Lightning Parameters for Engineering Applications

Report
IV International Conference on Lightning Protection
St. Petersburg, Russia, May 27-29, 2014
CIGRE Technical Brochure on
Lightning Parameters for Engineering
Applications
Vladimir A. Rakov
Department of Electrical and Computer Engineering
University of Florida, Gainesville, Florida
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.
Multiple Channel Terminations on Ground
Min = 0.3 km
Max = 7.3 km
GM = 1.7 km
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).
6
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.
Lightning Peak Current – Berger’s Distributions
Negative first strokes
Positive first strokes
Negative
subsequent strokes
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.
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).
8
Lightning Peak Current – IEEE and CIGRE Distributions
99.99
99.9
Percent exceeding abscissa value
99.5
99
98
For the CIGRE distribution, 98% of peak
currents exceed 4 kA, 80% exceed 20
kA, and 5% exceed 90 kA.
IEEE
95
CIGRE
90
For the IEEE distribution, the
“probability to exceed” values are given
by the following equation
80
70
60
50
40
30
PI 
20
10
5
2
1
0.5
 31 
1 I
2 .6
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.
0.1
0.01
1
4
10
100
1000
Peak current, kA
Cumulative statistical distributions of
peak currents for negative first strokes
adopted by IEEE and CIGRE (N = 408).
Taken from CIGRE Report 63 (1991).
9
1
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
I30
I90
I100= II
IF
T10/90
T30/90
S10
S10/90
10% intercept along the stroke current waveshape
30% intercept along the stroke current waveshape
90% intercept along the stroke current waveshape
Initial peak of current
Final (global) peak of current (same as peak current without an adjective)
Time between I10 and I90 intercepts on the wavefront
Time between I30 and I90 intercepts on the wavefront
Instantaneous rate-of-rise of current at I10
S30/90
Sm
td 10/90
td 30/90
tm
QI
Average steepness (through I30 and I90 intercepts)
Maximum rate-of-rise of current along wavefront, typically at I90
Equivalent linear wavefront duration derived from IF / S10/90
Equivalent linear wavefront duration derived from IF / S30/90
Equivalent linear waveform duration derived from IF / Sm
Impulse charge (time integral of current)
Average steepness (through I10 and I90 intercepts)
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.
Lightning current parameters (based on Berger’s data) recommend by CIGRÉ
Document 63 (1991) and IEEE Std 1410-2010
Parameters of log-normal distribution for negative downward flashes
First stroke
Parameter
M, Median
β, logarithmic
(base e)
standard
deviation
Subsequent stroke
M, Median
β, 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
0.530
IF, final
31.1
0.484
12.3
0.530
0.9
0.230
0.9
0.207
Ratio, II/IF
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-ofrise 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).
(a)
(b)
S10/90, kA/μS
Scatter plots relating return-stroke current waveform parameters for rockettriggered 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).
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.
Positive Lightning
Lightning current parameters for positive flashes (Berger et al., 1975)
Parameters
Sample Percent Exceeding Tabulated Value
Size
95%
50%
kA
26
4.6
35
250
80
Charge (total charge)
C
26
20
80
350
24
Impulse charge (excluding
continuing current )
C
25
2.0
16
150
20
Front Duration (2 kA to peak)
μs
19
3.5
22
200
18
kA/μs
21
0.20
2.4
32
32
Stroke duration ( 2 kA to half
peak value on the tail)
μs
16
25
230
2000
200
Action integral ( ∫i2dt )
A2s
26
Flash Duration
ms
24
Peak current (minimum 2 kA)
Maximum di/dt
23
Units
5% Value
for
Negative
First
First
Strokes
2.5x105
14
6.5x105
85
1.5x107 5.5x105
500
-
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 downwardleader/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.
Negative downward leader
Positive upward connecting
leader (~400 m)
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)
Assumptions on Vd/Vu in
leader-progression-type
models
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).
Reference
Vd/Vu
Eriksson
[1987]
1
Rizk [1990]
1
Dellera and
Garbagnati
[1990]
Decreasing
from 4 to 1
Mazur et al.
[2000]
2
Monte San Salvatore Tower (70 m), Lugano, Switzerland
Courtesy of Prof. R.E. Orville, Texas A&M
31
32
Lightning Parameters Derived from Direct Current Measurements
Parameters
Peak current (minimum 2 kA)
First strokes
Subsequent strokes
Charge (total charge)
First strokes
Subsequent strokes
Complete flash
Impulse charge (excluding
continuing current)
First strokes
Subsequent strokes
Front duration (2 kA to peak)
First strokes
Subsequent strokes
Maximum dI/dt
First strokes
Subsequent strokes
Units
Sample
Size
Percent Exceeding Tabulated Value
95%
50%
5%
kA
101
135
14
4.6
30
12
80
30
C
93
122
94
1.1
0.2
1.3
5.2
1.4
7.5
24
11
40
90
117
1.1
0.22
4.5
0.95
20
4
μs
89
118
1.8
0.22
5.5
1.1
18
4.5
kA μs-1
92
122
5.5
12
12
40
32
120
90
115
30
6.5
75
32
200
140
91
88
6.0 x 103
5.5 x 102
5.5 x 104
6.0 x 103
5.5 x 105
5.2 x 104
C
Stroke duration (2 kA to half
peak value on the tail)
First strokes
Subsequent strokes
μs
Action integral (∫I2dt)
First strokes
Subsequent strokes
A2s
Lightning-induced voltages on overhead power lines
V = 50 kV
I = -22.3 kA
Typical Induced Voltage at a distance of 145 m and Corresponding Stroke Current (93-05)
34
Electrogeometrical Model (EGM)
Ng=const
Capture surfaces
rs
rs
rs
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).
35
Electrogeometrical Model (EGM)
4
3
1
2
{
rs = 10 I0.65, m
where I is in kA
I, kA
r s, m
10
45
30
91
170
282
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 twodimensional photographs by Eriksson (1978); , estimates from three-dimensional photography by
Eriksson (1978). Adapted from Golde (1977) and Eriksson (1978).
36
Electrogeometrical Model (EGM)
102
Finding rs = f(I)
•
101
For Q = 5 C
I = 33 kA
Q
Assume leader geometry,
total leader charge Q, and
distribution of this charge
along the channel.
I = 10.6 Q0.7
•
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)
•
100
I peak/ Q impulse
neg. first strokes
n=89
Find rs = f(Q)
•
Use an empirical relation
between Q and I to find
rs = f(I)
37
10-1
100
101
I
102
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).
Lightning Attachment Process
First optical image of upward connecting leader in rocket-triggered
lightning (Wang et al. 1999a)
38
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 triggeredlightning 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.
r = 10 · I0.65
Natural flash first stroke
at LOG (h < 25 m)
Anomalous flash first
stroke at CB (h = 10 m)
<
Subsequent
strokes (h = 10 m)
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 triggeredlightning 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.
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
25 m
56 m
16 m
1 frame before return stroke 8
2 frames before return stroke 8
Biagi et al. (2009, GRL)
41
180
Striking distance (m)
160
140
120
r = 10 I 0.65
100
80
60
(2009)
40
20
0
0
(2009)
10
20
Peak current (kA)
30
40
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.
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: TriggeredLightning Data vs. Berger’s Natural-Lightning Data
(a)
10 – 90% Average Slope (S10/90)
(b)
30 – 90% Average Slope (S30/90)
Trigg.
Natur.
(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).
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).
Stroke order
Height
range, m
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 cloudto-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.
Number of strokes per negative flash and percentage of single-stroke flashes.
Location
(Reference)
Average Number
of Strokes per
Flash
Percentage of
Single-Stroke
Flashes
Sample 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

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