Geophysical Research Letters
RESEARCH LETTER
10.1002/2018GL077628
Key Points:• Lightning 3-D mapping with highaccuracy and great details has beenrealized by the Fast Antenna
Lightning Mapping Array (FALMA)• Stepped leaders with multiple
branches, K changes, and dart leaders7
with speeds up to 2.4 × 10 m/s arewell imaged• Horizontal location accuracy isestimated to be around 20 m bycomparing locations of successive
return strokes in CG ﬂashes

Supporting Information:• Supporting Information S1• Movie S1• Movie S2• Movie S3• Movie S4• Movie S5• Movie S6• Movie S7
Correspondence to:T. Wu,
tingwu@gifu-u.ac.jp

Lightning Mapping With an Array of Fast Antennas
Ting Wu1
1, Daohong Wang1, and Nobuyuki Takagi1

Department of Electrical, Electronic and Computer Engineering, Gifu University, Gifu, Japan

Abstract Fast Antenna Lightning Mapping Array (FALMA), a low-frequency lightning mapping systemcomprising an array of fast antennas, was developed and established in Gifu, Japan, during the summer of
2017. Location results of two hybrid ﬂashes and a cloud-to-ground ﬂash comprising 11 return strokes (RSs)are described in detail in this paper. Results show that concurrent branches of stepped leaders can be readily
resolved, and K changes and dart leaders with speeds up to 2.4 × 107 m/s are also well imaged. These results
demonstrate that FALMA can reconstruct three-dimensional structures of lightning ﬂashes with great details.
Location accuracy of FALMA is estimated by comparing the located striking points of successive RSs incloud-to-ground ﬂashes. Results show that distances between successive RSs are mainly below 25 m,
indicating exceptionally high location accuracy of FALMA.

Plain Language Summary We have developed a lightning mapping system called Fast Antenna
Lightning Mapping Array (FALMA). FALMA detects low-frequency radio waves produced by lightning
discharges at multiple sites and can reconstruct 3-D structures of lightning ﬂashes. Three lightning ﬂashes areanalyzed in detail in this paper, and animations of seven cases are provided in the supporting information.
These results demonstrate that FALMA can show development of lightning discharges in great details andaccuracy. Types and polarities of lightning discharges can also be determined by the recorded electric ﬁeld
change waveforms. FALMA is expected to become a unique tool for lightning and thunderstorm researches.
Research studies of several topics are already underway based on the observation data in the summer of 2017.

1. Introduction
Citation:
Wu, T., Wang, D., & Takagi, N. (2018).
Lightning mapping with an array of fastantennas. Geophysical Research Letters,
45, 3698–3705. https://doi.org/10.1002/
2018GL077628
Received 20 FEB 2018
Accepted 21 MAR 2018
Accepted article online 26 MAR 2018
Published online 16 APR 2018

Lightning discharges produce a wideband of electromagnetic radiation, among which radio waves are widelyused for ground-based lightning locating. Depending on different purposes, various frequency ranges ofradio waves are utilized in different lightning locating systems. Well-known lightning locating systems
include, among others, the World Wide Lightning Location Network (e.g., Rudlosky & Shea, 2013), which
detects very low-frequency radio waves; the U.S. National Lightning Detection Network (e.g., Cummins &Murphy, 2009), which operates in very low frequency and low-frequency (LF) bands; and the Lightning
Mapping Array (LMA) (Rison et al., 1999) working in the very high frequency (VHF) band.
Most operational lightning locating systems can only do two-dimensional (2-D) locating, which is sufﬁcientfor most practical purposes such as locating lightning-caused damages. However, for research purposes,
especially those involving lightning channel development, lightning initiation, and thunderstorm charge
structures and so on, height information and detailed three-dimensional (3-D) structures of lightning
discharges are necessary. The most successful 3-D lightning locating system is the LMA. As a VHF system,
the location accuracy of the LMA is about 6 to 12 m in the horizontal direction and 20 to 30 m in the verticaldirection for sources over the network (Thomas et al., 2004). Detailed 3-D structures of lightning ﬂashes canbe mapped with the LMA, which has signiﬁcantly facilitated lightning and thunderstorm research studies.
In recent years, 3-D locating in the LF band is rapidly developing (Bitzer et al., 2013; Karunarathne et al., 2013;
Yoshida et al., 2014). The major advantage of observations in the LF band is that the recorded electric ﬁeld
change (E-change) waveforms can be used to determine discharge types, polarities, and to infer currents.
However, compared to VHF systems, the location accuracy is generally lower, and sources that can be locatedare much fewer. Recent studies by Lyu et al. (2014, 2016) made signiﬁcant improvements on LF 3-D mappingby using a hybrid interferometric-time of arrival (TOA) technique combined with a continuous data recording
scheme. They reported that thousands of sources can be located for a typical lightning ﬂash by their ﬁvestation magnetic sensors.

©2018. American Geophysical Union.
All Rights Reserved.

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Due to the valuable waveform information, an LF system with a high 3-D mapping capability can be evenmore useful as a lightning research tool than VHF systems. In this paper, we will introduce our newly

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developed LF lightning locating system called Fast Antenna Lightning
Mapping Array (FALMA). As the name suggests, it is a system comprising
an array of fast antennas. This paper serves as a prompt report based on
the observation in the summer of 2017 to show the capability of FALMA
to do exceptionally detailed 3-D mapping with high accuracy and demonstrate that LF systems are indeed capable of 3-D mapping similar to the
LMA operating in the VHF band.

2. Experiment and Methods
FALMA is a system consisting of multiple sites of fast antennas. During its
observation in the summer of 2017, 12 sites were set up. Figure 1 shows
the network, which covers an area of about 90 × 90 km2. The distances
between neighboring sites are about 20 to 30 km. At each site, there is afast antenna, an AD converter, a computer, and some devices for internet
connection. All sites are synchronized with Global Positioning System.
Figure 1. Network of Fast Antenna Lightning Mapping Array during thesummer observation in 2017. The black squares represent 12 sites. The latitude and longitude of the site at (0, 0) is (35.475°E, 136.960°N). Sources ofthree lightning ﬂashes described in section 3 are also plotted. The black dots
represent locations of return strokes analyzed in section 4.

The fast antenna is a ﬂat plate antenna similar in principle to that
described by Kitagawa and Brook (1960). It has a time constant of 200 μs
and records radio waves in the frequency band of about 500 Hz to
500 kHz. The AD converter has a resolution of 16 bits. In order to achievea timing accuracy as high as possible, we use a sampling rate of 25 MS/s.
The recording length of each trigger is 1 s with a pretrigger length of
100 ms. Full waveform data are recorded for post processing.

A lot of efforts have been made to overcome shortcomings of an LF system and to achieve location results as
good as a VHF system. Features of FALMA that are important for improving the performance of 3-D mapping
are described as follows.
2.1. High Sensitivity of the Fast Antenna
Fast antennas of FALMA were newly designed and manufactured. Fast antennas with various structures were
tested. They were set up at the same location, and signals from the same lightning discharges were compared to ﬁnd out the structure with the highest signal-to-noise ratio (SNR). For example, our tests indicatethat antennas with upward facing ﬂat plates generally have a higher SNR than those with downward facing
ﬂat plates. A higher SNR means that more pulses can emerge from the background noise and be located,
contributing to a more complete image of reconstructed lightning channels.
2.2. High Timing Accuracy
A sampling rate of 25 MS/s is used for FALMA, corresponding to the timing accuracy of 40 ns. As the timing
accuracy of Global Positioning System is about 40 to 50 ns, 25 MS/s is the highest meaningful sampling rate.
Although the effective timing error for location will not be as small as 40 ns due to the limited analog bandwidth, sampling at 25 MS/s minimizes timing uncertainty as much as possible.
2.3. Continuous Data Recording Capability
Normally during the period when the triggered data are being written to the hard drive, new signals cannot
be processed and are lost, and the so-called “dead time” arises. The dead time problem is especially serious
when the sampling rate is high and the data recording length is long. In order to solve the dead time
problem, we developed a new recording scheme by fully utilizing the computer memory. When there comesa trigger and the triggered data are being written to the hard drive, the input data from the AD converter are
temporarily stored in the memory and are processed after the writing of the triggered data is ﬁnished. In thisway, all waveform data can be fully recorded. This is especially important when a ﬂash lasts for a long time.
Similarly, the improvement made by Stock et al. (2014) on VHF interferometry was primarily due to thecontinuous recording capability.

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2.4. Waveform Correlation for Pulse Matching
FALMA uses the TOA method for 3-D locating. The most difﬁcult part in the TOA method is accurately matching pulses recorded at different sites. Since every site of FALMA records the full waveform, it is preferable touse waveform correlation to match pulses at different sites, which is more accurate and efﬁcient than purely
trying different combinations. The waveform correlation method was also used by Lyu et al. (2014) in theirinterferometric-TOA technique, which largely improved location results of their LF system.
2.5. Relatively High-Frequency Band for Locating
The frequency band of the recorded waveform is about 500 Hz to 500 kHz. However, it is not necessary to use
the full bandwidth for locating; it is more advantageous to use a relatively high frequency part for locating.
Frequency is directly related with the spatial scale of the discharge, so higher frequency components can theoretically yield location results with higher accuracy. Moreover, a narrower frequency band means many
noise signals can be excluded, and more pulses produced by lightning discharges can be detected andlocated. FALMA uses a frequency band of 200 to 500 kHz for locating.

3. Location Results
In this section, we will describe location results of three ﬂashes in detail. E-change waveforms, which use theatmospheric sign convention, are also provided, but as the fast antenna has not been calibrated, the waveform magnitude is not shown. Animations of the second example and six more ﬂashes are provided as
Movies S1–S7 in the supporting information to give a visual demonstration of the 3-D mapping capabilityof FALMA.
3.1. A Bolt-From-the-Blue Type Hybrid FlashThe ﬁrst case is a bolt-from-the-blue type hybrid ﬂash (e.g., Krehbiel et al., 2008) started as a typical intracloud(IC) ﬂash and produced a return stroke (RS) at the end. This ﬂash lasted for 423.3 ms, and a total of 2,880
sources were located. Figure 2 shows the waveform and 3-D location results.
The ﬁrst half of this ﬂash looks like a typical IC ﬂash. It started with an upward negative leader, forming analmost vertical channel, presumably between the main negative charge layer and the upper positive charge
layer. The vertical channel is dark blue sources and is labeled as “a” in Figure 2. The speed of the initial upward
propagation is about 7.1 × 105 m/s. The upward negative leader then turned to a horizontal direction andpropagated to the north before it split to two branches, which are labeled as “b1” and “b2.” The branch b2
developed to the east. Its altitude decreased from about 10 to 8 km and at last it developed almost verticallyback to about 10 km. The ﬁnal vertical propagation is labeled as “c.” From the E-change waveform, we candetermine that this is also a negative leader. The speed of the upward propagation c is about 1.1 × 105 m/s.
The branch b1 developed to the west and soon turned to the south. It progressed for more than 10 km andhad at least four clear branches labeled as d1–d4. The branch d4 turned to the ground and produced an RS.
The speed of the downward negative leader appeared to increase as it approached to the ground. The overall
speed is about 1.3 × 105 m/s, typical for a stepped leader.
While branches b1 and b2 were developing from the top of the initial vertical channel a, some sources werealso located from the bottom of the vertical channel. According to the bidirectional leader concept (e.g.,
Mazur et al., 2013), as the initial negative leader develops upward, a positive leader develops in the opposite
direction. In Figure 2 we can see some scattered sources at the height of about 6 km. These sources are probably produced from the main negative charge layer. They may be produced by the positive leader or recoil
leaders traveling from the head of the positive leader back to the origin.
3.2. A Hybrid Flash With Multiple K Changes
The second case is shown in Figure 3. It is also a hybrid ﬂash, but it is different from the ﬁrst case in that the IC
processes and the RS are initiated by different leaders. This type of hybrid ﬂash has also been analyzed by Lu
et al. (2012). Animation of this ﬂash is provided as Movie S3 in the supporting information.
This ﬂash started with a succession of negative leaders propagating upward from the main negative charge
region, but all of them stopped developing before forming typical horizontal propagations in the upper positive charge region. At the time of about 300 ms, a downward stepped leader was formed and it produced an

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Figure 2. E-change waveform and 3-D location results of case 1 in Figure 1. (a) E-change waveform. (b) Height-time view. (c) Height-distance (from west to east) view.
(d) Plan view. (e) Distance (from south to north)-height view. (f) Source distribution along the height. The color scale indicates the time corresponding to the time
coordinate of Figure 2b.

RS. From Movie S3, we can see that the downward leader was initiated from the head of an old channel that
had stopped developing. From Figures 2c and 2e we can see that the downward leader had at least threebranches traveling simultaneously. All of them reached very close to the ground but only one successfully
touched the ground and produced an RS (cross sign).
After the RS, ﬁve K changes were clearly imaged and labeled as k1–k5 in Figure 3b. From Figures 3c and 3e,sources from k1–k4 cannot be seen as they are completely covered by sources of k5. This feature also indicates the high location accuracy of FALMA.
3.3. A Negative Cloud-to-Ground Flash Comprising 11 RSs
The third example is a negative cloud-to-ground (CG) ﬂash comprising 11 RSs as shown in Figure 4. Eachpanel in Figure 4 shows the location results in height-time view along with E-change waveforms. Eleven
RSs are labeled as R1–R11. Sources of this ﬂash are also plotted in Figure 1 and labeled as “Case 3.”
This ﬂash started with a direct downward propagation as shown in Figure 4b. Normally, a CG ﬂash starts withthe preliminary breakdown and followed by a stepped leader. In this case, these is no clear boundary

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Figure 3. (a–f) E-change waveform and 3-D location results of case 2 in Figure 1. Subplots are arranged as in Figure 2. The cross sign indicates the return stroke (RS).

between the preliminary breakdown and the stepped leader, and for simplicity, the whole processes before
R1 are considered as one stepped leader. The speed of the stepped leader is about 2.0 × 105 m/s. A few
sources (dark red) are also located for the RS R1.
The second RS R2 occurred about 187 ms after R1. About 10 ms before R2, a K change was located as shownin Figure 4c. This K change reached very close to the ground, but actually, it did not reach the ground.
According to the E-change waveform, there was no RS at the end of this K change and this K change had
no direct connection with R2. Therefore, this K change may also be called “attempted leader” (Rhodes
et al., 1994), which is a dart leader that does not reach the ground. This K change was clearly imaged, andits overall speed was about 2.6 × 106 m/s. This example shows the importance of the E-change waveform
data in identifying discharge processes. Without the waveform, this K change could be easily misinterpreted
as a dart leader reaching the ground.
Subsequent RSs (R2–R11) occurred with time intervals of 25 to 60 ms. Leaders before these RSs were all
located, four of which are shown in Figures 4d–4g. All of these leaders seem to be dart leaders. The dart leader in Figure 4d had a large speed of 2.4 × 107 m/s. Probably because of its large speed, only a few sourceswere located. The speed for leaders in Figures 4e–4g ranged from 5.5 to 8.1 × 106 m/s. These leaders were all
well located.

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Figure 4. (a–g) E-change waveform and location results of a negative cloud-to-ground ﬂash comprising 11 return strokes. Each subplot is shown in height-time view
with the color scale indicating time. Figures 4b–4g are some enlarged portions in Figure 4a.

We can notice one problem from the results that when a leader gets close to the ground, location results
seem to be more scattered. This is a common problem that the location accuracy for discharges with a
low altitude is relatively low. One possible reason is that radio waves produced by discharges near the
ground are easily affected by the lossy ground and the topography when propagating toobservation sites.
From Figure 4a we can also see that some sources are located at the height of 6 to 9 km throughout this ﬂash.
This indicates that the main negative charge layer is at the height of 6 to 9 km and all RSs are produced fromthis negative charge layer.
Lyu et al. (2014) reported that their LF system could also locate dart leaders in CG ﬂashes, but the dart leadersreported by them had the downward speed of 0.8 to 2 × 106 m/s. Lyu et al. (2016) also located dart leaders in
IC ﬂashes with a speed range of 0.9 to 7.1 × 106 m/s. To our best knowledge, no LF system has ever reported
locating of dart leaders with the speed on the order of 107 m/s.

4. Estimation of Location Accuracy Using Multistroke Lightning Flashes
In this analysis, we will evaluate the location accuracy of FALMA by comparing the distances between
different RSs in CG ﬂashes. For most CG ﬂashes producing multiple RSs, these RSs strike at the same point.
However, the location results of these RSs always have some differences due to location uncertainties.
Because different RSs are independently located, differences of their locations can indicate the location
accuracy of the system. Based on this principle, we located a large amount of RSs produced in a thunderstorm over the network. For every RS, the ﬁrst RS that follows it is found out, and if their time difference is
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Figure 5. (a and b) Distribution of the distance between successive RSs. The y axis in Figure 5a is in the logarithmic scale.

less than 500 ms, their horizontal distance is calculated. As an example, for the CG ﬂash in Figure 4, whichcontains 11 RSs, distances between ith and (i + 1)th RSs (1 ≤ i ≤ 10) are calculated and 10 results are
obtained. A total of 1684 results are obtained, and locations of contributing RSs are plotted as black
dots in Figure 1.
The distribution of the calculated distances is shown in Figure 5. Figure 5a shows in the range of 0 to 1,600 m
and Figure 5b in the range of 0 to 200 m. Note that the y axis of Figure 5a is shown in the logarithmic scale.
The distance between successive RSs has a very wide distribution. The main reason is that some CG ﬂashes
have multiple ground terminations. As reported by Valine and Krider (2002), 35% CG ﬂashes had two or morestriking points separated by tens of meters or more. Another reason is that some successive RSs are actually
produced in different CG ﬂashes. Results below 200 m are replotted in Figure 5b. There are 1,274 results
below 200 m, accounting for 75.7% of all results. We can see that the majority of results are smaller than
25 m. For simplicity, here we consider that all results below 200 m are due to location uncertainties. The meanvalue and median value of these results are 20.9 and 11.0 m, respectively, and 79.8% of these results are
below 25 m.
This result indicates the high accuracy of about 20 m, at least for RSs. However, this method may not be able
to evaluate systematic errors. For example, multiple RSs in a CG ﬂash are located very close to each other, butthey may be all located away from the real striking point due to certain systematic errors. We will try to do amore comprehensive analysis on the location accuracy in the future.

5. Conclusions
The capability of lightning 3-D mapping by FALMA is demonstrated in this paper. Different from traditional
lightning mapping in the VHF band, FALMA uses an array of fast antennas to sense lightning radiation signals
in the LF band. Location results of three lightning ﬂashes are described in detail to demonstrate the 3-D
mapping capability of FALMA. Animations of seven ﬂashes are provided in the supporting information.
Due to many improvements on both the hardware and software, FALMA can map 3-D structures of various
types of lightning ﬂashes in high accuracy and great details, representing a new level of lightning mapping
capability for LF systems.
As an LF system, FALMA records the full E-change waveforms at every site. By combining waveforms and 3-D
location results, we can unambiguously determine discharge types and leader polarities. It is also possible toinfer discharge currents and thunderstorm charge structures. FALMA can be expected to become a uniquetool for lightning and thunderstorm researches.

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Acknowledgments
This work was supported by the Ministryof Education, Culture, Sports, Science,
and Technology of Japan (grants
15H02597 and 16H04315). Location
results used in this paper can be downloaded at https://doi.org/10.5281/
zenodo.1202489. More examples oflightning ﬂashes imaged by FALMA canbe found at https://www1.gifu-u.ac.jp/~lrg/falma.html. The authors thank two
anonymous reviewers for their constructive comments.

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