mean ms Sample

Size

13 plusmn03 x 108

19 plusmn07 x 108

12 plusmn03 x 108

14 plusmn04 x 108

Summary of measured return stroke speeds averaged over the visible part of the channel in natural and triggered negative lightning Adapted from Rakov

et al (1992b)

Return-Stroke Speed Near Ground

24

Height Above Ground

7-63 m

63-117 m

117-170

m

12

16

15

12121213

18

16

16

17

18 18

1512

Return-stroke speed profiles estimated tracking the 20 point on the light-pulse front for triggered lightning flash F0336 (Olsen et al 2004)

Return-Stroke Speed vs Return-Stroke Peak Current

25

Return-stroke speed vs peak current for 29 triggered-lightning strokes observed at the Kennedy Space Center (KSC) Florida in 1986 and reported by Mach and Rust (1989a) and 18 triggered-lightning strokes from the 1987 KSC experiments reported by Willett et al

(1989a) Peak curent shown in the scatter plot as 38 kA may be an underestimate Note that the linear correlation coefficients (r) for both data sets are low and negative not in support of the often assumed relationship between these two lightning parameters

00

05

10

15

20

25

0 5 10 15 20 25 30 35 40 45

Return-Stroke Peak Current kA

Ret

urn-

Stro

ke S

peed

108 m

s

Mach and Rust (1989a) r = -008

Willett el al (1998a) r = -027

First Return Stroke

Electric field waveforms of a first return stroke The waveform is shown on two time scales 5 μsdiv

and 10 μsdiv The fields are normalized to a distance of 100 km L denotes individual leader pulses F slow front and R fast transition Also marked are the small secondary peak or shoulder α

and the larger subsidiary peaks a b and c Adapted from Weidman and Krider

(1978)

-20 -15 -10 -5 0 5 10 15 20

5

microsdiv

10

microsdiv

-60 -40 -20 0 20 40 60 80

26

Subsequent Return Strokes

-20 -15 -10 -5 0 5 10 15 20

5 microsdiv

5 microsdiv

10 microsdiv

10 microsdiv

-60 -40 -20 0 20 40 60 80

Electric field waveforms of (b) a subsequent return stroke initiated by a dart-stepped leader and (c) a subsequent return stroke initiated by a dart leader showing the fine structure both before and after the initial field peak Each waveform is shown on two time scales 5 μsdiv

and 10 μsdiv The fields are normalized to a distance of 100 km L denotes individual leader pulses F slow front and R fast transition Also marked are the small secondary peak or shoulder α

and the larger subsidiary peaks a b and c Adapted from Weidman and Krider

(1978)

27

First Return Stroke Electric Field Derivative

Examples of (top) the time derivative of the electric field intensity dEdt

and (bottom)

the electric field intensity E produced by a first return stroke at a distance of about 36 km over the Atlantic Ocean The propagation path was almost entirely over salt water The vertical arrow under the E record shows the time of the dEdt

trigger Adapted from Krider

et al (1996)

28

Return Strokes Measured Parameters

Parameters of microsecond-scale electric field waveforms produced by negative return strokes

Parameter Location First strokes Subsequent strokes

Sample size Mean SD Sample size Mean SD

Initial peak (V m‐1) (normalized to 100 km)Rakov

and Uman

(1990b)

Cooray

and Lundquist (1982)Lin et al (1979)

Florida

SwedenKSCOcala

76

5535129

59 (GM)

536758

273825

232a

38b

8359

27(GM)41(GM)

5043

2215

Zero‐crossing time (μs)Cooray

and Lundquist (1985)

Lin et al (1979)

SwedenSri LankaFlorida

1029146c

498954

123018

9414377c

394236

81417

Zero‐to‐peak rise time (μs)Master et al (1984)Cooray

and Lundquist (1982)Lin et al (1979)

FloridaSwedenKSCOcala

1051405129

44702427

18201213

220

8359

28

1519

15

0807

10‐90 percent rise time (μs)Master et al (1984) Florida 105 26 12 220 15 09

Slow front duration

(μs)Master et al (1984)Cooray

and Lundquist (1982)Weidman and Krider

(1978)

FloridaSwedenFlorida

105826290

29504041

13201716

44 120 34d

060921

020509

29

Return Strokes Measured ParametersParameters of microsecond-scale electric field waveforms produced by negative return strokes (contrsquod)

Parameter Locatio

nFirst strokes Subsequent strokes

Sample size

Mean SD Sample size Mean SD

Slow front amplitude as percentage of peakMaster et al (1984)Cooray

and Lundquist (1982)Weidman and Krider

(1978)

FloridaSwedenFlorida

105836290

28415040

15112020

4412034d

202540

101020

Fast

transition 10-90 percent risetime

(ns)Master et al (1984)Weidman and Krider

(1978)

Weidman and Krider

(1980a 1984)

Weidman (1982)

FloridaFlorida

Florida

1023815125

97020020090

68010010040

2178034

610200150

27040100

Peak time derivative (normalized to100 km ) (V m-1

μs-1)Krider

et al (1996) Florida 63 39 11

Time derivative pulse width at half-peak value (ns)

Krider

et al (1996) Florida 61 100 20

If not specicied

otherwise multiple lines for a given source for the same location correspond to different thunderstorms GM = geometric mean value a better characteristic of the distribution of initial field peaks since this distribution is approximately log-normala

Strokes following previously formed channelb

Strokes creating new termination on groundcBoth

electric and magnetic fieldsd

Subsequent strokes initiated by dart-stepped leaders Other subsequent strokes studied by Weidman and

Krider

(1978) were initiated by dart leaders

30

• Slide Number 1
• Slide Number 2
• Slide Number 3
• Slide Number 4
• Slide Number 5
• Slide Number 6
• Slide Number 7
• Slide Number 8
• Slide Number 9
• Slide Number 10
• Slide Number 11
• Slide Number 12
• Return-Stroke Fields Variation with Distance
• Return-Stroke Fields Variation with Distance
• Slide Number 15
• Slide Number 16
• Slide Number 17
• Slide Number 18
• Slide Number 19
• Slide Number 20
• Slide Number 21
• Slide Number 22
• Slide Number 23
• Slide Number 24
• Slide Number 25
• First Return Stroke
• Subsequent Return Strokes
• First Return Stroke Electric Field Derivative
• Return Strokes Measured Parameters
• Return Strokes Measured Parameters

9

Illustration of capture surfaces of two towers and earthrsquos surface in the electrogeometrical

model (EGM) rs

is the striking distance defined as the distance from the tip of the descending leader to the object to be struck at the instant when an upward connecting leader is initiated from this object

Vertical arrows represent descending leaders assumed to be uniformly distributed (Ng=const) above the capture surfaces Adapted from Bazelyan

and Raizer

(2000)

Electrogeometrical Model (EGM)

rs

rsrs

Capture surfaces

Ng=const

10

Electrogeometrical Model (EGM)

rs

= 10 I065 m where I

is in kA

4

3

12

Striking distance rs

versus return-stroke peak current I

[curve 1 Golde

(1945) curve 2 Wagner (1963) curve 3 Love (1973) curve 4 Ruhling

(1972) x theory of Davis (1962) estimates from two-

dimensional photographs by Eriksson (1978) estimates from three-dimensional photography by Eriksson (1978) Adapted from Golde

(1977) and Eriksson (1978)

I kA rs m

10 45

30 91

170 282

11

Scatter plot of impulse charge Q versus return-stroke peak current

I Note that both vertical and horizontal scales are logarithmic The best fit to data I

= 106 Q07 where Q is in coulombs and I

is in kiloamperes was used in deriving rs

= 10 I065

Adapted from Berger (1972)

Electrogeometrical Model (EGM)

Finding rs = f(I)

bull

Assume critical average electric field between the leader tip and the strike object at the time of initiation of upward connecting leader from the object (200-600 kVm)

bull

Use an empirical relation between Q and I

to find rs

= f(I)

bull

Find rs

= f(Q)

bull

Assume leader geometry total leader charge Q and distribution of this charge along the channel

Q

10-1

100

101

102

100 101 102I

I

peak Q impulseneg first strokes n=89

I

= 106 Q07

For Q = 5 CI

= 33 kA

12

Electrogeometrical Model (EGM)

Illustration of the rolling-sphere method (RSM) The shaded area is that area into which it is postulated lightning cannot enter Adapted from Szczerbinski

(2000)

rs

rsrs

rs = 45 m (150 ft) (NFPA 780 2004) corresponds to I

= 10 kA (95 of currents exceed this value)

Rolling-Sphere Method

Return‐Stroke Fields Variation with Distance

Typical vertical electric field intensity (left column) and azimuthal

magnetic flux density (right column) waveforms for first (solid line) and subsequent (dashed line) return strokes at distances of 1 2 and 5 km Adapted from Lin et al (1979)

Electric Field Intensity Magnetic Flux Density

Return‐Stroke Fields Variation with Distance

Electric Field IntensityMagnetic Flux Density

Typical vertical electric field intensity (left column) and azimuthal

magnetic flux density (right column) waveforms for first (solid line) and subsequent (dashed line) return strokes at distances of 10 15 50 and 200 km Adapted from Lin et al (1979)

Return-Stroke Current Waveshapes

ndash

Switzerland (Berger et al 1975)

15

Average negative first and subsequent-stroke current waveshapes

each shown on two time scales A

and B The lower time scales (A) correspond to the solid curves while the upper time scales (B) correspond to the broken curves The vertical (amplitude) scale is in relative units the peak values being equal to negative unity Adapted from Berger et al (1975)

Lightning Parameters Derived from Direct Current Measurements

Parameters Units Sample Size

Percent Exceeding Tabulated Value

95 50 5

Peak current

(minimum 2 kA)First strokesSubsequent strokes

kA 101135

1446

3012

8030

Charge

(total charge)First strokesSubsequent strokesComplete flash

C 9312294

110213

521475

241140

Impulse charge

(excluding continuing current)

First strokesSubsequent strokes

C90

11711

02245

09520

4Front duration

(2 kA to peak)First strokesSubsequent strokes

μs 89118

18022

5511

1845

Maximum dIdtFirst strokesSubsequent strokes

kA μs-1 92122

5512

1240

32120

Stroke duration

(2 kA to half peak value on the tail)

First strokesSubsequent strokes

μs90

1153065

7532

200140

Action integral (intI2dt)First strokesSubsequent strokes

A2s 9188

60 x 103

55 x 10255 x 104

60 x 10355 x 105

52 x 104

17

Cumulative statistical distributions of lightning peak currents

giving percent of cases exceeding abscissa value from direct measurements in Switzerland (Berger 1972 Berger et al 1975) The distributions are assumed to be lognormal and given for (1) negative first strokes (2) positive first strokes (3) negative and positive first strokes and (4) negative subsequent strokes Adapted from Bazelyan

et al (1978)

Lightning peak currents for first strokes vary by a factor of 50 or more from about 5 to 250 kA

The probability of occurrence of a given value rapidly increases up to 25 kA

or so and then slowly decreasesStatistical distributions of this type are often assumed to be lognormal

Lightning Peak Current ndash

Bergerrsquos Distributions

18

Cumulative statistical distributions of peak currents (percent values on the vertical axis should be subtracted from 100 to obtain the probability to exceed the peak current value on the horizontal axis) for negative first strokes adopted by IEEE

and CIGRE Taken from CIGRE Document 63 (1991)

For the CIGRE

distribution 98 of peak currents exceed 4 kA 80 exceed 20 kA and 5 exceed 90 kA

For the IEEE

distribution the ldquoprobability to exceedrdquo

values are given by the following equation

where PI

is in per unit and I is in kA This equation applies to values of I up to 200 kA The median (50) peak current value is equal to 31 kA

Peak current I kA(IEEE

distribution) 5 10 20 40 60 80 100 200

Percentage exceeding tabulated value PI

10099 95 76 34 15 78 45 08

( ) 62

311

1I

PI+

=

Lightning Peak Current ndash

IEEE and CIGRE Distributions

dIdt

in Rocket-Triggered Lightning ( ~100 kAμs)

19

Relation between the peak rate of current rise dIdt and the peak current I from triggered-lightning experiments conducted at the NASA Kennedy Space Center Florida in 19851987 and 1988 and in France in 1986 The regression line for each year is shown the sample size N and the regression equation are given in table Adapted from Leteinturier

et al (1991)

Morro Do Cachimbo

Tower (60 m) Belo Horizonte Brazil

20

Courtesy Prof Dr Silverio Visacro Filho Lightning Research Center (UFMG-CEMIG)

Lightning Parameters Derived from Direct Current Measurements ndash

Brazil

21

First Stroke

Subsequent Strokes

404

52

163

099

Optical Measurements of Return-Stroke Speed

22

Optical intensity (in millivolts

at the input of the oscilloscope) vs time waveforms at four different heights 7 63 117 and 170 m

above the lightning termination point for stroke 1 in flash F0336 Adapted from Olsen et al (2004)

23

Reference St Dev ms Comments

Natural Lightning

Boyle and Orville (1976)

20 x 107 12 x 108 071 x 108 26 x 107 12 Streak camera 2-D speed

Idone and Orville (1982)

29 x 107 24 x 108 11 x 108 47 x 107 63 Streak camera2-D speed

Mach and Rust (1989a Fig 7)

20 x 107

80 x 10726 x 108

gt28 x 1085 x 107

7 x 1075443

Long channelShort channel (Photoelectric 2-D)

Triggered Lightning

Hubert and Mouget (1981)

45 x 107 17 x 108 99 x 107 41 x 107 13 Photoelectric3-D speed

Idone et al (1984) 67 x 107 17 x 108 12 x 108 27 x 107 56 Streak camera 3-D speed

Willett et al (1988)

10 x 108 15 x 108 12 x 108 16 x 107 9 Streak camera 2-D speed

Willett et al (1989a)

12 x 108 19 x 108 15 x 108 17 x 107 18 Streak camera 2-D speed

Mach and Rust (1989a Fig 8)

60 x 107

60 x 10716 x 108

20 x 1082 x 107

4 x 1074039

Long channelShort channel(Photoelectric 2-D)

Min ms Max ms Mean ms Sample

Size

13 plusmn03 x 108

19 plusmn07 x 108

12 plusmn03 x 108

14 plusmn04 x 108

Summary of measured return stroke speeds averaged over the visible part of the channel in natural and triggered negative lightning Adapted from Rakov

et al (1992b)

Return-Stroke Speed Near Ground

24

Height Above Ground

7-63 m

63-117 m

117-170

m

12

16

15

12121213

18

16

16

17

18 18

1512

Return-stroke speed profiles estimated tracking the 20 point on the light-pulse front for triggered lightning flash F0336 (Olsen et al 2004)

Return-Stroke Speed vs Return-Stroke Peak Current

25

Return-stroke speed vs peak current for 29 triggered-lightning strokes observed at the Kennedy Space Center (KSC) Florida in 1986 and reported by Mach and Rust (1989a) and 18 triggered-lightning strokes from the 1987 KSC experiments reported by Willett et al

(1989a) Peak curent shown in the scatter plot as 38 kA may be an underestimate Note that the linear correlation coefficients (r) for both data sets are low and negative not in support of the often assumed relationship between these two lightning parameters

00

05

10

15

20

25

0 5 10 15 20 25 30 35 40 45

Return-Stroke Peak Current kA

Ret

urn-

Stro

ke S

peed

108 m

s

Mach and Rust (1989a) r = -008

Willett el al (1998a) r = -027

First Return Stroke

Electric field waveforms of a first return stroke The waveform is shown on two time scales 5 μsdiv

and 10 μsdiv The fields are normalized to a distance of 100 km L denotes individual leader pulses F slow front and R fast transition Also marked are the small secondary peak or shoulder α

and the larger subsidiary peaks a b and c Adapted from Weidman and Krider

(1978)

-20 -15 -10 -5 0 5 10 15 20

5

microsdiv

10

microsdiv

-60 -40 -20 0 20 40 60 80

26

Subsequent Return Strokes

-20 -15 -10 -5 0 5 10 15 20

5 microsdiv

5 microsdiv

10 microsdiv

10 microsdiv

-60 -40 -20 0 20 40 60 80

Electric field waveforms of (b) a subsequent return stroke initiated by a dart-stepped leader and (c) a subsequent return stroke initiated by a dart leader showing the fine structure both before and after the initial field peak Each waveform is shown on two time scales 5 μsdiv

and 10 μsdiv The fields are normalized to a distance of 100 km L denotes individual leader pulses F slow front and R fast transition Also marked are the small secondary peak or shoulder α

and the larger subsidiary peaks a b and c Adapted from Weidman and Krider

(1978)

27

First Return Stroke Electric Field Derivative

Examples of (top) the time derivative of the electric field intensity dEdt

and (bottom)

the electric field intensity E produced by a first return stroke at a distance of about 36 km over the Atlantic Ocean The propagation path was almost entirely over salt water The vertical arrow under the E record shows the time of the dEdt

trigger Adapted from Krider

et al (1996)

28

Return Strokes Measured Parameters

Parameters of microsecond-scale electric field waveforms produced by negative return strokes

Parameter Location First strokes Subsequent strokes

Sample size Mean SD Sample size Mean SD

Initial peak (V m‐1) (normalized to 100 km)Rakov

and Uman

(1990b)

Cooray

and Lundquist (1982)Lin et al (1979)

Florida

SwedenKSCOcala

76

5535129

59 (GM)

536758

273825

232a

38b

8359

27(GM)41(GM)

5043

2215

Zero‐crossing time (μs)Cooray

and Lundquist (1985)

Lin et al (1979)

SwedenSri LankaFlorida

1029146c

498954

123018

9414377c

394236

81417

Zero‐to‐peak rise time (μs)Master et al (1984)Cooray

and Lundquist (1982)Lin et al (1979)

FloridaSwedenKSCOcala

1051405129

44702427

18201213

220

8359

28

1519

15

0807

10‐90 percent rise time (μs)Master et al (1984) Florida 105 26 12 220 15 09

Slow front duration

(μs)Master et al (1984)Cooray

and Lundquist (1982)Weidman and Krider

(1978)

FloridaSwedenFlorida

105826290

29504041

13201716

44 120 34d

060921

020509

29

Return Strokes Measured ParametersParameters of microsecond-scale electric field waveforms produced by negative return strokes (contrsquod)

Parameter Locatio

nFirst strokes Subsequent strokes

Sample size

Mean SD Sample size Mean SD

Slow front amplitude as percentage of peakMaster et al (1984)Cooray

and Lundquist (1982)Weidman and Krider

(1978)

FloridaSwedenFlorida

105836290

28415040

15112020

4412034d

202540

101020

Fast

transition 10-90 percent risetime

(ns)Master et al (1984)Weidman and Krider

(1978)

Weidman and Krider

(1980a 1984)

Weidman (1982)

FloridaFlorida

Florida

1023815125

97020020090

68010010040

2178034

610200150

27040100

Peak time derivative (normalized to100 km ) (V m-1

μs-1)Krider

et al (1996) Florida 63 39 11

Time derivative pulse width at half-peak value (ns)

Krider

et al (1996) Florida 61 100 20

If not specicied

otherwise multiple lines for a given source for the same location correspond to different thunderstorms GM = geometric mean value a better characteristic of the distribution of initial field peaks since this distribution is approximately log-normala

Strokes following previously formed channelb

Strokes creating new termination on groundcBoth

electric and magnetic fieldsd

Subsequent strokes initiated by dart-stepped leaders Other subsequent strokes studied by Weidman and

Krider

(1978) were initiated by dart leaders

30

• Slide Number 1
• Slide Number 2
• Slide Number 3
• Slide Number 4
• Slide Number 5
• Slide Number 6
• Slide Number 7
• Slide Number 8
• Slide Number 9
• Slide Number 10
• Slide Number 11
• Slide Number 12
• Return-Stroke Fields Variation with Distance
• Return-Stroke Fields Variation with Distance
• Slide Number 15
• Slide Number 16
• Slide Number 17
• Slide Number 18
• Slide Number 19
• Slide Number 20
• Slide Number 21
• Slide Number 22
• Slide Number 23
• Slide Number 24
• Slide Number 25
• First Return Stroke
• Subsequent Return Strokes
• First Return Stroke Electric Field Derivative
• Return Strokes Measured Parameters
• Return Strokes Measured Parameters

10

Electrogeometrical Model (EGM)

rs

= 10 I065 m where I

is in kA

4

3

12

Striking distance rs

versus return-stroke peak current I

[curve 1 Golde

(1945) curve 2 Wagner (1963) curve 3 Love (1973) curve 4 Ruhling

(1972) x theory of Davis (1962) estimates from two-

dimensional photographs by Eriksson (1978) estimates from three-dimensional photography by Eriksson (1978) Adapted from Golde

(1977) and Eriksson (1978)

I kA rs m

10 45

30 91

170 282

11

Scatter plot of impulse charge Q versus return-stroke peak current

I Note that both vertical and horizontal scales are logarithmic The best fit to data I

= 106 Q07 where Q is in coulombs and I

is in kiloamperes was used in deriving rs

= 10 I065

Adapted from Berger (1972)

Electrogeometrical Model (EGM)

Finding rs = f(I)

bull

Assume critical average electric field between the leader tip and the strike object at the time of initiation of upward connecting leader from the object (200-600 kVm)

bull

Use an empirical relation between Q and I

to find rs

= f(I)

bull

Find rs

= f(Q)

bull

Assume leader geometry total leader charge Q and distribution of this charge along the channel

Q

10-1

100

101

102

100 101 102I

I

peak Q impulseneg first strokes n=89

I

= 106 Q07

For Q = 5 CI

= 33 kA

12

Electrogeometrical Model (EGM)

Illustration of the rolling-sphere method (RSM) The shaded area is that area into which it is postulated lightning cannot enter Adapted from Szczerbinski

(2000)

rs

rsrs

rs = 45 m (150 ft) (NFPA 780 2004) corresponds to I

= 10 kA (95 of currents exceed this value)

Rolling-Sphere Method

Return‐Stroke Fields Variation with Distance

Typical vertical electric field intensity (left column) and azimuthal

magnetic flux density (right column) waveforms for first (solid line) and subsequent (dashed line) return strokes at distances of 1 2 and 5 km Adapted from Lin et al (1979)

Electric Field Intensity Magnetic Flux Density

Return‐Stroke Fields Variation with Distance

Electric Field IntensityMagnetic Flux Density

Typical vertical electric field intensity (left column) and azimuthal

magnetic flux density (right column) waveforms for first (solid line) and subsequent (dashed line) return strokes at distances of 10 15 50 and 200 km Adapted from Lin et al (1979)

Return-Stroke Current Waveshapes

ndash

Switzerland (Berger et al 1975)

15

Average negative first and subsequent-stroke current waveshapes

each shown on two time scales A

and B The lower time scales (A) correspond to the solid curves while the upper time scales (B) correspond to the broken curves The vertical (amplitude) scale is in relative units the peak values being equal to negative unity Adapted from Berger et al (1975)

Lightning Parameters Derived from Direct Current Measurements

Parameters Units Sample Size

Percent Exceeding Tabulated Value

95 50 5

Peak current

(minimum 2 kA)First strokesSubsequent strokes

kA 101135

1446

3012

8030

Charge

(total charge)First strokesSubsequent strokesComplete flash

C 9312294

110213

521475

241140

Impulse charge

(excluding continuing current)

First strokesSubsequent strokes

C90

11711

02245

09520

4Front duration

(2 kA to peak)First strokesSubsequent strokes

μs 89118

18022

5511

1845

Maximum dIdtFirst strokesSubsequent strokes

kA μs-1 92122

5512

1240

32120

Stroke duration

(2 kA to half peak value on the tail)

First strokesSubsequent strokes

μs90

1153065

7532

200140

Action integral (intI2dt)First strokesSubsequent strokes

A2s 9188

60 x 103

55 x 10255 x 104

60 x 10355 x 105

52 x 104

17

Cumulative statistical distributions of lightning peak currents

giving percent of cases exceeding abscissa value from direct measurements in Switzerland (Berger 1972 Berger et al 1975) The distributions are assumed to be lognormal and given for (1) negative first strokes (2) positive first strokes (3) negative and positive first strokes and (4) negative subsequent strokes Adapted from Bazelyan

et al (1978)

Lightning peak currents for first strokes vary by a factor of 50 or more from about 5 to 250 kA

The probability of occurrence of a given value rapidly increases up to 25 kA

or so and then slowly decreasesStatistical distributions of this type are often assumed to be lognormal

Lightning Peak Current ndash

Bergerrsquos Distributions

18

Cumulative statistical distributions of peak currents (percent values on the vertical axis should be subtracted from 100 to obtain the probability to exceed the peak current value on the horizontal axis) for negative first strokes adopted by IEEE

and CIGRE Taken from CIGRE Document 63 (1991)

For the CIGRE

distribution 98 of peak currents exceed 4 kA 80 exceed 20 kA and 5 exceed 90 kA

For the IEEE

distribution the ldquoprobability to exceedrdquo

values are given by the following equation

where PI

is in per unit and I is in kA This equation applies to values of I up to 200 kA The median (50) peak current value is equal to 31 kA

Peak current I kA(IEEE

distribution) 5 10 20 40 60 80 100 200

Percentage exceeding tabulated value PI

10099 95 76 34 15 78 45 08

( ) 62

311

1I

PI+

=

Lightning Peak Current ndash

IEEE and CIGRE Distributions

dIdt

in Rocket-Triggered Lightning ( ~100 kAμs)

19

Relation between the peak rate of current rise dIdt and the peak current I from triggered-lightning experiments conducted at the NASA Kennedy Space Center Florida in 19851987 and 1988 and in France in 1986 The regression line for each year is shown the sample size N and the regression equation are given in table Adapted from Leteinturier

et al (1991)

Morro Do Cachimbo

Tower (60 m) Belo Horizonte Brazil

20

Courtesy Prof Dr Silverio Visacro Filho Lightning Research Center (UFMG-CEMIG)

Lightning Parameters Derived from Direct Current Measurements ndash

Brazil

21

First Stroke

Subsequent Strokes

404

52

163

099

Optical Measurements of Return-Stroke Speed

22

Optical intensity (in millivolts

at the input of the oscilloscope) vs time waveforms at four different heights 7 63 117 and 170 m

above the lightning termination point for stroke 1 in flash F0336 Adapted from Olsen et al (2004)

23

Reference St Dev ms Comments

Natural Lightning

Boyle and Orville (1976)

20 x 107 12 x 108 071 x 108 26 x 107 12 Streak camera 2-D speed

Idone and Orville (1982)

29 x 107 24 x 108 11 x 108 47 x 107 63 Streak camera2-D speed

Mach and Rust (1989a Fig 7)

20 x 107

80 x 10726 x 108

gt28 x 1085 x 107

7 x 1075443

Long channelShort channel (Photoelectric 2-D)

Triggered Lightning

Hubert and Mouget (1981)

45 x 107 17 x 108 99 x 107 41 x 107 13 Photoelectric3-D speed

Idone et al (1984) 67 x 107 17 x 108 12 x 108 27 x 107 56 Streak camera 3-D speed

Willett et al (1988)

10 x 108 15 x 108 12 x 108 16 x 107 9 Streak camera 2-D speed

Willett et al (1989a)

12 x 108 19 x 108 15 x 108 17 x 107 18 Streak camera 2-D speed

Mach and Rust (1989a Fig 8)

60 x 107

60 x 10716 x 108

20 x 1082 x 107

4 x 1074039

Long channelShort channel(Photoelectric 2-D)

Min ms Max ms Mean ms Sample

Size

13 plusmn03 x 108

19 plusmn07 x 108

12 plusmn03 x 108

14 plusmn04 x 108

Summary of measured return stroke speeds averaged over the visible part of the channel in natural and triggered negative lightning Adapted from Rakov

et al (1992b)

Return-Stroke Speed Near Ground

24

Height Above Ground

7-63 m

63-117 m

117-170

m

12

16

15

12121213

18

16

16

17

18 18

1512

Return-stroke speed profiles estimated tracking the 20 point on the light-pulse front for triggered lightning flash F0336 (Olsen et al 2004)

Return-Stroke Speed vs Return-Stroke Peak Current

25

Return-stroke speed vs peak current for 29 triggered-lightning strokes observed at the Kennedy Space Center (KSC) Florida in 1986 and reported by Mach and Rust (1989a) and 18 triggered-lightning strokes from the 1987 KSC experiments reported by Willett et al

(1989a) Peak curent shown in the scatter plot as 38 kA may be an underestimate Note that the linear correlation coefficients (r) for both data sets are low and negative not in support of the often assumed relationship between these two lightning parameters

00

05

10

15

20

25

0 5 10 15 20 25 30 35 40 45

Return-Stroke Peak Current kA

Ret

urn-

Stro

ke S

peed

108 m

s

Mach and Rust (1989a) r = -008

Willett el al (1998a) r = -027

First Return Stroke

Electric field waveforms of a first return stroke The waveform is shown on two time scales 5 μsdiv

and 10 μsdiv The fields are normalized to a distance of 100 km L denotes individual leader pulses F slow front and R fast transition Also marked are the small secondary peak or shoulder α

and the larger subsidiary peaks a b and c Adapted from Weidman and Krider

(1978)

-20 -15 -10 -5 0 5 10 15 20

5

microsdiv

10

microsdiv

-60 -40 -20 0 20 40 60 80

26

Subsequent Return Strokes

-20 -15 -10 -5 0 5 10 15 20

5 microsdiv

5 microsdiv

10 microsdiv

10 microsdiv

-60 -40 -20 0 20 40 60 80

Electric field waveforms of (b) a subsequent return stroke initiated by a dart-stepped leader and (c) a subsequent return stroke initiated by a dart leader showing the fine structure both before and after the initial field peak Each waveform is shown on two time scales 5 μsdiv

and 10 μsdiv The fields are normalized to a distance of 100 km L denotes individual leader pulses F slow front and R fast transition Also marked are the small secondary peak or shoulder α

and the larger subsidiary peaks a b and c Adapted from Weidman and Krider

(1978)

27

First Return Stroke Electric Field Derivative

Examples of (top) the time derivative of the electric field intensity dEdt

and (bottom)

the electric field intensity E produced by a first return stroke at a distance of about 36 km over the Atlantic Ocean The propagation path was almost entirely over salt water The vertical arrow under the E record shows the time of the dEdt

trigger Adapted from Krider

et al (1996)

28

Return Strokes Measured Parameters

Parameters of microsecond-scale electric field waveforms produced by negative return strokes

Parameter Location First strokes Subsequent strokes

Sample size Mean SD Sample size Mean SD

Initial peak (V m‐1) (normalized to 100 km)Rakov

and Uman

(1990b)

Cooray

and Lundquist (1982)Lin et al (1979)

Florida

SwedenKSCOcala

76

5535129

59 (GM)

536758

273825

232a

38b

8359

27(GM)41(GM)

5043

2215

Zero‐crossing time (μs)Cooray

and Lundquist (1985)

Lin et al (1979)

SwedenSri LankaFlorida

1029146c

498954

123018

9414377c

394236

81417

Zero‐to‐peak rise time (μs)Master et al (1984)Cooray

and Lundquist (1982)Lin et al (1979)

FloridaSwedenKSCOcala

1051405129

44702427

18201213

220

8359

28

1519

15

0807

10‐90 percent rise time (μs)Master et al (1984) Florida 105 26 12 220 15 09

Slow front duration

(μs)Master et al (1984)Cooray

and Lundquist (1982)Weidman and Krider

(1978)

FloridaSwedenFlorida

105826290

29504041

13201716

44 120 34d

060921

020509

29

Return Strokes Measured ParametersParameters of microsecond-scale electric field waveforms produced by negative return strokes (contrsquod)

Parameter Locatio

nFirst strokes Subsequent strokes

Sample size

Mean SD Sample size Mean SD

Slow front amplitude as percentage of peakMaster et al (1984)Cooray

and Lundquist (1982)Weidman and Krider

(1978)

FloridaSwedenFlorida

105836290

28415040

15112020

4412034d

202540

101020

Fast

transition 10-90 percent risetime

(ns)Master et al (1984)Weidman and Krider

(1978)

Weidman and Krider

(1980a 1984)

Weidman (1982)

FloridaFlorida

Florida

1023815125

97020020090

68010010040

2178034

610200150

27040100

Peak time derivative (normalized to100 km ) (V m-1

μs-1)Krider

et al (1996) Florida 63 39 11

Time derivative pulse width at half-peak value (ns)

Krider

et al (1996) Florida 61 100 20

If not specicied

otherwise multiple lines for a given source for the same location correspond to different thunderstorms GM = geometric mean value a better characteristic of the distribution of initial field peaks since this distribution is approximately log-normala

Strokes following previously formed channelb

Strokes creating new termination on groundcBoth

electric and magnetic fieldsd

Subsequent strokes initiated by dart-stepped leaders Other subsequent strokes studied by Weidman and

Krider

(1978) were initiated by dart leaders

30

• Slide Number 1
• Slide Number 2
• Slide Number 3
• Slide Number 4
• Slide Number 5
• Slide Number 6
• Slide Number 7
• Slide Number 8
• Slide Number 9
• Slide Number 10
• Slide Number 11
• Slide Number 12
• Return-Stroke Fields Variation with Distance
• Return-Stroke Fields Variation with Distance
• Slide Number 15
• Slide Number 16
• Slide Number 17
• Slide Number 18
• Slide Number 19
• Slide Number 20
• Slide Number 21
• Slide Number 22
• Slide Number 23
• Slide Number 24
• Slide Number 25
• First Return Stroke
• Subsequent Return Strokes
• First Return Stroke Electric Field Derivative
• Return Strokes Measured Parameters
• Return Strokes Measured Parameters

11

Scatter plot of impulse charge Q versus return-stroke peak current

I Note that both vertical and horizontal scales are logarithmic The best fit to data I

= 106 Q07 where Q is in coulombs and I

is in kiloamperes was used in deriving rs

= 10 I065

Adapted from Berger (1972)

Electrogeometrical Model (EGM)

Finding rs = f(I)

bull

Assume critical average electric field between the leader tip and the strike object at the time of initiation of upward connecting leader from the object (200-600 kVm)

bull

Use an empirical relation between Q and I

to find rs

= f(I)

bull

Find rs

= f(Q)

bull

Assume leader geometry total leader charge Q and distribution of this charge along the channel

Q

10-1

100

101

102

100 101 102I

I

peak Q impulseneg first strokes n=89

I

= 106 Q07

For Q = 5 CI

= 33 kA

12

Electrogeometrical Model (EGM)

Illustration of the rolling-sphere method (RSM) The shaded area is that area into which it is postulated lightning cannot enter Adapted from Szczerbinski

(2000)

rs

rsrs

rs = 45 m (150 ft) (NFPA 780 2004) corresponds to I

= 10 kA (95 of currents exceed this value)

Rolling-Sphere Method

Return‐Stroke Fields Variation with Distance

Typical vertical electric field intensity (left column) and azimuthal

magnetic flux density (right column) waveforms for first (solid line) and subsequent (dashed line) return strokes at distances of 1 2 and 5 km Adapted from Lin et al (1979)

Electric Field Intensity Magnetic Flux Density

Return‐Stroke Fields Variation with Distance

Electric Field IntensityMagnetic Flux Density

Typical vertical electric field intensity (left column) and azimuthal

magnetic flux density (right column) waveforms for first (solid line) and subsequent (dashed line) return strokes at distances of 10 15 50 and 200 km Adapted from Lin et al (1979)

Return-Stroke Current Waveshapes

ndash

Switzerland (Berger et al 1975)

15

Average negative first and subsequent-stroke current waveshapes

each shown on two time scales A

and B The lower time scales (A) correspond to the solid curves while the upper time scales (B) correspond to the broken curves The vertical (amplitude) scale is in relative units the peak values being equal to negative unity Adapted from Berger et al (1975)

Lightning Parameters Derived from Direct Current Measurements

Parameters Units Sample Size

Percent Exceeding Tabulated Value

95 50 5

Peak current

(minimum 2 kA)First strokesSubsequent strokes

kA 101135

1446

3012

8030

Charge

(total charge)First strokesSubsequent strokesComplete flash

C 9312294

110213

521475

241140

Impulse charge

(excluding continuing current)

First strokesSubsequent strokes

C90

11711

02245

09520

4Front duration

(2 kA to peak)First strokesSubsequent strokes

μs 89118

18022

5511

1845

Maximum dIdtFirst strokesSubsequent strokes

kA μs-1 92122

5512

1240

32120

Stroke duration

(2 kA to half peak value on the tail)

First strokesSubsequent strokes

μs90

1153065

7532

200140

Action integral (intI2dt)First strokesSubsequent strokes

A2s 9188

60 x 103

55 x 10255 x 104

60 x 10355 x 105

52 x 104

17

Cumulative statistical distributions of lightning peak currents

giving percent of cases exceeding abscissa value from direct measurements in Switzerland (Berger 1972 Berger et al 1975) The distributions are assumed to be lognormal and given for (1) negative first strokes (2) positive first strokes (3) negative and positive first strokes and (4) negative subsequent strokes Adapted from Bazelyan

et al (1978)

Lightning peak currents for first strokes vary by a factor of 50 or more from about 5 to 250 kA

The probability of occurrence of a given value rapidly increases up to 25 kA

or so and then slowly decreasesStatistical distributions of this type are often assumed to be lognormal

Lightning Peak Current ndash

Bergerrsquos Distributions

18

Cumulative statistical distributions of peak currents (percent values on the vertical axis should be subtracted from 100 to obtain the probability to exceed the peak current value on the horizontal axis) for negative first strokes adopted by IEEE

and CIGRE Taken from CIGRE Document 63 (1991)

For the CIGRE

distribution 98 of peak currents exceed 4 kA 80 exceed 20 kA and 5 exceed 90 kA

For the IEEE

distribution the ldquoprobability to exceedrdquo

values are given by the following equation

where PI

is in per unit and I is in kA This equation applies to values of I up to 200 kA The median (50) peak current value is equal to 31 kA

Peak current I kA(IEEE

distribution) 5 10 20 40 60 80 100 200

Percentage exceeding tabulated value PI

10099 95 76 34 15 78 45 08

( ) 62

311

1I

PI+

=

Lightning Peak Current ndash

IEEE and CIGRE Distributions

dIdt

in Rocket-Triggered Lightning ( ~100 kAμs)

19

Relation between the peak rate of current rise dIdt and the peak current I from triggered-lightning experiments conducted at the NASA Kennedy Space Center Florida in 19851987 and 1988 and in France in 1986 The regression line for each year is shown the sample size N and the regression equation are given in table Adapted from Leteinturier

et al (1991)

Morro Do Cachimbo

Tower (60 m) Belo Horizonte Brazil

20

Courtesy Prof Dr Silverio Visacro Filho Lightning Research Center (UFMG-CEMIG)

Lightning Parameters Derived from Direct Current Measurements ndash

Brazil

21

First Stroke

Subsequent Strokes

404

52

163

099

Optical Measurements of Return-Stroke Speed

22

Optical intensity (in millivolts

at the input of the oscilloscope) vs time waveforms at four different heights 7 63 117 and 170 m

above the lightning termination point for stroke 1 in flash F0336 Adapted from Olsen et al (2004)

23

Reference St Dev ms Comments

Natural Lightning

Boyle and Orville (1976)

20 x 107 12 x 108 071 x 108 26 x 107 12 Streak camera 2-D speed

Idone and Orville (1982)

29 x 107 24 x 108 11 x 108 47 x 107 63 Streak camera2-D speed

Mach and Rust (1989a Fig 7)

20 x 107

80 x 10726 x 108

gt28 x 1085 x 107

7 x 1075443

Long channelShort channel (Photoelectric 2-D)

Triggered Lightning

Hubert and Mouget (1981)

45 x 107 17 x 108 99 x 107 41 x 107 13 Photoelectric3-D speed

Idone et al (1984) 67 x 107 17 x 108 12 x 108 27 x 107 56 Streak camera 3-D speed

Willett et al (1988)

10 x 108 15 x 108 12 x 108 16 x 107 9 Streak camera 2-D speed

Willett et al (1989a)

12 x 108 19 x 108 15 x 108 17 x 107 18 Streak camera 2-D speed

Mach and Rust (1989a Fig 8)

60 x 107

60 x 10716 x 108

20 x 1082 x 107

4 x 1074039

Long channelShort channel(Photoelectric 2-D)

Min ms Max ms Mean ms Sample

Size

13 plusmn03 x 108

19 plusmn07 x 108

12 plusmn03 x 108

14 plusmn04 x 108

Summary of measured return stroke speeds averaged over the visible part of the channel in natural and triggered negative lightning Adapted from Rakov

et al (1992b)

Return-Stroke Speed Near Ground

24

Height Above Ground

7-63 m

63-117 m

117-170

m

12

16

15

12121213

18

16

16

17

18 18

1512

Return-stroke speed profiles estimated tracking the 20 point on the light-pulse front for triggered lightning flash F0336 (Olsen et al 2004)

Return-Stroke Speed vs Return-Stroke Peak Current

25

Return-stroke speed vs peak current for 29 triggered-lightning strokes observed at the Kennedy Space Center (KSC) Florida in 1986 and reported by Mach and Rust (1989a) and 18 triggered-lightning strokes from the 1987 KSC experiments reported by Willett et al

(1989a) Peak curent shown in the scatter plot as 38 kA may be an underestimate Note that the linear correlation coefficients (r) for both data sets are low and negative not in support of the often assumed relationship between these two lightning parameters

00

05

10

15

20

25

0 5 10 15 20 25 30 35 40 45

Return-Stroke Peak Current kA

Ret

urn-

Stro

ke S

peed

108 m

s

Mach and Rust (1989a) r = -008

Willett el al (1998a) r = -027

First Return Stroke

Electric field waveforms of a first return stroke The waveform is shown on two time scales 5 μsdiv

and 10 μsdiv The fields are normalized to a distance of 100 km L denotes individual leader pulses F slow front and R fast transition Also marked are the small secondary peak or shoulder α

and the larger subsidiary peaks a b and c Adapted from Weidman and Krider

(1978)

-20 -15 -10 -5 0 5 10 15 20

5

microsdiv

10

microsdiv

-60 -40 -20 0 20 40 60 80

26

Subsequent Return Strokes

-20 -15 -10 -5 0 5 10 15 20

5 microsdiv

5 microsdiv

10 microsdiv

10 microsdiv

-60 -40 -20 0 20 40 60 80

Electric field waveforms of (b) a subsequent return stroke initiated by a dart-stepped leader and (c) a subsequent return stroke initiated by a dart leader showing the fine structure both before and after the initial field peak Each waveform is shown on two time scales 5 μsdiv

and 10 μsdiv The fields are normalized to a distance of 100 km L denotes individual leader pulses F slow front and R fast transition Also marked are the small secondary peak or shoulder α

and the larger subsidiary peaks a b and c Adapted from Weidman and Krider

(1978)

27

First Return Stroke Electric Field Derivative

Examples of (top) the time derivative of the electric field intensity dEdt

and (bottom)

the electric field intensity E produced by a first return stroke at a distance of about 36 km over the Atlantic Ocean The propagation path was almost entirely over salt water The vertical arrow under the E record shows the time of the dEdt

trigger Adapted from Krider

et al (1996)

28

Return Strokes Measured Parameters

Parameters of microsecond-scale electric field waveforms produced by negative return strokes

Parameter Location First strokes Subsequent strokes

Sample size Mean SD Sample size Mean SD

Initial peak (V m‐1) (normalized to 100 km)Rakov

and Uman

(1990b)

Cooray

and Lundquist (1982)Lin et al (1979)

Florida

SwedenKSCOcala

76

5535129

59 (GM)

536758

273825

232a

38b

8359

27(GM)41(GM)

5043

2215

Zero‐crossing time (μs)Cooray

and Lundquist (1985)

Lin et al (1979)

SwedenSri LankaFlorida

1029146c

498954

123018

9414377c

394236

81417

Zero‐to‐peak rise time (μs)Master et al (1984)Cooray

and Lundquist (1982)Lin et al (1979)

FloridaSwedenKSCOcala

1051405129

44702427

18201213

220

8359

28

1519

15

0807

10‐90 percent rise time (μs)Master et al (1984) Florida 105 26 12 220 15 09

Slow front duration

(μs)Master et al (1984)Cooray

and Lundquist (1982)Weidman and Krider

(1978)

FloridaSwedenFlorida

105826290

29504041

13201716

44 120 34d

060921

020509

29

Return Strokes Measured ParametersParameters of microsecond-scale electric field waveforms produced by negative return strokes (contrsquod)

Parameter Locatio

nFirst strokes Subsequent strokes

Sample size

Mean SD Sample size Mean SD

Slow front amplitude as percentage of peakMaster et al (1984)Cooray

and Lundquist (1982)Weidman and Krider

(1978)

FloridaSwedenFlorida

105836290

28415040

15112020

4412034d

202540

101020

Fast

transition 10-90 percent risetime

(ns)Master et al (1984)Weidman and Krider

(1978)

Weidman and Krider

(1980a 1984)

Weidman (1982)

FloridaFlorida

Florida

1023815125

97020020090

68010010040

2178034

610200150

27040100

Peak time derivative (normalized to100 km ) (V m-1

μs-1)Krider

et al (1996) Florida 63 39 11

Time derivative pulse width at half-peak value (ns)

Krider

et al (1996) Florida 61 100 20

If not specicied

otherwise multiple lines for a given source for the same location correspond to different thunderstorms GM = geometric mean value a better characteristic of the distribution of initial field peaks since this distribution is approximately log-normala

Strokes following previously formed channelb

Strokes creating new termination on groundcBoth

electric and magnetic fieldsd

Subsequent strokes initiated by dart-stepped leaders Other subsequent strokes studied by Weidman and

Krider

(1978) were initiated by dart leaders

30

• Slide Number 1
• Slide Number 2
• Slide Number 3
• Slide Number 4
• Slide Number 5
• Slide Number 6
• Slide Number 7
• Slide Number 8
• Slide Number 9
• Slide Number 10
• Slide Number 11
• Slide Number 12
• Return-Stroke Fields Variation with Distance
• Return-Stroke Fields Variation with Distance
• Slide Number 15
• Slide Number 16
• Slide Number 17
• Slide Number 18
• Slide Number 19
• Slide Number 20
• Slide Number 21
• Slide Number 22
• Slide Number 23
• Slide Number 24
• Slide Number 25
• First Return Stroke
• Subsequent Return Strokes
• First Return Stroke Electric Field Derivative
• Return Strokes Measured Parameters
• Return Strokes Measured Parameters

12

Electrogeometrical Model (EGM)

Illustration of the rolling-sphere method (RSM) The shaded area is that area into which it is postulated lightning cannot enter Adapted from Szczerbinski

(2000)

rs

rsrs

rs = 45 m (150 ft) (NFPA 780 2004) corresponds to I

= 10 kA (95 of currents exceed this value)

Rolling-Sphere Method

Return‐Stroke Fields Variation with Distance

Typical vertical electric field intensity (left column) and azimuthal

magnetic flux density (right column) waveforms for first (solid line) and subsequent (dashed line) return strokes at distances of 1 2 and 5 km Adapted from Lin et al (1979)

Electric Field Intensity Magnetic Flux Density

Return‐Stroke Fields Variation with Distance

Electric Field IntensityMagnetic Flux Density

Typical vertical electric field intensity (left column) and azimuthal

magnetic flux density (right column) waveforms for first (solid line) and subsequent (dashed line) return strokes at distances of 10 15 50 and 200 km Adapted from Lin et al (1979)

Return-Stroke Current Waveshapes

ndash

Switzerland (Berger et al 1975)

15

Average negative first and subsequent-stroke current waveshapes

each shown on two time scales A

and B The lower time scales (A) correspond to the solid curves while the upper time scales (B) correspond to the broken curves The vertical (amplitude) scale is in relative units the peak values being equal to negative unity Adapted from Berger et al (1975)

Lightning Parameters Derived from Direct Current Measurements

Parameters Units Sample Size

Percent Exceeding Tabulated Value

95 50 5

Peak current

(minimum 2 kA)First strokesSubsequent strokes

kA 101135

1446

3012

8030

Charge

(total charge)First strokesSubsequent strokesComplete flash

C 9312294

110213

521475

241140

Impulse charge

(excluding continuing current)

First strokesSubsequent strokes

C90

11711

02245

09520

4Front duration

(2 kA to peak)First strokesSubsequent strokes

μs 89118

18022

5511

1845

Maximum dIdtFirst strokesSubsequent strokes

kA μs-1 92122

5512

1240

32120

Stroke duration

(2 kA to half peak value on the tail)

First strokesSubsequent strokes

μs90

1153065

7532

200140

Action integral (intI2dt)First strokesSubsequent strokes

A2s 9188

60 x 103

55 x 10255 x 104

60 x 10355 x 105

52 x 104

17

Cumulative statistical distributions of lightning peak currents

giving percent of cases exceeding abscissa value from direct measurements in Switzerland (Berger 1972 Berger et al 1975) The distributions are assumed to be lognormal and given for (1) negative first strokes (2) positive first strokes (3) negative and positive first strokes and (4) negative subsequent strokes Adapted from Bazelyan

et al (1978)

Lightning peak currents for first strokes vary by a factor of 50 or more from about 5 to 250 kA

The probability of occurrence of a given value rapidly increases up to 25 kA

or so and then slowly decreasesStatistical distributions of this type are often assumed to be lognormal

Lightning Peak Current ndash

Bergerrsquos Distributions

18

Cumulative statistical distributions of peak currents (percent values on the vertical axis should be subtracted from 100 to obtain the probability to exceed the peak current value on the horizontal axis) for negative first strokes adopted by IEEE

and CIGRE Taken from CIGRE Document 63 (1991)

For the CIGRE

distribution 98 of peak currents exceed 4 kA 80 exceed 20 kA and 5 exceed 90 kA

For the IEEE

distribution the ldquoprobability to exceedrdquo

values are given by the following equation

where PI

is in per unit and I is in kA This equation applies to values of I up to 200 kA The median (50) peak current value is equal to 31 kA

Peak current I kA(IEEE

distribution) 5 10 20 40 60 80 100 200

Percentage exceeding tabulated value PI

10099 95 76 34 15 78 45 08

( ) 62

311

1I

PI+

=

Lightning Peak Current ndash

IEEE and CIGRE Distributions

dIdt

in Rocket-Triggered Lightning ( ~100 kAμs)

19

Relation between the peak rate of current rise dIdt and the peak current I from triggered-lightning experiments conducted at the NASA Kennedy Space Center Florida in 19851987 and 1988 and in France in 1986 The regression line for each year is shown the sample size N and the regression equation are given in table Adapted from Leteinturier

et al (1991)

Morro Do Cachimbo

Tower (60 m) Belo Horizonte Brazil

20

Courtesy Prof Dr Silverio Visacro Filho Lightning Research Center (UFMG-CEMIG)

Lightning Parameters Derived from Direct Current Measurements ndash

Brazil

21

First Stroke

Subsequent Strokes

404

52

163

099

Optical Measurements of Return-Stroke Speed

22

Optical intensity (in millivolts

at the input of the oscilloscope) vs time waveforms at four different heights 7 63 117 and 170 m

above the lightning termination point for stroke 1 in flash F0336 Adapted from Olsen et al (2004)

23

Reference St Dev ms Comments

Natural Lightning

Boyle and Orville (1976)

20 x 107 12 x 108 071 x 108 26 x 107 12 Streak camera 2-D speed

Idone and Orville (1982)

29 x 107 24 x 108 11 x 108 47 x 107 63 Streak camera2-D speed

Mach and Rust (1989a Fig 7)

20 x 107

80 x 10726 x 108

gt28 x 1085 x 107

7 x 1075443

Long channelShort channel (Photoelectric 2-D)

Triggered Lightning

Hubert and Mouget (1981)

45 x 107 17 x 108 99 x 107 41 x 107 13 Photoelectric3-D speed

Idone et al (1984) 67 x 107 17 x 108 12 x 108 27 x 107 56 Streak camera 3-D speed

Willett et al (1988)

10 x 108 15 x 108 12 x 108 16 x 107 9 Streak camera 2-D speed

Willett et al (1989a)

12 x 108 19 x 108 15 x 108 17 x 107 18 Streak camera 2-D speed

Mach and Rust (1989a Fig 8)

60 x 107

60 x 10716 x 108

20 x 1082 x 107

4 x 1074039

Long channelShort channel(Photoelectric 2-D)

Min ms Max ms Mean ms Sample

Size

13 plusmn03 x 108

19 plusmn07 x 108

12 plusmn03 x 108

14 plusmn04 x 108

Summary of measured return stroke speeds averaged over the visible part of the channel in natural and triggered negative lightning Adapted from Rakov

et al (1992b)

Return-Stroke Speed Near Ground

24

Height Above Ground

7-63 m

63-117 m

117-170

m

12

16

15

12121213

18

16

16

17

18 18

1512

Return-stroke speed profiles estimated tracking the 20 point on the light-pulse front for triggered lightning flash F0336 (Olsen et al 2004)

Return-Stroke Speed vs Return-Stroke Peak Current

25

Return-stroke speed vs peak current for 29 triggered-lightning strokes observed at the Kennedy Space Center (KSC) Florida in 1986 and reported by Mach and Rust (1989a) and 18 triggered-lightning strokes from the 1987 KSC experiments reported by Willett et al

(1989a) Peak curent shown in the scatter plot as 38 kA may be an underestimate Note that the linear correlation coefficients (r) for both data sets are low and negative not in support of the often assumed relationship between these two lightning parameters

00

05

10

15

20

25

0 5 10 15 20 25 30 35 40 45

Return-Stroke Peak Current kA

Ret

urn-

Stro

ke S

peed

108 m

s

Mach and Rust (1989a) r = -008

Willett el al (1998a) r = -027

First Return Stroke

Electric field waveforms of a first return stroke The waveform is shown on two time scales 5 μsdiv

and 10 μsdiv The fields are normalized to a distance of 100 km L denotes individual leader pulses F slow front and R fast transition Also marked are the small secondary peak or shoulder α

and the larger subsidiary peaks a b and c Adapted from Weidman and Krider

(1978)

-20 -15 -10 -5 0 5 10 15 20

5

microsdiv

10

microsdiv

-60 -40 -20 0 20 40 60 80

26

Subsequent Return Strokes

-20 -15 -10 -5 0 5 10 15 20

5 microsdiv

5 microsdiv

10 microsdiv

10 microsdiv

-60 -40 -20 0 20 40 60 80

Electric field waveforms of (b) a subsequent return stroke initiated by a dart-stepped leader and (c) a subsequent return stroke initiated by a dart leader showing the fine structure both before and after the initial field peak Each waveform is shown on two time scales 5 μsdiv

and 10 μsdiv The fields are normalized to a distance of 100 km L denotes individual leader pulses F slow front and R fast transition Also marked are the small secondary peak or shoulder α

and the larger subsidiary peaks a b and c Adapted from Weidman and Krider

(1978)

27

First Return Stroke Electric Field Derivative

Examples of (top) the time derivative of the electric field intensity dEdt

and (bottom)

the electric field intensity E produced by a first return stroke at a distance of about 36 km over the Atlantic Ocean The propagation path was almost entirely over salt water The vertical arrow under the E record shows the time of the dEdt

trigger Adapted from Krider

et al (1996)

28

Return Strokes Measured Parameters

Parameters of microsecond-scale electric field waveforms produced by negative return strokes

Parameter Location First strokes Subsequent strokes

Sample size Mean SD Sample size Mean SD

Initial peak (V m‐1) (normalized to 100 km)Rakov

and Uman

(1990b)

Cooray

and Lundquist (1982)Lin et al (1979)

Florida

SwedenKSCOcala

76

5535129

59 (GM)

536758

273825

232a

38b

8359

27(GM)41(GM)

5043

2215

Zero‐crossing time (μs)Cooray

and Lundquist (1985)

Lin et al (1979)

SwedenSri LankaFlorida

1029146c

498954

123018

9414377c

394236

81417

Zero‐to‐peak rise time (μs)Master et al (1984)Cooray

and Lundquist (1982)Lin et al (1979)

FloridaSwedenKSCOcala

1051405129

44702427

18201213

220

8359

28

1519

15

0807

10‐90 percent rise time (μs)Master et al (1984) Florida 105 26 12 220 15 09

Slow front duration

(μs)Master et al (1984)Cooray

and Lundquist (1982)Weidman and Krider

(1978)

FloridaSwedenFlorida

105826290

29504041

13201716

44 120 34d

060921

020509

29

Return Strokes Measured ParametersParameters of microsecond-scale electric field waveforms produced by negative return strokes (contrsquod)

Parameter Locatio

nFirst strokes Subsequent strokes

Sample size

Mean SD Sample size Mean SD

Slow front amplitude as percentage of peakMaster et al (1984)Cooray

and Lundquist (1982)Weidman and Krider

(1978)

FloridaSwedenFlorida

105836290

28415040

15112020

4412034d

202540

101020

Fast

transition 10-90 percent risetime

(ns)Master et al (1984)Weidman and Krider

(1978)

Weidman and Krider

(1980a 1984)

Weidman (1982)

FloridaFlorida

Florida

1023815125

97020020090

68010010040

2178034

610200150

27040100

Peak time derivative (normalized to100 km ) (V m-1

μs-1)Krider

et al (1996) Florida 63 39 11

Time derivative pulse width at half-peak value (ns)

Krider

et al (1996) Florida 61 100 20

If not specicied

otherwise multiple lines for a given source for the same location correspond to different thunderstorms GM = geometric mean value a better characteristic of the distribution of initial field peaks since this distribution is approximately log-normala

Strokes following previously formed channelb

Strokes creating new termination on groundcBoth

electric and magnetic fieldsd

Subsequent strokes initiated by dart-stepped leaders Other subsequent strokes studied by Weidman and

Krider

(1978) were initiated by dart leaders

30

• Slide Number 1
• Slide Number 2
• Slide Number 3
• Slide Number 4
• Slide Number 5
• Slide Number 6
• Slide Number 7
• Slide Number 8
• Slide Number 9
• Slide Number 10
• Slide Number 11
• Slide Number 12
• Return-Stroke Fields Variation with Distance
• Return-Stroke Fields Variation with Distance
• Slide Number 15
• Slide Number 16
• Slide Number 17
• Slide Number 18
• Slide Number 19
• Slide Number 20
• Slide Number 21
• Slide Number 22
• Slide Number 23
• Slide Number 24
• Slide Number 25
• First Return Stroke
• Subsequent Return Strokes
• First Return Stroke Electric Field Derivative
• Return Strokes Measured Parameters
• Return Strokes Measured Parameters

Return‐Stroke Fields Variation with Distance

Typical vertical electric field intensity (left column) and azimuthal

magnetic flux density (right column) waveforms for first (solid line) and subsequent (dashed line) return strokes at distances of 1 2 and 5 km Adapted from Lin et al (1979)

Electric Field Intensity Magnetic Flux Density

Return‐Stroke Fields Variation with Distance

Electric Field IntensityMagnetic Flux Density

Typical vertical electric field intensity (left column) and azimuthal

magnetic flux density (right column) waveforms for first (solid line) and subsequent (dashed line) return strokes at distances of 10 15 50 and 200 km Adapted from Lin et al (1979)

Return-Stroke Current Waveshapes

ndash

Switzerland (Berger et al 1975)

15

Average negative first and subsequent-stroke current waveshapes

each shown on two time scales A

and B The lower time scales (A) correspond to the solid curves while the upper time scales (B) correspond to the broken curves The vertical (amplitude) scale is in relative units the peak values being equal to negative unity Adapted from Berger et al (1975)

Lightning Parameters Derived from Direct Current Measurements

Parameters Units Sample Size

Percent Exceeding Tabulated Value

95 50 5

Peak current

(minimum 2 kA)First strokesSubsequent strokes

kA 101135

1446

3012

8030

Charge

(total charge)First strokesSubsequent strokesComplete flash

C 9312294

110213

521475

241140

Impulse charge

(excluding continuing current)

First strokesSubsequent strokes

C90

11711

02245

09520

4Front duration

(2 kA to peak)First strokesSubsequent strokes

μs 89118

18022

5511

1845

Maximum dIdtFirst strokesSubsequent strokes

kA μs-1 92122

5512

1240

32120

Stroke duration

(2 kA to half peak value on the tail)

First strokesSubsequent strokes

μs90

1153065

7532

200140

Action integral (intI2dt)First strokesSubsequent strokes

A2s 9188

60 x 103

55 x 10255 x 104

60 x 10355 x 105

52 x 104

17

Cumulative statistical distributions of lightning peak currents

giving percent of cases exceeding abscissa value from direct measurements in Switzerland (Berger 1972 Berger et al 1975) The distributions are assumed to be lognormal and given for (1) negative first strokes (2) positive first strokes (3) negative and positive first strokes and (4) negative subsequent strokes Adapted from Bazelyan

et al (1978)

Lightning peak currents for first strokes vary by a factor of 50 or more from about 5 to 250 kA

The probability of occurrence of a given value rapidly increases up to 25 kA

or so and then slowly decreasesStatistical distributions of this type are often assumed to be lognormal

Lightning Peak Current ndash

Bergerrsquos Distributions

18

Cumulative statistical distributions of peak currents (percent values on the vertical axis should be subtracted from 100 to obtain the probability to exceed the peak current value on the horizontal axis) for negative first strokes adopted by IEEE

and CIGRE Taken from CIGRE Document 63 (1991)

For the CIGRE

distribution 98 of peak currents exceed 4 kA 80 exceed 20 kA and 5 exceed 90 kA

For the IEEE

distribution the ldquoprobability to exceedrdquo

values are given by the following equation

where PI

is in per unit and I is in kA This equation applies to values of I up to 200 kA The median (50) peak current value is equal to 31 kA

Peak current I kA(IEEE

distribution) 5 10 20 40 60 80 100 200

Percentage exceeding tabulated value PI

10099 95 76 34 15 78 45 08

( ) 62

311

1I

PI+

=

Lightning Peak Current ndash

IEEE and CIGRE Distributions

dIdt

in Rocket-Triggered Lightning ( ~100 kAμs)

19

Relation between the peak rate of current rise dIdt and the peak current I from triggered-lightning experiments conducted at the NASA Kennedy Space Center Florida in 19851987 and 1988 and in France in 1986 The regression line for each year is shown the sample size N and the regression equation are given in table Adapted from Leteinturier

et al (1991)

Morro Do Cachimbo

Tower (60 m) Belo Horizonte Brazil

20

Courtesy Prof Dr Silverio Visacro Filho Lightning Research Center (UFMG-CEMIG)

Lightning Parameters Derived from Direct Current Measurements ndash

Brazil

21

First Stroke

Subsequent Strokes

404

52

163

099

Optical Measurements of Return-Stroke Speed

22

Optical intensity (in millivolts

at the input of the oscilloscope) vs time waveforms at four different heights 7 63 117 and 170 m

above the lightning termination point for stroke 1 in flash F0336 Adapted from Olsen et al (2004)

23

Reference St Dev ms Comments

Natural Lightning

Boyle and Orville (1976)

20 x 107 12 x 108 071 x 108 26 x 107 12 Streak camera 2-D speed

Idone and Orville (1982)

29 x 107 24 x 108 11 x 108 47 x 107 63 Streak camera2-D speed

Mach and Rust (1989a Fig 7)

20 x 107

80 x 10726 x 108

gt28 x 1085 x 107

7 x 1075443

Long channelShort channel (Photoelectric 2-D)

Triggered Lightning

Hubert and Mouget (1981)

45 x 107 17 x 108 99 x 107 41 x 107 13 Photoelectric3-D speed

Idone et al (1984) 67 x 107 17 x 108 12 x 108 27 x 107 56 Streak camera 3-D speed

Willett et al (1988)

10 x 108 15 x 108 12 x 108 16 x 107 9 Streak camera 2-D speed

Willett et al (1989a)

12 x 108 19 x 108 15 x 108 17 x 107 18 Streak camera 2-D speed

Mach and Rust (1989a Fig 8)

60 x 107

60 x 10716 x 108

20 x 1082 x 107

4 x 1074039

Long channelShort channel(Photoelectric 2-D)

Min ms Max ms Mean ms Sample

Size

13 plusmn03 x 108

19 plusmn07 x 108

12 plusmn03 x 108

14 plusmn04 x 108

Summary of measured return stroke speeds averaged over the visible part of the channel in natural and triggered negative lightning Adapted from Rakov

et al (1992b)

Return-Stroke Speed Near Ground

24

Height Above Ground

7-63 m

63-117 m

117-170

m

12

16

15

12121213

18

16

16

17

18 18

1512

Return-stroke speed profiles estimated tracking the 20 point on the light-pulse front for triggered lightning flash F0336 (Olsen et al 2004)

Return-Stroke Speed vs Return-Stroke Peak Current

25

Return-stroke speed vs peak current for 29 triggered-lightning strokes observed at the Kennedy Space Center (KSC) Florida in 1986 and reported by Mach and Rust (1989a) and 18 triggered-lightning strokes from the 1987 KSC experiments reported by Willett et al

(1989a) Peak curent shown in the scatter plot as 38 kA may be an underestimate Note that the linear correlation coefficients (r) for both data sets are low and negative not in support of the often assumed relationship between these two lightning parameters

00

05

10

15

20

25

0 5 10 15 20 25 30 35 40 45

Return-Stroke Peak Current kA

Ret

urn-

Stro

ke S

peed

108 m

s

Mach and Rust (1989a) r = -008

Willett el al (1998a) r = -027

First Return Stroke

Electric field waveforms of a first return stroke The waveform is shown on two time scales 5 μsdiv

and 10 μsdiv The fields are normalized to a distance of 100 km L denotes individual leader pulses F slow front and R fast transition Also marked are the small secondary peak or shoulder α

and the larger subsidiary peaks a b and c Adapted from Weidman and Krider

(1978)

-20 -15 -10 -5 0 5 10 15 20

5

microsdiv

10

microsdiv

-60 -40 -20 0 20 40 60 80

26

Subsequent Return Strokes

-20 -15 -10 -5 0 5 10 15 20

5 microsdiv

5 microsdiv

10 microsdiv

10 microsdiv

-60 -40 -20 0 20 40 60 80

Electric field waveforms of (b) a subsequent return stroke initiated by a dart-stepped leader and (c) a subsequent return stroke initiated by a dart leader showing the fine structure both before and after the initial field peak Each waveform is shown on two time scales 5 μsdiv

and 10 μsdiv The fields are normalized to a distance of 100 km L denotes individual leader pulses F slow front and R fast transition Also marked are the small secondary peak or shoulder α

and the larger subsidiary peaks a b and c Adapted from Weidman and Krider

(1978)

27

First Return Stroke Electric Field Derivative

Examples of (top) the time derivative of the electric field intensity dEdt

and (bottom)

the electric field intensity E produced by a first return stroke at a distance of about 36 km over the Atlantic Ocean The propagation path was almost entirely over salt water The vertical arrow under the E record shows the time of the dEdt

trigger Adapted from Krider

et al (1996)

28

Return Strokes Measured Parameters

Parameters of microsecond-scale electric field waveforms produced by negative return strokes

Parameter Location First strokes Subsequent strokes

Sample size Mean SD Sample size Mean SD

Initial peak (V m‐1) (normalized to 100 km)Rakov

and Uman

(1990b)

Cooray

and Lundquist (1982)Lin et al (1979)

Florida

SwedenKSCOcala

76

5535129

59 (GM)

536758

273825

232a

38b

8359

27(GM)41(GM)

5043

2215

Zero‐crossing time (μs)Cooray

and Lundquist (1985)

Lin et al (1979)

SwedenSri LankaFlorida

1029146c

498954

123018

9414377c

394236

81417

Zero‐to‐peak rise time (μs)Master et al (1984)Cooray

and Lundquist (1982)Lin et al (1979)

FloridaSwedenKSCOcala

1051405129

44702427

18201213

220

8359

28

1519

15

0807

10‐90 percent rise time (μs)Master et al (1984) Florida 105 26 12 220 15 09

Slow front duration

(μs)Master et al (1984)Cooray

and Lundquist (1982)Weidman and Krider

(1978)

FloridaSwedenFlorida

105826290

29504041

13201716

44 120 34d

060921

020509

29

Return Strokes Measured ParametersParameters of microsecond-scale electric field waveforms produced by negative return strokes (contrsquod)

Parameter Locatio

nFirst strokes Subsequent strokes

Sample size

Mean SD Sample size Mean SD

Slow front amplitude as percentage of peakMaster et al (1984)Cooray

and Lundquist (1982)Weidman and Krider

(1978)

FloridaSwedenFlorida

105836290

28415040

15112020

4412034d

202540

101020

Fast

transition 10-90 percent risetime

(ns)Master et al (1984)Weidman and Krider

(1978)

Weidman and Krider

(1980a 1984)

Weidman (1982)

FloridaFlorida

Florida

1023815125

97020020090

68010010040

2178034

610200150

27040100

Peak time derivative (normalized to100 km ) (V m-1

μs-1)Krider

et al (1996) Florida 63 39 11

Time derivative pulse width at half-peak value (ns)

Krider

et al (1996) Florida 61 100 20

If not specicied

otherwise multiple lines for a given source for the same location correspond to different thunderstorms GM = geometric mean value a better characteristic of the distribution of initial field peaks since this distribution is approximately log-normala

Strokes following previously formed channelb

Strokes creating new termination on groundcBoth

electric and magnetic fieldsd

Subsequent strokes initiated by dart-stepped leaders Other subsequent strokes studied by Weidman and

Krider

(1978) were initiated by dart leaders

30

• Slide Number 1
• Slide Number 2
• Slide Number 3
• Slide Number 4
• Slide Number 5
• Slide Number 6
• Slide Number 7
• Slide Number 8
• Slide Number 9
• Slide Number 10
• Slide Number 11
• Slide Number 12
• Return-Stroke Fields Variation with Distance
• Return-Stroke Fields Variation with Distance
• Slide Number 15
• Slide Number 16
• Slide Number 17
• Slide Number 18
• Slide Number 19
• Slide Number 20
• Slide Number 21
• Slide Number 22
• Slide Number 23
• Slide Number 24
• Slide Number 25
• First Return Stroke
• Subsequent Return Strokes
• First Return Stroke Electric Field Derivative
• Return Strokes Measured Parameters
• Return Strokes Measured Parameters

Return‐Stroke Fields Variation with Distance

Electric Field IntensityMagnetic Flux Density

Typical vertical electric field intensity (left column) and azimuthal

magnetic flux density (right column) waveforms for first (solid line) and subsequent (dashed line) return strokes at distances of 10 15 50 and 200 km Adapted from Lin et al (1979)

Return-Stroke Current Waveshapes

ndash

Switzerland (Berger et al 1975)

15

Average negative first and subsequent-stroke current waveshapes

each shown on two time scales A

and B The lower time scales (A) correspond to the solid curves while the upper time scales (B) correspond to the broken curves The vertical (amplitude) scale is in relative units the peak values being equal to negative unity Adapted from Berger et al (1975)

Lightning Parameters Derived from Direct Current Measurements

Parameters Units Sample Size

Percent Exceeding Tabulated Value

95 50 5

Peak current

(minimum 2 kA)First strokesSubsequent strokes

kA 101135

1446

3012

8030

Charge

(total charge)First strokesSubsequent strokesComplete flash

C 9312294

110213

521475

241140

Impulse charge

(excluding continuing current)

First strokesSubsequent strokes

C90

11711

02245

09520

4Front duration

(2 kA to peak)First strokesSubsequent strokes

μs 89118

18022

5511

1845

Maximum dIdtFirst strokesSubsequent strokes

kA μs-1 92122

5512

1240

32120

Stroke duration

(2 kA to half peak value on the tail)

First strokesSubsequent strokes

μs90

1153065

7532

200140

Action integral (intI2dt)First strokesSubsequent strokes

A2s 9188

60 x 103

55 x 10255 x 104

60 x 10355 x 105

52 x 104

17

Cumulative statistical distributions of lightning peak currents

giving percent of cases exceeding abscissa value from direct measurements in Switzerland (Berger 1972 Berger et al 1975) The distributions are assumed to be lognormal and given for (1) negative first strokes (2) positive first strokes (3) negative and positive first strokes and (4) negative subsequent strokes Adapted from Bazelyan

et al (1978)

Lightning peak currents for first strokes vary by a factor of 50 or more from about 5 to 250 kA

The probability of occurrence of a given value rapidly increases up to 25 kA

or so and then slowly decreasesStatistical distributions of this type are often assumed to be lognormal

Lightning Peak Current ndash

Bergerrsquos Distributions

18

Cumulative statistical distributions of peak currents (percent values on the vertical axis should be subtracted from 100 to obtain the probability to exceed the peak current value on the horizontal axis) for negative first strokes adopted by IEEE

and CIGRE Taken from CIGRE Document 63 (1991)

For the CIGRE

distribution 98 of peak currents exceed 4 kA 80 exceed 20 kA and 5 exceed 90 kA

For the IEEE

distribution the ldquoprobability to exceedrdquo

values are given by the following equation

where PI

is in per unit and I is in kA This equation applies to values of I up to 200 kA The median (50) peak current value is equal to 31 kA

Peak current I kA(IEEE

distribution) 5 10 20 40 60 80 100 200

Percentage exceeding tabulated value PI

10099 95 76 34 15 78 45 08

( ) 62

311

1I

PI+

=

Lightning Peak Current ndash

IEEE and CIGRE Distributions

dIdt

in Rocket-Triggered Lightning ( ~100 kAμs)

19

Relation between the peak rate of current rise dIdt and the peak current I from triggered-lightning experiments conducted at the NASA Kennedy Space Center Florida in 19851987 and 1988 and in France in 1986 The regression line for each year is shown the sample size N and the regression equation are given in table Adapted from Leteinturier

et al (1991)

Morro Do Cachimbo

Tower (60 m) Belo Horizonte Brazil

20

Courtesy Prof Dr Silverio Visacro Filho Lightning Research Center (UFMG-CEMIG)

Lightning Parameters Derived from Direct Current Measurements ndash

Brazil

21

First Stroke

Subsequent Strokes

404

52

163

099

Optical Measurements of Return-Stroke Speed

22

Optical intensity (in millivolts

at the input of the oscilloscope) vs time waveforms at four different heights 7 63 117 and 170 m

above the lightning termination point for stroke 1 in flash F0336 Adapted from Olsen et al (2004)

23

Reference St Dev ms Comments

Natural Lightning

Boyle and Orville (1976)

20 x 107 12 x 108 071 x 108 26 x 107 12 Streak camera 2-D speed

Idone and Orville (1982)

29 x 107 24 x 108 11 x 108 47 x 107 63 Streak camera2-D speed

Mach and Rust (1989a Fig 7)

20 x 107

80 x 10726 x 108

gt28 x 1085 x 107

7 x 1075443

Long channelShort channel (Photoelectric 2-D)

Triggered Lightning

Hubert and Mouget (1981)

45 x 107 17 x 108 99 x 107 41 x 107 13 Photoelectric3-D speed

Idone et al (1984) 67 x 107 17 x 108 12 x 108 27 x 107 56 Streak camera 3-D speed

Willett et al (1988)

10 x 108 15 x 108 12 x 108 16 x 107 9 Streak camera 2-D speed

Willett et al (1989a)

12 x 108 19 x 108 15 x 108 17 x 107 18 Streak camera 2-D speed

Mach and Rust (1989a Fig 8)

60 x 107

60 x 10716 x 108

20 x 1082 x 107

4 x 1074039

Long channelShort channel(Photoelectric 2-D)

Min ms Max ms Mean ms Sample

Size

13 plusmn03 x 108

19 plusmn07 x 108

12 plusmn03 x 108

14 plusmn04 x 108

Summary of measured return stroke speeds averaged over the visible part of the channel in natural and triggered negative lightning Adapted from Rakov

et al (1992b)

Return-Stroke Speed Near Ground

24

Height Above Ground

7-63 m

63-117 m

117-170

m

12

16

15

12121213

18

16

16

17

18 18

1512

Return-stroke speed profiles estimated tracking the 20 point on the light-pulse front for triggered lightning flash F0336 (Olsen et al 2004)

Return-Stroke Speed vs Return-Stroke Peak Current

25

Return-stroke speed vs peak current for 29 triggered-lightning strokes observed at the Kennedy Space Center (KSC) Florida in 1986 and reported by Mach and Rust (1989a) and 18 triggered-lightning strokes from the 1987 KSC experiments reported by Willett et al

(1989a) Peak curent shown in the scatter plot as 38 kA may be an underestimate Note that the linear correlation coefficients (r) for both data sets are low and negative not in support of the often assumed relationship between these two lightning parameters

00

05

10

15

20

25

0 5 10 15 20 25 30 35 40 45

Return-Stroke Peak Current kA

Ret

urn-

Stro

ke S

peed

108 m

s

Mach and Rust (1989a) r = -008

Willett el al (1998a) r = -027

First Return Stroke

Electric field waveforms of a first return stroke The waveform is shown on two time scales 5 μsdiv

and 10 μsdiv The fields are normalized to a distance of 100 km L denotes individual leader pulses F slow front and R fast transition Also marked are the small secondary peak or shoulder α

and the larger subsidiary peaks a b and c Adapted from Weidman and Krider

(1978)

-20 -15 -10 -5 0 5 10 15 20

5

microsdiv

10

microsdiv

-60 -40 -20 0 20 40 60 80

26

Subsequent Return Strokes

-20 -15 -10 -5 0 5 10 15 20

5 microsdiv

5 microsdiv

10 microsdiv

10 microsdiv

-60 -40 -20 0 20 40 60 80

Electric field waveforms of (b) a subsequent return stroke initiated by a dart-stepped leader and (c) a subsequent return stroke initiated by a dart leader showing the fine structure both before and after the initial field peak Each waveform is shown on two time scales 5 μsdiv

and 10 μsdiv The fields are normalized to a distance of 100 km L denotes individual leader pulses F slow front and R fast transition Also marked are the small secondary peak or shoulder α

and the larger subsidiary peaks a b and c Adapted from Weidman and Krider

(1978)

27

First Return Stroke Electric Field Derivative

Examples of (top) the time derivative of the electric field intensity dEdt

and (bottom)

the electric field intensity E produced by a first return stroke at a distance of about 36 km over the Atlantic Ocean The propagation path was almost entirely over salt water The vertical arrow under the E record shows the time of the dEdt

trigger Adapted from Krider

et al (1996)

28

Return Strokes Measured Parameters

Parameters of microsecond-scale electric field waveforms produced by negative return strokes

Parameter Location First strokes Subsequent strokes

Sample size Mean SD Sample size Mean SD

Initial peak (V m‐1) (normalized to 100 km)Rakov

and Uman

(1990b)

Cooray

and Lundquist (1982)Lin et al (1979)

Florida

SwedenKSCOcala

76

5535129

59 (GM)

536758

273825

232a

38b

8359

27(GM)41(GM)

5043

2215

Zero‐crossing time (μs)Cooray

and Lundquist (1985)

Lin et al (1979)

SwedenSri LankaFlorida

1029146c

498954

123018

9414377c

394236

81417

Zero‐to‐peak rise time (μs)Master et al (1984)Cooray

and Lundquist (1982)Lin et al (1979)

FloridaSwedenKSCOcala

1051405129

44702427

18201213

220

8359

28

1519

15

0807

10‐90 percent rise time (μs)Master et al (1984) Florida 105 26 12 220 15 09

Slow front duration

(μs)Master et al (1984)Cooray

and Lundquist (1982)Weidman and Krider

(1978)

FloridaSwedenFlorida

105826290

29504041

13201716

44 120 34d

060921

020509

29

Return Strokes Measured ParametersParameters of microsecond-scale electric field waveforms produced by negative return strokes (contrsquod)

Parameter Locatio

nFirst strokes Subsequent strokes

Sample size

Mean SD Sample size Mean SD

Slow front amplitude as percentage of peakMaster et al (1984)Cooray

and Lundquist (1982)Weidman and Krider

(1978)

FloridaSwedenFlorida

105836290

28415040

15112020

4412034d

202540

101020

Fast

transition 10-90 percent risetime

(ns)Master et al (1984)Weidman and Krider

(1978)

Weidman and Krider

(1980a 1984)

Weidman (1982)

FloridaFlorida

Florida

1023815125

97020020090

68010010040

2178034

610200150

27040100

Peak time derivative (normalized to100 km ) (V m-1

μs-1)Krider

et al (1996) Florida 63 39 11

Time derivative pulse width at half-peak value (ns)

Krider

et al (1996) Florida 61 100 20

If not specicied

otherwise multiple lines for a given source for the same location correspond to different thunderstorms GM = geometric mean value a better characteristic of the distribution of initial field peaks since this distribution is approximately log-normala

Strokes following previously formed channelb

Strokes creating new termination on groundcBoth

electric and magnetic fieldsd

Subsequent strokes initiated by dart-stepped leaders Other subsequent strokes studied by Weidman and

Krider

(1978) were initiated by dart leaders

30

• Slide Number 1
• Slide Number 2
• Slide Number 3
• Slide Number 4
• Slide Number 5
• Slide Number 6
• Slide Number 7
• Slide Number 8
• Slide Number 9
• Slide Number 10
• Slide Number 11
• Slide Number 12
• Return-Stroke Fields Variation with Distance
• Return-Stroke Fields Variation with Distance
• Slide Number 15
• Slide Number 16
• Slide Number 17
• Slide Number 18
• Slide Number 19
• Slide Number 20
• Slide Number 21
• Slide Number 22
• Slide Number 23
• Slide Number 24
• Slide Number 25
• First Return Stroke
• Subsequent Return Strokes
• First Return Stroke Electric Field Derivative
• Return Strokes Measured Parameters
• Return Strokes Measured Parameters

Return-Stroke Current Waveshapes

ndash

Switzerland (Berger et al 1975)

15

Average negative first and subsequent-stroke current waveshapes

each shown on two time scales A

and B The lower time scales (A) correspond to the solid curves while the upper time scales (B) correspond to the broken curves The vertical (amplitude) scale is in relative units the peak values being equal to negative unity Adapted from Berger et al (1975)

Lightning Parameters Derived from Direct Current Measurements

Parameters Units Sample Size

Percent Exceeding Tabulated Value

95 50 5

Peak current

(minimum 2 kA)First strokesSubsequent strokes

kA 101135

1446

3012

8030

Charge

(total charge)First strokesSubsequent strokesComplete flash

C 9312294

110213

521475

241140

Impulse charge

(excluding continuing current)

First strokesSubsequent strokes

C90

11711

02245

09520

4Front duration

(2 kA to peak)First strokesSubsequent strokes

μs 89118

18022

5511

1845

Maximum dIdtFirst strokesSubsequent strokes

kA μs-1 92122

5512

1240

32120

Stroke duration

(2 kA to half peak value on the tail)

First strokesSubsequent strokes

μs90

1153065

7532

200140

Action integral (intI2dt)First strokesSubsequent strokes

A2s 9188

60 x 103

55 x 10255 x 104

60 x 10355 x 105

52 x 104

17

Cumulative statistical distributions of lightning peak currents

giving percent of cases exceeding abscissa value from direct measurements in Switzerland (Berger 1972 Berger et al 1975) The distributions are assumed to be lognormal and given for (1) negative first strokes (2) positive first strokes (3) negative and positive first strokes and (4) negative subsequent strokes Adapted from Bazelyan

et al (1978)

Lightning peak currents for first strokes vary by a factor of 50 or more from about 5 to 250 kA

The probability of occurrence of a given value rapidly increases up to 25 kA

or so and then slowly decreasesStatistical distributions of this type are often assumed to be lognormal

Lightning Peak Current ndash

Bergerrsquos Distributions

18

Cumulative statistical distributions of peak currents (percent values on the vertical axis should be subtracted from 100 to obtain the probability to exceed the peak current value on the horizontal axis) for negative first strokes adopted by IEEE

and CIGRE Taken from CIGRE Document 63 (1991)

For the CIGRE

distribution 98 of peak currents exceed 4 kA 80 exceed 20 kA and 5 exceed 90 kA

For the IEEE

distribution the ldquoprobability to exceedrdquo

values are given by the following equation

where PI

is in per unit and I is in kA This equation applies to values of I up to 200 kA The median (50) peak current value is equal to 31 kA

Peak current I kA(IEEE

distribution) 5 10 20 40 60 80 100 200

Percentage exceeding tabulated value PI

10099 95 76 34 15 78 45 08

( ) 62

311

1I

PI+

=

Lightning Peak Current ndash

IEEE and CIGRE Distributions

dIdt

in Rocket-Triggered Lightning ( ~100 kAμs)

19

Relation between the peak rate of current rise dIdt and the peak current I from triggered-lightning experiments conducted at the NASA Kennedy Space Center Florida in 19851987 and 1988 and in France in 1986 The regression line for each year is shown the sample size N and the regression equation are given in table Adapted from Leteinturier

et al (1991)

Morro Do Cachimbo

Tower (60 m) Belo Horizonte Brazil

20

Courtesy Prof Dr Silverio Visacro Filho Lightning Research Center (UFMG-CEMIG)

Lightning Parameters Derived from Direct Current Measurements ndash

Brazil

21

First Stroke

Subsequent Strokes

404

52

163

099

Optical Measurements of Return-Stroke Speed

22

Optical intensity (in millivolts

at the input of the oscilloscope) vs time waveforms at four different heights 7 63 117 and 170 m

above the lightning termination point for stroke 1 in flash F0336 Adapted from Olsen et al (2004)

23

Reference St Dev ms Comments

Natural Lightning

Boyle and Orville (1976)

20 x 107 12 x 108 071 x 108 26 x 107 12 Streak camera 2-D speed

Idone and Orville (1982)

29 x 107 24 x 108 11 x 108 47 x 107 63 Streak camera2-D speed

Mach and Rust (1989a Fig 7)

20 x 107

80 x 10726 x 108

gt28 x 1085 x 107

7 x 1075443

Long channelShort channel (Photoelectric 2-D)

Triggered Lightning

Hubert and Mouget (1981)

45 x 107 17 x 108 99 x 107 41 x 107 13 Photoelectric3-D speed

Idone et al (1984) 67 x 107 17 x 108 12 x 108 27 x 107 56 Streak camera 3-D speed

Willett et al (1988)

10 x 108 15 x 108 12 x 108 16 x 107 9 Streak camera 2-D speed

Willett et al (1989a)

12 x 108 19 x 108 15 x 108 17 x 107 18 Streak camera 2-D speed

Mach and Rust (1989a Fig 8)

60 x 107

60 x 10716 x 108

20 x 1082 x 107

4 x 1074039

Long channelShort channel(Photoelectric 2-D)

Min ms Max ms Mean ms Sample

Size

13 plusmn03 x 108

19 plusmn07 x 108

12 plusmn03 x 108

14 plusmn04 x 108

Summary of measured return stroke speeds averaged over the visible part of the channel in natural and triggered negative lightning Adapted from Rakov

et al (1992b)

Return-Stroke Speed Near Ground

24

Height Above Ground

7-63 m

63-117 m

117-170

m

12

16

15

12121213

18

16

16

17

18 18

1512

Return-stroke speed profiles estimated tracking the 20 point on the light-pulse front for triggered lightning flash F0336 (Olsen et al 2004)

Return-Stroke Speed vs Return-Stroke Peak Current

25

Return-stroke speed vs peak current for 29 triggered-lightning strokes observed at the Kennedy Space Center (KSC) Florida in 1986 and reported by Mach and Rust (1989a) and 18 triggered-lightning strokes from the 1987 KSC experiments reported by Willett et al

(1989a) Peak curent shown in the scatter plot as 38 kA may be an underestimate Note that the linear correlation coefficients (r) for both data sets are low and negative not in support of the often assumed relationship between these two lightning parameters

00

05

10

15

20

25

0 5 10 15 20 25 30 35 40 45

Return-Stroke Peak Current kA

Ret

urn-

Stro

ke S

peed

108 m

s

Mach and Rust (1989a) r = -008

Willett el al (1998a) r = -027

First Return Stroke

Electric field waveforms of a first return stroke The waveform is shown on two time scales 5 μsdiv

and 10 μsdiv The fields are normalized to a distance of 100 km L denotes individual leader pulses F slow front and R fast transition Also marked are the small secondary peak or shoulder α

and the larger subsidiary peaks a b and c Adapted from Weidman and Krider

(1978)

-20 -15 -10 -5 0 5 10 15 20

5

microsdiv

10

microsdiv

-60 -40 -20 0 20 40 60 80

26

Subsequent Return Strokes

-20 -15 -10 -5 0 5 10 15 20

5 microsdiv

5 microsdiv

10 microsdiv

10 microsdiv

-60 -40 -20 0 20 40 60 80

Electric field waveforms of (b) a subsequent return stroke initiated by a dart-stepped leader and (c) a subsequent return stroke initiated by a dart leader showing the fine structure both before and after the initial field peak Each waveform is shown on two time scales 5 μsdiv

and 10 μsdiv The fields are normalized to a distance of 100 km L denotes individual leader pulses F slow front and R fast transition Also marked are the small secondary peak or shoulder α

and the larger subsidiary peaks a b and c Adapted from Weidman and Krider

(1978)

27

First Return Stroke Electric Field Derivative

Examples of (top) the time derivative of the electric field intensity dEdt

and (bottom)

the electric field intensity E produced by a first return stroke at a distance of about 36 km over the Atlantic Ocean The propagation path was almost entirely over salt water The vertical arrow under the E record shows the time of the dEdt

trigger Adapted from Krider

et al (1996)

28

Return Strokes Measured Parameters

Parameters of microsecond-scale electric field waveforms produced by negative return strokes

Parameter Location First strokes Subsequent strokes

Sample size Mean SD Sample size Mean SD

Initial peak (V m‐1) (normalized to 100 km)Rakov

and Uman

(1990b)

Cooray

and Lundquist (1982)Lin et al (1979)

Florida

SwedenKSCOcala

76

5535129

59 (GM)

536758

273825

232a

38b

8359

27(GM)41(GM)

5043

2215

Zero‐crossing time (μs)Cooray

and Lundquist (1985)

Lin et al (1979)

SwedenSri LankaFlorida

1029146c

498954

123018

9414377c

394236

81417

Zero‐to‐peak rise time (μs)Master et al (1984)Cooray

and Lundquist (1982)Lin et al (1979)

FloridaSwedenKSCOcala

1051405129

44702427

18201213

220

8359

28

1519

15

0807

10‐90 percent rise time (μs)Master et al (1984) Florida 105 26 12 220 15 09

Slow front duration

(μs)Master et al (1984)Cooray

and Lundquist (1982)Weidman and Krider

(1978)

FloridaSwedenFlorida

105826290

29504041

13201716

44 120 34d

060921

020509

29

Return Strokes Measured ParametersParameters of microsecond-scale electric field waveforms produced by negative return strokes (contrsquod)

Parameter Locatio

nFirst strokes Subsequent strokes

Sample size

Mean SD Sample size Mean SD

Slow front amplitude as percentage of peakMaster et al (1984)Cooray

and Lundquist (1982)Weidman and Krider

(1978)

FloridaSwedenFlorida

105836290

28415040

15112020

4412034d

202540

101020

Fast

transition 10-90 percent risetime

(ns)Master et al (1984)Weidman and Krider

(1978)

Weidman and Krider

(1980a 1984)

Weidman (1982)

FloridaFlorida

Florida

1023815125

97020020090

68010010040

2178034

610200150

27040100

Peak time derivative (normalized to100 km ) (V m-1

μs-1)Krider

et al (1996) Florida 63 39 11

Time derivative pulse width at half-peak value (ns)

Krider

et al (1996) Florida 61 100 20

If not specicied

otherwise multiple lines for a given source for the same location correspond to different thunderstorms GM = geometric mean value a better characteristic of the distribution of initial field peaks since this distribution is approximately log-normala

Strokes following previously formed channelb

Strokes creating new termination on groundcBoth

electric and magnetic fieldsd

Subsequent strokes initiated by dart-stepped leaders Other subsequent strokes studied by Weidman and

Krider

(1978) were initiated by dart leaders

30

• Slide Number 1
• Slide Number 2
• Slide Number 3
• Slide Number 4
• Slide Number 5
• Slide Number 6
• Slide Number 7
• Slide Number 8
• Slide Number 9
• Slide Number 10
• Slide Number 11
• Slide Number 12
• Return-Stroke Fields Variation with Distance
• Return-Stroke Fields Variation with Distance
• Slide Number 15
• Slide Number 16
• Slide Number 17
• Slide Number 18
• Slide Number 19
• Slide Number 20
• Slide Number 21
• Slide Number 22
• Slide Number 23
• Slide Number 24
• Slide Number 25
• First Return Stroke
• Subsequent Return Strokes
• First Return Stroke Electric Field Derivative
• Return Strokes Measured Parameters
• Return Strokes Measured Parameters

Lightning Parameters Derived from Direct Current Measurements

Parameters Units Sample Size

Percent Exceeding Tabulated Value

95 50 5

Peak current

(minimum 2 kA)First strokesSubsequent strokes

kA 101135

1446

3012

8030

Charge

(total charge)First strokesSubsequent strokesComplete flash

C 9312294

110213

521475

241140

Impulse charge

(excluding continuing current)

First strokesSubsequent strokes

C90

11711

02245

09520

4Front duration

(2 kA to peak)First strokesSubsequent strokes

μs 89118

18022

5511

1845

Maximum dIdtFirst strokesSubsequent strokes

kA μs-1 92122

5512

1240

32120

Stroke duration

(2 kA to half peak value on the tail)

First strokesSubsequent strokes

μs90

1153065

7532

200140

Action integral (intI2dt)First strokesSubsequent strokes

A2s 9188

60 x 103

55 x 10255 x 104

60 x 10355 x 105

52 x 104

17

Cumulative statistical distributions of lightning peak currents

giving percent of cases exceeding abscissa value from direct measurements in Switzerland (Berger 1972 Berger et al 1975) The distributions are assumed to be lognormal and given for (1) negative first strokes (2) positive first strokes (3) negative and positive first strokes and (4) negative subsequent strokes Adapted from Bazelyan

et al (1978)

Lightning peak currents for first strokes vary by a factor of 50 or more from about 5 to 250 kA

The probability of occurrence of a given value rapidly increases up to 25 kA

or so and then slowly decreasesStatistical distributions of this type are often assumed to be lognormal

Lightning Peak Current ndash

Bergerrsquos Distributions

18

Cumulative statistical distributions of peak currents (percent values on the vertical axis should be subtracted from 100 to obtain the probability to exceed the peak current value on the horizontal axis) for negative first strokes adopted by IEEE

and CIGRE Taken from CIGRE Document 63 (1991)

For the CIGRE

distribution 98 of peak currents exceed 4 kA 80 exceed 20 kA and 5 exceed 90 kA

For the IEEE

distribution the ldquoprobability to exceedrdquo

values are given by the following equation

where PI

is in per unit and I is in kA This equation applies to values of I up to 200 kA The median (50) peak current value is equal to 31 kA

Peak current I kA(IEEE

distribution) 5 10 20 40 60 80 100 200

Percentage exceeding tabulated value PI

10099 95 76 34 15 78 45 08

( ) 62

311

1I

PI+

=

Lightning Peak Current ndash

IEEE and CIGRE Distributions

dIdt

in Rocket-Triggered Lightning ( ~100 kAμs)

19

Relation between the peak rate of current rise dIdt and the peak current I from triggered-lightning experiments conducted at the NASA Kennedy Space Center Florida in 19851987 and 1988 and in France in 1986 The regression line for each year is shown the sample size N and the regression equation are given in table Adapted from Leteinturier

et al (1991)

Morro Do Cachimbo

Tower (60 m) Belo Horizonte Brazil

20

Courtesy Prof Dr Silverio Visacro Filho Lightning Research Center (UFMG-CEMIG)

Lightning Parameters Derived from Direct Current Measurements ndash

Brazil

21

First Stroke

Subsequent Strokes

404

52

163

099

Optical Measurements of Return-Stroke Speed

22

Optical intensity (in millivolts

at the input of the oscilloscope) vs time waveforms at four different heights 7 63 117 and 170 m

above the lightning termination point for stroke 1 in flash F0336 Adapted from Olsen et al (2004)

23

Reference St Dev ms Comments

Natural Lightning

Boyle and Orville (1976)

20 x 107 12 x 108 071 x 108 26 x 107 12 Streak camera 2-D speed

Idone and Orville (1982)

29 x 107 24 x 108 11 x 108 47 x 107 63 Streak camera2-D speed

Mach and Rust (1989a Fig 7)

20 x 107

80 x 10726 x 108

gt28 x 1085 x 107

7 x 1075443

Long channelShort channel (Photoelectric 2-D)

Triggered Lightning

Hubert and Mouget (1981)

45 x 107 17 x 108 99 x 107 41 x 107 13 Photoelectric3-D speed

Idone et al (1984) 67 x 107 17 x 108 12 x 108 27 x 107 56 Streak camera 3-D speed

Willett et al (1988)

10 x 108 15 x 108 12 x 108 16 x 107 9 Streak camera 2-D speed

Willett et al (1989a)

12 x 108 19 x 108 15 x 108 17 x 107 18 Streak camera 2-D speed

Mach and Rust (1989a Fig 8)

60 x 107

60 x 10716 x 108

20 x 1082 x 107

4 x 1074039

Long channelShort channel(Photoelectric 2-D)

Min ms Max ms Mean ms Sample

Size

13 plusmn03 x 108

19 plusmn07 x 108

12 plusmn03 x 108

14 plusmn04 x 108

Summary of measured return stroke speeds averaged over the visible part of the channel in natural and triggered negative lightning Adapted from Rakov

et al (1992b)

Return-Stroke Speed Near Ground

24

Height Above Ground

7-63 m

63-117 m

117-170

m

12

16

15

12121213

18

16

16

17

18 18

1512

Return-stroke speed profiles estimated tracking the 20 point on the light-pulse front for triggered lightning flash F0336 (Olsen et al 2004)

Return-Stroke Speed vs Return-Stroke Peak Current

25

Return-stroke speed vs peak current for 29 triggered-lightning strokes observed at the Kennedy Space Center (KSC) Florida in 1986 and reported by Mach and Rust (1989a) and 18 triggered-lightning strokes from the 1987 KSC experiments reported by Willett et al

(1989a) Peak curent shown in the scatter plot as 38 kA may be an underestimate Note that the linear correlation coefficients (r) for both data sets are low and negative not in support of the often assumed relationship between these two lightning parameters

00

05

10

15

20

25

0 5 10 15 20 25 30 35 40 45

Return-Stroke Peak Current kA

Ret

urn-

Stro

ke S

peed

108 m

s

Mach and Rust (1989a) r = -008

Willett el al (1998a) r = -027

First Return Stroke

Electric field waveforms of a first return stroke The waveform is shown on two time scales 5 μsdiv

and 10 μsdiv The fields are normalized to a distance of 100 km L denotes individual leader pulses F slow front and R fast transition Also marked are the small secondary peak or shoulder α

and the larger subsidiary peaks a b and c Adapted from Weidman and Krider

(1978)

-20 -15 -10 -5 0 5 10 15 20

5

microsdiv

10

microsdiv

-60 -40 -20 0 20 40 60 80

26

Subsequent Return Strokes

-20 -15 -10 -5 0 5 10 15 20

5 microsdiv

5 microsdiv

10 microsdiv

10 microsdiv

-60 -40 -20 0 20 40 60 80

Electric field waveforms of (b) a subsequent return stroke initiated by a dart-stepped leader and (c) a subsequent return stroke initiated by a dart leader showing the fine structure both before and after the initial field peak Each waveform is shown on two time scales 5 μsdiv

and 10 μsdiv The fields are normalized to a distance of 100 km L denotes individual leader pulses F slow front and R fast transition Also marked are the small secondary peak or shoulder α

and the larger subsidiary peaks a b and c Adapted from Weidman and Krider

(1978)

27

First Return Stroke Electric Field Derivative

Examples of (top) the time derivative of the electric field intensity dEdt

and (bottom)

the electric field intensity E produced by a first return stroke at a distance of about 36 km over the Atlantic Ocean The propagation path was almost entirely over salt water The vertical arrow under the E record shows the time of the dEdt

trigger Adapted from Krider

et al (1996)

28

Return Strokes Measured Parameters

Parameters of microsecond-scale electric field waveforms produced by negative return strokes

Parameter Location First strokes Subsequent strokes

Sample size Mean SD Sample size Mean SD

Initial peak (V m‐1) (normalized to 100 km)Rakov

and Uman

(1990b)

Cooray

and Lundquist (1982)Lin et al (1979)

Florida

SwedenKSCOcala

76

5535129

59 (GM)

536758

273825

232a

38b

8359

27(GM)41(GM)

5043

2215

Zero‐crossing time (μs)Cooray

and Lundquist (1985)

Lin et al (1979)

SwedenSri LankaFlorida

1029146c

498954

123018

9414377c

394236

81417

Zero‐to‐peak rise time (μs)Master et al (1984)Cooray

and Lundquist (1982)Lin et al (1979)

FloridaSwedenKSCOcala

1051405129

44702427

18201213

220

8359

28

1519

15

0807

10‐90 percent rise time (μs)Master et al (1984) Florida 105 26 12 220 15 09

Slow front duration

(μs)Master et al (1984)Cooray

and Lundquist (1982)Weidman and Krider

(1978)

FloridaSwedenFlorida

105826290

29504041

13201716

44 120 34d

060921

020509

29

Return Strokes Measured ParametersParameters of microsecond-scale electric field waveforms produced by negative return strokes (contrsquod)

Parameter Locatio

nFirst strokes Subsequent strokes

Sample size

Mean SD Sample size Mean SD

Slow front amplitude as percentage of peakMaster et al (1984)Cooray

and Lundquist (1982)Weidman and Krider

(1978)

FloridaSwedenFlorida

105836290

28415040

15112020

4412034d

202540

101020

Fast

transition 10-90 percent risetime

(ns)Master et al (1984)Weidman and Krider

(1978)

Weidman and Krider

(1980a 1984)

Weidman (1982)

FloridaFlorida

Florida

1023815125

97020020090

68010010040

2178034

610200150

27040100

Peak time derivative (normalized to100 km ) (V m-1

μs-1)Krider

et al (1996) Florida 63 39 11

Time derivative pulse width at half-peak value (ns)

Krider

et al (1996) Florida 61 100 20

If not specicied

otherwise multiple lines for a given source for the same location correspond to different thunderstorms GM = geometric mean value a better characteristic of the distribution of initial field peaks since this distribution is approximately log-normala

Strokes following previously formed channelb

Strokes creating new termination on groundcBoth

electric and magnetic fieldsd

Subsequent strokes initiated by dart-stepped leaders Other subsequent strokes studied by Weidman and

Krider

(1978) were initiated by dart leaders

30

• Slide Number 1
• Slide Number 2
• Slide Number 3
• Slide Number 4
• Slide Number 5
• Slide Number 6
• Slide Number 7
• Slide Number 8
• Slide Number 9
• Slide Number 10
• Slide Number 11
• Slide Number 12
• Return-Stroke Fields Variation with Distance
• Return-Stroke Fields Variation with Distance
• Slide Number 15
• Slide Number 16
• Slide Number 17
• Slide Number 18
• Slide Number 19
• Slide Number 20
• Slide Number 21
• Slide Number 22
• Slide Number 23
• Slide Number 24
• Slide Number 25
• First Return Stroke
• Subsequent Return Strokes
• First Return Stroke Electric Field Derivative
• Return Strokes Measured Parameters
• Return Strokes Measured Parameters

17

Cumulative statistical distributions of lightning peak currents

giving percent of cases exceeding abscissa value from direct measurements in Switzerland (Berger 1972 Berger et al 1975) The distributions are assumed to be lognormal and given for (1) negative first strokes (2) positive first strokes (3) negative and positive first strokes and (4) negative subsequent strokes Adapted from Bazelyan

et al (1978)

Lightning peak currents for first strokes vary by a factor of 50 or more from about 5 to 250 kA

The probability of occurrence of a given value rapidly increases up to 25 kA

or so and then slowly decreasesStatistical distributions of this type are often assumed to be lognormal

Lightning Peak Current ndash

Bergerrsquos Distributions

18

Cumulative statistical distributions of peak currents (percent values on the vertical axis should be subtracted from 100 to obtain the probability to exceed the peak current value on the horizontal axis) for negative first strokes adopted by IEEE

and CIGRE Taken from CIGRE Document 63 (1991)

For the CIGRE

distribution 98 of peak currents exceed 4 kA 80 exceed 20 kA and 5 exceed 90 kA

For the IEEE

distribution the ldquoprobability to exceedrdquo

values are given by the following equation

where PI

is in per unit and I is in kA This equation applies to values of I up to 200 kA The median (50) peak current value is equal to 31 kA

Peak current I kA(IEEE

distribution) 5 10 20 40 60 80 100 200

Percentage exceeding tabulated value PI

10099 95 76 34 15 78 45 08

( ) 62

311

1I

PI+

=

Lightning Peak Current ndash

IEEE and CIGRE Distributions

dIdt

in Rocket-Triggered Lightning ( ~100 kAμs)

19

Relation between the peak rate of current rise dIdt and the peak current I from triggered-lightning experiments conducted at the NASA Kennedy Space Center Florida in 19851987 and 1988 and in France in 1986 The regression line for each year is shown the sample size N and the regression equation are given in table Adapted from Leteinturier

et al (1991)

Morro Do Cachimbo

Tower (60 m) Belo Horizonte Brazil

20

Courtesy Prof Dr Silverio Visacro Filho Lightning Research Center (UFMG-CEMIG)

Lightning Parameters Derived from Direct Current Measurements ndash

Brazil

21

First Stroke

Subsequent Strokes

404

52

163

099

Optical Measurements of Return-Stroke Speed

22

Optical intensity (in millivolts

at the input of the oscilloscope) vs time waveforms at four different heights 7 63 117 and 170 m

above the lightning termination point for stroke 1 in flash F0336 Adapted from Olsen et al (2004)

23

Reference St Dev ms Comments

Natural Lightning

Boyle and Orville (1976)

20 x 107 12 x 108 071 x 108 26 x 107 12 Streak camera 2-D speed

Idone and Orville (1982)

29 x 107 24 x 108 11 x 108 47 x 107 63 Streak camera2-D speed

Mach and Rust (1989a Fig 7)

20 x 107

80 x 10726 x 108

gt28 x 1085 x 107

7 x 1075443

Long channelShort channel (Photoelectric 2-D)

Triggered Lightning

Hubert and Mouget (1981)

45 x 107 17 x 108 99 x 107 41 x 107 13 Photoelectric3-D speed

Idone et al (1984) 67 x 107 17 x 108 12 x 108 27 x 107 56 Streak camera 3-D speed

Willett et al (1988)

10 x 108 15 x 108 12 x 108 16 x 107 9 Streak camera 2-D speed

Willett et al (1989a)

12 x 108 19 x 108 15 x 108 17 x 107 18 Streak camera 2-D speed

Mach and Rust (1989a Fig 8)

60 x 107

60 x 10716 x 108

20 x 1082 x 107

4 x 1074039

Long channelShort channel(Photoelectric 2-D)

Min ms Max ms Mean ms Sample

Size

13 plusmn03 x 108

19 plusmn07 x 108

12 plusmn03 x 108

14 plusmn04 x 108

Summary of measured return stroke speeds averaged over the visible part of the channel in natural and triggered negative lightning Adapted from Rakov

et al (1992b)

Return-Stroke Speed Near Ground

24

Height Above Ground

7-63 m

63-117 m

117-170

m

12

16

15

12121213

18

16

16

17

18 18

1512

Return-stroke speed profiles estimated tracking the 20 point on the light-pulse front for triggered lightning flash F0336 (Olsen et al 2004)

Return-Stroke Speed vs Return-Stroke Peak Current

25

Return-stroke speed vs peak current for 29 triggered-lightning strokes observed at the Kennedy Space Center (KSC) Florida in 1986 and reported by Mach and Rust (1989a) and 18 triggered-lightning strokes from the 1987 KSC experiments reported by Willett et al

(1989a) Peak curent shown in the scatter plot as 38 kA may be an underestimate Note that the linear correlation coefficients (r) for both data sets are low and negative not in support of the often assumed relationship between these two lightning parameters

00

05

10

15

20

25

0 5 10 15 20 25 30 35 40 45

Return-Stroke Peak Current kA

Ret

urn-

Stro

ke S

peed

108 m

s

Mach and Rust (1989a) r = -008

Willett el al (1998a) r = -027

First Return Stroke

Electric field waveforms of a first return stroke The waveform is shown on two time scales 5 μsdiv

and 10 μsdiv The fields are normalized to a distance of 100 km L denotes individual leader pulses F slow front and R fast transition Also marked are the small secondary peak or shoulder α

and the larger subsidiary peaks a b and c Adapted from Weidman and Krider

(1978)

-20 -15 -10 -5 0 5 10 15 20

5

microsdiv

10

microsdiv

-60 -40 -20 0 20 40 60 80

26

Subsequent Return Strokes

-20 -15 -10 -5 0 5 10 15 20

5 microsdiv

5 microsdiv

10 microsdiv

10 microsdiv

-60 -40 -20 0 20 40 60 80

Electric field waveforms of (b) a subsequent return stroke initiated by a dart-stepped leader and (c) a subsequent return stroke initiated by a dart leader showing the fine structure both before and after the initial field peak Each waveform is shown on two time scales 5 μsdiv

and 10 μsdiv The fields are normalized to a distance of 100 km L denotes individual leader pulses F slow front and R fast transition Also marked are the small secondary peak or shoulder α

and the larger subsidiary peaks a b and c Adapted from Weidman and Krider

(1978)

27

First Return Stroke Electric Field Derivative

Examples of (top) the time derivative of the electric field intensity dEdt

and (bottom)

the electric field intensity E produced by a first return stroke at a distance of about 36 km over the Atlantic Ocean The propagation path was almost entirely over salt water The vertical arrow under the E record shows the time of the dEdt

trigger Adapted from Krider

et al (1996)

28

Return Strokes Measured Parameters

Parameters of microsecond-scale electric field waveforms produced by negative return strokes

Parameter Location First strokes Subsequent strokes

Sample size Mean SD Sample size Mean SD

Initial peak (V m‐1) (normalized to 100 km)Rakov

and Uman

(1990b)

Cooray

and Lundquist (1982)Lin et al (1979)

Florida

SwedenKSCOcala

76

5535129

59 (GM)

536758

273825

232a

38b

8359

27(GM)41(GM)

5043

2215

Zero‐crossing time (μs)Cooray

and Lundquist (1985)

Lin et al (1979)

SwedenSri LankaFlorida

1029146c

498954

123018

9414377c

394236

81417

Zero‐to‐peak rise time (μs)Master et al (1984)Cooray

and Lundquist (1982)Lin et al (1979)

FloridaSwedenKSCOcala

1051405129

44702427

18201213

220

8359

28

1519

15

0807

10‐90 percent rise time (μs)Master et al (1984) Florida 105 26 12 220 15 09

Slow front duration

(μs)Master et al (1984)Cooray

and Lundquist (1982)Weidman and Krider

(1978)

FloridaSwedenFlorida

105826290

29504041

13201716

44 120 34d

060921

020509

29

Return Strokes Measured ParametersParameters of microsecond-scale electric field waveforms produced by negative return strokes (contrsquod)

Parameter Locatio

nFirst strokes Subsequent strokes

Sample size

Mean SD Sample size Mean SD

Slow front amplitude as percentage of peakMaster et al (1984)Cooray

and Lundquist (1982)Weidman and Krider

(1978)

FloridaSwedenFlorida

105836290

28415040

15112020

4412034d

202540

101020

Fast

transition 10-90 percent risetime

(ns)Master et al (1984)Weidman and Krider

(1978)

Weidman and Krider

(1980a 1984)

Weidman (1982)

FloridaFlorida

Florida

1023815125

97020020090

68010010040

2178034

610200150

27040100

Peak time derivative (normalized to100 km ) (V m-1

μs-1)Krider

et al (1996) Florida 63 39 11

Time derivative pulse width at half-peak value (ns)

Krider

et al (1996) Florida 61 100 20

If not specicied

otherwise multiple lines for a given source for the same location correspond to different thunderstorms GM = geometric mean value a better characteristic of the distribution of initial field peaks since this distribution is approximately log-normala

Strokes following previously formed channelb

Strokes creating new termination on groundcBoth

electric and magnetic fieldsd

Subsequent strokes initiated by dart-stepped leaders Other subsequent strokes studied by Weidman and

Krider

(1978) were initiated by dart leaders

30

• Slide Number 1
• Slide Number 2
• Slide Number 3
• Slide Number 4
• Slide Number 5
• Slide Number 6
• Slide Number 7
• Slide Number 8
• Slide Number 9
• Slide Number 10
• Slide Number 11
• Slide Number 12
• Return-Stroke Fields Variation with Distance
• Return-Stroke Fields Variation with Distance
• Slide Number 15
• Slide Number 16
• Slide Number 17
• Slide Number 18
• Slide Number 19
• Slide Number 20
• Slide Number 21
• Slide Number 22
• Slide Number 23
• Slide Number 24
• Slide Number 25
• First Return Stroke
• Subsequent Return Strokes
• First Return Stroke Electric Field Derivative
• Return Strokes Measured Parameters
• Return Strokes Measured Parameters

18

Cumulative statistical distributions of peak currents (percent values on the vertical axis should be subtracted from 100 to obtain the probability to exceed the peak current value on the horizontal axis) for negative first strokes adopted by IEEE

and CIGRE Taken from CIGRE Document 63 (1991)

For the CIGRE

distribution 98 of peak currents exceed 4 kA 80 exceed 20 kA and 5 exceed 90 kA

For the IEEE

distribution the ldquoprobability to exceedrdquo

values are given by the following equation

where PI

is in per unit and I is in kA This equation applies to values of I up to 200 kA The median (50) peak current value is equal to 31 kA

Peak current I kA(IEEE

distribution) 5 10 20 40 60 80 100 200

Percentage exceeding tabulated value PI

10099 95 76 34 15 78 45 08

( ) 62

311

1I

PI+

=

Lightning Peak Current ndash

IEEE and CIGRE Distributions

dIdt

in Rocket-Triggered Lightning ( ~100 kAμs)

19

Relation between the peak rate of current rise dIdt and the peak current I from triggered-lightning experiments conducted at the NASA Kennedy Space Center Florida in 19851987 and 1988 and in France in 1986 The regression line for each year is shown the sample size N and the regression equation are given in table Adapted from Leteinturier

et al (1991)

Morro Do Cachimbo

Tower (60 m) Belo Horizonte Brazil

20

Courtesy Prof Dr Silverio Visacro Filho Lightning Research Center (UFMG-CEMIG)

Lightning Parameters Derived from Direct Current Measurements ndash

Brazil

21

First Stroke

Subsequent Strokes

404

52

163

099

Optical Measurements of Return-Stroke Speed

22

Optical intensity (in millivolts

at the input of the oscilloscope) vs time waveforms at four different heights 7 63 117 and 170 m

above the lightning termination point for stroke 1 in flash F0336 Adapted from Olsen et al (2004)

23

Reference St Dev ms Comments

Natural Lightning

Boyle and Orville (1976)

20 x 107 12 x 108 071 x 108 26 x 107 12 Streak camera 2-D speed

Idone and Orville (1982)

29 x 107 24 x 108 11 x 108 47 x 107 63 Streak camera2-D speed

Mach and Rust (1989a Fig 7)

20 x 107

80 x 10726 x 108

gt28 x 1085 x 107

7 x 1075443

Long channelShort channel (Photoelectric 2-D)

Triggered Lightning

Hubert and Mouget (1981)

45 x 107 17 x 108 99 x 107 41 x 107 13 Photoelectric3-D speed

Idone et al (1984) 67 x 107 17 x 108 12 x 108 27 x 107 56 Streak camera 3-D speed

Willett et al (1988)

10 x 108 15 x 108 12 x 108 16 x 107 9 Streak camera 2-D speed

Willett et al (1989a)

12 x 108 19 x 108 15 x 108 17 x 107 18 Streak camera 2-D speed

Mach and Rust (1989a Fig 8)

60 x 107

60 x 10716 x 108

20 x 1082 x 107

4 x 1074039

Long channelShort channel(Photoelectric 2-D)

Min ms Max ms Mean ms Sample

Size

13 plusmn03 x 108

19 plusmn07 x 108

12 plusmn03 x 108

14 plusmn04 x 108

Summary of measured return stroke speeds averaged over the visible part of the channel in natural and triggered negative lightning Adapted from Rakov

et al (1992b)

Return-Stroke Speed Near Ground

24

Height Above Ground

7-63 m

63-117 m

117-170

m

12

16

15

12121213

18

16

16

17

18 18

1512

Return-stroke speed profiles estimated tracking the 20 point on the light-pulse front for triggered lightning flash F0336 (Olsen et al 2004)

Return-Stroke Speed vs Return-Stroke Peak Current

25

Return-stroke speed vs peak current for 29 triggered-lightning strokes observed at the Kennedy Space Center (KSC) Florida in 1986 and reported by Mach and Rust (1989a) and 18 triggered-lightning strokes from the 1987 KSC experiments reported by Willett et al

(1989a) Peak curent shown in the scatter plot as 38 kA may be an underestimate Note that the linear correlation coefficients (r) for both data sets are low and negative not in support of the often assumed relationship between these two lightning parameters

00

05

10

15

20

25

0 5 10 15 20 25 30 35 40 45

Return-Stroke Peak Current kA

Ret

urn-

Stro

ke S

peed

108 m

s

Mach and Rust (1989a) r = -008

Willett el al (1998a) r = -027

First Return Stroke

Electric field waveforms of a first return stroke The waveform is shown on two time scales 5 μsdiv

and 10 μsdiv The fields are normalized to a distance of 100 km L denotes individual leader pulses F slow front and R fast transition Also marked are the small secondary peak or shoulder α

and the larger subsidiary peaks a b and c Adapted from Weidman and Krider

(1978)

-20 -15 -10 -5 0 5 10 15 20

5

microsdiv

10

microsdiv

-60 -40 -20 0 20 40 60 80

26

Subsequent Return Strokes

-20 -15 -10 -5 0 5 10 15 20

5 microsdiv

5 microsdiv

10 microsdiv

10 microsdiv

-60 -40 -20 0 20 40 60 80

Electric field waveforms of (b) a subsequent return stroke initiated by a dart-stepped leader and (c) a subsequent return stroke initiated by a dart leader showing the fine structure both before and after the initial field peak Each waveform is shown on two time scales 5 μsdiv

and 10 μsdiv The fields are normalized to a distance of 100 km L denotes individual leader pulses F slow front and R fast transition Also marked are the small secondary peak or shoulder α

and the larger subsidiary peaks a b and c Adapted from Weidman and Krider

(1978)

27

First Return Stroke Electric Field Derivative

Examples of (top) the time derivative of the electric field intensity dEdt

and (bottom)

the electric field intensity E produced by a first return stroke at a distance of about 36 km over the Atlantic Ocean The propagation path was almost entirely over salt water The vertical arrow under the E record shows the time of the dEdt

trigger Adapted from Krider

et al (1996)

28

Return Strokes Measured Parameters

Parameters of microsecond-scale electric field waveforms produced by negative return strokes

Parameter Location First strokes Subsequent strokes

Sample size Mean SD Sample size Mean SD

Initial peak (V m‐1) (normalized to 100 km)Rakov

and Uman

(1990b)

Cooray

and Lundquist (1982)Lin et al (1979)

Florida

SwedenKSCOcala

76

5535129

59 (GM)

536758

273825

232a

38b

8359

27(GM)41(GM)

5043

2215

Zero‐crossing time (μs)Cooray

and Lundquist (1985)

Lin et al (1979)

SwedenSri LankaFlorida

1029146c

498954

123018

9414377c

394236

81417

Zero‐to‐peak rise time (μs)Master et al (1984)Cooray

and Lundquist (1982)Lin et al (1979)

FloridaSwedenKSCOcala

1051405129

44702427

18201213

220

8359

28

1519

15

0807

10‐90 percent rise time (μs)Master et al (1984) Florida 105 26 12 220 15 09

Slow front duration

(μs)Master et al (1984)Cooray

and Lundquist (1982)Weidman and Krider

(1978)

FloridaSwedenFlorida

105826290

29504041

13201716

44 120 34d

060921

020509

29

Return Strokes Measured ParametersParameters of microsecond-scale electric field waveforms produced by negative return strokes (contrsquod)

Parameter Locatio

nFirst strokes Subsequent strokes

Sample size

Mean SD Sample size Mean SD

Slow front amplitude as percentage of peakMaster et al (1984)Cooray

and Lundquist (1982)Weidman and Krider

(1978)

FloridaSwedenFlorida

105836290

28415040

15112020

4412034d

202540

101020

Fast

transition 10-90 percent risetime

(ns)Master et al (1984)Weidman and Krider

(1978)

Weidman and Krider

(1980a 1984)

Weidman (1982)

FloridaFlorida

Florida

1023815125

97020020090

68010010040

2178034

610200150

27040100

Peak time derivative (normalized to100 km ) (V m-1

μs-1)Krider

et al (1996) Florida 63 39 11

Time derivative pulse width at half-peak value (ns)

Krider

et al (1996) Florida 61 100 20

If not specicied

otherwise multiple lines for a given source for the same location correspond to different thunderstorms GM = geometric mean value a better characteristic of the distribution of initial field peaks since this distribution is approximately log-normala

Strokes following previously formed channelb

Strokes creating new termination on groundcBoth

electric and magnetic fieldsd

Subsequent strokes initiated by dart-stepped leaders Other subsequent strokes studied by Weidman and

Krider

(1978) were initiated by dart leaders

30

• Slide Number 1
• Slide Number 2
• Slide Number 3
• Slide Number 4
• Slide Number 5
• Slide Number 6
• Slide Number 7
• Slide Number 8
• Slide Number 9
• Slide Number 10
• Slide Number 11
• Slide Number 12
• Return-Stroke Fields Variation with Distance
• Return-Stroke Fields Variation with Distance
• Slide Number 15
• Slide Number 16
• Slide Number 17
• Slide Number 18
• Slide Number 19
• Slide Number 20
• Slide Number 21
• Slide Number 22
• Slide Number 23
• Slide Number 24
• Slide Number 25
• First Return Stroke
• Subsequent Return Strokes
• First Return Stroke Electric Field Derivative
• Return Strokes Measured Parameters
• Return Strokes Measured Parameters

dIdt

in Rocket-Triggered Lightning ( ~100 kAμs)

19

Relation between the peak rate of current rise dIdt and the peak current I from triggered-lightning experiments conducted at the NASA Kennedy Space Center Florida in 19851987 and 1988 and in France in 1986 The regression line for each year is shown the sample size N and the regression equation are given in table Adapted from Leteinturier

et al (1991)

Morro Do Cachimbo

Tower (60 m) Belo Horizonte Brazil

20

Courtesy Prof Dr Silverio Visacro Filho Lightning Research Center (UFMG-CEMIG)

Lightning Parameters Derived from Direct Current Measurements ndash

Brazil

21

First Stroke

Subsequent Strokes

404

52

163

099

Optical Measurements of Return-Stroke Speed

22

Optical intensity (in millivolts

at the input of the oscilloscope) vs time waveforms at four different heights 7 63 117 and 170 m

above the lightning termination point for stroke 1 in flash F0336 Adapted from Olsen et al (2004)

23

Reference St Dev ms Comments

Natural Lightning

Boyle and Orville (1976)

20 x 107 12 x 108 071 x 108 26 x 107 12 Streak camera 2-D speed

Idone and Orville (1982)

29 x 107 24 x 108 11 x 108 47 x 107 63 Streak camera2-D speed

Mach and Rust (1989a Fig 7)

20 x 107

80 x 10726 x 108

gt28 x 1085 x 107

7 x 1075443

Long channelShort channel (Photoelectric 2-D)

Triggered Lightning

Hubert and Mouget (1981)

45 x 107 17 x 108 99 x 107 41 x 107 13 Photoelectric3-D speed

Idone et al (1984) 67 x 107 17 x 108 12 x 108 27 x 107 56 Streak camera 3-D speed

Willett et al (1988)

10 x 108 15 x 108 12 x 108 16 x 107 9 Streak camera 2-D speed

Willett et al (1989a)

12 x 108 19 x 108 15 x 108 17 x 107 18 Streak camera 2-D speed

Mach and Rust (1989a Fig 8)

60 x 107

60 x 10716 x 108

20 x 1082 x 107

4 x 1074039

Long channelShort channel(Photoelectric 2-D)

Min ms Max ms Mean ms Sample

Size

13 plusmn03 x 108

19 plusmn07 x 108

12 plusmn03 x 108

14 plusmn04 x 108

Summary of measured return stroke speeds averaged over the visible part of the channel in natural and triggered negative lightning Adapted from Rakov

et al (1992b)

Return-Stroke Speed Near Ground

24

Height Above Ground

7-63 m

63-117 m

117-170

m

12

16

15

12121213

18

16

16

17

18 18

1512

Return-stroke speed profiles estimated tracking the 20 point on the light-pulse front for triggered lightning flash F0336 (Olsen et al 2004)

Return-Stroke Speed vs Return-Stroke Peak Current

25

Return-stroke speed vs peak current for 29 triggered-lightning strokes observed at the Kennedy Space Center (KSC) Florida in 1986 and reported by Mach and Rust (1989a) and 18 triggered-lightning strokes from the 1987 KSC experiments reported by Willett et al

(1989a) Peak curent shown in the scatter plot as 38 kA may be an underestimate Note that the linear correlation coefficients (r) for both data sets are low and negative not in support of the often assumed relationship between these two lightning parameters

00

05

10

15

20

25

0 5 10 15 20 25 30 35 40 45

Return-Stroke Peak Current kA

Ret

urn-

Stro

ke S

peed

108 m

s

Mach and Rust (1989a) r = -008

Willett el al (1998a) r = -027

First Return Stroke

Electric field waveforms of a first return stroke The waveform is shown on two time scales 5 μsdiv

and 10 μsdiv The fields are normalized to a distance of 100 km L denotes individual leader pulses F slow front and R fast transition Also marked are the small secondary peak or shoulder α

and the larger subsidiary peaks a b and c Adapted from Weidman and Krider

(1978)

-20 -15 -10 -5 0 5 10 15 20

5

microsdiv

10

microsdiv

-60 -40 -20 0 20 40 60 80

26

Subsequent Return Strokes

-20 -15 -10 -5 0 5 10 15 20

5 microsdiv

5 microsdiv

10 microsdiv

10 microsdiv

-60 -40 -20 0 20 40 60 80

Electric field waveforms of (b) a subsequent return stroke initiated by a dart-stepped leader and (c) a subsequent return stroke initiated by a dart leader showing the fine structure both before and after the initial field peak Each waveform is shown on two time scales 5 μsdiv

and 10 μsdiv The fields are normalized to a distance of 100 km L denotes individual leader pulses F slow front and R fast transition Also marked are the small secondary peak or shoulder α

and the larger subsidiary peaks a b and c Adapted from Weidman and Krider

(1978)

27

First Return Stroke Electric Field Derivative

Examples of (top) the time derivative of the electric field intensity dEdt

and (bottom)

the electric field intensity E produced by a first return stroke at a distance of about 36 km over the Atlantic Ocean The propagation path was almost entirely over salt water The vertical arrow under the E record shows the time of the dEdt

trigger Adapted from Krider

et al (1996)

28

Return Strokes Measured Parameters

Parameters of microsecond-scale electric field waveforms produced by negative return strokes

Parameter Location First strokes Subsequent strokes

Sample size Mean SD Sample size Mean SD

Initial peak (V m‐1) (normalized to 100 km)Rakov

and Uman

(1990b)

Cooray

and Lundquist (1982)Lin et al (1979)

Florida

SwedenKSCOcala

76

5535129

59 (GM)

536758

273825

232a

38b

8359

27(GM)41(GM)

5043

2215

Zero‐crossing time (μs)Cooray

and Lundquist (1985)

Lin et al (1979)

SwedenSri LankaFlorida

1029146c

498954

123018

9414377c

394236

81417

Zero‐to‐peak rise time (μs)Master et al (1984)Cooray

and Lundquist (1982)Lin et al (1979)

FloridaSwedenKSCOcala

1051405129

44702427

18201213

220

8359

28

1519

15

0807

10‐90 percent rise time (μs)Master et al (1984) Florida 105 26 12 220 15 09

Slow front duration

(μs)Master et al (1984)Cooray

and Lundquist (1982)Weidman and Krider

(1978)

FloridaSwedenFlorida

105826290

29504041

13201716

44 120 34d

060921

020509

29

Return Strokes Measured ParametersParameters of microsecond-scale electric field waveforms produced by negative return strokes (contrsquod)

Parameter Locatio

nFirst strokes Subsequent strokes

Sample size

Mean SD Sample size Mean SD

Slow front amplitude as percentage of peakMaster et al (1984)Cooray

and Lundquist (1982)Weidman and Krider

(1978)

FloridaSwedenFlorida

105836290

28415040

15112020

4412034d

202540

101020

Fast

transition 10-90 percent risetime

(ns)Master et al (1984)Weidman and Krider

(1978)

Weidman and Krider

(1980a 1984)

Weidman (1982)

FloridaFlorida

Florida

1023815125

97020020090

68010010040

2178034

610200150

27040100

Peak time derivative (normalized to100 km ) (V m-1

μs-1)Krider

et al (1996) Florida 63 39 11

Time derivative pulse width at half-peak value (ns)

Krider

et al (1996) Florida 61 100 20

If not specicied

otherwise multiple lines for a given source for the same location correspond to different thunderstorms GM = geometric mean value a better characteristic of the distribution of initial field peaks since this distribution is approximately log-normala

Strokes following previously formed channelb

Strokes creating new termination on groundcBoth

electric and magnetic fieldsd

Subsequent strokes initiated by dart-stepped leaders Other subsequent strokes studied by Weidman and

Krider

(1978) were initiated by dart leaders

30

• Slide Number 1
• Slide Number 2
• Slide Number 3
• Slide Number 4
• Slide Number 5
• Slide Number 6
• Slide Number 7
• Slide Number 8
• Slide Number 9
• Slide Number 10
• Slide Number 11
• Slide Number 12
• Return-Stroke Fields Variation with Distance
• Return-Stroke Fields Variation with Distance
• Slide Number 15
• Slide Number 16
• Slide Number 17
• Slide Number 18
• Slide Number 19
• Slide Number 20
• Slide Number 21
• Slide Number 22
• Slide Number 23
• Slide Number 24
• Slide Number 25
• First Return Stroke
• Subsequent Return Strokes
• First Return Stroke Electric Field Derivative
• Return Strokes Measured Parameters
• Return Strokes Measured Parameters

Morro Do Cachimbo

Tower (60 m) Belo Horizonte Brazil

20

Courtesy Prof Dr Silverio Visacro Filho Lightning Research Center (UFMG-CEMIG)

Lightning Parameters Derived from Direct Current Measurements ndash

Brazil

21

First Stroke

Subsequent Strokes

404

52

163

099

Optical Measurements of Return-Stroke Speed

22

Optical intensity (in millivolts

at the input of the oscilloscope) vs time waveforms at four different heights 7 63 117 and 170 m

above the lightning termination point for stroke 1 in flash F0336 Adapted from Olsen et al (2004)

23

Reference St Dev ms Comments

Natural Lightning

Boyle and Orville (1976)

20 x 107 12 x 108 071 x 108 26 x 107 12 Streak camera 2-D speed

Idone and Orville (1982)

29 x 107 24 x 108 11 x 108 47 x 107 63 Streak camera2-D speed

Mach and Rust (1989a Fig 7)

20 x 107

80 x 10726 x 108

gt28 x 1085 x 107

7 x 1075443

Long channelShort channel (Photoelectric 2-D)

Triggered Lightning

Hubert and Mouget (1981)

45 x 107 17 x 108 99 x 107 41 x 107 13 Photoelectric3-D speed

Idone et al (1984) 67 x 107 17 x 108 12 x 108 27 x 107 56 Streak camera 3-D speed

Willett et al (1988)

10 x 108 15 x 108 12 x 108 16 x 107 9 Streak camera 2-D speed

Willett et al (1989a)

12 x 108 19 x 108 15 x 108 17 x 107 18 Streak camera 2-D speed

Mach and Rust (1989a Fig 8)

60 x 107

60 x 10716 x 108

20 x 1082 x 107

4 x 1074039

Long channelShort channel(Photoelectric 2-D)

Min ms Max ms Mean ms Sample

Size

13 plusmn03 x 108

19 plusmn07 x 108

12 plusmn03 x 108

14 plusmn04 x 108

Summary of measured return stroke speeds averaged over the visible part of the channel in natural and triggered negative lightning Adapted from Rakov

et al (1992b)

Return-Stroke Speed Near Ground

24

Height Above Ground

7-63 m

63-117 m

117-170

m

12

16

15

12121213

18

16

16

17

18 18

1512

Return-stroke speed profiles estimated tracking the 20 point on the light-pulse front for triggered lightning flash F0336 (Olsen et al 2004)

Return-Stroke Speed vs Return-Stroke Peak Current

25

Return-stroke speed vs peak current for 29 triggered-lightning strokes observed at the Kennedy Space Center (KSC) Florida in 1986 and reported by Mach and Rust (1989a) and 18 triggered-lightning strokes from the 1987 KSC experiments reported by Willett et al

(1989a) Peak curent shown in the scatter plot as 38 kA may be an underestimate Note that the linear correlation coefficients (r) for both data sets are low and negative not in support of the often assumed relationship between these two lightning parameters

00

05

10

15

20

25

0 5 10 15 20 25 30 35 40 45

Return-Stroke Peak Current kA

Ret

urn-

Stro

ke S

peed

108 m

s

Mach and Rust (1989a) r = -008

Willett el al (1998a) r = -027

First Return Stroke

Electric field waveforms of a first return stroke The waveform is shown on two time scales 5 μsdiv

and 10 μsdiv The fields are normalized to a distance of 100 km L denotes individual leader pulses F slow front and R fast transition Also marked are the small secondary peak or shoulder α

and the larger subsidiary peaks a b and c Adapted from Weidman and Krider

(1978)

-20 -15 -10 -5 0 5 10 15 20

5

microsdiv

10

microsdiv

-60 -40 -20 0 20 40 60 80

26

Subsequent Return Strokes

-20 -15 -10 -5 0 5 10 15 20

5 microsdiv

5 microsdiv

10 microsdiv

10 microsdiv

-60 -40 -20 0 20 40 60 80

Electric field waveforms of (b) a subsequent return stroke initiated by a dart-stepped leader and (c) a subsequent return stroke initiated by a dart leader showing the fine structure both before and after the initial field peak Each waveform is shown on two time scales 5 μsdiv

and 10 μsdiv The fields are normalized to a distance of 100 km L denotes individual leader pulses F slow front and R fast transition Also marked are the small secondary peak or shoulder α

and the larger subsidiary peaks a b and c Adapted from Weidman and Krider

(1978)

27

First Return Stroke Electric Field Derivative

Examples of (top) the time derivative of the electric field intensity dEdt

and (bottom)

the electric field intensity E produced by a first return stroke at a distance of about 36 km over the Atlantic Ocean The propagation path was almost entirely over salt water The vertical arrow under the E record shows the time of the dEdt

trigger Adapted from Krider

et al (1996)

28

Return Strokes Measured Parameters

Parameters of microsecond-scale electric field waveforms produced by negative return strokes

Parameter Location First strokes Subsequent strokes

Sample size Mean SD Sample size Mean SD

Initial peak (V m‐1) (normalized to 100 km)Rakov

and Uman

(1990b)

Cooray

and Lundquist (1982)Lin et al (1979)

Florida

SwedenKSCOcala

76

5535129

59 (GM)

536758

273825

232a

38b

8359

27(GM)41(GM)

5043

2215

Zero‐crossing time (μs)Cooray

and Lundquist (1985)

Lin et al (1979)

SwedenSri LankaFlorida

1029146c

498954

123018

9414377c

394236

81417

Zero‐to‐peak rise time (μs)Master et al (1984)Cooray

and Lundquist (1982)Lin et al (1979)

FloridaSwedenKSCOcala

1051405129

44702427

18201213

220

8359

28

1519

15

0807

10‐90 percent rise time (μs)Master et al (1984) Florida 105 26 12 220 15 09

Slow front duration

(μs)Master et al (1984)Cooray

and Lundquist (1982)Weidman and Krider

(1978)

FloridaSwedenFlorida

105826290

29504041

13201716

44 120 34d

060921

020509

29

Return Strokes Measured ParametersParameters of microsecond-scale electric field waveforms produced by negative return strokes (contrsquod)

Parameter Locatio

nFirst strokes Subsequent strokes

Sample size

Mean SD Sample size Mean SD

Slow front amplitude as percentage of peakMaster et al (1984)Cooray

and Lundquist (1982)Weidman and Krider

(1978)

FloridaSwedenFlorida

105836290

28415040

15112020

4412034d

202540

101020

Fast

transition 10-90 percent risetime

(ns)Master et al (1984)Weidman and Krider

(1978)

Weidman and Krider

(1980a 1984)

Weidman (1982)

FloridaFlorida

Florida

1023815125

97020020090

68010010040

2178034

610200150

27040100

Peak time derivative (normalized to100 km ) (V m-1

μs-1)Krider

et al (1996) Florida 63 39 11

Time derivative pulse width at half-peak value (ns)

Krider

et al (1996) Florida 61 100 20

If not specicied

otherwise multiple lines for a given source for the same location correspond to different thunderstorms GM = geometric mean value a better characteristic of the distribution of initial field peaks since this distribution is approximately log-normala

Strokes following previously formed channelb

Strokes creating new termination on groundcBoth

electric and magnetic fieldsd

Subsequent strokes initiated by dart-stepped leaders Other subsequent strokes studied by Weidman and

Krider

(1978) were initiated by dart leaders

30

• Slide Number 1
• Slide Number 2
• Slide Number 3
• Slide Number 4
• Slide Number 5
• Slide Number 6
• Slide Number 7
• Slide Number 8
• Slide Number 9
• Slide Number 10
• Slide Number 11
• Slide Number 12
• Return-Stroke Fields Variation with Distance
• Return-Stroke Fields Variation with Distance
• Slide Number 15
• Slide Number 16
• Slide Number 17
• Slide Number 18
• Slide Number 19
• Slide Number 20
• Slide Number 21
• Slide Number 22
• Slide Number 23
• Slide Number 24
• Slide Number 25
• First Return Stroke
• Subsequent Return Strokes
• First Return Stroke Electric Field Derivative
• Return Strokes Measured Parameters
• Return Strokes Measured Parameters

Lightning Parameters Derived from Direct Current Measurements ndash

Brazil

21

First Stroke

Subsequent Strokes

404

52

163

099

Optical Measurements of Return-Stroke Speed

22

Optical intensity (in millivolts

at the input of the oscilloscope) vs time waveforms at four different heights 7 63 117 and 170 m

above the lightning termination point for stroke 1 in flash F0336 Adapted from Olsen et al (2004)

23

Reference St Dev ms Comments

Natural Lightning

Boyle and Orville (1976)

20 x 107 12 x 108 071 x 108 26 x 107 12 Streak camera 2-D speed

Idone and Orville (1982)

29 x 107 24 x 108 11 x 108 47 x 107 63 Streak camera2-D speed

Mach and Rust (1989a Fig 7)

20 x 107

80 x 10726 x 108

gt28 x 1085 x 107

7 x 1075443

Long channelShort channel (Photoelectric 2-D)

Triggered Lightning

Hubert and Mouget (1981)

45 x 107 17 x 108 99 x 107 41 x 107 13 Photoelectric3-D speed

Idone et al (1984) 67 x 107 17 x 108 12 x 108 27 x 107 56 Streak camera 3-D speed

Willett et al (1988)

10 x 108 15 x 108 12 x 108 16 x 107 9 Streak camera 2-D speed

Willett et al (1989a)

12 x 108 19 x 108 15 x 108 17 x 107 18 Streak camera 2-D speed

Mach and Rust (1989a Fig 8)

60 x 107

60 x 10716 x 108

20 x 1082 x 107

4 x 1074039

Long channelShort channel(Photoelectric 2-D)

Min ms Max ms Mean ms Sample

Size

13 plusmn03 x 108

19 plusmn07 x 108

12 plusmn03 x 108

14 plusmn04 x 108

Summary of measured return stroke speeds averaged over the visible part of the channel in natural and triggered negative lightning Adapted from Rakov

et al (1992b)

Return-Stroke Speed Near Ground

24

Height Above Ground

7-63 m

63-117 m

117-170

m

12

16

15

12121213

18

16

16

17

18 18

1512

Return-stroke speed profiles estimated tracking the 20 point on the light-pulse front for triggered lightning flash F0336 (Olsen et al 2004)

Return-Stroke Speed vs Return-Stroke Peak Current

25

Return-stroke speed vs peak current for 29 triggered-lightning strokes observed at the Kennedy Space Center (KSC) Florida in 1986 and reported by Mach and Rust (1989a) and 18 triggered-lightning strokes from the 1987 KSC experiments reported by Willett et al

(1989a) Peak curent shown in the scatter plot as 38 kA may be an underestimate Note that the linear correlation coefficients (r) for both data sets are low and negative not in support of the often assumed relationship between these two lightning parameters

00

05

10

15

20

25

0 5 10 15 20 25 30 35 40 45

Return-Stroke Peak Current kA

Ret

urn-

Stro

ke S

peed

108 m

s

Mach and Rust (1989a) r = -008

Willett el al (1998a) r = -027

First Return Stroke

Electric field waveforms of a first return stroke The waveform is shown on two time scales 5 μsdiv

and 10 μsdiv The fields are normalized to a distance of 100 km L denotes individual leader pulses F slow front and R fast transition Also marked are the small secondary peak or shoulder α

and the larger subsidiary peaks a b and c Adapted from Weidman and Krider

(1978)

-20 -15 -10 -5 0 5 10 15 20

5

microsdiv

10

microsdiv

-60 -40 -20 0 20 40 60 80

26

Subsequent Return Strokes

-20 -15 -10 -5 0 5 10 15 20

5 microsdiv

5 microsdiv

10 microsdiv

10 microsdiv

-60 -40 -20 0 20 40 60 80

Electric field waveforms of (b) a subsequent return stroke initiated by a dart-stepped leader and (c) a subsequent return stroke initiated by a dart leader showing the fine structure both before and after the initial field peak Each waveform is shown on two time scales 5 μsdiv

and 10 μsdiv The fields are normalized to a distance of 100 km L denotes individual leader pulses F slow front and R fast transition Also marked are the small secondary peak or shoulder α

and the larger subsidiary peaks a b and c Adapted from Weidman and Krider

(1978)

27

First Return Stroke Electric Field Derivative

Examples of (top) the time derivative of the electric field intensity dEdt

and (bottom)

the electric field intensity E produced by a first return stroke at a distance of about 36 km over the Atlantic Ocean The propagation path was almost entirely over salt water The vertical arrow under the E record shows the time of the dEdt

trigger Adapted from Krider

et al (1996)

28

Return Strokes Measured Parameters

Parameters of microsecond-scale electric field waveforms produced by negative return strokes

Parameter Location First strokes Subsequent strokes

Sample size Mean SD Sample size Mean SD

Initial peak (V m‐1) (normalized to 100 km)Rakov

and Uman

(1990b)

Cooray

and Lundquist (1982)Lin et al (1979)

Florida

SwedenKSCOcala

76

5535129

59 (GM)

536758

273825

232a

38b

8359

27(GM)41(GM)

5043

2215

Zero‐crossing time (μs)Cooray

and Lundquist (1985)

Lin et al (1979)

SwedenSri LankaFlorida

1029146c

498954

123018

9414377c

394236

81417

Zero‐to‐peak rise time (μs)Master et al (1984)Cooray

and Lundquist (1982)Lin et al (1979)

FloridaSwedenKSCOcala

1051405129

44702427

18201213

220

8359

28

1519

15

0807

10‐90 percent rise time (μs)Master et al (1984) Florida 105 26 12 220 15 09

Slow front duration

(μs)Master et al (1984)Cooray

and Lundquist (1982)Weidman and Krider

(1978)

FloridaSwedenFlorida

105826290

29504041

13201716

44 120 34d

060921

020509

29

Return Strokes Measured ParametersParameters of microsecond-scale electric field waveforms produced by negative return strokes (contrsquod)

Parameter Locatio

nFirst strokes Subsequent strokes

Sample size

Mean SD Sample size Mean SD

Slow front amplitude as percentage of peakMaster et al (1984)Cooray

and Lundquist (1982)Weidman and Krider

(1978)

FloridaSwedenFlorida

105836290

28415040

15112020

4412034d

202540

101020

Fast

transition 10-90 percent risetime

(ns)Master et al (1984)Weidman and Krider

(1978)

Weidman and Krider

(1980a 1984)

Weidman (1982)

FloridaFlorida

Florida

1023815125

97020020090

68010010040

2178034

610200150

27040100

Peak time derivative (normalized to100 km ) (V m-1

μs-1)Krider

et al (1996) Florida 63 39 11

Time derivative pulse width at half-peak value (ns)

Krider

et al (1996) Florida 61 100 20

If not specicied

otherwise multiple lines for a given source for the same location correspond to different thunderstorms GM = geometric mean value a better characteristic of the distribution of initial field peaks since this distribution is approximately log-normala

Strokes following previously formed channelb

Strokes creating new termination on groundcBoth

electric and magnetic fieldsd

Subsequent strokes initiated by dart-stepped leaders Other subsequent strokes studied by Weidman and

Krider

(1978) were initiated by dart leaders

30

• Slide Number 1
• Slide Number 2
• Slide Number 3
• Slide Number 4
• Slide Number 5
• Slide Number 6
• Slide Number 7
• Slide Number 8
• Slide Number 9
• Slide Number 10
• Slide Number 11
• Slide Number 12
• Return-Stroke Fields Variation with Distance
• Return-Stroke Fields Variation with Distance
• Slide Number 15
• Slide Number 16
• Slide Number 17
• Slide Number 18
• Slide Number 19
• Slide Number 20
• Slide Number 21
• Slide Number 22
• Slide Number 23
• Slide Number 24
• Slide Number 25
• First Return Stroke
• Subsequent Return Strokes
• First Return Stroke Electric Field Derivative
• Return Strokes Measured Parameters
• Return Strokes Measured Parameters

Optical Measurements of Return-Stroke Speed

22

Optical intensity (in millivolts

at the input of the oscilloscope) vs time waveforms at four different heights 7 63 117 and 170 m

above the lightning termination point for stroke 1 in flash F0336 Adapted from Olsen et al (2004)

23

Reference St Dev ms Comments

Natural Lightning

Boyle and Orville (1976)

20 x 107 12 x 108 071 x 108 26 x 107 12 Streak camera 2-D speed

Idone and Orville (1982)

29 x 107 24 x 108 11 x 108 47 x 107 63 Streak camera2-D speed

Mach and Rust (1989a Fig 7)

20 x 107

80 x 10726 x 108

gt28 x 1085 x 107

7 x 1075443

Long channelShort channel (Photoelectric 2-D)

Triggered Lightning

Hubert and Mouget (1981)

45 x 107 17 x 108 99 x 107 41 x 107 13 Photoelectric3-D speed

Idone et al (1984) 67 x 107 17 x 108 12 x 108 27 x 107 56 Streak camera 3-D speed

Willett et al (1988)

10 x 108 15 x 108 12 x 108 16 x 107 9 Streak camera 2-D speed

Willett et al (1989a)

12 x 108 19 x 108 15 x 108 17 x 107 18 Streak camera 2-D speed

Mach and Rust (1989a Fig 8)

60 x 107

60 x 10716 x 108

20 x 1082 x 107

4 x 1074039

Long channelShort channel(Photoelectric 2-D)

Min ms Max ms Mean ms Sample

Size

13 plusmn03 x 108

19 plusmn07 x 108

12 plusmn03 x 108

14 plusmn04 x 108

Summary of measured return stroke speeds averaged over the visible part of the channel in natural and triggered negative lightning Adapted from Rakov

et al (1992b)

Return-Stroke Speed Near Ground

24

Height Above Ground

7-63 m

63-117 m

117-170

m

12

16

15

12121213

18

16

16

17

18 18

1512

Return-stroke speed profiles estimated tracking the 20 point on the light-pulse front for triggered lightning flash F0336 (Olsen et al 2004)

Return-Stroke Speed vs Return-Stroke Peak Current

25

Return-stroke speed vs peak current for 29 triggered-lightning strokes observed at the Kennedy Space Center (KSC) Florida in 1986 and reported by Mach and Rust (1989a) and 18 triggered-lightning strokes from the 1987 KSC experiments reported by Willett et al

(1989a) Peak curent shown in the scatter plot as 38 kA may be an underestimate Note that the linear correlation coefficients (r) for both data sets are low and negative not in support of the often assumed relationship between these two lightning parameters

00

05

10

15

20

25

0 5 10 15 20 25 30 35 40 45

Return-Stroke Peak Current kA

Ret

urn-

Stro

ke S

peed

108 m

s

Mach and Rust (1989a) r = -008

Willett el al (1998a) r = -027

First Return Stroke

Electric field waveforms of a first return stroke The waveform is shown on two time scales 5 μsdiv

and 10 μsdiv The fields are normalized to a distance of 100 km L denotes individual leader pulses F slow front and R fast transition Also marked are the small secondary peak or shoulder α

and the larger subsidiary peaks a b and c Adapted from Weidman and Krider

(1978)

-20 -15 -10 -5 0 5 10 15 20

5

microsdiv

10

microsdiv

-60 -40 -20 0 20 40 60 80

26

Subsequent Return Strokes

-20 -15 -10 -5 0 5 10 15 20

5 microsdiv

5 microsdiv

10 microsdiv

10 microsdiv

-60 -40 -20 0 20 40 60 80

Electric field waveforms of (b) a subsequent return stroke initiated by a dart-stepped leader and (c) a subsequent return stroke initiated by a dart leader showing the fine structure both before and after the initial field peak Each waveform is shown on two time scales 5 μsdiv

and 10 μsdiv The fields are normalized to a distance of 100 km L denotes individual leader pulses F slow front and R fast transition Also marked are the small secondary peak or shoulder α

and the larger subsidiary peaks a b and c Adapted from Weidman and Krider

(1978)

27

First Return Stroke Electric Field Derivative

Examples of (top) the time derivative of the electric field intensity dEdt

and (bottom)

the electric field intensity E produced by a first return stroke at a distance of about 36 km over the Atlantic Ocean The propagation path was almost entirely over salt water The vertical arrow under the E record shows the time of the dEdt

trigger Adapted from Krider

et al (1996)

28

Return Strokes Measured Parameters

Parameters of microsecond-scale electric field waveforms produced by negative return strokes

Parameter Location First strokes Subsequent strokes

Sample size Mean SD Sample size Mean SD

Initial peak (V m‐1) (normalized to 100 km)Rakov

and Uman

(1990b)

Cooray

and Lundquist (1982)Lin et al (1979)

Florida

SwedenKSCOcala

76

5535129

59 (GM)

536758

273825

232a

38b

8359

27(GM)41(GM)

5043

2215

Zero‐crossing time (μs)Cooray

and Lundquist (1985)

Lin et al (1979)

SwedenSri LankaFlorida

1029146c

498954

123018

9414377c

394236

81417

Zero‐to‐peak rise time (μs)Master et al (1984)Cooray

and Lundquist (1982)Lin et al (1979)

FloridaSwedenKSCOcala

1051405129

44702427

18201213

220

8359

28

1519

15

0807

10‐90 percent rise time (μs)Master et al (1984) Florida 105 26 12 220 15 09

Slow front duration

(μs)Master et al (1984)Cooray

and Lundquist (1982)Weidman and Krider

(1978)

FloridaSwedenFlorida

105826290

29504041

13201716

44 120 34d

060921

020509

29

Return Strokes Measured ParametersParameters of microsecond-scale electric field waveforms produced by negative return strokes (contrsquod)

Parameter Locatio

nFirst strokes Subsequent strokes

Sample size

Mean SD Sample size Mean SD

Slow front amplitude as percentage of peakMaster et al (1984)Cooray

and Lundquist (1982)Weidman and Krider

(1978)

FloridaSwedenFlorida

105836290

28415040

15112020

4412034d

202540

101020

Fast

transition 10-90 percent risetime

(ns)Master et al (1984)Weidman and Krider

(1978)

Weidman and Krider

(1980a 1984)

Weidman (1982)

FloridaFlorida

Florida

1023815125

97020020090

68010010040

2178034

610200150

27040100

Peak time derivative (normalized to100 km ) (V m-1

μs-1)Krider

et al (1996) Florida 63 39 11

Time derivative pulse width at half-peak value (ns)

Krider

et al (1996) Florida 61 100 20

If not specicied

otherwise multiple lines for a given source for the same location correspond to different thunderstorms GM = geometric mean value a better characteristic of the distribution of initial field peaks since this distribution is approximately log-normala

Strokes following previously formed channelb

Strokes creating new termination on groundcBoth

electric and magnetic fieldsd

Subsequent strokes initiated by dart-stepped leaders Other subsequent strokes studied by Weidman and

Krider

(1978) were initiated by dart leaders

30

• Slide Number 1
• Slide Number 2
• Slide Number 3
• Slide Number 4
• Slide Number 5
• Slide Number 6
• Slide Number 7
• Slide Number 8
• Slide Number 9
• Slide Number 10
• Slide Number 11
• Slide Number 12
• Return-Stroke Fields Variation with Distance
• Return-Stroke Fields Variation with Distance
• Slide Number 15
• Slide Number 16
• Slide Number 17
• Slide Number 18
• Slide Number 19
• Slide Number 20
• Slide Number 21
• Slide Number 22
• Slide Number 23
• Slide Number 24
• Slide Number 25
• First Return Stroke
• Subsequent Return Strokes
• First Return Stroke Electric Field Derivative
• Return Strokes Measured Parameters
• Return Strokes Measured Parameters

23

Reference St Dev ms Comments

Natural Lightning

Boyle and Orville (1976)

20 x 107 12 x 108 071 x 108 26 x 107 12 Streak camera 2-D speed

Idone and Orville (1982)

29 x 107 24 x 108 11 x 108 47 x 107 63 Streak camera2-D speed

Mach and Rust (1989a Fig 7)

20 x 107

80 x 10726 x 108

gt28 x 1085 x 107

7 x 1075443

Long channelShort channel (Photoelectric 2-D)

Triggered Lightning

Hubert and Mouget (1981)

45 x 107 17 x 108 99 x 107 41 x 107 13 Photoelectric3-D speed

Idone et al (1984) 67 x 107 17 x 108 12 x 108 27 x 107 56 Streak camera 3-D speed

Willett et al (1988)

10 x 108 15 x 108 12 x 108 16 x 107 9 Streak camera 2-D speed

Willett et al (1989a)

12 x 108 19 x 108 15 x 108 17 x 107 18 Streak camera 2-D speed

Mach and Rust (1989a Fig 8)

60 x 107

60 x 10716 x 108

20 x 1082 x 107

4 x 1074039

Long channelShort channel(Photoelectric 2-D)

Min ms Max ms Mean ms Sample

Size

13 plusmn03 x 108

19 plusmn07 x 108

12 plusmn03 x 108

14 plusmn04 x 108

Summary of measured return stroke speeds averaged over the visible part of the channel in natural and triggered negative lightning Adapted from Rakov

et al (1992b)

Return-Stroke Speed Near Ground

24

Height Above Ground

7-63 m

63-117 m

117-170

m

12

16

15

12121213

18

16

16

17

18 18

1512

Return-stroke speed profiles estimated tracking the 20 point on the light-pulse front for triggered lightning flash F0336 (Olsen et al 2004)

Return-Stroke Speed vs Return-Stroke Peak Current

25

Return-stroke speed vs peak current for 29 triggered-lightning strokes observed at the Kennedy Space Center (KSC) Florida in 1986 and reported by Mach and Rust (1989a) and 18 triggered-lightning strokes from the 1987 KSC experiments reported by Willett et al

(1989a) Peak curent shown in the scatter plot as 38 kA may be an underestimate Note that the linear correlation coefficients (r) for both data sets are low and negative not in support of the often assumed relationship between these two lightning parameters

00

05

10

15

20

25

0 5 10 15 20 25 30 35 40 45

Return-Stroke Peak Current kA

Ret

urn-

Stro

ke S

peed

108 m

s

Mach and Rust (1989a) r = -008

Willett el al (1998a) r = -027

First Return Stroke

Electric field waveforms of a first return stroke The waveform is shown on two time scales 5 μsdiv

and 10 μsdiv The fields are normalized to a distance of 100 km L denotes individual leader pulses F slow front and R fast transition Also marked are the small secondary peak or shoulder α

and the larger subsidiary peaks a b and c Adapted from Weidman and Krider

(1978)

-20 -15 -10 -5 0 5 10 15 20

5

microsdiv

10

microsdiv

-60 -40 -20 0 20 40 60 80

26

Subsequent Return Strokes

-20 -15 -10 -5 0 5 10 15 20

5 microsdiv

5 microsdiv

10 microsdiv

10 microsdiv

-60 -40 -20 0 20 40 60 80

Electric field waveforms of (b) a subsequent return stroke initiated by a dart-stepped leader and (c) a subsequent return stroke initiated by a dart leader showing the fine structure both before and after the initial field peak Each waveform is shown on two time scales 5 μsdiv

and 10 μsdiv The fields are normalized to a distance of 100 km L denotes individual leader pulses F slow front and R fast transition Also marked are the small secondary peak or shoulder α

and the larger subsidiary peaks a b and c Adapted from Weidman and Krider

(1978)

27

First Return Stroke Electric Field Derivative

Examples of (top) the time derivative of the electric field intensity dEdt

and (bottom)

the electric field intensity E produced by a first return stroke at a distance of about 36 km over the Atlantic Ocean The propagation path was almost entirely over salt water The vertical arrow under the E record shows the time of the dEdt

trigger Adapted from Krider

et al (1996)

28

Return Strokes Measured Parameters

Parameters of microsecond-scale electric field waveforms produced by negative return strokes

Parameter Location First strokes Subsequent strokes

Sample size Mean SD Sample size Mean SD

Initial peak (V m‐1) (normalized to 100 km)Rakov

and Uman

(1990b)

Cooray

and Lundquist (1982)Lin et al (1979)

Florida

SwedenKSCOcala

76

5535129

59 (GM)

536758

273825

232a

38b

8359

27(GM)41(GM)

5043

2215

Zero‐crossing time (μs)Cooray

and Lundquist (1985)

Lin et al (1979)

SwedenSri LankaFlorida

1029146c

498954

123018

9414377c

394236

81417

Zero‐to‐peak rise time (μs)Master et al (1984)Cooray

and Lundquist (1982)Lin et al (1979)

FloridaSwedenKSCOcala

1051405129

44702427

18201213

220

8359

28

1519

15

0807

10‐90 percent rise time (μs)Master et al (1984) Florida 105 26 12 220 15 09

Slow front duration

(μs)Master et al (1984)Cooray

and Lundquist (1982)Weidman and Krider

(1978)

FloridaSwedenFlorida

105826290

29504041

13201716

44 120 34d

060921

020509

29

Return Strokes Measured ParametersParameters of microsecond-scale electric field waveforms produced by negative return strokes (contrsquod)

Parameter Locatio

nFirst strokes Subsequent strokes

Sample size

Mean SD Sample size Mean SD

Slow front amplitude as percentage of peakMaster et al (1984)Cooray

and Lundquist (1982)Weidman and Krider

(1978)

FloridaSwedenFlorida

105836290

28415040

15112020

4412034d

202540

101020

Fast

transition 10-90 percent risetime

(ns)Master et al (1984)Weidman and Krider

(1978)

Weidman and Krider

(1980a 1984)

Weidman (1982)

FloridaFlorida

Florida

1023815125

97020020090

68010010040

2178034

610200150

27040100

Peak time derivative (normalized to100 km ) (V m-1

μs-1)Krider

et al (1996) Florida 63 39 11

Time derivative pulse width at half-peak value (ns)

Krider

et al (1996) Florida 61 100 20

If not specicied

otherwise multiple lines for a given source for the same location correspond to different thunderstorms GM = geometric mean value a better characteristic of the distribution of initial field peaks since this distribution is approximately log-normala

Strokes following previously formed channelb

Strokes creating new termination on groundcBoth

electric and magnetic fieldsd

Subsequent strokes initiated by dart-stepped leaders Other subsequent strokes studied by Weidman and

Krider

(1978) were initiated by dart leaders

30

• Slide Number 1
• Slide Number 2
• Slide Number 3
• Slide Number 4
• Slide Number 5
• Slide Number 6
• Slide Number 7
• Slide Number 8
• Slide Number 9
• Slide Number 10
• Slide Number 11
• Slide Number 12
• Return-Stroke Fields Variation with Distance
• Return-Stroke Fields Variation with Distance
• Slide Number 15
• Slide Number 16
• Slide Number 17
• Slide Number 18
• Slide Number 19
• Slide Number 20
• Slide Number 21
• Slide Number 22
• Slide Number 23
• Slide Number 24
• Slide Number 25
• First Return Stroke
• Subsequent Return Strokes
• First Return Stroke Electric Field Derivative
• Return Strokes Measured Parameters
• Return Strokes Measured Parameters

Return-Stroke Speed Near Ground

24

Height Above Ground

7-63 m

63-117 m

117-170

m

12

16

15

12121213

18

16

16

17

18 18

1512

Return-stroke speed profiles estimated tracking the 20 point on the light-pulse front for triggered lightning flash F0336 (Olsen et al 2004)

Return-Stroke Speed vs Return-Stroke Peak Current

25

Return-stroke speed vs peak current for 29 triggered-lightning strokes observed at the Kennedy Space Center (KSC) Florida in 1986 and reported by Mach and Rust (1989a) and 18 triggered-lightning strokes from the 1987 KSC experiments reported by Willett et al

(1989a) Peak curent shown in the scatter plot as 38 kA may be an underestimate Note that the linear correlation coefficients (r) for both data sets are low and negative not in support of the often assumed relationship between these two lightning parameters

00

05

10

15

20

25

0 5 10 15 20 25 30 35 40 45

Return-Stroke Peak Current kA

Ret

urn-

Stro

ke S

peed

108 m

s

Mach and Rust (1989a) r = -008

Willett el al (1998a) r = -027

First Return Stroke

Electric field waveforms of a first return stroke The waveform is shown on two time scales 5 μsdiv

and 10 μsdiv The fields are normalized to a distance of 100 km L denotes individual leader pulses F slow front and R fast transition Also marked are the small secondary peak or shoulder α

and the larger subsidiary peaks a b and c Adapted from Weidman and Krider

(1978)

-20 -15 -10 -5 0 5 10 15 20

5

microsdiv

10

microsdiv

-60 -40 -20 0 20 40 60 80

26

Subsequent Return Strokes

-20 -15 -10 -5 0 5 10 15 20

5 microsdiv

5 microsdiv

10 microsdiv

10 microsdiv

-60 -40 -20 0 20 40 60 80

Electric field waveforms of (b) a subsequent return stroke initiated by a dart-stepped leader and (c) a subsequent return stroke initiated by a dart leader showing the fine structure both before and after the initial field peak Each waveform is shown on two time scales 5 μsdiv

and 10 μsdiv The fields are normalized to a distance of 100 km L denotes individual leader pulses F slow front and R fast transition Also marked are the small secondary peak or shoulder α

and the larger subsidiary peaks a b and c Adapted from Weidman and Krider

(1978)

27

First Return Stroke Electric Field Derivative

Examples of (top) the time derivative of the electric field intensity dEdt

and (bottom)

the electric field intensity E produced by a first return stroke at a distance of about 36 km over the Atlantic Ocean The propagation path was almost entirely over salt water The vertical arrow under the E record shows the time of the dEdt

trigger Adapted from Krider

et al (1996)

28

Return Strokes Measured Parameters

Parameters of microsecond-scale electric field waveforms produced by negative return strokes

Parameter Location First strokes Subsequent strokes

Sample size Mean SD Sample size Mean SD

Initial peak (V m‐1) (normalized to 100 km)Rakov

and Uman

(1990b)

Cooray

and Lundquist (1982)Lin et al (1979)

Florida

SwedenKSCOcala

76

5535129

59 (GM)

536758

273825

232a

38b

8359

27(GM)41(GM)

5043

2215

Zero‐crossing time (μs)Cooray

and Lundquist (1985)

Lin et al (1979)

SwedenSri LankaFlorida

1029146c

498954

123018

9414377c

394236

81417

Zero‐to‐peak rise time (μs)Master et al (1984)Cooray

and Lundquist (1982)Lin et al (1979)

FloridaSwedenKSCOcala

1051405129

44702427

18201213

220

8359

28

1519

15

0807

10‐90 percent rise time (μs)Master et al (1984) Florida 105 26 12 220 15 09

Slow front duration

(μs)Master et al (1984)Cooray

and Lundquist (1982)Weidman and Krider

(1978)

FloridaSwedenFlorida

105826290

29504041

13201716

44 120 34d

060921

020509

29

Return Strokes Measured ParametersParameters of microsecond-scale electric field waveforms produced by negative return strokes (contrsquod)

Parameter Locatio

nFirst strokes Subsequent strokes

Sample size

Mean SD Sample size Mean SD

Slow front amplitude as percentage of peakMaster et al (1984)Cooray

and Lundquist (1982)Weidman and Krider

(1978)

FloridaSwedenFlorida

105836290

28415040

15112020

4412034d

202540

101020

Fast

transition 10-90 percent risetime

(ns)Master et al (1984)Weidman and Krider

(1978)

Weidman and Krider

(1980a 1984)

Weidman (1982)

FloridaFlorida

Florida

1023815125

97020020090

68010010040

2178034

610200150

27040100

Peak time derivative (normalized to100 km ) (V m-1

μs-1)Krider

et al (1996) Florida 63 39 11

Time derivative pulse width at half-peak value (ns)

Krider

et al (1996) Florida 61 100 20

If not specicied

otherwise multiple lines for a given source for the same location correspond to different thunderstorms GM = geometric mean value a better characteristic of the distribution of initial field peaks since this distribution is approximately log-normala

Strokes following previously formed channelb

Strokes creating new termination on groundcBoth

electric and magnetic fieldsd

Subsequent strokes initiated by dart-stepped leaders Other subsequent strokes studied by Weidman and

Krider

(1978) were initiated by dart leaders

30

• Slide Number 1
• Slide Number 2
• Slide Number 3
• Slide Number 4
• Slide Number 5
• Slide Number 6
• Slide Number 7
• Slide Number 8
• Slide Number 9
• Slide Number 10
• Slide Number 11
• Slide Number 12
• Return-Stroke Fields Variation with Distance
• Return-Stroke Fields Variation with Distance
• Slide Number 15
• Slide Number 16
• Slide Number 17
• Slide Number 18
• Slide Number 19
• Slide Number 20
• Slide Number 21
• Slide Number 22
• Slide Number 23
• Slide Number 24
• Slide Number 25
• First Return Stroke
• Subsequent Return Strokes
• First Return Stroke Electric Field Derivative
• Return Strokes Measured Parameters
• Return Strokes Measured Parameters

Return-Stroke Speed vs Return-Stroke Peak Current

25

Return-stroke speed vs peak current for 29 triggered-lightning strokes observed at the Kennedy Space Center (KSC) Florida in 1986 and reported by Mach and Rust (1989a) and 18 triggered-lightning strokes from the 1987 KSC experiments reported by Willett et al

(1989a) Peak curent shown in the scatter plot as 38 kA may be an underestimate Note that the linear correlation coefficients (r) for both data sets are low and negative not in support of the often assumed relationship between these two lightning parameters

00

05

10

15

20

25

0 5 10 15 20 25 30 35 40 45

Return-Stroke Peak Current kA

Ret

urn-

Stro

ke S

peed

108 m

s

Mach and Rust (1989a) r = -008

Willett el al (1998a) r = -027

First Return Stroke

Electric field waveforms of a first return stroke The waveform is shown on two time scales 5 μsdiv

and 10 μsdiv The fields are normalized to a distance of 100 km L denotes individual leader pulses F slow front and R fast transition Also marked are the small secondary peak or shoulder α

and the larger subsidiary peaks a b and c Adapted from Weidman and Krider

(1978)

-20 -15 -10 -5 0 5 10 15 20

5

microsdiv

10

microsdiv

-60 -40 -20 0 20 40 60 80

26

Subsequent Return Strokes

-20 -15 -10 -5 0 5 10 15 20

5 microsdiv

5 microsdiv

10 microsdiv

10 microsdiv

-60 -40 -20 0 20 40 60 80

Electric field waveforms of (b) a subsequent return stroke initiated by a dart-stepped leader and (c) a subsequent return stroke initiated by a dart leader showing the fine structure both before and after the initial field peak Each waveform is shown on two time scales 5 μsdiv

and 10 μsdiv The fields are normalized to a distance of 100 km L denotes individual leader pulses F slow front and R fast transition Also marked are the small secondary peak or shoulder α

and the larger subsidiary peaks a b and c Adapted from Weidman and Krider

(1978)

27

First Return Stroke Electric Field Derivative

Examples of (top) the time derivative of the electric field intensity dEdt

and (bottom)

the electric field intensity E produced by a first return stroke at a distance of about 36 km over the Atlantic Ocean The propagation path was almost entirely over salt water The vertical arrow under the E record shows the time of the dEdt

trigger Adapted from Krider

et al (1996)

28

Return Strokes Measured Parameters

Parameters of microsecond-scale electric field waveforms produced by negative return strokes

Parameter Location First strokes Subsequent strokes

Sample size Mean SD Sample size Mean SD

Initial peak (V m‐1) (normalized to 100 km)Rakov

and Uman

(1990b)

Cooray

and Lundquist (1982)Lin et al (1979)

Florida

SwedenKSCOcala

76

5535129

59 (GM)

536758

273825

232a

38b

8359

27(GM)41(GM)

5043

2215

Zero‐crossing time (μs)Cooray

and Lundquist (1985)

Lin et al (1979)

SwedenSri LankaFlorida

1029146c

498954

123018

9414377c

394236

81417

Zero‐to‐peak rise time (μs)Master et al (1984)Cooray

and Lundquist (1982)Lin et al (1979)

FloridaSwedenKSCOcala

1051405129

44702427

18201213

220

8359

28

1519

15

0807

10‐90 percent rise time (μs)Master et al (1984) Florida 105 26 12 220 15 09

Slow front duration

(μs)Master et al (1984)Cooray

and Lundquist (1982)Weidman and Krider

(1978)

FloridaSwedenFlorida

105826290

29504041

13201716

44 120 34d

060921

020509

29

Return Strokes Measured ParametersParameters of microsecond-scale electric field waveforms produced by negative return strokes (contrsquod)

Parameter Locatio

nFirst strokes Subsequent strokes

Sample size

Mean SD Sample size Mean SD

Slow front amplitude as percentage of peakMaster et al (1984)Cooray

and Lundquist (1982)Weidman and Krider

(1978)

FloridaSwedenFlorida

105836290

28415040

15112020

4412034d

202540

101020

Fast

transition 10-90 percent risetime

(ns)Master et al (1984)Weidman and Krider

(1978)

Weidman and Krider

(1980a 1984)

Weidman (1982)

FloridaFlorida

Florida

1023815125

97020020090

68010010040

2178034

610200150

27040100

Peak time derivative (normalized to100 km ) (V m-1

μs-1)Krider

et al (1996) Florida 63 39 11

Time derivative pulse width at half-peak value (ns)

Krider

et al (1996) Florida 61 100 20

If not specicied

otherwise multiple lines for a given source for the same location correspond to different thunderstorms GM = geometric mean value a better characteristic of the distribution of initial field peaks since this distribution is approximately log-normala

Strokes following previously formed channelb

Strokes creating new termination on groundcBoth

electric and magnetic fieldsd

Subsequent strokes initiated by dart-stepped leaders Other subsequent strokes studied by Weidman and

Krider

(1978) were initiated by dart leaders

30

• Slide Number 1
• Slide Number 2
• Slide Number 3
• Slide Number 4
• Slide Number 5
• Slide Number 6
• Slide Number 7
• Slide Number 8
• Slide Number 9
• Slide Number 10
• Slide Number 11
• Slide Number 12
• Return-Stroke Fields Variation with Distance
• Return-Stroke Fields Variation with Distance
• Slide Number 15
• Slide Number 16
• Slide Number 17
• Slide Number 18
• Slide Number 19
• Slide Number 20
• Slide Number 21
• Slide Number 22
• Slide Number 23
• Slide Number 24
• Slide Number 25
• First Return Stroke
• Subsequent Return Strokes
• First Return Stroke Electric Field Derivative
• Return Strokes Measured Parameters
• Return Strokes Measured Parameters

First Return Stroke

Electric field waveforms of a first return stroke The waveform is shown on two time scales 5 μsdiv

and 10 μsdiv The fields are normalized to a distance of 100 km L denotes individual leader pulses F slow front and R fast transition Also marked are the small secondary peak or shoulder α

and the larger subsidiary peaks a b and c Adapted from Weidman and Krider

(1978)

-20 -15 -10 -5 0 5 10 15 20

5

microsdiv

10

microsdiv

-60 -40 -20 0 20 40 60 80

26

Subsequent Return Strokes

-20 -15 -10 -5 0 5 10 15 20

5 microsdiv

5 microsdiv

10 microsdiv

10 microsdiv

-60 -40 -20 0 20 40 60 80

Electric field waveforms of (b) a subsequent return stroke initiated by a dart-stepped leader and (c) a subsequent return stroke initiated by a dart leader showing the fine structure both before and after the initial field peak Each waveform is shown on two time scales 5 μsdiv

and 10 μsdiv The fields are normalized to a distance of 100 km L denotes individual leader pulses F slow front and R fast transition Also marked are the small secondary peak or shoulder α

and the larger subsidiary peaks a b and c Adapted from Weidman and Krider

(1978)

27

First Return Stroke Electric Field Derivative

Examples of (top) the time derivative of the electric field intensity dEdt

and (bottom)

the electric field intensity E produced by a first return stroke at a distance of about 36 km over the Atlantic Ocean The propagation path was almost entirely over salt water The vertical arrow under the E record shows the time of the dEdt

trigger Adapted from Krider

et al (1996)

28

Return Strokes Measured Parameters

Parameters of microsecond-scale electric field waveforms produced by negative return strokes

Parameter Location First strokes Subsequent strokes

Sample size Mean SD Sample size Mean SD

Initial peak (V m‐1) (normalized to 100 km)Rakov

and Uman

(1990b)

Cooray

and Lundquist (1982)Lin et al (1979)

Florida

SwedenKSCOcala

76

5535129

59 (GM)

536758

273825

232a

38b

8359

27(GM)41(GM)

5043

2215

Zero‐crossing time (μs)Cooray

and Lundquist (1985)

Lin et al (1979)

SwedenSri LankaFlorida

1029146c

498954

123018

9414377c

394236

81417

Zero‐to‐peak rise time (μs)Master et al (1984)Cooray

and Lundquist (1982)Lin et al (1979)

FloridaSwedenKSCOcala

1051405129

44702427

18201213

220

8359

28

1519

15

0807

10‐90 percent rise time (μs)Master et al (1984) Florida 105 26 12 220 15 09

Slow front duration

(μs)Master et al (1984)Cooray

and Lundquist (1982)Weidman and Krider

(1978)

FloridaSwedenFlorida

105826290

29504041

13201716

44 120 34d

060921

020509

29

Return Strokes Measured ParametersParameters of microsecond-scale electric field waveforms produced by negative return strokes (contrsquod)

Parameter Locatio

nFirst strokes Subsequent strokes

Sample size

Mean SD Sample size Mean SD

Slow front amplitude as percentage of peakMaster et al (1984)Cooray

and Lundquist (1982)Weidman and Krider

(1978)

FloridaSwedenFlorida

105836290

28415040

15112020

4412034d

202540

101020

Fast

transition 10-90 percent risetime

(ns)Master et al (1984)Weidman and Krider

(1978)

Weidman and Krider

(1980a 1984)

Weidman (1982)

FloridaFlorida

Florida

1023815125

97020020090

68010010040

2178034

610200150

27040100

Peak time derivative (normalized to100 km ) (V m-1

μs-1)Krider

et al (1996) Florida 63 39 11

Time derivative pulse width at half-peak value (ns)

Krider

et al (1996) Florida 61 100 20

If not specicied

otherwise multiple lines for a given source for the same location correspond to different thunderstorms GM = geometric mean value a better characteristic of the distribution of initial field peaks since this distribution is approximately log-normala

Strokes following previously formed channelb

Strokes creating new termination on groundcBoth

electric and magnetic fieldsd

Subsequent strokes initiated by dart-stepped leaders Other subsequent strokes studied by Weidman and

Krider

(1978) were initiated by dart leaders

30

• Slide Number 1
• Slide Number 2
• Slide Number 3
• Slide Number 4
• Slide Number 5
• Slide Number 6
• Slide Number 7
• Slide Number 8
• Slide Number 9
• Slide Number 10
• Slide Number 11
• Slide Number 12
• Return-Stroke Fields Variation with Distance
• Return-Stroke Fields Variation with Distance
• Slide Number 15
• Slide Number 16
• Slide Number 17
• Slide Number 18
• Slide Number 19
• Slide Number 20
• Slide Number 21
• Slide Number 22
• Slide Number 23
• Slide Number 24
• Slide Number 25
• First Return Stroke
• Subsequent Return Strokes
• First Return Stroke Electric Field Derivative
• Return Strokes Measured Parameters
• Return Strokes Measured Parameters

Subsequent Return Strokes

-20 -15 -10 -5 0 5 10 15 20

5 microsdiv

5 microsdiv

10 microsdiv

10 microsdiv

-60 -40 -20 0 20 40 60 80

Electric field waveforms of (b) a subsequent return stroke initiated by a dart-stepped leader and (c) a subsequent return stroke initiated by a dart leader showing the fine structure both before and after the initial field peak Each waveform is shown on two time scales 5 μsdiv

and 10 μsdiv The fields are normalized to a distance of 100 km L denotes individual leader pulses F slow front and R fast transition Also marked are the small secondary peak or shoulder α

and the larger subsidiary peaks a b and c Adapted from Weidman and Krider

(1978)

27

First Return Stroke Electric Field Derivative

Examples of (top) the time derivative of the electric field intensity dEdt

and (bottom)

the electric field intensity E produced by a first return stroke at a distance of about 36 km over the Atlantic Ocean The propagation path was almost entirely over salt water The vertical arrow under the E record shows the time of the dEdt

trigger Adapted from Krider

et al (1996)

28

Return Strokes Measured Parameters

Parameters of microsecond-scale electric field waveforms produced by negative return strokes

Parameter Location First strokes Subsequent strokes

Sample size Mean SD Sample size Mean SD

Initial peak (V m‐1) (normalized to 100 km)Rakov

and Uman

(1990b)

Cooray

and Lundquist (1982)Lin et al (1979)

Florida

SwedenKSCOcala

76

5535129

59 (GM)

536758

273825

232a

38b

8359

27(GM)41(GM)

5043

2215

Zero‐crossing time (μs)Cooray

and Lundquist (1985)

Lin et al (1979)

SwedenSri LankaFlorida

1029146c

498954

123018

9414377c

394236

81417

Zero‐to‐peak rise time (μs)Master et al (1984)Cooray

and Lundquist (1982)Lin et al (1979)

FloridaSwedenKSCOcala

1051405129

44702427

18201213

220

8359

28

1519

15

0807

10‐90 percent rise time (μs)Master et al (1984) Florida 105 26 12 220 15 09

Slow front duration

(μs)Master et al (1984)Cooray

and Lundquist (1982)Weidman and Krider

(1978)

FloridaSwedenFlorida

105826290

29504041

13201716

44 120 34d

060921

020509

29

Return Strokes Measured ParametersParameters of microsecond-scale electric field waveforms produced by negative return strokes (contrsquod)

Parameter Locatio

nFirst strokes Subsequent strokes

Sample size

Mean SD Sample size Mean SD

Slow front amplitude as percentage of peakMaster et al (1984)Cooray

and Lundquist (1982)Weidman and Krider

(1978)

FloridaSwedenFlorida

105836290

28415040

15112020

4412034d

202540

101020

Fast

transition 10-90 percent risetime

(ns)Master et al (1984)Weidman and Krider

(1978)

Weidman and Krider

(1980a 1984)

Weidman (1982)

FloridaFlorida

Florida

1023815125

97020020090

68010010040

2178034

610200150

27040100

Peak time derivative (normalized to100 km ) (V m-1

μs-1)Krider

et al (1996) Florida 63 39 11

Time derivative pulse width at half-peak value (ns)

Krider

et al (1996) Florida 61 100 20

If not specicied

otherwise multiple lines for a given source for the same location correspond to different thunderstorms GM = geometric mean value a better characteristic of the distribution of initial field peaks since this distribution is approximately log-normala

Strokes following previously formed channelb

Strokes creating new termination on groundcBoth

electric and magnetic fieldsd

Subsequent strokes initiated by dart-stepped leaders Other subsequent strokes studied by Weidman and

Krider

(1978) were initiated by dart leaders

30

• Slide Number 1
• Slide Number 2
• Slide Number 3
• Slide Number 4
• Slide Number 5
• Slide Number 6
• Slide Number 7
• Slide Number 8
• Slide Number 9
• Slide Number 10
• Slide Number 11
• Slide Number 12
• Return-Stroke Fields Variation with Distance
• Return-Stroke Fields Variation with Distance
• Slide Number 15
• Slide Number 16
• Slide Number 17
• Slide Number 18
• Slide Number 19
• Slide Number 20
• Slide Number 21
• Slide Number 22
• Slide Number 23
• Slide Number 24
• Slide Number 25
• First Return Stroke
• Subsequent Return Strokes
• First Return Stroke Electric Field Derivative
• Return Strokes Measured Parameters
• Return Strokes Measured Parameters

First Return Stroke Electric Field Derivative

Examples of (top) the time derivative of the electric field intensity dEdt

and (bottom)

the electric field intensity E produced by a first return stroke at a distance of about 36 km over the Atlantic Ocean The propagation path was almost entirely over salt water The vertical arrow under the E record shows the time of the dEdt

trigger Adapted from Krider

et al (1996)

28

Return Strokes Measured Parameters

Parameters of microsecond-scale electric field waveforms produced by negative return strokes

Parameter Location First strokes Subsequent strokes

Sample size Mean SD Sample size Mean SD

Initial peak (V m‐1) (normalized to 100 km)Rakov

and Uman

(1990b)

Cooray

and Lundquist (1982)Lin et al (1979)

Florida

SwedenKSCOcala

76

5535129

59 (GM)

536758

273825

232a

38b

8359

27(GM)41(GM)

5043

2215

Zero‐crossing time (μs)Cooray

and Lundquist (1985)

Lin et al (1979)

SwedenSri LankaFlorida

1029146c

498954

123018

9414377c

394236

81417

Zero‐to‐peak rise time (μs)Master et al (1984)Cooray

and Lundquist (1982)Lin et al (1979)

FloridaSwedenKSCOcala

1051405129

44702427

18201213

220

8359

28

1519

15

0807

10‐90 percent rise time (μs)Master et al (1984) Florida 105 26 12 220 15 09

Slow front duration

(μs)Master et al (1984)Cooray

and Lundquist (1982)Weidman and Krider

(1978)

FloridaSwedenFlorida

105826290

29504041

13201716

44 120 34d

060921

020509

29

Return Strokes Measured ParametersParameters of microsecond-scale electric field waveforms produced by negative return strokes (contrsquod)

Parameter Locatio

nFirst strokes Subsequent strokes

Sample size

Mean SD Sample size Mean SD

Slow front amplitude as percentage of peakMaster et al (1984)Cooray

and Lundquist (1982)Weidman and Krider

(1978)

FloridaSwedenFlorida

105836290

28415040

15112020

4412034d

202540

101020

Fast

transition 10-90 percent risetime

(ns)Master et al (1984)Weidman and Krider

(1978)

Weidman and Krider

(1980a 1984)

Weidman (1982)

FloridaFlorida

Florida

1023815125

97020020090

68010010040

2178034

610200150

27040100

Peak time derivative (normalized to100 km ) (V m-1

μs-1)Krider

et al (1996) Florida 63 39 11

Time derivative pulse width at half-peak value (ns)

Krider

et al (1996) Florida 61 100 20

If not specicied

otherwise multiple lines for a given source for the same location correspond to different thunderstorms GM = geometric mean value a better characteristic of the distribution of initial field peaks since this distribution is approximately log-normala

Strokes following previously formed channelb

Strokes creating new termination on groundcBoth

electric and magnetic fieldsd

Subsequent strokes initiated by dart-stepped leaders Other subsequent strokes studied by Weidman and

Krider

(1978) were initiated by dart leaders

30

• Slide Number 1
• Slide Number 2
• Slide Number 3
• Slide Number 4
• Slide Number 5
• Slide Number 6
• Slide Number 7
• Slide Number 8
• Slide Number 9
• Slide Number 10
• Slide Number 11
• Slide Number 12
• Return-Stroke Fields Variation with Distance
• Return-Stroke Fields Variation with Distance
• Slide Number 15
• Slide Number 16
• Slide Number 17
• Slide Number 18
• Slide Number 19
• Slide Number 20
• Slide Number 21
• Slide Number 22
• Slide Number 23
• Slide Number 24
• Slide Number 25
• First Return Stroke
• Subsequent Return Strokes
• First Return Stroke Electric Field Derivative
• Return Strokes Measured Parameters
• Return Strokes Measured Parameters

Return Strokes Measured Parameters

Parameters of microsecond-scale electric field waveforms produced by negative return strokes

Parameter Location First strokes Subsequent strokes

Sample size Mean SD Sample size Mean SD

Initial peak (V m‐1) (normalized to 100 km)Rakov

and Uman

(1990b)

Cooray

and Lundquist (1982)Lin et al (1979)

Florida

SwedenKSCOcala

76

5535129

59 (GM)

536758

273825

232a

38b

8359

27(GM)41(GM)

5043

2215

Zero‐crossing time (μs)Cooray

and Lundquist (1985)

Lin et al (1979)

SwedenSri LankaFlorida

1029146c

498954

123018

9414377c

394236

81417

Zero‐to‐peak rise time (μs)Master et al (1984)Cooray

and Lundquist (1982)Lin et al (1979)

FloridaSwedenKSCOcala

1051405129

44702427

18201213

220

8359

28

1519

15

0807

10‐90 percent rise time (μs)Master et al (1984) Florida 105 26 12 220 15 09

Slow front duration

(μs)Master et al (1984)Cooray

and Lundquist (1982)Weidman and Krider

(1978)

FloridaSwedenFlorida

105826290

29504041

13201716

44 120 34d

060921

020509

29

Return Strokes Measured ParametersParameters of microsecond-scale electric field waveforms produced by negative return strokes (contrsquod)

Parameter Locatio

nFirst strokes Subsequent strokes

Sample size

Mean SD Sample size Mean SD

Slow front amplitude as percentage of peakMaster et al (1984)Cooray

and Lundquist (1982)Weidman and Krider

(1978)

FloridaSwedenFlorida

105836290

28415040

15112020

4412034d

202540

101020

Fast

transition 10-90 percent risetime

(ns)Master et al (1984)Weidman and Krider

(1978)

Weidman and Krider

(1980a 1984)

Weidman (1982)

FloridaFlorida

Florida

1023815125

97020020090

68010010040

2178034

610200150

27040100

Peak time derivative (normalized to100 km ) (V m-1

μs-1)Krider

et al (1996) Florida 63 39 11

Time derivative pulse width at half-peak value (ns)

Krider

et al (1996) Florida 61 100 20

If not specicied

otherwise multiple lines for a given source for the same location correspond to different thunderstorms GM = geometric mean value a better characteristic of the distribution of initial field peaks since this distribution is approximately log-normala

Strokes following previously formed channelb

Strokes creating new termination on groundcBoth

electric and magnetic fieldsd

Subsequent strokes initiated by dart-stepped leaders Other subsequent strokes studied by Weidman and

Krider

(1978) were initiated by dart leaders

30

• Slide Number 1
• Slide Number 2
• Slide Number 3
• Slide Number 4
• Slide Number 5
• Slide Number 6
• Slide Number 7
• Slide Number 8
• Slide Number 9
• Slide Number 10
• Slide Number 11
• Slide Number 12
• Return-Stroke Fields Variation with Distance
• Return-Stroke Fields Variation with Distance
• Slide Number 15
• Slide Number 16
• Slide Number 17
• Slide Number 18
• Slide Number 19
• Slide Number 20
• Slide Number 21
• Slide Number 22
• Slide Number 23
• Slide Number 24
• Slide Number 25
• First Return Stroke
• Subsequent Return Strokes
• First Return Stroke Electric Field Derivative
• Return Strokes Measured Parameters
• Return Strokes Measured Parameters

Return Strokes Measured ParametersParameters of microsecond-scale electric field waveforms produced by negative return strokes (contrsquod)

Parameter Locatio

nFirst strokes Subsequent strokes

Sample size

Mean SD Sample size Mean SD

Slow front amplitude as percentage of peakMaster et al (1984)Cooray

and Lundquist (1982)Weidman and Krider

(1978)

FloridaSwedenFlorida

105836290

28415040

15112020

4412034d

202540

101020

Fast

transition 10-90 percent risetime

(ns)Master et al (1984)Weidman and Krider

(1978)

Weidman and Krider

(1980a 1984)

Weidman (1982)

FloridaFlorida

Florida

1023815125

97020020090

68010010040

2178034

610200150

27040100

Peak time derivative (normalized to100 km ) (V m-1

μs-1)Krider

et al (1996) Florida 63 39 11

Time derivative pulse width at half-peak value (ns)

Krider

et al (1996) Florida 61 100 20

If not specicied

otherwise multiple lines for a given source for the same location correspond to different thunderstorms GM = geometric mean value a better characteristic of the distribution of initial field peaks since this distribution is approximately log-normala

Strokes following previously formed channelb

Strokes creating new termination on groundcBoth

electric and magnetic fieldsd

Subsequent strokes initiated by dart-stepped leaders Other subsequent strokes studied by Weidman and

Krider

(1978) were initiated by dart leaders

30

• Slide Number 1
• Slide Number 2
• Slide Number 3
• Slide Number 4
• Slide Number 5
• Slide Number 6
• Slide Number 7
• Slide Number 8
• Slide Number 9
• Slide Number 10
• Slide Number 11
• Slide Number 12
• Return-Stroke Fields Variation with Distance
• Return-Stroke Fields Variation with Distance
• Slide Number 15
• Slide Number 16
• Slide Number 17
• Slide Number 18
• Slide Number 19
• Slide Number 20
• Slide Number 21
• Slide Number 22
• Slide Number 23
• Slide Number 24
• Slide Number 25
• First Return Stroke
• Subsequent Return Strokes
• First Return Stroke Electric Field Derivative
• Return Strokes Measured Parameters
• Return Strokes Measured Parameters