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International Journal on Electrical Engineering and Informatics - Volume 11, Number 2, June 2019
Reconstruction of Lightning Channel Based on Acoustic Radiation
Ariadi Hazmi1, Primas Emeraldi1, Muhammad Imran Hamid1, Suci Melati1, and Nobuyuki Takagi2
1Andalas University, Department of Electrical Engineering, Padang, Indonesia
2Gifu University, Department of Electrical, Electronic and Computer Engineering, Gifu, Japan
Abstract: The acoustic radiation of lightning was used to get information on the lightning
channel, such as images and locations. A single station of short baseline lightning location was
installed to record the acoustic signals of lightning using a microphone array observation system
(MAOS). In this study, the differential time of arrival (DTOA) method was used to examine the
time variation in the acoustic signals of lightning and to reconstruct the 3D lightning channel
imaging. The results showed that there was good agreement between images recorded by
cameras and MAOS. The height of negative charge center in thundercloud is at 4.37-4.83 km.
The azimuth and elevation angles of the acoustic radiation source at higher latitude inside a
thundercloud of two recorded natural lightning discharges were 70.67o, 90o and 67.83o, 73.82o,
respectively. The acoustic signal of thunder lasted about 15.15-16.038 s. The system was able to
reconstruct the 3D lightning channel imaging.
Keywords: Lightning; cloud to ground; image; mapping; acoustic radiation.
1. Introduction
The stepped leader and attachment process prior to return strokes are closely related to
thundercloud to produce the electric field. The height of the bottom of the thundercloud to the
ground plays a significant role in increasing the leader step length occurring in virgin air [1]. It
is generally believed that the lightning stroke distance has been determined by the height of the
bottom of the thundercloud to ground. The leader propagation of natural lightning also plays an
important role in the lightning protection designs of tall objects on the ground has become a
concern of many researchers [2-5].
When the stepped leader approaches the ground (downward leader), its negative charge
attracts concentrated positive charge on the ground (upward leader) [6-9]. Furthermore, one of
these upward leaders will attach with a branch of the downward leader, causing a return stroke.
The return stroke impulsively heats the current-carrying air which then generates thunder and
radiates acoustic signals. The largest amplitudes of the acoustic signal are usually associated
with the return stroke of the lightning discharge. The acoustic signal can provide information on
the image of the lightning channel. The frequency range of acoustic emissions from lightning is
20-20,000 Hz [10-17]. Because the acoustic radiations from lightning include low frequencies,
a short baseline lightning location can be applied to reconstruct the lightning channel imaging
using a microphone array observation system (MAOS) with a single station. The method used
in finding the height of thundercloud and lightning location are the differential time of arrival
(DTOA). In addition, the acoustic radiation of lightning can be captured in a 360° perspective
and flashes hidden in clouds can be observed, which could increase the probability of capturing
lightning flashes compared with using the cameras [18-21].
The purpose of this study is to determine the height of thundercloud to ground and reconstruct
the lightning channel based on the acoustic radiation sources. As far we know, this is the first
time to measure the height of negative charge center in thundercloud in Padang, Indonesia. Our
observation results are compared with a few of previous studies in other regions.
2. Method
In this study, to analyze the acoustic signals of a lightning discharge and to reconstruct the
Received: April 12nd, 2019. Accepted: June 30th, 2019
DOI: 10.15676/ijeei.2019.11.2.8
341
3D imaging of the lightning channel, differential time of arrival (DTOA) was used as described
in the following section.
Differential time of arrival
The acoustic radiation of lightning discharges was recorded simultaneously by four different
microphones (for convenience ‘mic’ refers to microphone). Next, to obtain the DTOA at the
different microphones, all acoustic signals were examined by cross correlation. The equations of
DTOA used in this study are similar with used by Zhang et al. [18]. The time difference between
signal 2 (S2) and signal 3 (S3) is ∆𝑡 = 𝑡2 − 𝑡3 as shown in Figure 1.
|𝐷𝐻| = 𝑣 ∙ ∆𝑡 (1)
𝑣 = 322 + 0.6 𝑇 (2)
𝑣 = 353 𝑚/𝑠
Where v and T are the speed of thunder sound propagation and temperature, respectively.
cos(∠ 𝑂𝐷𝐻) =|𝐷𝐻|
|𝑂𝐷|=
𝑣×Δ𝑡
𝐿2 (3)
cos(∠ 𝐸𝐷𝐻) =|𝐷𝐸|
|𝐷𝐻|=
𝑣×Δ𝑡
𝐿2 (4)
|𝐷𝐸| = |𝐷𝐹| × cos(∠𝐺𝑂𝐹) (5)
|𝐷𝐸| = |𝐷𝐻| × cos(∠𝐻𝐷𝐹) cos(∠𝐺𝐷𝐹)
𝑣 × ∆𝑡
𝐿2
=|𝐷𝐻| × cos(∠𝐻𝐷𝐹) cos(∠𝐺𝐷𝐹)
|𝐷𝐻|= cos 𝛼 sin 𝛽
𝐿2 × cos 𝛼 cos 𝛽 = 𝑣 × ∆𝑡 = 𝑣 × |𝑡2 − 𝑡3| (7)
Figure 1. Schematic diagram of differential time of arrival of acoustic signals [18].
The azimuth (β) and elevation (α) in Figure 1 can be resolved by least square method for
nonlinear equations 8-10 as follows:
𝐿1 × 𝑠𝑖𝑛 𝛼 = 𝑣 × |𝑡2 − 𝑡1| = 𝑣 × ∆𝑡1 (8)
𝐿2 × 𝑐𝑜𝑠 𝛼 𝑐𝑜𝑠 𝛽 = 𝑣 × |𝑡2 − 𝑡3| = 𝑣 × ∆𝑡2 (9)
𝐿3 × 𝑐𝑜𝑠 𝛼 𝑠𝑖𝑛 𝛽 = 𝑣 × |𝑡2 − 𝑡4| = 𝑣 × ∆𝑡3 (10)
Where L is distance between the microphones.
Ariadi Hazmi, et al.
342
3. Observation and Data
Acoustic radiation of lightning was recorded using a single station of MAOS located in
Padang, Indonesia (-0.912° N, 100.418° E). The system consisted of one slow, one fast and one
loop antenna, two surveillance video cameras, four condenser microphones with a frequency
range of 20-20,000 Hz, and two digitizers. All the equipment was controlled by a computer that
was used to capture the electromagnetic, optic and acoustic signals of lightning. The slow
antenna was used as an external trigger to simultaneously trigger the acoustic signals of the
lightning discharge by the four microphones. The four acoustic signals were amplified by an
audiophile vacuum tube preamplifier with gain at 26-60 dB and maximum output at 10 dB. The
record length was set to 20 s with a pre-trigger of 10% of the record length and a sampling rate
of 100 kS/s. A schematic of the MAOS is shown in Figure 2, with the distance between the
microphones at 2 m.
Figure 2. Schematic of the MAOS.
4. Result and Discussions
In this study, two negative cloud to ground (-CG) lightning discharges were examined to
evaluate the MAOS and the algorithm of the DTOA lightning mapping system based on acoustic
radiation. Due to limited data, in this study only two acoustic signals of natural lightning were
analyzed, which were recorded at 16:49:28 PM and 19:02:33 PM on 8 September 2018 and 9
December 2018, respectively. The following section analyzes in detail the two -CG lightning
discharges, which will be referred to as -CG A and -CG B, respectively.
Detailed description of -CG A
The -CG A lightning discharge was recorded at 16:49:28 PM (local time). One of the video
camera frames that captured the lightning is shown in Figure 3. The electric field and magnetic
field changes recorded by the fast antenna and the loop antenna respectively are presented in
Figure 4a. Figure 4a indicates that 6 return strokes (RS) occurred in the lightning event. At the
same time, the associated acoustic signal of the lightning discharge was recorded by four
microphones, namely mic 1, mic 2, mic 3, and mic 4, respectively, as shown in Figure 4b.
According to the time difference between the optic and the first acoustic data records, the
lightning discharge occurred around 1 km from the observation site. Furthermore, using the
DTOA method, the azimuth-elevation angles and time of the acoustic signals were obtained by
calculating the different times of arrival for each microphone using the least square method and
cross correlation to find the peak values of the four microphone signals (see appendix A). The
3D lightning channel mapping can be reconstructed from the acoustic signal, the height of
Mic
rophones
Video Camera
Slow antenna
Fast antenna
Loop antenna
Dig
itiz
er 1
Dig
itiz
er 2
PCP
rea
mp
lifie
r
Amplifier
Amplifier
Amplifier
Ground
Thundercloud
Downward
leader
Upward
leader
Height
-
-
-
-
+
+
+
Reconstruction of Lightning Channel Based on Acoustic Radiation
343
negative charges of thundercloud was 4.83 km as shown in Figure 5. The x, y, z directions and
time order origin from the azimuth and elevation angles and the acoustic signal of the lightning
channel, respectively, are displayed in Table 1.
Detailed description of -CG B
The -CG B lightning discharge was recorded at 16:49:28 PM (local time). One of the video
camera frames associated with the lightning discharge is displayed in Figure 3. In addition, the
electric field and magnetic field changes recorded by the fast antenna and the loop antenna,
respectively, are shown in Figure 6a. The recorded acoustic signals of the lightning discharge by
the four microphones, namely mic 1, mic 2, mic 3, and mic 4, respectively, are shown in Figure
4b. Based on the time difference between the optic and the first acoustic data records, the
lightning discharge occurred around 0.2 km from the observation site. The location of -CG B
was closer than that of -CG A, as can be seen in Figures 6 and 7b. The amplitude of the acoustic
signal of -CG B was higher than that of -CG A. Moreover, in the same way (see appendix A),
the azimuth-elevation angles and time for the acoustic signal were obtained by using the DTOA
method. A projection of the 3D lightning mapping results can be seen in Figure 5. The height of
negative charges of thundercloud was 4.37 km. The Cartesian coordinates (x, y, z) of the
radiation source and time order origin from the azimuth and elevation angles and acoustic signal
of the lightning channel, respectively, are presented in Table 2.
Figure 3. –CG A lightning flash image. (a) One of video camera frames, (b) The expanded
lightning channel image.
Table 1 and 2 tell us that the azimuth and elevation angles of the radiation sources at higher
latitude inside the thundercloud of both lightning were at 70.67°, 90° and 67.83°, 73.82°,
respectively. The minimum values of the azimuth and elevation angles were 56.16°, 2.38° and
1.28°, 0.56°, respectively. In the previous study, in China [18] using a rocket triggered lightning
and Sri Lanka [19] with natural lightning reported that they found the height of negative charges
of thundercloud were 0.74 km and 4.56 km, respectively. Compared with the value revealed in
China, the height of thundercloud in Indonesia and Sri Lanka were higher. The differences may
be due to different thundersorm types between the two regions. The propagation path of the
acoustic radiation sources was initiated from the ground to the cloud can be seen from the 3D
lightning mapping in Figures 5 and 8. Because the video camera speed was 30 fps, the cameras
were not able to record the branches of the lightning channels so that there are slight differences
between the lightning images recorded by the camera and the lightning images detected by the
MAOS. This may also be caused by errors in calculating the time difference measurements
because of background noise. The accuracy of the DTOA also depends on the time difference
measurement between the microphones. Furthermore, the acoustic signal of thunder lasted about
15.15-16.038 s as can be seen in Table 1 and 2.
(a) (b)
Ariadi Hazmi, et al.
344
Figure 4. The measured lightning discharge of –CG A. (a) Electric field and magnetic field
changes, (b) Acoustic radiation.
Figure 5. 3D lightning channel mapping of –CG A.
Figure 6. –CG B lightning flash image. (a) One of video camera frames, (b) The expanded
lightning channel image.
RS1 RS2RS3 RS4
RS5 RS6
(a) (b)
(a) (b)
Reconstruction of Lightning Channel Based on Acoustic Radiation
345
Figure 7. The measured lightning discharge of –CG B. (a) Electric field and magnetic field
changes, (b) Acoustic radiation.
Table 1. 2D location of –CG A. Table 2. 2D location of –CG B.
Azimuth
(o)
Elevation
(o) Time (s) Azimuth (o)
Elevation
(o) Time (s)
68.78 7.39 0.077 67.00 4.82 0.507
70.15 2.65 0.095 43.67 12.08 1.510
69.85 9.28 0.136 17.69 55.06 2.149
74.76 7.09 0.199 7.80 23.66 4.032
69.31 11.17 0.227 10.58 17.16 4.066
66.87 31.65 0.812 34.81 0.59 4.109
78.11 11.58 1.739 6.62 63.10 4.334
73.59 11.17 1.985 2.38 59.04 4.380
74.96 16.54 2.147 13.24 66.32 5.586
72.46 47.81 3.252 40.21 66.32 5.647
75.99 30.39 3.273 52.66 67.83 6.030
77.93 39.51 4.710 85.46 66.32 7.987
75.96 48.54 4.957 80.74 66.08 8.752
73.98 48.69 5.876 85.34 65.84 8.938
76.09 50.51 5.911 86.82 65.13 9.276
80.21 48.25 6.376 78.27 59.23 10.232
89.19 56.64 7.677 85.68 57.54 10.411
70.87 60.60 8.233 81.78 65.84 11.506
56.16 11.47 8.495 87.03 63.32 12.077
67.38 1.28 9.698 82.43 59.61 12.909
84.31 52.89 10.796 87.03 61.41 13.148
80.05 57.18 10.919 88.81 63.10 13.699
62.76 62.46 10.987 87.14 62.88 14.111
70.67 67.83 11.053 89.71 60.60 14.231
85.87 57.73 14.152 87.71 60.01 14.535
83.07 61.41 15.014 85.43 33.52 14.627
82.61 45.66 15.333 90.00 73.82 14.912
90.00 61.41 16.038 90.00 55.06 15.150
(a) (b)
Ariadi Hazmi, et al.
346
Figure 8. 3D lightning channel mapping of –CG B.
5. Conclusion
A microphone array observation system (MAOS) with a short baseline lightning mapping
system was used to record and analyze the acoustic radiation from natural lightning. The system
utilized the TDOA method and a number of signal processing tools, such as cross correlation
method to calculate the time delay and the least square method to estimate the azimuth and
elevation angles. The system was able to determine the height of thundercloud and reconstruct
the 3D imaging of the lightning channel. More data are needed to perfect and complement the
understanding of the acoustic radiation of the lightning channel.
6. Acknowledgment
This work is supported by Universitas Andalas of KRP2GB-PDU scheme, with grant no.
046/UN.16.17/PP.MGB/LPPM/2018.
Appendix A
Here t1, t2, t3 and t4 are the time values at correlated peaks of the same phase of the four signals
cross correlated the time values. t0 is the time difference between the light and the sound signal
of the lightning and t21, t31 and t41 are time differences between relevant microphone pairs.
Table 3. Time differences of –CG A
Time values of each considered signals (s) Time differences (s)
t1(sig1) t2(sig2) t3(sig3) t4(sig4) t21 t31 t41 t0
0.077 0.079 0.072 0.076 0.002 -0.005 -0.001 3.000
0.095 0.097 0.090 0.095 0.002 -0.005 0.000 3.018
0.136 0.138 0.131 0.135 0.002 -0.005 -0.001 3.059
0.199 0.200 0.194 0.198 0.001 -0.005 -0.001 3.122
0.227 0.229 0.222 0.226 0.002 -0.005 -0.001 3.150
0.812 0.814 0.808 0.809 0.002 -0.004 -0.003 3.735
1.739 1.740 1.734 1.738 0.001 -0.005 -0.001 4.662
1.985 1.987 1.980 1.984 0.001 -0.005 -0.001 4.908
2.147 2.148 2.142 2.145 0.001 -0.005 -0.002 5.070
3.252 3.253 3.249 3.247 0.001 -0.003 -0.004 6.175
3.273 3.274 3.269 3.270 0.001 -0.004 -0.003 6.196
Reconstruction of Lightning Channel Based on Acoustic Radiation
347
Time values of each considered signals (s) Time differences (s)
t1(sig1) t2(sig2) t3(sig3) t4(sig4) t21 t31 t41 t0
4.710 4.710 4.706 4.706 0.001 -0.004 -0.004 7.633
4.957 4.958 4.954 4.953 0.001 -0.003 -0.004 7.880
5.876 5.877 5.873 5.871 0.001 -0.003 -0.004 8.799
5.911 5.912 5.908 5.907 0.001 -0.003 -0.004 8.834
6.376 6.376 6.373 6.372 0.001 -0.003 -0.004 9.299
7.677 7.677 7.675 7.673 0.000 -0.003 -0.005 10.601
8.233 8.233 8.232 8.228 -0.001 -0.002 -0.005 11.156
8.495 8.497 8.497 8.494 0.001 0.002 -0.001 11.418
9.698 9.698 9.699 9.697 0.001 0.002 0.000 12.621
10.796 10.796 10.794 10.792 0.000 -0.002 -0.005 13.719
10.919 10.919 10.916 10.914 0.000 -0.002 -0.005 13.842
10.987 10.988 10.985 10.982 0.001 -0.002 -0.005 13.910
11.053 11.054 11.051 11.047 0.001 -0.002 -0.005 13.976
14.152 14.153 14.151 14.147 0.000 -0.002 -0.005 17.075
15.014 15.014 15.013 15.009 0.000 -0.001 -0.005 17.938
15.333 15.334 15.332 15.329 0.000 -0.002 -0.004 18.256
16.038 16.038 16.037 16.033 0.000 -0.002 -0.005 18.961
Table 4. Time differences of –CG B
Time values of each considered signals (s) Time differences (s)
t1(sig1) t2(sig2) t3(sig3) t4(sig4) t21 t31 t41 t0
0.507 0.506 0.505 0.506 -0.001 -0.001 0.000 0.500
1.510 1.513 1.507 1.511 0.003 -0.003 0.001 1.503
2.149 2.151 2.148 2.144 0.003 -0.001 -0.005 2.142
4.032 4.034 4.031 4.029 0.002 0.000 -0.002 4.025
4.066 4.068 4.065 4.064 0.003 0.000 -0.002 4.059
4.109 4.106 4.111 4.109 -0.003 0.002 0.000 4.102
4.334 4.336 4.333 4.328 0.002 0.000 -0.005 4.327
4.380 4.382 4.380 4.375 0.002 0.000 -0.005 4.373
5.586 5.587 5.586 5.580 0.002 0.000 -0.005 5.579
5.647 5.648 5.648 5.641 0.001 0.001 -0.005 5.640
6.030 6.031 6.031 6.025 0.001 0.001 -0.005 6.024
7.987 7.987 7.988 7.981 0.000 0.001 -0.005 7.980
8.752 8.752 8.753 8.747 0.000 0.001 -0.005 8.745
8.938 8.938 8.939 8.932 0.000 0.001 -0.005 8.931
9.276 9.276 9.278 9.271 0.000 0.001 -0.005 9.270
10.232 10.233 10.234 10.227 0.000 0.002 -0.005 10.226
10.411 10.411 10.412 10.406 0.000 0.002 -0.005 10.404
11.506 11.507 11.508 11.501 0.000 0.002 -0.005 11.500
Ariadi Hazmi, et al.
348
Time values of each considered signals (s) Time differences (s)
t1(sig1) t2(sig2) t3(sig3) t4(sig4) t21 t31 t41 t0
12.909 12.909 12.911 12.904 0.000 0.002 -0.005 12.902
13.148 13.148 13.149 13.143 0.000 0.002 -0.005 13.141
13.699 13.699 13.701 13.694 0.000 0.002 -0.005 13.692
14.111 14.111 14.113 14.106 0.000 0.002 -0.005 14.104
14.231 14.231 14.233 14.226 0.000 0.002 -0.005 14.224
14.535 14.535 14.537 14.530 0.000 0.002 -0.005 14.528
14.627 14.627 14.629 14.630 0.000 0.002 0.003 14.620
14.912 14.912 14.914 14.906 0.000 0.002 -0.006 14.905
15.150 15.150 15.152 15.145 0.000 0.002 -0.005 15.143
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Ariadi Hazmi was born in Lahat, South Sumatra, Indonesia in 1975. He
received B. Eng., M. Eng., and Dr. Eng. degrees in Electrical Engineering
from Universitas Sriwijaya, Institut Teknologi Bandung, Indonesia, and Gifu
University of Japan in 1998, 2002, 2008, respectively. Since 1999, He is
lecturer at Universitas Andalas of Indonesia and now serves as a Professor.
His research interest is lightning and plasma physics and lightning protection.
He is a member of the Society of Atmospheric Electricity of Japan and IEEE.
Primas Emeraldi was born in Pariaman, West Sumatera, Indonesia in 1986.
He received B. Eng., M. Eng. degrees in Electrical Engineering from
Universitas Andalas and Institut Teknologi Bandung, Indonesia, in 2009,
2013, respectively. Since 2015, He is a lecturer at Universitas Andalas,
Indonesia. His research interest is plasma physics and lightning protection.
Ariadi Hazmi, et al.
350
Muhammad Imran Hamid was born in Bulukumba, South Sulawesi,
Indonesia in 1971. He received B. Eng., M. Eng., and Ph.D. in Electrical
Engineering from Universitas Hasanuddin, Institut Teknologi Bandung,
Indonesia, and University Technology Malaysia in 1996, 2001, 2014,
respectively. Since 1999, He is a lecturer at Universitas Andalas, Indonesia.
His research interest is power electronics for electrical energy conversion and
high voltage application.
Suci Melati was born in Padang, West Sumatra, Indonesia in 1993. She
received B. Eng. in Electrical Engineering from Universitas Andalas,
Indonesia in 2015. Now, she is a master student in Electrical Engineering of
Universitas Andalas.
Nobuyuki Takagi was born in 1957. He received MS and Ph.D from Nagoya
University of Japan. He joined Gifu University from 1985 and presently serves
as a professor. His research interests are atmospheric electricity, lightning
physics and lightning protection. He is a member of the Society of
Atmospheric Electricity of Japan and AGU.
Reconstruction of Lightning Channel Based on Acoustic Radiation
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