CIGRE Technical Brochure on Lightning Parameters for Engineering

Applications

Department of Electrical and Computer EngineeringUniversity of Florida, Gainesville, Florida

IV International Conference on Lightning ProtectionSt. Petersburg, Russia, May 27-29, 2014

Vladimir A. Rakov

1

In April 2008, CIGRE (International Council on Large Electric Systems) formed a new Working Group C4.407, named “Lightning Parameters for Engineering Applications”.

That was an initiative of Prof. C.A. Nucci (then Convener of the CIGRE Study Committee C4) and Prof. M. Ishii (Convener of the Advisory Group C4.4).

The WG C4.407 was composed of 21 members from North and South America, Europe, and Asia. It was tasked to prepare a CIGRE Reference Document (Technical Brochure) on lightning parameters needed for engineering applications.

CIGRE WG C4.407 has completed its work on the Technical Brochure in May 2013. This Brochure (CIGRE TB 549, 2013) can be viewed as an update on previous CIGRE documents on the subject published in Electra more than three decades ago: Berger et al. (1975) and Anderson and Eriksson (1980).

This lecture is largely a presentation of the Executive Summary of CIGRE TB 549 (2013), expanded to include some illustrations.

Anderson, R.B., and Eriksson, A.J. 1980. Lightning parameters for engineering application. Electra, No. 69, pp. 65-102.

Berger, K., Anderson, R.B., and Kroninger, H. 1975. Parameters of lightning flashes. Electra, No. 41, pp. 23-37.

CIGRE TB 549, Lightning Parameters for Engineering Applications, WG C4.407, V.A. Rakov, Convenor (US), A. Borghetti, Secretary (IT), C. Bouquegneau (BE), W.A. Chisholm (CA), V. Cooray (SE), K. Cummins (US), G. Diendorfer (AT), F. Heidler (DE), A. Hussein (CA), M. Ishii (JP), C.A. Nucci (IT), A. Piantini (BR), O. Pinto, Jr. (BR), X. Qie (CN), F. Rachidi (CH), M.M.F. Saba (BR), T. Shindo (JP), W. Schulz (AT), R. Thottappillil (SE), S. Visacro (BR), W. Zischank (DE), 117 p., August 2013.

General Characterization of Lightning

About 80% or more of negative cloud-to-ground lightning flashes are composed of two or more strokes. This percentage is appreciably higher than 55% previously estimated by Anderson and Eriksson (1980), based on a variety of less accurate records.

Roughly one-third to one-half of lightning flashes create two or more terminations on ground separated by up to several kilometers.

In order to account for multiple channel terminations on ground, a correction factor of 1.5-1.7 (considerably larger than 1.1 previously estimated by Anderson and Eriksson (1980)) for the ground flash density is needed. Bouquegneau et al. (2012) suggested a conservative value of 2 for lightning risk calculations recommended by the IEC Standard.

6

Histogram of the distances between the multiple terminations of 22 individual ground flashes in Florida. The distances were determined using optical triangulation and thunder ranging. Adapted from Thottappillil et al. (1992).

Multiple Channel Terminations on Ground

Min = 0.3 kmMax = 7.3 kmGM = 1.7 km

Return-Stroke Parameters Derived from Current Measurements

Direct current measurements by K. Berger and co-workers in Switzerland remain the primary reference for both lightning research and lightning protection studies. Berger’s peak current distributions are generally confirmed by recent direct current measurements, particularly by those with larger sample sizes obtained in Japan (N=120), Austria (N=615), and Florida (N=165).

From direct current measurements, the median return-stroke peak current is about 30 kA for negative first strokes and typically 10-15 kA for subsequent strokes. Additional measurements are needed to determine more reliably the tails of the statistical distributions. As of today, there is no experimental evidence that peak current distributions for downward lightning significantly depends on strike-object height.

8

Cumulative statistical distributions of lightning peak currents, giving percent of cases exceeding abscissa value, from direct measurements in Switzerland (Berger et al. 1975). The distributions are assumed to be lognormal and given for (1) negative first strokes (N=101), (2) positive first strokes (N=26), and (3) negative subsequent strokes (N=135).

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 decreases.Statistical distributions of this type are often assumed to be lognormal.

Lightning Peak Current – Berger’s Distributions

Negative first strokes

Negativesubsequent strokes

Positive first strokes

9

Cumulative statistical distributions of peak currents for negative first strokes adopted by IEEE and CIGRE (N = 408). Taken from CIGRE Report 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 “probability to exceed” values are given by the following equation

where ΡI 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.

6.2

311

1I

PI

Lightning Peak Current – IEEE and CIGRE Distributions

1 4 10 100 10000.01

0.1

0.512

5

10

20

3040506070

80

90

95

9899

99.5

99.9

99.99

Per

cent

exc

eedi

ng a

bsci

ssa

valu

e

Peak current, kA

CIGRE

IEEE

Return-Stroke Parameters Derived from Current Measurements

Direct lightning current measurements on instrumented towers should be continued. Currently, direct current measurements are performed on instrumented towers in- Austria (Gaisberg Tower, 100 m), - Brazil (Morro do Cachimbo Tower, 60 m), - Canada (CN Tower, 553 m), - Germany (Peissenberg Tower, 160 m), - Japan (Tokyo Sky Tree, 634 m), and- Switzerland (Santis Tower, 124 m),

although the overwhelming majority of observed flashes (except for Brazil and possibly Japan (20 upward and 14 downward in 2012-2014)) are of upward type.

Return-Stroke Parameters Derived from Current Measurements

Recommended lightning current waveshape parameters are still based on Berger et al.’s (1975) data, although the current rate-of-rise parameters estimated by Anderson and Eriksson (1980) from Berger et al.'s oscillograms are likely to be significantly underestimated, due to limitations of the instrumentation used by Berger et al.

Triggered-lightning data for current rates of rise (acquired using modern instrumentation) can be applied to subsequent strokes in natural lightning.

Parameter Description

I10 10% intercept along the stroke current waveshapeI30 30% intercept along the stroke current waveshapeI90 90% intercept along the stroke current waveshape

I100= II Initial peak of currentIF Final (global) peak of current (same as peak current without an adjective)

T10/90 Time between I10 and I90 intercepts on the wavefrontT30/90 Time between I30 and I90 intercepts on the wavefront

S10 Instantaneous rate-of-rise of current at I10S10/90 Average steepness (through I10 and I90 intercepts)S30/90 Average steepness (through I30 and I90 intercepts)

Sm Maximum rate-of-rise of current along wavefront, typically at I90td 10/90 Equivalent linear wavefront duration derived from IF / S10/90td 30/90 Equivalent linear wavefront duration derived from IF / S30/90

t m Equivalent linear waveform duration derived from IF / SmQI Impulse charge (time integral of current)

Description of lightning current waveform parameters. The waveform corresponds to the typical negative first return stroke. Adapted from CIGRE Document 63 (1991) and IEEE Std 1410-2010.

 Parameters of log-normal distribution for negative downward flashes

  Parameter

First stroke Subsequent stroke

M, Medianβ, logarithmic

(base e) standard deviation

M, Medianβ, logarithmic

(base e) standard deviation

FRONT TIME (µs) td10/90 = T10/90/0.8 5.63 0.576 0.75 0.921 td30/90 = T30/90/0.6 3.83 0.553 0.67 1.013

tm=IF / Sm 1.28 0.611 0.308 0.708

STEEPNESS (kA/µs) Sm, Maximum 24.3 0.599 39.9 0.852 S10, at 10% 2.6 0.921 18.9 1.404

S10/90, 10-90% 5.0 0.645 15.4 0.944 S30/90, 30-90% 7.2 0.622 20.1 0.967

PEAK (CREST) CURRENT (kA)II, initial 27.7 0.461 11.8 0.530IF, final 31.1 0.484 12.3 0.530

Ratio, II/IF 0.9 0.230 0.9 0.207

Lightning current parameters (based on Berger’s data) recommend by CIGRÉ Document 63 (1991) and IEEE Std 1410-2010

Relation between the peak value of (maximum) current rate of rise and peak current from triggered-lightning experiments conducted at the NASA Kennedy Space Center, Florida, in 1985, 1987, and 1988 and in France in 1986. The regression line for each year is shown, and the sample size and the regression equation are given. Adapted from Leteinturier et al. (1991).

Return-Stroke Parameters Derived from Current Measurements

Relatively strong correlation is observed between the lightning peak current and charge transfer and between the current rate-of-rise and current peak. Relatively weak or no correlation is observed between the current peak and current risetime and between the current peak and current duration (from 2 kA to Ip/2).

Scatter plots relating return-stroke current waveform parameters for rocket-triggered lightning in Florida (1990) and Alabama (1991). (a) Current peak versus S10/90; (b) current peak versus 10-90% risetime. Adapted from Fisher et al. (1993).

S10/90, kA/μS

(a) (b)

Peak Current Inferred from Measured Electromagnetic Field

The field-to-current conversion procedure employed by the U.S. National Lightning Detection Network (NLDN) and other similar lightning locating systems has been calibrated, using rocket-triggered lightning data and tower-initiated lightning data, only for negative subsequent strokes, with the median absolute error being 10 to 20%. Peak current estimation errors for negative first strokes and for positive lightning are presently unknown.

Besides systems of NLDN type, there are other lightning locating systems that are also reporting lightning peak currents inferred from measured fields, including LINET (mostly in Europe), USPLN (in the U.S., but similar systems operate in other countries), ENTLN (in the U.S. and other countries), WWLLN (global), and GLD360 (global). Peak current estimation errors for the latter three systems are presently being examined using triggered-lightning data.

NLDN reported peak currents vs. those directly measured at Camp Blanding, Florida, for 268 negative strokes in lightning triggered in 2004-2013. The diagonal represents the ideal situation when the NLDN-reported and directly-measured peak currents are equal to each other. Adapted from Mallick et al. (2014).

Continuing Currents

The percentage of positive flashes or strokes containing continuing currents (CC) is much higher than that of negative flashes or strokes. Positive strokes tend to be followed by longer and more intense CC than negative strokes.

Negative strokes initiating long (>40 ms) continuing currents tend to have a lower peak current (also to be preceded by higher-peak-current strokes and by relatively short interstroke intervals), while positive strokes can produce both a high peak current and a long CC.

Peak current (Ip) versus CC duration for 586 negative strokes and 141 positive strokes. Provided by M.M.F. Saba.

Lightning Return Stroke Propagation Speed

The lightning return-stroke speed is needed in computing lightning electromagnetic fields that cause induced overvoltages in power distribution lines. It is also explicitly or implicitly assumed in procedures to infer lightning currents from measured fields.

The average propagation speed of a negative return stroke (first or subsequent) below the lower cloud boundary is typically between one-third and one-half of the speed of light.

It appears that the return-stroke speed for first strokes is lower than that for subsequent strokes, although the difference is not very large (9.6 × 107 vs. 1.2 × 108 m/s).

Equivalent Impedance of the Lightning Channel

The equivalent impedance of the lightning channel, Zch, is needed for specifying the source in studies of either direct-strike or induced lightning effects.

The estimates of this impedance from limited experimental data suggest values ranging from several hundred ohms to a few kiloohms. In many practical situations the impedance “seen” by lightning at the strike point is some tens of ohms or less, which allows one to assume infinitely large equivalent impedance of the lightning channel. In other words, lightning in these situations can be viewed as an ideal current source.

Representation of lightning by a current source with internal impedance of 400 ohm, similar to that of an overhead wire, is probably not justified (particularly at early times).

Positive and Bipolar Lightning Discharges

In spite of the recent progress, our knowledge of the physics of positive lightning remains considerably poorer than that of negative lightning.

Because of the absence of other direct current measurements for positive lightning return strokes, it is still recommended to use the peak current distribution based on the 26 events recorded by K. Berger, even though some of those 26 events are likely to be not of “classical” return-stroke type.

Clearly, additional measurements for positive lightning return strokes are needed to establish reliable distributions of peak current and other parameters for this type of lightning.

Bipolar lightning discharges are usually initiated by upward leaders from tall objects. However, natural downward flashes also can be bipolar.

23

Positive Lightning

Lightning current parameters for positive flashes (Berger et al., 1975)

4.6

20

2.0

3.5

0.20

25

2.5x105

14

35

80

16

22

2.4

230

6.5x105

85

250

350

150

200

32

2000

1.5x107

500

80

24

20

18

32

200

5.5x105

-

26

26

25

19

21

16

26

24

Percent Exceeding Tabulated ValueSampleSize

UnitsParameters

95% 50%First

5% ValueforNegativeFirstStrokes

kA

C

C

μs

kA/μs

μs

A2s

ms

Peak current (minimum 2 kA)

Charge (total charge)

Impulse charge (excludingcontinuing current )

Front Duration (2 kA to peak)

Maximum di/dt

Action integral ( ∫i2dt )

Flash Duration

Stroke duration ( 2 kA to halfpeak value on the tail)

Upward Lightning Discharges

Tall objects (higher than 100 m or so) located on flat terrain and objects of moderate height (some tens of meters) located on mountain tops experience primarily upward lightning discharges that are initiated by upward-propagating leaders.

Upward (object-initiated) lightning discharges always involve an initial stage that may or may not be followed by downward-leader/upward-return-stroke sequences. The percentage of upward flashes with return strokes varies from 20 to 50%.

The initial-stage steady current typically has a magnitude of some hundreds of amperes and typical charge transfers of 30-40 C, and often exhibits superimposed pulses whose peaks range from tens of amperes to several kiloamperes (occasionally a few tens of kiloamperes).

Schematic current record of upward-initiated flash. Labeled are the initial continuous current (ICC) with three superimposed ICC pulses, a period of no current flow, and two return strokes (RS). Adapted from Diendorfer et al. (2009).

Geographical and Seasonal Variations in Lightning Parameters

At the present time, the available information is not sufficient to confirm or refute a hypothesis on dependence of negative CG lightning parameters on geographical location or season.

On the other hand, some local conditions may exist (for example, winter storms in Japan) that give rise to more frequent occurrence of unusual types of lightning, primarily of upward type, whose parameters may differ significantly from those of “ordinary” lightning. Further studies are necessary to clarify those conditions and their possible dependence on geographical location.

Percentage of flashes that produce a given number of ground contacts in Arizona, USA, and São Paulo, Brazil. The average number of ground contacts in both locations is 1.7. Adapted from Saraiva et al. (2010).

Lightning Parameters Needed for Different Engineering Applications

This chapter of the Technical Brochure was envisioned to serve as a "bridge" between the description of lightning parameters found in the preceding chapters and the existing standards and other literature on specific applications of those parameters.

No attempt was made to present detailed descriptions of the various procedures in which lightning parameters are used as an input. Instead, references to the pertinent CIGRE documents, standards, and published papers are given.

Positive upward connecting leader (~400 m)

Negative downward leader

A downward negative flash terminating on the 440-m Guangzhou International Finance Center, China. Adapted from Lu et al. (2013).

Time variation of the ratio of speeds of downward (negative) and upward connecting (positive) leaders (Vd/Vu)

Reference Vd/Vu

Eriksson [1987] 1

Rizk [1990] 1Dellera and Garbagnati

[1990]Decreasingfrom 4 to 1

Mazur et al. [2000] 2

The length of the upward connecting leader was ~400 m, with the initial ~100 m being too faint for speed measurements. Adapted from Lu et al. (2013).

Assumptions on Vd/Vu in leader-progression-type

models

Monte San Salvatore Tower (70 m), Lugano, Switzerland

31

Courtesy of Prof. R.E. Orville, Texas A&M

Thank You

32

Lightning Parameters Derived from Direct Current Measurements

 Parameters Units Sample Size

Percent Exceeding Tabulated Value

95% 50% 5%

 Peak current (minimum 2 kA) First strokes Subsequent strokes

kA  

101135

144.6

3012

8030

 Charge (total charge) First strokes Subsequent strokes Complete flash

C

  93

12294

  1.10.21.3

  5.21.47.5

  241140

Impulse charge (excluding continuing current) First strokes Subsequent strokes

C

   90

117

   1.10.22

   4.50.95

   204

 Front duration (2 kA to peak) First strokes Subsequent strokes

μs  89

1181.80.22

  5.51.1

   18

4.5

 Maximum dI/dt First strokes Subsequent strokes

kA μs-1 92122

5.512

1240

   32120

Stroke duration (2 kA to half peak value on the tail) First strokes Subsequent strokes

μs90115

306.5

7532

  

200140

 Action integral (∫I2dt) First strokes Subsequent strokes

A2s 9188

6.0 x 103

5.5 x 102

  5.5 x 104

6.0 x 103

  5.5 x 105

5.2 x 104

34

Typical Induced Voltage at a distance of 145 m and Corresponding Stroke Current (93-05)

Lightning-induced voltages on overhead power lines

V = 50 kV

I = -22.3 kA

35

Illustration of capture surfaces of two towers and earth’s 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

36

Electrogeometrical Model (EGM)

rs = 10 I0.65, 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

{

37

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 = 10.6 Q0.7, where Q is in coulombs and I is in kiloamperes, was used

in deriving rs = 10 I0.65 Adapted from Berger (1972).

Electrogeometrical Model (EGM)

Finding rs = f(I)

• 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 kV/m)

• Use an empirical relation

between Q and I to find rs = f(I)

• Find rs = f(Q)

• 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 = 10.6 Q0.7

For Q = 5 CI = 33 kA

38

Lightning Attachment Process

First optical image of upward connecting leader in rocket-triggered lightning (Wang et al. 1999a)

Striking distance (2 times the return-stroke initiation height) vs. return-stroke peak current derived from luminosity for 7 strokes in the anomalous flash (h = 10 m) triggered at Camp Blanding in 2012. The red curve is based on data for 14 classical triggered-lightning strokes (with directly measured currents, h = 5 m) from 2011 experiments at Camp Blanding. The blue curve is recommended for first strokes by the IEC standard.

Wang et al. (2014)

Striking distance (2 times the return-stroke initiation height) vs. return-stroke peak current derived from luminosity for 7 strokes in the anomalous flash (h = 10 m) triggered at Camp Blanding in 2012. The red curve is based on data for 14 classical triggered-lightning strokes (directly measured currents, h = 5 m) from 2011 experiments at Camp Blanding. The blue curve is recommended for first strokes by the IEC standard.

r = 10 · I0.65

Natural flash first stroke at LOG (h < 25 m)

Anomalous flash first stroke at CB (h = 10 m)

<

Subsequentstrokes (h = 10 m)

41

Optical Images of Leader and Attachment Process – Triggered Lightning

Dart-stepped leader and attachement process in rocket-triggered lightning (Sept. 17, 2008) at Camp Blanding, Florida; Photron FASTCAM SA1.1, 50000 fps (20 µs per frame); h = 17 m

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

56 m

16 m

25 m

Striking distance (2 times the total upward connecting leader length) vs. peak current for 11 classical triggered-lightning strokes from 2008 (h = 17 m) and 2009 (h = 15 m) Camp Blanding experiments (based on work of Biagi (2011)). Also shown is the IEC standard dependence.

0 10 20 30 400

20

40

60

80

100

120

140

160

180

Peak current (kA)

Strik

ing

dist

ance

(m)

r = 10 I 0.65

(2009)

(2009)

CIGRE WG C4.407 Scope• Evaluation of current measurements on instrumented towers

• Evaluation of current measurements for rocket-triggered lightning

• Evaluation of the procedures used to estimate lightning currents from measured fields, with emphasis on those implemented in lightning locating systems

• Inclusion of additional lightning parameters (e.g., characteristics of continuing currents, return-stroke propagation speed, equivalent lightning channel impedance, etc.) that are presently not on the CIGRE list, but needed in engineering applications

• Further characterization of positive and bipolar lightning discharges

• Characterization of upward lightning discharges

• Search for any geographical, seasonal and other variations in lightning parameters

• Preparation of a reference document (technical brochure) “Lightning Parameters for Engineering Applications”

Return-Stroke Parameters Derived from Current Measurements

The “global” distributions of lightning peak currents for negative first strokes currently recommended by CIGRE and IEEE are each based on a mix of direct current measurements and less accurate indirect measurements, some of which are of questionable quality.

However, since the “global” distributions have been widely used in lightning protection studies and are not much different from that based on direct measurements only, continued use of these “global” distributions for representing negative first strokes is recommended, along with Berger’s distribution having a median of 30 kA, σlgI = 0.265.

For negative subsequent strokes and for positive lightning strokes, Berger’s peak current distributions are still recommended. For negative subsequent strokes, a log-normal distribution with median = 12 kA and σlgI = 0.265 should be used. For positive lightning strokes, a log-normal distribution with median = 35 kA and σlgI = 0.544 is recommended.

10-to-90% and 30-to-90% Average Slopes: Triggered-Lightning Data vs. Berger’s Natural-Lightning Data

(a) (b)

(a) The 10-90% average (steepness): S-10 = 0.8Ip/T-10. (b) The 30-90% average (steepness): S-30 = 0.6Ip/T-30. GM is the geometric mean and SD is the standard deviation of the logarithm (base 10) of the parameter. Adapted from Fisher et al. (1993).

10 – 90% Average Slope (S10/90)

30 – 90% Average Slope (S30/90)

Trigg.

Natur.

46

Lightning Return Stroke Propagation Speed

There exists some experimental evidence that the negative return stroke speed may vary non-monotonically along the lightning channel, initially increasing and then decreasing with increasing height.

Return-stroke speeds (×108 m/s) at different heights for five strokes in a triggered lightning flash. Adapted from Olsen et al. (2004).

Height range, m

Stroke order Estimated error, %

1 2 4 5 6

7 – 63 1.3 1.2 1.2 1.2 1.2 10

63 – 117 1.6 1.8 1.8 1.8 1.6 15

117 – 170 1.7 1.2 1.5 1.6 1.5 21

No data are available for stroke 3.

Engineering models of lightning strikes (a) to lumped grounding impedance and (b) to a tall grounded object, in which lightning is represented by the Norton equivalent circuit, labeled ‘‘source’’. Adapted from Baba and Rakov (2005).

Positive and Bipolar Lightning Discharges

Although positive lightning discharges account for 10% or less of global cloud-to-ground lightning activity, there are several situations, including, for example, winter storms, that appear to be conducive to the more frequent occurrence of positive lightning.

The highest directly measured lightning currents (near 300 kA vs. a maximum of about 200 kA or less for negative lightning) and the largest charge transfers (hundreds of coulombs or more) are associated with positive lightning.

Positive flashes are usually composed of a single stroke, although up to four strokes per flash have been observed. Subsequent strokes in positive flashes can occur either in a new (a more common situation) or in the previously-formed channel.

Examples of two types of positive lightning current waveforms observed by K. Berger: (a) microsecond-scale waveform, similar to those produced by downward negative return strokes, and a sketch illustrating the lightning processes that might have led to the production of this waveform; (b) millisecond-scale waveform and a sketch illustrating the lightning processes that might have led to the production of this current waveform. Adapted from Rakov (2003).

Geographical and Seasonal Variations in Lightning Parameters

From the information available in the literature at the present time, there is no evidence of a systematic dependence of negative cloud-to-ground lightning parameters on geographical location, except maybe for first and subsequent return-stroke peak currents, for which relatively insignificant (less than 50%), from the engineering point of view, variations may exist.

It is important to note, however, that it cannot be ruled out that the observed differences in current measurements are due to reasons other than "geographical location“, with the limited sample size for some observations being of particular concern.

Similarly, no reliable information on seasonal dependence is available.

Location(Reference)

Average Number of Strokes per

Flash

Percentage of Single-Stroke

FlashesSample Size

New Mexico(Kitagawa et al., 1962) 6.4 13% 83

Florida(Rakov and Uman, 1990) 4.6 17% 76

Sweden(Cooray and Perez, 1994) 3.4 18% 137

Sri Lanka(Cooray and Jayaratne,

1994)4.5 21% 81

Brazil(Ballarotti et al., 2012) 4.6 17% 883

Arizona(Saraiva et al., 2010) 3.9 19% 209

Malaysia(Baharudin et al., 2014) 4.0 16% 100

Number of strokes per negative flash and percentage of single-stroke flashes.