Atmospheric Research 91 (2009) 316–325
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Atmospheric Research
j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / a t m o s
Analysis of microsecond- and submicrosecond-scale electric field pulses
produced by cloud and ground lightning discharges
Amitabh Nag ⁎, Brian A. DeCarlo, Vladimir A. Rakov
Department of Electrical and Computer Engineering, University of Florida, P.O. Box 116130, Gainesville, FL 32611-6130, USA
a r t i c l e
i n f o
Article history:
Received 24 October 2007
Accepted 29 January 2008
Keywords:
Lightning
Electric field
Cloud discharge
Cloud-to-ground discharge
Submicrosecond-scale pulses
Microsecond-scale pulses
a b s t r a c t
We examined microsecond- and submicrosecond-scale pulses in electric field records of cloud
and cloud-to-ground lightning discharges acquired in summer 2006, in Gainesville, Florida. A
total of 12 cloud and 12 ground flashes were analyzed in detail, with the electric field record
length being 96 or 200 ms and sampling interval being 4 or 10 ns. The majority of pulses in both
cloud and ground discharges analyzed in this study were associated with the initial breakdown
process and were relatively small in amplitude and duration. The typical durations were an
order of magnitude smaller than tens of microseconds characteristic of “classical” preliminary
breakdown pulses. We estimated that 26% of the pulses in the 12 cloud discharges and 22% of
the pulses in the 12 cloud-to-ground discharges had total durations less that 1 µs.
© 2008 Elsevier B.V. All rights reserved.
1. Introduction
Cloud discharges can be viewed as being composed of an
early or active stage and a late or final stage. The beginning of a
cloud discharge is typically marked by the largest microsecondscale pulses in its wideband electric field record that are
presumably related to the flash initiating breakdown process.
The typical total pulse duration of individual initial breakdown
pulses is in the range of 50 to 80 µs with typical interpulse
interval of 600 to 800 µs (Rakov et al., 1996). Microsecond-scale
pulses in cloud discharges were analyzed by Villanueva et al.
(1994), although pulses that were smaller than 12.5% of the
average amplitude of the five largest pulses in a flash (in some
flashes there were hundreds of them) were not included in the
analysis. In the present study, we extend the work of Villanueva
et al. (1994) to additionally include these smaller pulses by
examining their total duration, amplitude, and occurrence.
Additionally, our sampling interval of 10 ns (for cloud
discharges) versus 500 ns in Villanueva et al.'s (1994) study
allowed us to include submicrosecond-scale pulses in the
analysis. Examined here are pulses occurring primarily during
the early stage of cloud flashes. The final stage of cloud flashes
⁎ Corresponding author. Tel.: +1 352 392 4240.
E-mail address: amitabh@ufl.edu (A. Nag).
0169-8095/$ – see front matter © 2008 Elsevier B.V. All rights reserved.
doi:10.1016/j.atmosres.2008.01.014
generally could not be examined due to limited record length
(200 ms for cloud discharges).
In cloud-to-ground discharges, a predominantly bipolar
pulse train sometimes appears a few to several tens of
milliseconds before the first return-stroke. This pulse train is
commonly attributed to preliminary (initial) breakdown and
hence referred to as the preliminary breakdown pulse train. The
typical total pulse duration of individual pulses in the train is 20
to 40 µs with typical interpulse interval in the range of 70 to
130 µs (Rakov et al., 1996). In this paper, we examine only pulses
occurring prior to the first return-stroke pulse, most of which
were associated with the preliminary breakdown pulse train.
2. Instrumentation and methodology
The data used in this study were acquired during summer
2006 in Gainesville, Florida. A total of 12 cloud discharges and
12 negative cloud-to-ground discharges with a relatively
large number of pulses within the length of the record (96 or
200 ms) were selected for analysis. Using thunder ranging
and the characteristic features of return-stroke electric field
waveforms at known distances in the 50 to 250 km range
(Pavlick et al., 2002; Fig. 5), we estimated that the majority of
our records are due to lightning discharges occurring at
distances ranging from a few to about a hundred kilometers.
A. Nag et al. / Atmospheric Research 91 (2009) 316–325
Table 1
Categorization of pulses according to normalized amplitude
Normalized pulse amplitude
Category
≤0.25
N 0.25 and ≤ 0.5
N 0.5 and ≤0.75
N 0.75 and ≤ 1.0
Very small
Small
Medium
Large
The electric field measuring system included a circular flatplate antenna followed by an integrator and a unity-gain, highinput-impedance amplifier. The antenna was installed on the
roof of a three-storey building on the University of Florida
Campus. A Nicolet ISOBE 3000 fiber-optic link was used to
transmit signals from the antenna and associated electronics to
a LeCroy 8-bit digitizing oscilloscope. The system had a useful
frequency bandwidth of 16 Hz to 10 MHz, the lower and upper
limits being determined by the instrumentation RC decay time
317
constant and the amplifier, respectively. The instrumentation
decay time constant (τ = 9.9 ms) was long enough for faithful
reproduction of microsecond- and submicrosecond-scale
pulses examined here. The sampling interval was 4 or 10 ns.
Each electric field record was examined using different
time windows (mostly tens of microseconds). Only pulses
with peak-to-peak amplitudes equal to or exceeding twice
that of the local average noise level were considered. All
detected pulses were classified depending on their polarity
(positive or negative) and detectable opposite polarity overshoot (bipolar or unipolar).
3. Analysis and discussion
3.1. Cloud discharges
The peak-to-peak amplitude of each bipolar pulse and
zero-to-peak amplitude of each unipolar pulse in a particular
Fig. 1. Electric field record of cloud flash 05/24/06_299.
Fig. 2. Examples of (a) “classical” and (b) “narrow” pulses in the early stage of cloud discharges analyzed in this study.
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A. Nag et al. / Atmospheric Research 91 (2009) 316–325
Fig. 3. Occurrence of pulses of different amplitude in different parts of cloud flash whose electric field record is shown in Fig. 1.
cloud discharge was normalized with respect to that of the
largest pulse in the flash. Pulses were grouped into four
different categories depending upon the value of its normalized amplitude as shown in Table 1. The time at which the
pulse having the largest peak-to-peak amplitude in a
particular flash occurred was relabeled as the zero of the
time scale (t = 0) and positions of all other pulses on the time
axis were determined with respect to it. For each of the 12
cloud discharges the following characteristics were examined:
• Occurrence of pulses of different amplitude in different
parts of the flash (its early stage, to be exact).
• Occurrence of pulses of different total duration in different
parts of the flash.
Fig. 4. Occurrence of pulses of different total duration in different parts of cloud flash whose electric field record is shown in Fig. 1.
A. Nag et al. / Atmospheric Research 91 (2009) 316–325
319
Fig. 5. Histogram of pulse amplitude for four different types of pulses in the cloud flash whose electric field record is shown in Fig. 1.
• Statistical distribution of pulse amplitude.
• Statistical distribution of total pulse duration.
Fig. 1 shows an example of the measured electric field waveform of a cloud discharge. In addition to “classical” initial breakdown pulses (see Fig. 2a) having durations of the order of tens of
microseconds, “narrow” pulses, defined here as those having
durations less than or equal to 4 µs (see Fig. 2b), were also
observed. Figs. 3–6 show results of the analysis for the flash
shown in Fig.1. Typically, the majority of the pulses in a flash were
found to be small or very small in amplitude and having durations
less than or equal to 4 µs. Also, pulses with durations less than or
equal to 4 µs (including submicrosecond-scale pulses) were found
to occur both before and after the largest pulse in the flash.
Table 2 summarizes the occurrence of smaller and
narrower pulses in the 12 selected cloud discharges. We
Fig. 6. Histogram of total pulse duration for four different types of pulses in the cloud flash whose electric field record is shown in Fig. 1.
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A. Nag et al. / Atmospheric Research 91 (2009) 316–325
Table 2
Summary of occurrence of smaller and narrower pulses in the 12 selected cloud discharges
Flash ID
Total number
of pulses
05/24/06_49
05/24/06_52
05/24/06_54
05/24/06_57
05/24/06_226
05/24/06_299
07/17/06_555
07/17/06_559
07/17/06_565
07/21/06_1013
07/21/06_1015
07/21/06_1018
Total
105
129
187
152
183
185
124
143
49
19
23
24
1323
Number of pulses in the small and very small
categories (%)
Number of pulses having durations less than or
equal to 4 µs (%)
Bipolar
Unipolar
Total
Bipolar
Unipolar
Total
85 (81)
110 (85)
135 (72)
121 (80)
119 (65)
115 (62)
74 (60)
84 (59)
21 (43)
8 (42)
7 (30)
11 (46)
890 (67)
19 (18)
15 (12)
51 (27)
29 (19)
62 (34)
62 (34)
45 (36)
54 (38)
17 (35)
2 (11)
5 (21)
5 (21)
366 (28)
104 (99)
125 (97)
186 (99)
150 (99)
181 (99)
177 (96)
119 (96)
138 (97)
38 (78)
10 (53)
12 (52)
16 (76)
1266 (96)
70 (67)
85 (66)
122 (65)
100 (66)
108 (59)
88 (48)
70 (56)
70 (49)
27 (55)
16 (84)
13 (57)
14 (59)
783 (59)
17 (16)
13 (10)
47 (25)
28 (18)
61 (33)
47 (25)
42 (34)
51 (36)
19 (39)
2 (11)
8 (35)
7 (29)
342 (26)
87 (83)
98 (76)
169 (90)
128 (84)
169 (92)
135 (73)
112 (90)
121 (85)
46 (94)
18 (95)
21 (91)
21 (88)
1125 (85)
found that, for individual flashes, 52 to 99% of the pulses
belonged to the small and very small amplitude categories.
Further, 73 to 95% of the pulses had durations less than or
equal to 4 µs. Fig. 7 shows the distribution of total durations
of pulses in all the 12 cloud flashes. One can see from this
Figure that 85% (1125 out of 1323) of the pulses had
durations less than or equal to 4 µs, of which 70% (783 out of
1125) were bipolar, and that 26% (338 out of 1323) of the
pulses had durations less than 1 µs. The arithmetic mean
pulse duration was 3.5 µs, which is outside the 50–80 µs
range of typical durations usually given for “classical” initial
breakdown pulses in cloud discharges (e.g., Rakov and
Uman, 2003). The discrepancy is apparently due to our
inclusion of smaller pulses that were ignored in previous
studies. We found a moderate linear correlation between
the amplitude and duration of pulses (on average, the
smaller the amplitude the smaller the duration). In Weidman and Krider's (1979) study only a few (2 out of 137)
negative pulses had durations less than 10 µs.
• Statistical distribution of pulse amplitude.
• Statistical distribution of total pulse duration.
Fig. 8 shows an example of the measured electric field
waveform of a cloud-to-ground discharge. Similar to cloud
discharges, in addition to “classical” preliminary breakdown
pulses (see Fig. 9a) having durations of the order of tens of
microseconds, previously not reported (to the best of our
knowledge) “narrow” pulses with durations less than or equal
to 4 µs (see Fig. 9b) were also observed. Figs. 10–13 show
results of the analysis for the flash presented in Fig. 8. The
overwhelming majority (about 93%) of the 706 pulses in the
3.2. Cloud-to-ground discharges
As noted in Section 1, only pulses prior to the first return
stroke in each flash were examined. The peak-to-peak
amplitude of each bipolar pulse and zero-to-peak amplitude
of each unipolar pulse in a particular cloud-to-ground
discharge was normalized with respect to that of the largest
preliminary breakdown pulse (which was also the largest
pulse prior to the first return stroke) in that flash. Pulses were
classified into four different categories depending upon the
value of their normalized amplitude as shown in Table 1. The
time at which the first return-stroke of each cloud-to-ground
discharge occurred was relabeled as the zero of the time scale
(t = 0) and positions of all other pulses on the time axis were
determined with respect to it. For each of the 12 cloud-toground discharges the following characteristics were examined (essentially the same as for cloud discharges):
• Occurrence of pulses of different amplitude in different
parts of the flash (prior to the first return stroke).
• Occurrence of pulses of different total duration in different
parts of the flash.
Fig. 7. Histogram of total duration of unipolar and bipolar pulses in 12
selected cloud discharges.
A. Nag et al. / Atmospheric Research 91 (2009) 316–325
Fig. 8. Electric field record of cloud-to-ground flash 05/24/06_1078.
Fig. 9. Examples of (a) “classical” and (b) “narrow” preliminary breakdown pulses in cloud-to-ground discharges analyzed in this study.
321
322
A. Nag et al. / Atmospheric Research 91 (2009) 316–325
Fig. 10. Occurrence of pulses of different amplitude prior to the first return stroke of cloud-to-ground flash whose electric field record is shown in Fig. 8. Inset shows
the occurrence of pulses of different amplitude between −19.5 ms and −14 ms using bin size of 500 µs.
12 cloud-to-ground discharges examined in this study were
associated with the preliminary breakdown pulse trains
typically occurring tens of milliseconds before the first
return-strokes of the flashes and lasting for a few milli-
seconds, as seen in Figs. 10 and 11. Typically, the majority of
pulses in a flash were found to be small or very small in
amplitude and to have durations less than or equal to 4 µs.
Also, pulses with durations less than or equal to 4 µs
Fig. 11. Occurrence of pulses of different total duration prior to the first return stroke of cloud-to-ground flash whose electric field record is shown in Fig. 8. Inset
shows the occurrence of pulses of different total duration between − 19.5 ms and −14 ms using bin size of 500 µs.
A. Nag et al. / Atmospheric Research 91 (2009) 316–325
323
Fig. 12. Histogram of pulse amplitude for four different types of pulses in the cloud-to-ground flash whose electric field record is shown in Fig. 8.
(including submicrosecond-scale pulses) were found to occur
both before and after the largest pulse in the preliminary
breakdown pulse train.
Table 3 summarizes the occurrence of smaller and
narrower pulses in the 12 selected cloud-to-ground discharges. We found that, for individual flashes, 57 to 98% of the
pulses belonged to the small and very small amplitude
categories. Further, 22 to 89% of the pulses had durations
less than or equal to 4 µs. Fig. 14 shows the distribution of total
durations of pulses in all the 12 cloud-to-ground flashes. It
can be seen from this Figure that 78% (553 out of 706) of the
pulses had durations less than or equal to 4 µs, of which 87%
(479 out of 553) were bipolar, and that 22% (157 out of 706) of
the pulses had durations less than 1 µs. The arithmetic mean
Fig. 13. Histogram of total pulse duration for four different types of pulses in the cloud-to-ground flash whose electric field record is shown in Fig. 8.
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A. Nag et al. / Atmospheric Research 91 (2009) 316–325
Table 3
Summary of occurrence of smaller and narrower pulses observed in the 12 selected cloud-to-ground discharges
Flash ID
Total number
of pulses
05/24/06_224
05/24/06_228
05/24/06_1078
05/28/06_1152
05/28/06_1360
06/01/06_21
06/02/06_120
06/02/06_139
06/02/06_207
06/02/06_212
07/15/06_23
07/17/06_54
Total
169
27
97
23
41
44
25
72
48
65
73
22
706
Number of pulses in the small and very small
categories (%)
Number of pulses having durations less than or
equal to 4 µs (%)
Bipolar
Unipolar
Total
Bipolar
Unipolar
Total
141 (83)
19 (70)
83 (86)
13 (57)
35 (85)
38 (86)
19 (76)
58 (81)
36 (75)
48 (74)
58 (79)
14 (64)
562 (80)
23
6
12
0
1
2
2
6
6
9
11
2
80
164
25
95
13
36
40
21
64
42
57
69
16
642
127 (75)
7 (26)
70 (72)
5 (22)
33 (80)
29 (66)
8 (32)
58 (81)
34 (71)
43 (66)
52 (71)
13 (59)
479 (68)
22 (13)
4 (15)
12 (12)
0
1 (2.4)
2 (4.6)
1 (4.0)
6 (8.3)
6 (13)
9 (14)
9 (12)
2 (9.1)
74 (10)
149 (88)
11 (41)
82 (85)
5 (22)
34 (83)
31 (71)
9 (36)
64 (89)
40 (83)
52 (80)
61 (84)
15 (68)
553 (78)
(14)
(22)
(12)
(0)
(2.4)
(4.6)
(8.0)
(8)
(13)
(14)
(15)
(9.1)
(11)
pulse duration was 4.7 µs, which is outside the 20–40 µs range
of typical durations usually given for “classical” preliminary
breakdown pulses in ground discharges (e.g., Rakov and
Uman, 2003). Similar to cloud-discharge pulses, a moderate
linear correlation was found between the amplitude and
duration of pulses. In Weidman and Krider's (1979) study the
minimum duration of positive pulses included in the analysis
was between 10 and 15 µs versus less than 1 µs in our study.
(97)
(93)
(98)
(57)
(88)
(91)
(84)
(89)
(88)
(88)
(95)
(73)
(91)
both amplitude and duration. Amplitudes of these most
common pulses are 50% or less than that of the largest pulse,
and their durations are less than or equal to 4 µs. In contrast,
total durations of “classical” initial breakdown pulses in both
cloud and cloud-to-ground flashes are thought to be
considerably longer, typically some tens of microseconds. A
significant fraction of examined pulses (26% in cloud flashes
and 22% in cloud-to-ground flashes) had total durations less
than 1 µs.
4. Conclusions
Acknowledgment
The majority of pulses in the early stage of cloud
discharges and those occurring prior to the first return
stroke in cloud-to-ground discharges are typically small in
This study was supported in part by NSF grant ATM0346164.
Fig. 14. Histogram of total duration of unipolar and bipolar pulses in 12 selected cloud-to-ground discharges.
A. Nag et al. / Atmospheric Research 91 (2009) 316–325
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