RESEARCH ARTICLE
10.1029/2020JD033039
Key Points:• Forty‐seven multi‐stroke +CG
ﬂashes containing two to ﬁve
positive strokes observed in winterthunderstorms in Japan are
analyzed• Interstroke intervals, distances
between sequential strokes and peak
amplitudes of ﬁrst and subsequent
strokes are statistically analyzed• Positive leaders initiating mostsubsequent strokes are originatedfrom in‐cloud negative leader
channels
Supporting Information:• Supporting Information S1

Correspondence to:T. Wu,
tingwu@gifu-u.ac.jp

Citation:
Wu, T., Wang, D., & Takagi, N. (2020).
Multiple‐stroke positive cloud‐to‐ground lightning observed by the
FALMA in winter thunderstorms inJapan. Journal of Geophysical Research:
Atmospheres, 125, e2020JD033039.
https://doi.org/10.1029/2020JD033039
Received 1 MAY 2020
Accepted 23 SEP 2020
Accepted article online 30 SEP 2020

Multiple‐Stroke Positive Cloud‐to‐Ground Lightning
Observed by the FALMA in WinterThunderstorms in Japan
Ting Wu1, Daohong Wang1, and Nobuyuki Takagi1

1

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

Abstract Multiple‐stroke (MS) positive cloud‐to‐ground (+CG) lightning ﬂashes are rarely reported,
especially those with high‐quality location information. In this study, we report 47 MS +CG ﬂashes
observed in winter thunderstorms in Japan with a 14‐site fast antenna lightning mapping array (FALMA).
MS +CG ﬂashes account for 18% of +CG ﬂashes. The mean multiplicity of all +CG ﬂashes is 1.24, and the
maximum multiplicity is 5. Interstroke intervals have a very large range from 1.0 to 1,320.6 ms with thegeometric mean of 64.4 ms. In three ﬂashes, interstroke intervals smaller than 2 ms are observed, andcorresponding positive strokes are inferred to be produced by two branches of the same positive leader.
Horizontal distances between sequential positive strokes range from 1.1 to 37.3 km with the geometric meanof 9.7 km. No subsequent strokes struck at the same location as a previous stroke. Distances between
sequential strokes are generally much larger than distances between ﬁrst strokes and lightning initiation
locations. Subsequent stroke peak amplitudes are on average 0.45 of ﬁrst stroke peak amplitudes. In 39
ﬂashes (83%), the ﬁrst stroke is stronger than the largest subsequent stroke in the same ﬂash. Subsequent
stroke amplitudes are weakly correlated with the time difference from the previous stroke. Origination
mechanisms of positive leaders initiating ﬁrst and subsequent positive strokes are discussed. It is very likelythat positive leaders for most subsequent strokes originate from in‐cloud negative leader channels, but
origination mechanisms for positive leaders initiating ﬁrst strokes are more varied.

1. Introduction
Positive cloud‐to‐ground (+CG) lightning ﬂashes are usually much less frequent than negative CG (−CG)
ﬂashes. It is estimated that less than 10% of CG ﬂashes globally are positive ﬂashes (e.g., Rakov, 2003).
However, positive return strokes (RSs) are more likely to carry extremely large peak currents (e.g., Lyons
et al., 1998) and thus pose particular threats to various objects. It is also well known that transient luminous
events such as sprites are almost always associated with +CG ﬂashes (e.g., Williams et al., 2007). Therefore,+CG ﬂashes have attracted considerable research interest in recent years.
An interesting feature of +CG lightning that is not well understood is that most +CG ﬂashes contain only
one RS. Multiple‐stroke (MS) +CG ﬂashes do occur but are uncommon. Table 1 summarizes studies reporting MS +CG ﬂashes, and we can see that the percentage of MS +CG ﬂashes relative to all +CG ﬂashes isgenerally from 10% to 20%. As a result, high‐quality data of MS +CG ﬂashes are extremely difﬁcult to obtain.
In fact, most studies summarized in Table 1 were based on electric ﬁeld records and/or nationwide lightning
location systems, from which it is even difﬁcult to unambiguously determine whether two RSs belong to thesame ﬂash.

©2020. American Geophysical Union.
All Rights Reserved.

WU ET AL.

Although +CG ﬂashes are generally rare, they are more frequent in some situations as reviewed by
Rakov (2003). One of the situations is winter thunderstorms. Based on the observation in one winter season
in the Hokuriku region in Japan, we recorded 47 MS +CG ﬂashes, the largest sample reported so far. These
ﬂashes were recorded by a low‐frequency (LF) lightning mapping system called fast antenna lightning
mapping array (FALMA), with which we can obtain electric ﬁeld change (E change) waveforms at
multiple sites and image lightning channel developments with great detail. With this high‐quality dataset, we will clarify some basic properties of MS +CG ﬂashes and will investigate the origination
mechanism of positive leaders for ﬁrst and subsequent strokes in MS +CG ﬂashes.
1 of 17

Journal of Geophysical Research: Atmospheres

10.1029/2020JD033039

Table 1
Summary of Studies on MS +CG Flashes
MS +CGs
Study
Present study
Cooray & Pérez (1994)
Heidler & Hopf (1998)
Qie et al. (2002)
Fleenor et al. (2009)
Saba et al. (2010)
Nag & Rakov (2012)
Qie et al. (2013)
Adhikari et al. (2016)
Baharudin et al. (2016)
Hazmi et al. (2017)
Johari et al. (2017)
Wu et al. (2018a)

Multiplicity

Interstroke interval (ms)Horizontal distance (km)Number%Mean

Maximum

Range

47
c
29
12
3
9
20
10
10
11
40
13
6
7

18

1.24

5

1.0–1320.6
6.8–290

27
13
4
19
19
5
8
37
17
12
15

1.13
1.04
1.20
1.21
1.06
1.10
1.50
1.18
1.20
1.15

4
2
2
3
3
3
4
4
3
4
2

b

13–155
14–406
8.5–201
6.5–290.7
0.3–80.3
2.9–518
16–45825–124

AM

GM

Range

AM

GM

Asub/
a
A1st

122.2
92
120

64.4
64
101

1.1–37.3

13.1

9.7

0.45

143
77
97.8
33.8
116
163.9
71

94
54
64.2
16.7
70
113.3
60

0–
0–53
0.22–29

12.3

11.8

0.74
0.73

d

4.9–46.4

0.48
d
0.29
0.46

Ratio of mean peak amplitude of subsequent strokes to that of ﬁrst strokes. bExcluding the extreme case with the value of 1,320.6 ms, the range is 1.0–469.2 ms,
the AM is 103.2 ms, and the GM is 61.4 ms. cStroke number. dMean value of the ratio of peak amplitudes of subsequent strokes to those of ﬁrst strokes.

a

2. Observation and Data
Winter lightning observation was carried out in the Hokuriku region of Japan from December 2018 to March
2019. A FALMA system consisting of 14 sites was set up as shown in Figure 1. The FALMA is athree‐dimensional (3‐D) lightning mapping system working in the low‐frequency band. Lightning radiation
signals are received by a fast antenna with a time constant of 200 μs at each site, and 3‐D source locations arecalculated with an improved time‐of‐arrival method. Details about the summer observation with the
FALMA in Gifu, Japan, can be found in Wu et al. (2018b).
2.1. Data
Only +CG ﬂashes whose leader channels are mainly within about 60 km
from the center of the FALMA network are selected for this study toensure that at least 2‐D mapping of leader channels and localization of
RSs can be made accurately. As a result, a total of 263 +CG ﬂashes is identiﬁed from the data obtained during the winter, including 216 single‐
stroke +CG ﬂashes and 47 MS +CG ﬂashes. These +CG ﬂashes produced
327 positive RSs. Locations of these positive RSs are shown in Figure 1
with red dots representing RSs in MS +CG ﬂashes, and blue dots representing RSs in single‐stroke +CG ﬂashes.
Eleven of these MS +CG ﬂashes are actually bipolar ﬂashes; they also contain at least one negative RS. In six cases, all negative RSs occurred after
all positive RSs. In one case, a negative RS occurred before the ﬁrst positive RS. In another case, one negative RS occurred before and anotherafter all positive RSs. For these cases, it is assumed that occurrences ofnegative RSs do not inﬂuence most analyses in this study, so these ﬂashes
are analyzed as normal MS +CG ﬂashes. In the remaining three cases, one
or two negative RSs occurred between two positive RSs. One case has anextremely long interstroke interval and is analyzed separately in section 3.2. The other two cases do not seem to have any special characteristics and are analyzed as normal MS +CG ﬂashes for simplicity.
Figure 1. Locations of positive RSs observed during the winter observationin Hokuriku region of Japan. Red dots represent RSs in MS +CGs, andblue dots represent RSs in single‐stroke +CGs. Black squares represent 14
sites of the FALMA. The origin (0, 0) corresponds to the latitude andlongitude of (36.76°N, 136.76°E).

WU ET AL.

Figure 2 shows distributions of daily numbers of single‐stroke and MS+CG ﬂashes. It is clear that MS +CG ﬂashes are generally produced in
the same periods as single‐stroke +CG ﬂashes. It is also clear from
Figure 1 that MS +CG ﬂashes are produced in the same area as single‐
2 of 17

Journal of Geophysical Research: Atmospheres

10.1029/2020JD033039

Figure 2. Distributions of daily numbers of (a) single‐stroke +CGs and (b) MS +CGs.

stroke +CG ﬂashes. Therefore, it seems that MS +CG ﬂashes are produced in the same thunderstorm
conditions as single‐stroke +CG ﬂashes.
The atmospheric electricity sign convention is used in this paper, so a positive RS produces a negative Echange pulse.

2.2. Evaluation of the Location Accuracy
The FALMA for this study has different site number and baseline distances and is set up in an entirely different area from that used in our summer observation (Wu et al., 2018b). Additionally, lightning discharges
in winter have some special characteristics that may also inﬂuence the location accuracy. Therefore, it isnecessary to have an evaluation of the location accuracy for the FALMA in this study.
Similar to the method used by Wu et al. (2018b), we identiﬁed 206 −CG ﬂashes with at least two RSs in thesame area as Figure 1 and calculated distances between sequential RSs in the same −CG ﬂash. There were
763 RSs in these −CG ﬂashes, and a total of 557 results of distances between sequential RSs was obtained.
Distributions of the distances are shown in Figure 3. Figure 3a shows the distribution for distances smaller
than 2,000 m (457 results), and Figure 3b shows the distribution for distances smaller than 500 m (315results). Locations of these results are shown as points in Figure 3c with the color indicating the distance.
Apparently part of the results in Figure 3 are due to −CG ﬂashes with multiple terminations, but it is difﬁcult
to determine which of them are due to multiple terminations and which of them are due to location errors.
However, from Figure 3 we can get a general picture that the location accuracy for RSs in this area is basically better than 200 m but the accuracy for RSs outside of the network of observation sites can be lower.
Using the same method, Wu et al. (2018b) showed that the distances between sequential RSs in −CGs aremostly smaller than 25 m during the summer observation in Gifu, Japan. The much lower accuracy in thisstudy is due to several possible reasons. One apparent reason is that the evaluation above includes RSs tensof kilometers from the observation network, while the evaluation by Wu et al. (2018b) only considered RSs
inside the network. Indeed, from Figure 3c we can see RSs with very large distances from previous strokes
are mostly outside of the observation network. Second, the complex topography in this area may have contributed to the low accuracy (e.g., Li et al., 2016). As can be seen in Figure 3c, there are mountain areas both
inside and outside of the observation network as well as large sea areas nearby. Another possible reason isthat RSs in winter may be more complicated than those in summer, resulting in lower location accuracy.
We have seen many peculiar waveforms produced by RSs in winter, but the effect on location accuracy is
not well understood so far.
WU ET AL.

3 of 17

Journal of Geophysical Research: Atmospheres

10.1029/2020JD033039

Figure 3. Distances from previous strokes for negative RSs in −CG ﬂashes. (a) Distribution of the distances in the rangeof 0 to 2,000 m. (b) Distribution of the distances in the range of 0 to 500 m. (c) Locations of the analyzed negative
RSs with the color indicating distances from previous strokes.

During the summer observation, we were able to do high‐quality 3‐D imaging of lightning ﬂashes and infercharge structures of thunderstorms (Wu et al., 2020). However, 3‐D imaging in winter seems to be very difﬁcult. According to our analysis of the winter data so far, it seems that only some simple processes (such as
upward negative leaders from high objects) at the right locations (surrounded by multiple observation sites)
can be well imaged in 3‐D. One important reason for the difﬁculty in 3‐D imaging in winter is that lightning
discharges in winter generally have much lower altitudes than those in summer. In fact, the lightning mapping array, which works in the VHF band, also seems to have similar difﬁculties when imaging winter lightning (e.g., Figures 7 and 8 in Schultz et al., 2018). Therefore, height results of MS +CG ﬂashes analyzed inthis study are generally considered not reliable, and only 2‐D location results will be used.
WU ET AL.

4 of 17

Journal of Geophysical Research: Atmospheres

10.1029/2020JD033039

3. Results
3.1. Return Stroke Multiplicity
The distribution of multiplicity of positive RSs in +CG ﬂashes is shown in
Figure 4. There are 216 single‐stroke ﬂashes, 34 two‐stroke ﬂashes, 10
three‐stroke ﬂashes, 2 four‐stroke ﬂashes, and 1 ﬁve‐stroke ﬂash. A totalof 327 positive RSs was produced by 263 +CG ﬂashes, corresponding to
an average of 1.24 strokes per ﬂash.
Mean multiplicities reported by previous studies are summarized inTable 1. The mean multiplicity of 1.24 in this study is larger than all but
one previous studies. However, the mean multiplicity reported by several
studies are around 1.20 (Hazmi et al., 2017; Johari et al., 2017; Nag &Rakov, 2012; Saba et al., 2010), very close to the current study. If we conFigure 4. Distribution of the multiplicity of positive RSs in +CGs.
sider the percentage of MS +CG ﬂashes relative to all +CG ﬂashes, thepercentage in this study (18%) is just about the average level of other studies summarized in Table 1. Therefore, although winter thunderstorms in Japan have a clear tendency to
produce more frequent +CG ﬂashes, these +CG ﬂashes do not seem to have a higher chance to produce
multiple strokes.
The maximum multiplicity in this study is 5. MS +CG ﬂashes containing more than three positive RSs are
rarely reported (Lang et al., 2017; Lyons et al., 2020; Soula et al., 2010). This ﬁve‐stroke ﬂash is shown in
Figure 5. Figure 5a shows the plan view of the location results of the ﬂash with the red diamond representing the initiation location and black triangles representing positive RSs. Figure 5b shows the
distance‐time view (relative to the initiation location and time) similar
to the analysis made by van der Velde and Montanyà (2013), andFigure 5c shows the E change waveform recorded at one site. E change
waveforms of the ﬁve strokes recorded by all sites are shown in
Figures S1–S5 in the supporting information. This ﬂash has a large horizontal extent of about 50 × 30 km. The duration of the ﬂash is about
900 ms. Sources of this ﬂash superimposed on the radar reﬂectivity
are shown in Figure S6.
3.2. Interstroke Intervals

Figure 5. The +CG ﬂash with ﬁve positive RSs. (a) Plan view. (b)Horizontal distance (relative to the initiation location) versus time. (c) Echange waveform. The red diamond represents the initiation location.
Black triangles represent positive RSs. The color scale of source points
indicates the time corresponding to the time coordinate of Figure 5c. Slopes
5
6of two black dashed lines represent velocities of 10 and 10 m/s.

WU ET AL.

Interstroke intervals are calculated for all strokes in 47 MS +CG
ﬂashes. The distribution is shown in Figure 6a. Interstroke intervals
have a very large range from 1.0 to 1,320.6 ms. However, it should be
noted that the ﬂash with the largest interstroke interval of 1,320.6 ms
is actually a bipolar ﬂash and will be analyzed in more detail. Exceptof this extreme value, all interstroke intervals are smaller than
470 ms, and from Figure 6a, we can see interstroke intervals are mainly
smaller than 120 ms. The arithmetic mean (AM) and geometric mean
(GM) of interstroke intervals are 122.2 and 64.4 ms when including
the largest value and 103.2 and 61.4 ms when excluding the largest
value. As summarized in Table 1, many other studies also reported
the large range of interstroke intervals from several milliseconds tohundreds of milliseconds (Adhikari et al., 2016; Baharudin et al., 2016;
Cooray & Pérez, 1994; Nag & Rakov, 2012; Qie et al., 2013). As for themean values, the AM is easily inﬂuenced by extremely small or large
values, so the GM is more appropriate to measure the average interstroke interval, and as summarized in Table 1, GM values in most studies are in the range of 50 to 100 ms. These results are generally similar
to interstroke intervals for subsequent strokes in −CG ﬂashes. For
example, Cooray and Pérez (1994) reported that interstroke intervalsof 568 subsequent strokes in 271 −CG ﬂashes, without differentiating
strokes creating new terminations, had an AM of 65 ms and a GM of
5 of 17

Journal of Geophysical Research: Atmospheres

10.1029/2020JD033039

Figure 6. Distributions of (a) interstroke interval and (b) time difference between ﬂash initiation and the ﬁrst stroke in
MS +CG ﬂashes.

48 ms. Stolzenburg et al. (2019), based on high‐speed video and E change records, reported that themean and median values of interstroke intervals for 488 subsequent strokes were 87 and 65 ms, andamong these subsequent strokes, 88 strokes producing new terminations had a mean value ofinterstroke interval of 94 ms.
As described above, the ﬂash with the largest interstroke interval is a bipolar ﬂash and is shown in Figure 7.
Sources of this ﬂash superimposed on the radar reﬂectivity are shown in Figure S7. The ﬁrst and the second
positive RSs are separated by 1,320.6 ms, but it is clear that there is also a negative RS between these two
positive RSs. E change waveforms of the negative RS recorded by all sites are shown in Figure S8. It should
be noted that the negative RS is located on the sea, so it is unlikely that the negative RS belongs to an upward
ﬂash triggered by the preceding positive RS. It is not clear whether the occurrence of the negative RS hascontributed to the extremely long interval between the two positive RSs. The time difference between thenegative RS and the second positive RS is 956.7 ms, still much larger than interstroke intervals in other
MS +CG ﬂashes. The duration and horizontal extent of this ﬂash is also very large. The ﬂash duration isabout 2.2 s, and the horizontal extent is about 110 × 60 km. This ﬂash is also special in that all three subsequent positive RSs are larger than the ﬁrst RS, possibly due to the extremely long interstroke interval. From
Figure 7b, it appears that leaders progressed with a velocity much slower than 1 × 105 m/s during the period
between the ﬁrst and the second positive RSs, implying that these leaders might be positive leaders.
However, the overall low velocity was actually due to leaders propagating mainly in the tangential direction(the plot for this period is shown in Figure S9), and we believe the detected sources were mainly from negative leaders.
Interstroke intervals of several milliseconds in +CG ﬂashes are also rarely reported. In this study, weobserved three MS +CG ﬂashes with interstroke intervals smaller than 2 ms (1.0, 1.3 and 1.8 ms).
Interestingly, the horizontal distances between corresponding RSs are also very small (1.1, 2.7, and3.2 km). As we will see in section 3.3, these strokes have smaller distances than most of other strokes. It is
likely that these sequential strokes are produced when two branches of a positive leader connect to theground sequentially, similar to the so‐called “multiple termination stroke” in −CG ﬂashes (e.g., Rakov &Uman, 1994; Sun et al., 2016). E change waveforms of two cases (interstroke intervals of 1.0 and 1.3 ms)
WU ET AL.

6 of 17

Journal of Geophysical Research: Atmospheres

10.1029/2020JD033039

are shown in Figure 8. Interestingly, in both cases, the two strokes havesome similar features. First, in both cases, the two strokes are subsequent
strokes. Second, in both cases, the two strokes have similar peak amplitudes. Third, in both cases, waveforms of the two strokes have certain
similarities, such as the pulse width.
We also calculated the time difference between the ﬁrst positive RS andthe ﬂash initiation in 47 MS +CG ﬂashes, and the distribution is shownin Figure 6b. We can see the distribution is generally similar to that of
the interstroke interval. The time differences range from 6.7 to734.5 ms. The AM and GM are 117.9 and 64.4 ms, respectively, also similar to those of interstroke intervals.
3.3. Horizontal Distances Between Sequential Return Strokes
Horizontal distances between sequential RSs (DRS) in 47 MS +CG ﬂashes
are calculated, and the distribution is shown in Figure 9a. The value of
DRS ranges from 1.1 to 37.3 km. The AM and GM are 13.1 and 9.7 km,
respectively. Only three studies so far provided distances between sequential RSs (Johari et al., 2017; Nag & Rakov, 2012; Saba et al., 2010), andresults in this study are in general agreement with previous studies assummarized in Table 1.
It is interesting to note that distances between RSs in MS +CG ﬂashes are
generally larger than those between RSs creating new terminations in−CG ﬂashes (Gao et al., 2019; Thottappillil et al., 1992). The difference
is probably due to different origination mechanisms of leaders for subseFigure 7. The +CG ﬂash with the largest interstroke interval (1,032.6 ms)
in this study. (a) Plan view. (b) Horizontal distance (relative to thequent strokes in +CG and −CG ﬂashes. As will be discussed in section 4,
initiation location) versus time. (c) E change waveform. The red diamond
most subsequent strokes in +CG ﬂashes are likely initiated by positive
represents the initiation location. Black triangles represent positive RSs.
leaders originating from in‐cloud negative leader channels, so the disRed minus sign represents the negative RS. The color scale of source points
indicates the time corresponding to the time coordinate of Figure 7c. Slopes tance between sequential positive strokes is approximately the distance5
6
traveled by a negative leader during the interstroke interval. On the otherof two black dashed lines represent velocities of 10 and 10 m/s.
hand, subsequent RSs in −CG ﬂashes are produced by recoil leaders
propagating backward from positive leader channels to the initiation location and then deﬂecting fromthe previous main channel during the downward propagation (Gao et al., 2019; Stolzenburg et al., 2019).
As a result, new terminations are usually very close to old terminations in −CG ﬂashes.
It has long been postulated that subsequent strokes in +CG ﬂashes cannot follow the same channel as a previous stroke (Mazur, 2002; Mazur & Ruhnke, 1993). However, video observations of MS +CG ﬂashes haveshown that some subsequent RSs in +CG ﬂashes indeed followed a previously created channel (Fleenor
et al., 2009; Saba et al., 2010), although such cases appear to be extremely rare. In this study, all subsequent
strokes in +CG ﬂashes created new terminations. The minimum horizontal distance between sequential
positive RSs is 1.1 km. The two strokes also had the minimum interstroke interval. They have been analyzed
in section 3.2, and their E change waveforms are shown in Figure 8a.
We also calculated horizontal distances between ﬂash initiation location and the ﬁrst positive RS (Dini) for
all MS +CG ﬂashes, and the distribution is shown in Figure 9b. The value of Dini ranges from 0.4 to42.1 km. The AM and GM are 6.1 and 3.6 km, respectively, much smaller than those of DRS. The differenceis also clear by comparing Figures 9a and 9b. Although the maximum of Dini is larger than that of DRS, mostvalues of Dini are smaller than 8 km. By contrary, values of DRS distribute relatively evenly from 0 to 32 km.
The distinctly different distributions of Dini and DRS indicate different origination mechanisms of positive
leaders responsible for ﬁrst and subsequent strokes in +CG ﬂashes. We will make further discussion insection 4.
3.4. Return Stroke Peak Amplitudes
In this section we analyze peak amplitudes of ﬁrst and subsequent RSs in MS +CG ﬂashes. In order to compare peak amplitudes of RSs measured at different distances and at different observation sites, peak
WU ET AL.

7 of 17

Journal of Geophysical Research: Atmospheres

10.1029/2020JD033039

Figure 8. E change waveforms of sequential positive RSs with minimum time intervals (1.0 and 1.3 ms) in this study. The
value of ΔD indicates the horizontal distance between two RSs. The value of Δt indicates the interstroke interval.
The value of D indicates the distance between the stroke and the observation site recording the displayed waveform.

amplitudes are normalized to 100 km, and conversion coefﬁcients between different sites are calculated.
Details of the normalization and the conversion are described in Shi et al. (2019). Range‐normalized peak
amplitudes in the digital unit (DU) used for the following analyses are theoretically proportional to peakcurrents of RSs.
Figure 10 shows distributions of peak amplitudes of ﬁrst and subsequent RSs in MS +CG ﬂashes. We can seethat ﬁrst strokes are clearly much stronger than subsequent strokes. The mean value of ﬁrst stroke peak
amplitude is 13,321 DU and that of subsequent stroke amplitude is 6,021 DU. Subsequent stroke amplitudes
are on average 0.45 of ﬁrst stroke amplitudes. As summarized in Table 1, this result is smaller than thosereported by Fleenor et al. (2009) and Saba et al. (2010) but is very close to those reported by Baharudin
et al. (2016) and Johari et al. (2017).
WU ET AL.

8 of 17

Journal of Geophysical Research: Atmospheres

10.1029/2020JD033039

Figure 9. Distributions of (a) horizontal distances between sequential RSs and (b) horizontal distances between ﬂash
initiation location and the ﬁrst RS.

For every MS +CG ﬂash, the ﬁrst stroke amplitude is compared to the amplitude of the largest subsequent
stroke, and the result is shown in Figure 11a. In 39 ﬂashes (83%), the ﬁrst stroke is stronger than the largest
subsequent stroke. These events are represented by blue bars in Figure 11a. For these events, the ratio of theﬁrst stroke amplitude to the strongest subsequent stroke amplitude is calculated, and the mean value is 3.0.
In the remaining eight ﬂashes (17%), the largest subsequent stroke is stronger than the ﬁrst stroke. These
events are represented by red bars in Figure 11a. For these events, the ratio of the strongest subsequent
stroke amplitude to the ﬁrst stroke amplitude is calculated, and the mean value is 2.0. This result indicatesthat ﬁrst strokes in MS +CG ﬂashes are usually much stronger than subsequent strokes. Similarly, ﬁrst
strokes in −CG ﬂashes are also usually stronger than subsequent strokes, even when subsequent strokes create new terminations (Gao et al., 2019; Rakov & Uman, 1990).
For MS +CG ﬂashes with at least three strokes, the amplitude of the nth (n > =2) stroke is compared withthat of the (n + 1)th stroke, and the result is shown in Figure 11b. There are nine strokes stronger than thefollowing stroke (blue bars) and eight strokes stronger than the previous stroke (red bars), indicating that
subsequent stroke amplitudes do not show any increasing or decreasing trend with the stroke order.
There have been reports that peak amplitudes of subsequent strokes in −CG ﬂashes are associated with thetime interval with the previous stroke (e.g., Diendorfer et al., 1998). Here we examine the relationshipbetween subsequent stroke amplitudes in +CG ﬂashes and time differences with the previous stroke, andthe result is shown in Figure 12a. Note that the maximum interstroke interval of 1,320.6 ms (Figure 7) is
not shown in Figure 12a. Figure 12a shows a weak positive correlation between interstroke intervals andpeak amplitudes with the correlation coefﬁcient of 0.29. If we exclude strokes with interstroke intervals larger than 300 ms, the correlation coefﬁcient increases to 0.48. Figure 12b shows the relationship between
peak amplitudes and distances with previous strokes, and it is clear that the correlation is much weaker.
These results indicate that peak amplitudes of subsequent strokes in +CG ﬂashes are more closely associatedwith time differences with previous strokes, especially when the time difference is not too large. It should be
noted that strokes in +CG ﬂashes normally do not follow a previous RS channel, so the reason of the
WU ET AL.

9 of 17

Journal of Geophysical Research: Atmospheres

10.1029/2020JD033039

Figure 10. Distributions of normalized peak amplitudes of ﬁrst and subsequent RSs in MS +CG ﬂashes.

correlation is different from that for strokes in −CG ﬂashes. One possible explanation is that different strokes
in the same +CG ﬂash, although they do not share the same channel, lower positive charges from the samecharge region, so the longer the time difference is, the larger the amount of charges built up by updrafts andavailable for the next stroke, and thus, the stronger the subsequent stroke is. Additionally, during strokeintervals, as in‐cloud negative leaders keep extending in the positive charge region, more and morepositive charges may be induced on the leader system, which may also contribute to stronger subsequent
strokes.
As analyzed previously, in eight MS +CG ﬂashes, the largest subsequent stroke is stronger than the ﬁrst
stroke. In these eight ﬂashes, there is a total of 10 subsequent strokes stronger than the corresponding ﬁrst
strokes. These 10 subsequent strokes are represented by red points in Figure 12. For nine strokes (the one
with the largest interstroke interval is not shown in Figures 12a and 12c), the interstroke interval is larger
than 100 ms. As analyzed in section 3.2, the GM of interstroke interval is only 64.4 ms. This result is in agreement with the correlation between peak amplitudes and interstroke intervals analyzed above.

4. Inferences on Origins of Positive Leaders for First and Subsequent Strokes in+CG Flashes
Due to the rarity of +CG ﬂashes and the low radiation power in radio frequencies produced by positive leaders (e.g., Shao et al., 1999), it is very difﬁcult to obtain direct evidence on how positive leaders initiating
positive RSs originate in thunderclouds (Li et al., 2020). Various scenarios for the origination of positive leaders initiating ﬁrst positive strokes were discussed by van der Velde et al. (2014) based on the bidirectional
leader concept and the lightning mapping array observation. Possible charge conﬁgurations responsible forthe production of +CG ﬂashes were also discussed by Nag and Rakov (2012). Some of the scenarios proposedby these studies also seem to be applicable for the origination of positive leaders initiating subsequent positive strokes, and these scenarios will be examined in this section.
The ﬁrst scenario is similar to the scenario “f” in Nag and Rakov (2012). Assuming an in‐cloud positive leader propagates forward, one branch turns to the ground and initiates an RS, while the main channel keeps
propagating forward. Later, another branch develops from the channel, propagates to the ground, and
WU ET AL.

10 of 17

Journal of Geophysical Research: Atmospheres

10.1029/2020JD033039

Figure 11. (a) Comparison between the amplitude of the ﬁrst stroke (A1st) and the amplitude of the largest subsequent
stroke (Asub) in the same +CG ﬂash. Blue bars represent events with larger A1st, and red bars represent events withlarger Asub. (b) Comparison between sequential subsequent strokes for +CG ﬂashes with at least three positive strokes.
Blue bars represent events with the amplitude of the Nth stroke (AN) larger than that of the following stroke (AN+1). Redbars represent events with larger AN+1 than AN.

initiates a subsequent stroke. In this scenario, the minimum required velocity of the positive leader roughly
equals to the horizontal distance between the two strokes divided by the interstroke interval. To examine this
scenario, the scatterplot of horizontal distances between sequential strokes versus interstroke intervals isshown in Figure 12c. We can see that for most of subsequent strokes, the distance and the time interval
correspond to a velocity value in the range of 0.5 to 5 × 105 m/s. In other words, for most MS +CG
ﬂashes, the in‐cloud leader connecting sequential RS channels should have a velocity larger than
0.5 × 105 m/s. However, as demonstrated by Wu et al. (2019), velocities of in‐cloud positive leaders aremainly in the range of 1 to 3 × 104 m/s. Although Wu et al. (2019) only analyzed positive leaders inintracloud (IC) and −CG ﬂashes, it is likely that in‐cloud horizontal positive leaders in +CG ﬂashes are
generally similar to those in IC and −CG ﬂashes. Therefore, the scenario that multiple branches of apositive leader channel produce multiple positive RSs does not seem to be applicable to most of cases.
The second scenario is that positive leaders initiating subsequent strokes originate from in‐cloud negative
leader channels with current cutoff, similar to the scenario “e” in Nag and Rakov (2012) and the scenario
5 in van der Velde et al. (2014). After the ﬁrst positive stroke, in‐cloud negative leaders keep propagating.
When the current cutoff occurs in a negative leader, a new positive leader may develop from the negative
leader channel and may initiate a subsequent positive stroke. Observations of positive RSs preceded byextensive IC discharges (Kong et al., 2008; Saba et al., 2009) also agree with this scenario. In this scenario,
it is the negative leader that traverses the distance between two sequential positive strokes, so it is in agreement with the relationship between horizontal distances and interstroke intervals in Figure 12c.
In order to further examine this scenario, we analyze the distance‐time relationship for sources before andafter each subsequent strokes similar to the analysis made by van der Velde et al. (2014). Results for six subsequent strokes are shown in Figure 13. In all subplots in Figure 13, the stroke under consideration is represented by a black cross sign at (0, 0). The blue, yellow, and red dashed lines represent velocities of 2 × 104,
1 × 105, and 1 × 106 m/s, respectively. For the strokes in Figures 13a–13d, a negative leader ﬁrst approaching
WU ET AL.

11 of 17

Journal of Geophysical Research: Atmospheres

10.1029/2020JD033039

Figure 12. Relationships among normalized peak amplitudes of subsequent strokes in +CG ﬂashes, interstrokeintervals, and distances with previous positive strokes. Red points represent subsequent strokes stronger thancorresponding ﬁrst strokes. A stroke with extremely large time difference (1,321 ms) is not shown in Figures 12a and 12c.
Correlation coefﬁcient r1 is for all events in Figure 12a. Correlation coefﬁcient r2 is for events on the left of the red
55dashed line. Slopes of two black dashed lines in Figure 12c represent velocities of 5 × 10 and 0.5 × 10 m/s.

the location of the positive stroke and then propagating away can be recognized. The distance between thenegative leader and the stroke decreases to near 0 at some tens of milliseconds before the stroke. These cases
are in perfect agreement with the notion that positive leaders for subsequent strokes initiate from in‐cloudnegative leader channels. It seems very likely that a positive leader develops from the point on the negative
leader channel that is very close (near 0) to the location of the positive stroke and after tens of milliseconds
the positive leader reaches the ground and initiates a positive RS. We examined all 64 subsequent positive
strokes in this study and found that at least 37 strokes are preceded by similar negative leaders.
Twenty‐two more examples are shown in Figures S10–S12 and S13a–S13d. The distance‐time plots for all
strokes are provided in the data repository (see Acknowledgments section). Excluding some subsequent
strokes with extremely small time differences from previous strokes (Figure 8) and also considering thefact that in some cases the location results are not good enough to make a correct determination of theprocesses before the positive strokes, we believe that for most subsequent strokes in MS +CG ﬂashes,
positive leaders originate from in‐cloud negative channels. This conclusion is also consistent with therecent observation of a MS +CG ﬂash by Yuan et al. (2020).
However, details on how positive leaders develop from negative leader channels are not clear. In the scenario “e” proposed by Nag and Rakov (2012) and the scenario 5 proposed by van der Velde et al. (2014),
the current cutoff of the in‐cloud negative leader is needed for a new positive leader to develop. According
to van der Velde et al. (2014), the new positive leader develops from the point on the old negative leader
where the current cutoff occurs. In other words, the current cutoff occurs at the point of the negative leader
very close to the location of the positive stroke. It is impossible for the current cutoff to occur right after thenegative leader passes the point; the negative leader needs to continue developing forward for a while before
the current cutoff occurs. However, according to Figures 13a–13d, the time difference between the positive
stroke and the moment when the distance is near 0 is only tens of milliseconds, which seems to be too shortfor the current cutoff to occur and for the new positive leader to start and to develop to the ground.
Additionally, the short time difference indicates that the current cutoff occurs at a point not very far awayfrom the head of the developing negative leader, which is somewhat difﬁcult to explain as it is expected thatthe current cutoff tends to occur at a relatively old part of the leader with reduced conductivity.
An alternative mechanism to explain the positive leader developing from the negative leader channel is similar to the polarity reversal mechanism proposed by Wang and Takagi (2008) and Shi et al. (2018). Suppose abranch of the negative leader, which is not well resolved by the location results, becomes defunct while themain channel keeps propagating forward, positive charges from the head of the main channel may be transferred back to the defunct branch. When enough positive charges are transferred to the branch, a new positive leader may be triggered, and it may develop to the ground and initiate a positive stroke. In thismechanism, the head of the defunct branch corresponds to the point with 0 distance in Figures 13a–13d.
This mechanism is also consistent with the report by Yuan et al. (2020) that a positive leader initiated froma decayed negative leader branch.
WU ET AL.

12 of 17

Journal of Geophysical Research: Atmospheres

10.1029/2020JD033039

Figure 13. The scatterplot of the distance versus time for sources before and after some subsequent positive RSs. The
distance and the time are calculated relative to the stroke shown at (0, 0). Black crosses not at (0, 0) are otherpositive RSs in the same ﬂash. The red square, if shown, is the ﬁrst source of the +CG ﬂash. The blue, yellow, and red
456
dashed lines represent velocities of 2 × 10 , 1 × 10 , and 1 × 10 m/s, respectively. The value of d indicates the
distance between the stroke at (0, 0) and the center of the FALMA network in Figure 1.

Apart from the characteristic V‐shaped distance‐time plots in Figures 13a–13d, we found two cases inwhich a negative leader can be seen approaching the location of the positive stroke but it just stops anddoes not propagate away. One example is shown in Figure 13e, and the other is shown in Figure S13e.
In these cases, positive leaders for subsequent strokes may develop from the head of decayed negative
leader channels. In another two cases shown in Figures 13f and S13f, only a negative leader propagating
away from the location of the positive stroke can be recognized. These cases may be similar to the scenario
4 in van der Velde et al. (2014), that is, the positive leader is initiated together with the negative leader by a
new bidirectional development. These special cases seem to be relatively rare for subsequent positive
strokes.
The origination mechanism of positive leaders for ﬁrst positive strokes seems to be varied and complicated asdemonstrated by van der Velde et al. (2014). If we compare Figures 9a and 9b, we can see that the distance

WU ET AL.

13 of 17

Journal of Geophysical Research: Atmospheres

10.1029/2020JD033039

Figure 14. The same as Figure 13 but for six ﬁrst RSs in MS +CG ﬂashes.

between the ﬁrst stroke and the ﬂash initiation location (Dini) is usually much smaller than the distance
between sequential strokes (DRS). This result indicates that the origination mechanism of positive leaders
for ﬁrst strokes is usually different from that for subsequent strokes. However, even for ﬁrst strokes withvery small Dini (<5 km), different mechanisms seem to be necessary. The distance‐time plots for six ﬁrst
strokes are shown in Figure 14. Plots for other ﬁrst strokes can be found in the data repository. For the
strokes in Figures 14a and 14b, we can see in each case the ﬂash starts with a negative leader propagating
away from the location of the positive stroke, indicating that a positive leader starting together as thenegative leader goes directly down to the ground and initiates the ﬁrst stroke. This mechanism is similar
to the scenario 1 or 2 in van der Velde et al. (2014). For the strokes in Figures 14c and 14d, some sources
are located before the initiation of a negative leader propagating away, and it is likely that the positive
leader initiating the ﬁrst stroke starts together as the negative leader sometime after the initiation of theﬂash. This mechanism may be similar to the scenario 4 in van der Velde et al. (2014) and also similar to
the mechanism for the subsequent stroke in Figure 13f. First strokes in Figures 14e and 14f are somewhat
similar to the subsequent strokes in Figures 13a–13d. It is possible that the positive leader initiating the
WU ET AL.

14 of 17

Journal of Geophysical Research: Atmospheres

10.1029/2020JD033039

ﬁrst stroke starts from the point on the negative leader channel that is very close to the positive stroke location, but we cannot rule out the possibility that the positive leader simply starts together with the negative
leader at the beginning of the ﬂash.
In summary, it is inferred that for the majority of MS +CG ﬂashes analyzed in this study, positive leaders
initiating subsequent strokes mainly originated from in‐cloud negative leader channels, but origination
mechanisms for positive leaders initiating ﬁrst positive strokes seem to be more varied and complicated.

5. Conclusion
During the winter observation in the Hokuriku region of Japan, we successfully recorded 47 MS +CG
ﬂashes, which were imaged by the FALMA consisting of 14 sites. With this high‐quality data set, various
characteristics of MS +CG ﬂashes are analyzed. Major ﬁndings are summarized as follows.
MS +CG ﬂashes observed in this study include 34 two‐stroke ﬂashes, 10 three‐stroke ﬂashes, 2 four‐stroke
ﬂashes, and 1 ﬁve‐stroke ﬂashes. We also observed 216 single‐stroke ﬂashes. The percentage of MS +CG
ﬂashes is 17.9%, and the mean multiplicity of +CG ﬂashes is 1.24.
Interstroke intervals range from 1.0 to 1,320.6 ms with the AM and GM of 122.2 and 64.4 ms. The ﬂash withthe maximum interstroke interval is actually a bipolar ﬂash. Excluding this ﬂash, the maximum interstrokeinterval is 469.2 ms, and the AM and GM are 103.2 and 61.4 ms. Interstroke intervals smaller than 2 ms areobserved in three ﬂashes. Corresponding RSs also have small horizontal distances, indicating that they may
be produced by two branches of the same positive leader, similar to the so‐called “multiple termination
stroke” in −CG ﬂashes.
Horizontal distances between sequential positive RSs range from 1.1 to 37.3 km with the AM and GM of 13.1
and 9.7 km. No subsequent strokes were found to strike at the same location as a previous stroke. Horizontal
distances between sequential positive RSs are usually much larger than distances between ﬁrst positive RSs
and lightning initiation locations.
Subsequent stroke peak amplitudes are on average 0.45 of ﬁrst stroke peak amplitudes. In 39 ﬂashes (83.0%),
the ﬁrst stroke is found to be stronger than the largest subsequent stroke. For subsequent strokes, peak
amplitudes do not seem to depend on the stroke order. Subsequent stroke amplitudes are weakly correlatedwith preceding interstroke intervals.
Various scenarios for the origination of positive leaders initiating subsequent strokes in MS +CG ﬂashes are
examined. For most subsequent strokes, a negative leader ﬁrst approaching and getting very close to thelocation of the positive stroke tens of milliseconds before the positive stroke and then propagating away
can be recognized. This result indicates that positive leaders initiating subsequent strokes mainly originate
from in‐cloud negative leader channels. On the other hand, the origination mechanism of positive leaders
initiating ﬁrst strokes seems to be more varied and complicated, in agreement with previous studies.

Data Availability Statement
Data of all positive strokes analyzed in this paper and distance‐time plots (section 4) for all positive strokes
can be downloaded online (http://doi.org/10.5281/zenodo.3937501).
Acknowledgments
This work was supported by the
Ministry of Education, Culture, Sports,
Science, and Technology of Japan(Grants 16H04315, 18K13618, and
20H02129). The authors thank Oscar
van der Velde and two anonymous
reviewers for their valuable comments,
which helped improve the quality ofthis paper.

WU ET AL.

References
Adhikari, P. B., Sharma, S., & Baral, K. (2016). Features of positive ground ﬂashes observed in Kathmandu Nepal. Journal of Atmosphericand Solar‐Terrestrial Physics, 145, 106–113. https://doi.org/10.1016/j.jastp.2016.04.016
Baharudin, Z. A., Cooray, V., Rahman, M., Hettiarachchi, P., & Ahmad, N. A. (2016). On the characteristics of positive lightning ground
ﬂashes in Sweden. Journal of Atmospheric and Solar‐Terrestrial Physics, 138–139, 106–111. https://doi.org/10.1016/j.jastp.2015.12.014
Cooray, V., & Pérez, H. (1994). Some features of lightning ﬂashes observed in Sweden. Journal of Geophysical Research, 99(D5),10,683–10,688. https://doi.org/10.1029/93JD02366
Diendorfer, G., Schultz, W., & Rakov, V. A. (1998). Lightning characteristics based on data from the Austrian lightning locating system.
IEEE Transactions on Electromagnetic Compatibility, 40(4), 452–464. https://doi.org/10.1109/15.736206
Fleenor, S. A., Biagi, C. J., Cummins, K. L., Krider, E. P., & Shao, X. M. (2009). Characteristics of cloud‐to‐ground lightning in warm‐season
thunderstorms in the Central Great Plains. Atmospheric Research, 91(2–4), 333–352. https://doi.org/10.1016/j.atmosres.2008.08.011
Gao, P., Wang, D., Shi, D., Wu, T., & Takagi, N. (2019). Characterization of multitermination CG ﬂashes using a 3D Lightning Mapping
System (FALMA). Atmosphere, 10, 625. https://doi.org/10.3390/atmos10100625
Hazmi, A., Emeraldi, P., Hamid, M. I., Takagi, N., & Wang, D. (2017). Characterization of positive cloud to ground ﬂashes observed inIndonesia. Atmosphere, 8, 4. https://doi.org/10.3390/atmos8010004

15 of 17

Journal of Geophysical Research: Atmospheres

10.1029/2020JD033039

Heidler, F., & Hopf, C. (1998). Measurement results of the electric ﬁelds in cloud‐to‐ground lightning in nearby Munich, Germany. IEEE
Transactions on Electromagnetic Compatibility, 40(4), 436–443. https://doi.org/10.1109/15.736204
Johari, D., Cooray, V., Rahman, M., Hettiarachchi, P., & Ismail, M. M. (2017). Features of the ﬁrst and the subsequent return strokes inpositive ground ﬂashes based on electric ﬁeld measurements. Electric Power Systems Research, 150, 55–62. https://doi.org/10.1016/j.
epsr.2017.04.031
Kong, X., Qie, X., & Zhao, Y. (2008). Characteristics of downward leader in a positive cloud‐to‐ground lightning ﬂash observed by high‐speed video camera and electric ﬁeld changes. Geophysical Research Letters, 35, L05816. https://doi.org/10.1029/2007GL032764
Lang, T. J., Pédeboy, S., Rison, W., Cerveny, R. S., Cerveny, R. S., Montanyà, J., et al. (2017). WMO world record lightning extremes: Longest
reported ﬂash distance and longest reported ﬂash duration. Bulletin of the American Meteorological Society, 98(6), 1153–1168. https://doi.
org/10.1175/BAMS‐D‐16‐0061.1
Li, D., Azadifar, M., Rachidi, F., Rubinstein, M., Diendorfer, G., Sheshyekani, K., et al. (2016). Analysis of lightning electromagnetic ﬁeld
propagation in mountainous terrain and its effects on ToA‐based lightning location systems. Journal of Geophysical Research:
Atmospheres, 121, 895–911. https://doi.org/10.1002/2015JD024234
Li, S., Qiu, S., Shi, L., & Li, Y. (2020). Broadband VHF observations of two natural positive cloud‐to‐ground lightning ﬂashes. GeophysicalResearch Letters, 47, e2019GL086915. https://doi.org/10.1029/2019GL086915
Lyons, W. A., Bruning, E. C., Warner, T. A., MacGorman, D. R., Edgington, S., Tillier, C., & Mlynarczyk, J. (2020). Megaﬂashes: Just how
long can a lightning discharge get? Bulletin of the American Meteorological Society, 101(1), E73–E86. https://doi.org/10.1175/BAMS‐D‐
19‐0033.1
Lyons, W. A., Uliasz, M., & Nelson, T. E. (1998). Large peak current cloud‐to‐ground lightning ﬂashes during the summer months in thecontiguous United States. Monthly Weather Review, 126(8), 2217–2233. https://doi.org/10.1175/1520‐0493(1998)126<2217:
LPCCTG>2.0.CO;2
Mazur, V. (2002). Physical processes during development of lightning ﬂashes. Comptes Rendus Physique, 3(10), 1393–1409. https://doi.org/
10.1016/S1631‐0705(02)01412‐3
Mazur, V., & Ruhnke, L. H. (1993). Common physical processes in natural and artiﬁcially triggered lightning. Journal of GeophysicalResearch, 98(D7), 12,913–12,930. https://doi.org/10.1029/93JD00626
Nag, A., & Rakov, V. A. (2012). Positive lightning: An overview, new observations, and inferences. Journal of Geophysical Research, 117,
D08109. https://doi.org/10.1029/2012JD017545
Qie, X., Wang, Z., Wang, D., & Liu, M. (2013). Characteristics of positive cloud‐to‐ground lightning in Da Hinggan Ling forest region at
relatively high latitude, northeastern China. Journal of Geophysical Research: Atmospheres, 118, 13,393–13,404. https://doi.org/10.1002/
2013JD020093
Qie, X., Yu, Y., Wang, D., Wang, H., & Chu, R. (2002). Characteristics of cloud‐to‐ground lightning in Chinese inland plateau. Journal of the
Meteorological Society of Japan, 80(4), 745–754. https://doi.org/10.2151/jmsj.80.745
Rakov, V. A. (2003). A review of positive and bipolar lightning discharges. Bulletin of the American Meteorological Society, 84(6), 767–776.
https://doi.org/10.1175/BAMS‐84‐6‐767
Rakov, V. A., & Uman, M. A. (1990). Some properties of negative cloud‐to‐ground lightning ﬂashes versus stroke order. Journal ofGeophysical Research, 95(D5), 5447–5453. https://doi.org/10.1029/JD095iD05p05447
Rakov, V. A., & Uman, M. A. (1994). Origin of lighting electric ﬁeld signatures showing two return‐stroke waveforms separated in time by amillisecond or less. Journal of Geophysical Research, 99(D4), 8157–8165. https://doi.org/10.1029/94JD00165
Saba, M. M. F., Campos, L. Z. S., Krider, E. P., & Pinto, O. Jr. (2009). High‐speed video observations of positive ground ﬂashes produced byintracloud lightning. Geophysical Research Letters, 36, L12811. https://doi.org/10.1029/2009GL038791
Saba, M. M. F., Schulz, W., Warner, T. A., Campos, L. Z. S., Schumann, C., Krider, E. P., et al. (2010). High‐speed video observations ofpositive lightning ﬂashes to ground. Journal of Geophysical Research, 115, D24201. https://doi.org/10.1029/2010JD014330
Schultz, C. J., Lang, T. J., Bruning, E. C., Calhoun, K. M., Harkema, S., & Curtis, N. (2018). Characteristics of lightning within electriﬁed
snowfall events using lightning mapping arrays. Journal of Geophysical Research: Atmospheres, 123, 2347–2367. https://doi.org/10.1002/
2017JD027821
Shao, X. M., Rhodes, C. T., & Holden, D. N. (1999). RF radiation observations of positive cloud‐to‐ground ﬂashes. Journal of GeophysicalResearch, 104(D8), 9601–9608. https://doi.org/10.1029/1999JD900036
Shi, D., Wang, D., Wu, T., & Takagi, N. (2019). Correlation between the ﬁrst return stroke of negative CG lightning and its preceding
discharge processes. Journal of Geophysical Research: Atmospheres, 124, 8501–8510. https://doi.org/10.1029/2019JD030593
Shi, D., Wang, D., Wu, T., Thomas, R. J., Edens, H. E., Rison, W., et al. (2018). Leader polarity‐reversal feature and charge structure ofthree upward bipolar lightning ﬂashes. Journal of Geophysical Research: Atmospheres, 123, 9430–9442. https://doi.org/10.1029/
2018JD028637
Soula, S., van der Velde, O., Palmiéri, J., Chanrion, O., Neubert, T., Montanyà, J., et al. (2010). Characteristics and conditions of productionof transient luminous events observed over a maritime storm. Journal of Geophysical Research, 115, D16118. https://doi.org/10.1029/
2009JD012066
Stolzenburg, M., Marshall, T. C., & Karunarathne, S. (2019). Inception of subsequent stepped leaders in lightning. Meteorology andAtmospheric Physics, 132(4), 489–514. https://doi.org/10.1007/s00703‐019‐00702‐8
Sun, Z., Qie, X., Liu, M., Jiang, R., Wang, Z., & Zhang, H. (2016). Characteristics of a negative lightning with multiple‐ground terminations
observed by a VHF lightning location system. Journal of Geophysical Research: Atmospheres, 121, 413–426. https://doi.org/10.1002/
2015JD023702
Thottappillil, R., Rakov, V. A., Uman, M. A., Beasley, W. H., Master, M. J., & Shelukhin, D. V. (1992). Lightning subsequent‐stroke electricﬁeld peak greater than the ﬁrst stroke peak and multiple ground terminations. Journal of Geophysical Research, 97(D7), 7503–7509.
https://doi.org/10.1029/92JD00557
van der Velde, O. A., & Montanyà, J. (2013). Asymmetries in bidirectional leader development of lightning ﬂashes. Journal of GeophysicalResearch: Atmospheres, 118, 13,504–13,519. https://doi.org/10.1002/2013JD020257
van der Velde, O. A., Montanyà, J., Soula, S., Pineda, N., & Mlynarczyk, J. (2014). Bidirectional leader development in sprite‐producing
positive cloud‐to‐ground ﬂashes: Origins and characteristics of positive and negative leaders. Journal of Geophysical Research:
Atmospheres, 119, 12,755–12,779. https://doi.org/10.1002/2013JD021291
Wang, D., & Takagi, N. (2008). Characteristics of upward bipolar lightning derived from simultaneous recording of electric current andelectric ﬁeld change, Paper presented at the XXIX General Assembly, Int. Union of Radio Sci., Chicago, Ill.
Williams, E. R., Downes, E., Boldi, R., Lyons, W., & Hechman, S. (2007). Polarity asymmetry of sprite‐producing lightning: A paradox.
Radio Science, 42, RS2S17. https://doi.org/10.1029/2006RS003488

WU ET AL.

16 of 17

Journal of Geophysical Research: Atmospheres

10.1029/2020JD033039

Wu, T., Wang, D., & Takagi, N. (2018a). Locating preliminary breakdown pulses in positive cloud‐to‐ground lightning. Journal ofGeophysical Research: Atmospheres, 123, 7989–7998. https://doi.org/10.1029/2018JD028716
Wu, T., Wang, D., & Takagi, N. (2018b). Lightning mapping with an array of fast antennas. Geophysical Research Letters, 45, 3698–3705.
https://doi.org/10.1002/2018GL077628
Wu, T., Wang, D., & Takagi, N. (2019). Velocities of positive leaders in intracloud and negative cloud‐to‐ground lightning ﬂashes. Journal ofGeophysical Research: Atmospheres, 124, 9983–9995. https://doi.org/10.1029/2019JD030783
Wu, T., Wang, D., & Takagi, N. (2020). A negative cloud‐to‐ground lightning ﬂash initiating at a high altitude and starting without classic
preliminary breakdown pulses. Journal of Atmospheric Electricity., 39(1), 16–32. https://doi.org/10.1541/jae.39.16
Yuan, S., Qie, X., Jiang, R., Wang, D., Sun, Z., Srivastava, A., & Williams, E. (2020). Origin of an uncommon multiple‐stroke positive cloud‐to‐ground lightning ﬂash with different terminations. Journal of Geophysical Research: Atmospheres, 125, e2019JD032098. https://doi.
org/10.1029/2019JD032098

WU ET AL.

17 of 17