4b. Properties of negative downward
lightning discharge to ground - II
1
Downward Negative Lightning Discharges to Ground
Cloud Charge Distribution
t = 0
Preliminary
Breakdown
Stepped
Leader
1.10 ms
1.00 ms
Attachment
Process
20.00 ms
19.00 ms
First Return
Stroke
20.10 ms
20.20 ms
Second Return
Stroke
Dart
Leader
K and J Process
40.00 ms
1.20 ms
60.00 ms
61.00 ms
62.05 ms
A drawing illustrating various processes comprising a negative cloud-to-ground lightning flash.
Adapted from Uman (1987, 2001).
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) Lightning Attachment Process
Adapted from Howard (2009)
5
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)
25 m
56 m
16 m
1 frame before return stroke 8
2 frames before return stroke 8
Biagi et al. (2009, GRL)
6
Optical Images of Leader and Attachment Process – Laboratory Sparks
4.5 m
-
Single-frame K008 images of four negative discharges (-2.2
MV,130/7500 μs) in a 4.5 m rod-rod gap. Frame duration in a, b,
and c is 2 µs, and in d it is 0.5 µs. L in b is the length of last
step. Adapted from Lebedev et al. (2007).
7
Optical Images of Attachment Process
HV rod
JP
5.5 m
JP
Single-frame image-converter-camera K008 images
of negative discharges in a 5.5-m rod-rod gap with
frame exposure of 0.2 μs. JP is the junction point
between downward negative and upward connecting
positive leaders. Adapted from Shcherbakov et al.
(2006).
8
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).
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).
9
Electrogeometrical Model (EGM)
4
3
1
2
{
rs = 10 I0.65, m
where I is in kA
I, kA
rs , 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).
10
Electrogeometrical Model (EGM)
102
Finding rs = f(I)
Assume leader geometry,
total leader charge Q, and
distribution of this charge
along the channel.
•
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)
•
101
For Q = 5 C
I = 33 kA
Q
•
I = 10.6 Q0.7
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)
11
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).
Electrogeometrical Model (EGM)
Rolling-Sphere Method
rs = 45 m (150 ft)
(NFPA 780, 2004),
corresponds to I = 10 kA
(95% of currents exceed this value)
rs
rs
rs
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).
12
Return‐Stroke Fields: Variation with Distance
Electric Field Intensity
Magnetic 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 1, 2 and 5 km. Adapted from Lin et al. (1979).
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 – Switzerland (Berger et al., 1975)
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).
15
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
Stroke duration (2 kA to half
peak value on the tail)
First strokes
Subsequent strokes
Action integral (∫I2dt)
First strokes
Subsequent strokes
Units
Sample
Size
Percent Exceeding Tabulated Value
95%
50%
5%
30
12
80
30
kA
101
135
14
4.6
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
C
μs
A2s
90
115
91
88
30
6.5
6.0 x 103
5.5 x 102
12
40
32
120
75
32
200
140
5.5 x 104
6.0 x 103
5.5 x 105
5.2 x 104
Lightning Peak Current – Berger’s Distributions
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, 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).
17
Lightning Peak Current – IEEE and CIGRE Distributions
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
PI =
1
2.6
1+ I
31
( )
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.
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) .
18
Peak current, I, kA
(IEEE distribution)
5
10
20
40
60
80
100
200
Percentage
exceeding tabulated
value, PI· 100%
99
95
76
34
15
7.8
4.5
0.8
dI/dt in Rocket-Triggered Lightning ( ~100 kA/μs)
Relation between the peak rate of current rise, dI/dt, and the peak current I,
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; the sample size N and the regression
equation are given in table. Adapted from Leteinturier et al. (1991).
19
Morro Do Cachimbo Tower (60 m), Belo Horizonte, Brazil
Courtesy Prof. Dr. Silverio Visacro Filho, Lightning Research Center (UFMG-CEMIG)
20
Lightning Parameters Derived from Direct Current Measurements – Brazil
First Stroke
40.4
5.2
Subsequent Strokes
16.3
0.99
21
Optical Measurements of Return-Stroke Speed
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).
22
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).
Mean, m/s
Sample
Size
Min, m/s
Max, m/s
Boyle and Orville
(1976)
2.0 x 107
1.2 x 108
0.71 x 108
2.6 x 107
12
Streak camera,
2-D speed
Idone and Orville
(1982)
2.9 x 107
2.4 x 108
1.1 x 108
4.7 x 107
63
Streak camera,
2-D speed
Mach and Rust
(1989a, Fig. 7)
2.0 x 107
8.0 x 107
2.6 x 108
>2.8 x 108
1.3 ±0.3 x 108
1.9 ±0.7 x 108
5 x 107
7 x 107
54
43
Long channel
Short channel
(Photoelectric, 2-D)
Hubert and Mouget
(1981)
4.5 x 107
1.7 x 108
9.9 x 107
4.1 x 107
13
Idone et al. (1984)
6.7 x 107
1.7 x 108
1.2 x 108
2.7 x 107
56
Willett et al.
(1988)
1.0 x 108
1.5 x 108
1.2 x 108
1.6 x 107
9
Photoelectric,
3-D speed
Streak camera,
3-D speed
Streak camera,
2-D speed
Willett et al.
(1989a)
1.2 x 108
1.9 x 108
1.5 x 108
1.7 x 107
18
Streak camera,
2-D speed
Mach and Rust
(1989a, Fig. 8)
6.0 x 107
6.0 x 107
1.6 x 108
2.0 x 108
1.2 ±0.3 x 108
1.4 ±0.4 x 108
2 x 107
4 x 107
40
39
Long channel
Short channel
(Photoelectric, 2-D)
Reference
St. Dev, m/s
Comments
Natural Lightning
Triggered Lightning
23
Return-Stroke Speed Near Ground
Return-stroke speed profiles estimated tracking the 20% point on the light-pulse front for
triggered lightning flash F0336 (Olsen et al., 2004)
1.2
1.5
1.7
1.6
1.5
1.6
1.8
1.8
1.8
1.6
1
1.3 1.2
1.2
1.2
1.2
24
3
m
m
ve
o
Ab
t
igh
e
H
63
6
7-
7
11
-1
17
70
m und
o
Gr
Return-Stroke Speed vs. Return-Stroke Peak Current
2.5
Return-Stroke Speed, 108 m/s
2.0
1.5
1.0
0.5
Mach and Rust (1989a), r = -0.08
Willett el al. (1998a), r = -0.27
0.0
0
5
10
15
20
25
30
35
40
45
Return-Stroke Peak Current, kA
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.
25
First Return Stroke
-20 -15 -10 -5
0
5
10 15 20
5 µs/div
10 µs/div
-60
-40
-20
0
20
40
60
80
Electric field waveforms of a first return stroke. The waveform is shown on two time
scales, 5 μs/div and 10 μs/div. 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).
26
Subsequent Return Strokes
-20 -15 -10
-5
0
5
10 15
20
5 µs/div
10 µs/div
5 µs/div
10 µs/div
-60
27
-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
μs/div and 10 μs/div. 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).
First Return Stroke: Electric Field Derivative
Examples of (top) the time
derivative of the electric field
intensity dE/dt 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
dE/dt 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
Sample size
Mean
Florida
76
5.9 (GM)
Sweden
KSC
Ocala
553
51
29
5.3
6.7
5.8
Sweden
Sri Lanka
Florida
102
91
46c
Florida
Sweden
KSC
Ocala
10‐90 percent rise time (μs)
Master et al. (1984)
Slow front duration (μs)
Master et al. (1984)
Cooray and Lundquist (1982)
Weidman and Krider (1978)
Initial peak (V m‐1) (normalized to 100 km)
Rakov and Uman (1990b)
Cooray and Lundquist (1982)
Lin et al. (1979)
Zero‐crossing time (μs)
Cooray and Lundquist (1985)
Lin et al. (1979)
Zero‐to‐peak rise time (μs)
Master et al. (1984)
Cooray and Lundquist (1982)
Lin et al. (1979)
29
Subsequent strokes
SD
Sample size
Mean
SD
232a
38b
2.7(GM)
4.1(GM)
2.7
3.8
2.5
83
59
5.0
4.3
2.2
1.5
49
89
54
12
30
18
94
143
77c
39
42
36
8
14
17
105
140
51
29
4.4
7.0
2.4
2.7
1.8
2.0
1.2
1.3
220
2.8
1.5
83
59
1.5
1.9
0.8
0.7
Florida
105
2.6
1.2
220
1.5
0.9
Florida
Sweden
Florida
105
82
62
90
2.9
5.0
4.0
4.1
1.3
2.0
1.7
1.6
44 120 34d
0.6
0.9
2.1
0.2
0.5
0.9
Return Strokes: Measured Parameters
Parameters of microsecond-scale electric field waveforms produced by negative return strokes (cont’d).
Parameter
Locatio
n
First strokes
Subsequent strokes
Sample
size
Mean
SD
Slow front, amplitude as percentage of peak
Master et al. (1984)
Cooray and Lundquist (1982)
Weidman and Krider (1978)
Florida
Sweden
Florida
105
83
62
90
28
41
50
40
15
11
20
20
Fast transition, 10-90 percent risetime (ns)
Master et al. (1984)
Weidman and Krider (1978)
Florida
Florida
Florida
102
38
15
125
970
200
200
90
680
100
100
40
Peak time derivative (normalized to
100 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
Weidman and Krider (1980a,
Sample size
Mean
SD
44
120
34d
20
25
40
10
10
20
217
80
34
610
200
150
270
40
100
1984);
Weidman (1982)
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-normal.
a Strokes following previously formed channel.
b Strokes creating new termination on ground.
cBoth electric and magnetic fields.
d Subsequent strokes initiated by dart-stepped leaders. Other subsequent strokes studied by Weidman and Krider (1978) were initiated by dart leaders.
30