RESEARCH ARTICLE
10.1029/2022JD037282
Key Points:• T he intensity of first positive returnstrokes (RSs) is positively correlatedwith rise time and pulse width ofE-change waveforms of the RSs• The intensity of first positive RSs
is related with the preliminary
breakdown and preceding leader
processes• Strongest positive RSs usuallyoccur in a short time (<10 ms) after
lightning initiation, preceded by a fast(∼10 6 m/s) positive leader
Supporting Information:

Supporting Information may be found in
the online version of this article.
Correspondence to:T. Wu,
tingwu@gifu-u.ac.jp
Citation:

Wu, T., Wang, D., & Takagi, N. (2022).
On the intensity of first return strokes
in positive cloud-to-ground lightning in
winter. Journal of Geophysical Research:
Atmospheres, 127, e2022JD037282.
https://doi.org/10.1029/2022JD037282
Received 10 JUN 2022
Accepted 2 NOV 2022

On the Intensity of First Return Strokes in Positive
Cloud-To-Ground Lightning in WinterTing Wu1, Daohong Wang1, and Nobuyuki Takagi1

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

1

Abstract Intensities of about 700 first return strokes (RSs) in positive cloud-to-ground lightning flashes
observed by a 14-site Fast Antenna Lightning Mapping Array in one winter season are analyzed. Peak currents
estimated from range-normalized peak amplitudes of electric field change (E-change) waveforms of RSs areused to represent their intensities. It is found that peak currents of positive RSs are positively correlated with
their waveform parameters including pulse width, rise time, fall time and half-peak width. Time differences
between lightning initiation and first RSs are closely related with peak currents of positive RSs, with strong
positive RSs usually associated with small time differences. Peak currents of positive RSs are also related withamplitudes of preceding leader pulses. Out of 674 positive RSs, 232 are preceded by positive leader pulses,
and amplitudes of these pulses are positively correlated with peak currents of RSs. Strong positive RSs withpeak currents larger than 150 kA are analyzed and compared with strong negative RSs. While strong negative
RSs usually produce abnormal E-change waveforms that are generally different from typical RS waveforms,
strong positive RSs do not have such special features. Strongest positive RSs usually occur within a very shorttime (usually smaller than 10 ms) after lightning initiation and are more likely to be associated with positive
preliminary breakdown pulses. It is inferred that these strongest RSs are usually preceded by a fast downward
positive leader with a speed on the order of 10 6 m/s. Charge structures responsible for strong positive RSs are
discussed.
Plain Language Summary It is well known that positive return strokes (RSs) are more likely to
be very strong compared with negative RSs, but the reason is not clear. In this study, we analyzed the intensityof about 700 first RSs in positive cloud-to-ground lightning flashes and investigated its relationship with otherparameters and discharge processes. With such a large sample, we demonstrated that strong positive RSs areusually associated with short time differences with lightning initiation and strong preceding leader pulses.
Particularly, the strongest positive RSs usually occur within a few milliseconds after lightning initiation and areusually preceded by a fast downward positive leader with a speed on the order of 10 6 m/s. It is speculated thata strong downward electric field near the ground is essential for the production of strong positive RSs. Possible
charge structures responsible for strong positive strokes are proposed.
1. Introduction
The return stroke (RS) is usually the strongest discharge process in a cloud-to-ground (CG) lightning flash andis thought to be responsible for most lightning-related damages. Although RSs in negative CG flashes havebeen well studied, those in positive CG flashes are still poorly understood, largely due to the fact that positive
CG flashes are much rarer than negative ones. Much knowledge about the intensity of positive RSs has beenobtained with observations of nationwide lightning location systems such as the National Lightning Detection
Network (NLDN) (e.g., Cummins & Murphy, 2009), and it has been well established that positive RSs are more
likely to carry very large peak currents than negative ones (Lyons et al., 1998). This has been confirmed by
space-based observations showing that the brightest lightning flashes are usually positive CG flashes (Peterson& Lay, 2020). However, these observations cannot provide detailed information on characteristics of individual
lightning flashes, so it is not clear if positive CG flashes producing strong RSs have any common characteristics,
which is a key question for understanding the mechanism responsible for large peak currents in positive RSs.

© 2022. American Geophysical Union.
All Rights Reserved.

WU ET AL.

Some advancements have been made in understanding intensities of RSs in negative CG flashes, which are much
more common. Shi et al. (2019), based on 3-D lightning mapping results of 279 negative CG flashes, reported
that the intensity of first RSs in negative CG flashes is related with preceding discharge processes including
the preliminary breakdown (PB) and stepped leaders. Their key finding is that strong negative RSs are usually
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preceded by a fast stepped leader. The same conclusion can also be inferred from analyses of electric field change(E-change) waveforms of negative CG flashes (Nag & Cummins, 2017; Zhu et al., 2015, 2016). A similar result
has also been reported for positive CG flashes by Wang et al. (2021) based on the analysis of 24 positive CG
flashes observed by the Lightning Mapping Array (Rison et al., 1999) in winter.
Recently, Wu, Wang, Huang, and Takagi (2021) reported that negative RSs with peak currents larger than 150 kA
in winter produce abnormal E-change waveforms that are generally different from those of typical RSs. Due to theabnormal waveforms, these strong discharges had not been recognized as RSs by the lightning research community. This finding raised a new question: do strong positive RSs produce abnormal E-change waveforms as well?
In this paper, we will analyze the intensity of about 700 first RSs in positive CG flashes observed in winterby the Fast Antenna Lightning Mapping Array (FALMA). Based on this large data set, we will investigate therelationship between the intensity of first positive RSs and characteristics of RS waveforms, PB and preceding
leader pulses. Special attention will be paid to strong positive RSs with peak currents larger than 150 kA, and acomparison with strong negative RSs will be made.

2. Observation and Data
Data analyzed in this paper were recorded by a 14-site FALMA during the winter observation in the Hokuriku
region of Japan from December 2018 to March 2019. The FALMA is a 3-D lightning mapping system using thefast antenna as the sensor, working in the frequency band of 500 Hz to 500 kHz (Wu et al., 2018a). During thewinter observation, however, source height results are not reliable as discussed by Wu et al. (2020), so we will
only use 2-D mapping results in this paper. With the 2-D mapping results, we can unambiguously determine PB
and leader pulses that belong to the same flash as an RS. Observation sites of the FALMA during the winterobservation are shown as black squares in Figure 1a.
All identified first RSs in positive CG flashes in a 200 × 200 km 2 region are shown in Figure 1a. RSs represented
by red cross signs in Figure 1a are those saturating all FALMA sites so their peak currents could not be estimatedand are not included in this study. The remaining 690 RSs are represented by colored plus signs with the color
indicating the peak current and will be analyzed in this paper. Note that positive CG flashes analyzed in thisstudy include bipolar CG flashes starting with a positive RS but do not include those starting with a negative RS.
Also note that the number of RSs used in different analyses will be slightly different as the data requirements fordifferent analyses are different. Details will be provided at the beginning of each analysis in Section 3.
Peak currents of RSs are estimated from range-normalized peak amplitudes of E-change waveforms of RSs.
Simply speaking, range-normalized peak amplitudes of some RSs measured by the FALMA were compared withpeak currents reported by the Japan Lightning Detection Network (JLDN) (e.g., Matsui et al., 2019) to calculate
a conversion coefficient (we purchased the JLDN data in a 4-hr period with frequent lightning activities), thenpeak currents of all RSs recorded by the FALMA can be calculated from range-normalized peak amplitudes andthe conversion coefficient. The detailed procedure for the current estimation was described by Wu, Wang, andTakagi (2021). Figure S1 in the Supporting Information shows peak currents of RSs versus distances (relative
to the origin in Figure 1a). We can see that peak currents are generally not related with distances, indicating that
there is no distance-related bias in the estimation of peak currents.
Positive RSs are all manually identified by their E-change waveforms. We did not set any quantitative criterion
on waveform characteristics for the identification, because any criterion would inevitably result in certain biases
in distributions of waveform characteristics and peak currents. Although manual identification will also introduce certain errors, we believe this is the most accurate, though laborious, way to identify RSs. Waveforms of
all identified positive RSs are provided in the data repository so readers can see what events have been analyzed
in this paper.
The physics sign convention is used in this paper, so a positive RS produces an initial positive electric fieldchange.

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Figure 1. (a) Locations of all first RSs in positive CG flashes. The color indicates the estimated peak current of the RS. Red
crosses represent RSs saturating all observation sites. Black squares represent observation sites of the FALMA. The origin (0,0) corresponds to the latitude and longitude of (36.76°N, 136.76°E). (b) Distributions of peak currents. Gray bars represent
first positive RSs on land and blue bars on the sea.

3. Results
3.1. Peak Current Statistics of Positive Return Strokes
The distribution of peak currents of all 690 first RSs in positive CG flashes is shown in Figure 1b along with somestatistical results. The maximum current is 476 kA and the minimum is 5 kA. The average value is 82 kA and the
median value is 63 kA. These values are generally higher than statistical results reported by nationwide lightning
location systems such as the NLDN (Orville et al., 2011; Rudlosky & Fuelberg, 2010; Wacker & Orville, 1999).
It is possible that some relatively weak positive RSs were not identified in this study, resulting in an overestimation of the statistical results, but it is also possible that positive RSs in winter thunderstorms in Japan are stronger
than those in other regions and seasons. Moreover, the focus of this study is to investigate possible parameters
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and discharge processes related with peak currents of positive RSs, so the possible overestimation will have very
limited influence.
In Figure 1b, gray bars represent RSs on land and blue bars represent RSs on the sea. There are 227 RSs on landand 463 RSs on the sea. There are no clear differences between peak current distributions of RSs on land and on
the sea. For the 227 RSs on land, the average value of the peak current is 77 kA and the median value is 63 kA.
The average and median values for the 463 RSs on the sea are 85 and 64 kA. Although average values show
certain difference, median values are very close for RSs on land and on the sea. It is well known that unlike negative RSs, peak currents of positive RSs on land and on the sea do not have clear systematic differences (Chronis
et al., 2016; Orville et al., 2011).
3.2. Relationship Between Peak Current and Return Stroke Waveform
The relationship between peak currents of first positive RSs and parameters of their E-change waveforms isinvestigated. In order to reduce the influence of distortions due to the static field component and local noises, only
first RSs farther than 50 km from at least two sites are included in this analysis. There are a total of 623 events
satisfying this condition. For each waveform parameter, waveforms recorded by all sites farther than 50 km awayfrom the event are used to calculate the parameter, and their median value is used as the result of the parameter.
Definitions of waveform parameters including pulse width, rise time and fall time are the same as those in Wu,
Wang, Huang, and Takagi (2021).
Relationships between peak currents and parameters of RS waveforms are shown in Figure 2. RSs on land andon the sea are represented by gray and blue points, respectively. The value of r represents the Pearson correlation
coefficient for each pair of parameters. Positive correlations can be seen between peak current and pulse width,rise time, fall time, and half-peak width. The correlation is strongest for the rise time. The positive correlation
between the peak current and the rise time was also reported for negative first RSs (Nag & Cummins, 2018).
These moderate or strong positive correlations in Figure 2 (except of the correlation for the ratio of fall time torise time in Figure 2e) may be simply because an RS with a larger peak current generally needs a longer time forthe current to reach the peak. However, these correlations indicate a fundamental difference from waveform characteristics of strong negative RSs in winter. Wu, Wang, Huang, and Takagi (2021) reported that strong negative
RSs with peak currents larger than 150 kA produce E-change waveforms that are generally different from normal
RSs. Particularly, their pulse width and fall time are generally smaller than those of normal RS waveforms. From
Figure 2, we can see that E-change waveforms of strong positive RSs do not have this special feature.
Figure 2 also shows distributions and statistical results of waveform parameters. Statistical results of waveform
pamameters of positive RSs have been reported by many studies, and our results are generally consistent withprevious studies (e.g., Nag & Rakov, 2014; Qie et al., 2013; Schumann et al., 2013). From Figure 2 we canalso see that distributions of waveform parameters of RSs on land and on the sea do not show clear differences.
Although it is expected that upward connecting leaders on land and on the sea may have certain differences due
to different surface conditions, this result indicates that different surface conditions of the land and the sea havevery limited influences on E-change waveforms of positive RSs.
3.3. Relationship Between Peak Current and Preliminary Breakdown
Relationships between peak currents of positive RSs and various properties of PB pulses are investigated, andthe results are shown in Figure 3. It should be noted that some positive CG flashes did not start with PB pulses
or PB pulses were too weak to determine their properties, and these cases are excluded, and finally 673 cases areincluded in this analysis. E-change waveforms of one typical flash that did not start with PB pulses are shownin Figure 4b. We can see that this flash started with some weak pulses with very large pulse widths, which are
distinctly different from typical PB pulses.
It is well known that positive CG flashes can start with positive PB pulses (the same polarity as positive RSs)or negative PB pulses. In this study, 317 positive flashes started with positive PB pulses and 356 started withnegative PB pulses. This is consistent with the observation in winter by Wu et al. (2013) who observed 11 positive
flashes starting with positive PB pulses and 15 with negative PB pulses, but it is different from the observation in
winter by Ushio et al. (1998) that 17 out of 19 positive CG flashes started with positive PB pulses. Additionally,
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Figure 2. Relationship between peak currents of first positive RSs and (a) pulse width, (b) rise time, (c) fall time, (d)half-peak width, and (e) ratio of fall time to rise time of RS waveforms. Gray points and bars represent positive RSs on landand blue ones represent those on the sea. The event with the maximum value in (e) is not shown. The value of r represents thePearson correlation coefficient.

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Figure 3. (a) Relationship between the time difference (from lightning initiation to the first positive RS) and the peakcurrent of positive RSs. (b) Relationship between the time difference and the peak current of the PB (estimated peak currentof the largest pulse in a PB pulse train). (c) The same as (a) but only shows the range of time differences from 0 to 20 ms.
(d) Relationship between the peak current of PB and RS. (e) Distribution of the time difference. (f) Distribution of the peakcurrent of RS. Red dots and bars represent positive PB pulses or RSs preceded by positive PB pulses, and blue ones represent
negative PB pulses or RSs preceded by negative PB pulses.

there is evidence that positive CG flashes in summer thunderstorms, especially in low- and mid-latitude regions,mostly start with positive PB pulses (Nag & Rakov, 2012; Wu et al., 2018b; Zhang et al., 2013).
Figure 3a shows the relationship between the time difference (from the initiation of the positive CG flash to
the first RS) and the peak current. The initiation of a positive CG flash is determined as the first pulse in a PB
pulse train, and 2-D mapping results are used to determine the PB pulse train that belongs to the same flash
as the first RS. Note that the first pulse of a flash is usually very small, likely corresponding to the so-called“initial E-change” reported by Marshall et al. (2014). A pronounced feature in Figure 3a is that RSs with large
peak currents are usually associated with small time differences, which is true for flashes with both positive
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Figure 4. (a) E-change waveforms of the positive CG flash with the smallest time difference between the initiation and thefirst RS. Ip is the peak current of the RS, and d is the distance between the RS and the site recording the waveforms. The
red arrow indicates the first pulse of this flash. (b) E-change waveforms of a positive CG flash starting without PB pulses.
Colored points represent distances of located sources relative to the RS. The red cross sign indicates the RS. The time scale ofthe figure indicates that the initial pulses have very large pulse widths, different from PB pulses.

and negative PB pulses. In other words, if the peak current of the first RS in a positive CG flash is very large, it
usually occurs soon after the initiation of the flash, no matter if the PB pulses are positive or negative. However,
the opposite is not true; as we can see in Figure 3a, there are plenty of cases with both small peak currents andsmall time differences.
Although the correlation between the peak current and the time difference does not seem to be related with thepolarity of PB pulses, positive PB pulses are more likely to be associated with extremely small time differences.
Figure 3c shows the same result as Figure 3a but zooms in on the range of time differences from 0 to 20 ms. We
can see that almost all cases with a time difference smaller than 5 ms are associated with positive PB pulses (25cases with positive PB pulses compared with 1 case with negative PB pulses). The minimum time difference
for cases with positive PB pulses is 1.28 ms while that for cases with negative PB pulses is 4.76 ms. The same
result can also be seen in Figure 3e, which shows distributions of time differences for positive flashes withpositive and negative PB pulses. We can see that although overall distributions are similar, positive PB pulses
are more likely to be associated with very small time differences while negative PB pulses are more likely to be
associated with very large time differences.
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E-change waveforms of the positive stroke with the minimum time difference of 1.28 ms are shown in Figure 4a.
The RS has a relatively large peak current of 160 kA. It is interesting to note that the duration of the whole flash
is also extremely short; there are no signatures of discharges after the RS. Previous studies reported that the timedifference between the initiation or the PB and the first RS in positive CG flashes is normally tens of milliseconds
or larger than 100 ms in summer (e.g., Qie et al., 2013; Schumann et al., 2013; Zhang et al., 2013) and can be as
short as several milliseconds in winter (Wu et al., 2013, 2020). We believe a positive RS with such a short timedifference of 1.28 ms from lightning initiation is reported for the first time.
The relationship between the time difference and the peak current of the PB is also investigated and the result inshown in Figure 3b. The peak current of the PB is calculated from the E-change magnitude and the 2-D locationof the largest PB pulse in a PB pulse train in the same manner as estimating RS peak currents. Therefore, the value
is unlikely accurate as the true peak current flowing during the PB process, but it is likely well correlated withthe peak current of the PB process. Figure 3b shows a similar, but weaker, relationship as that between the timedifference and the peak current of RSs in Figure 3a. It indicates that strong PB pulses are usually followed by apositive RS in a short time. But again, the opposite is not true—weak PB pulses can be followed by a positive RS
in either a very short or a very long time. Further, there is no clear correlation between the peak current of the
PB and that of RSs as shown in Figure 3d. The only feature that can be determined from Figure 3d is that strong
PB pulses are unlikely to be followed by very weak positive RSs. Finally, Figure 3f shows distributions of peakcurrents of positive RSs associated with positive and negative PB pulses. It shows that the polarity of PB pulses
has little influence on the peak current of positive RSs overall. However, as will be discussed in Section 4, thestrongest positive RSs are more likely to be associated with positive PB pulses.
3.4. Relationship Between Peak Current and Preceding Leader Pulses
The relationship between the peak current of positive RSs and the amplitude of pulses right before the RS isinvestigated. In this analysis, we include positive RSs observed by at least one site more than 50 km away, andthere are a total of 674 positive RSs. Many positive RSs are preceded by positive pulses (the same polarity as the
positive RS), but there are also many cases in which there are no identifiable pulses. For simplicity, we confine
this analysis to pulses within 500 μs before the peak of the RS. Further, in order to avoid the influence of theonset of the RS pulse, we exclude pulses within 50 μs before the peak of the RS. Therefore, pulses in the period of−500∼–50 μs before the peak of the RS are manually inspected for the selected 674 cases. These cases are classified into three types: type 1—predominantly positive pulses, type 2—predominantly negative pulses, and type3—no clear pulses or pulses with mixed polarities. We are aware that the classification is sometimes subjective,
so figures showing the preceding pulses with the designated type for all events are provided in the data repository.
There are 232 positive RSs preceded by predominantly positive pulses. One typical example is shown in
Figure 5a. By contrast, there are only 15 cases preceded by predominantly negative pulses. One case with clear
negative pulses is shown in Figure 5b. In the remaining 427 cases, there are no clear preceding pulses or there arepulses of both polarities. Note that the waveform in Figure 5b may appear somewhat atypical as an RS pulse; itis determined as an RS pulse because of the fast rise to the peak and the fine structure after the peak, which arecharacteristic of RS pulses.
The peak current of preceding pulses is calculated and its correlation with the peak current of positive RSs isshown in Figure 6. Positive RSs on land are shown in Figure 6a and those on the sea in Figure 6b. For pulses oftype 1, the amplitude of the largest positive pulse is used for the estimation of the peak current, and for pulses oftype 2, the amplitude of the largest negative pulse is used. For pulses of type 3, the amplitude of the largest pulse,
regardless of its polarity, is used. The peak current is estimated in the same manner as the estimation of the RS
peak current.
From Figure 6, first we can see that most of type-3 pulses are associated with relatively weak RSs, mostly withpeak currents smaller than 100 kA. For type-1 pulses, their peak currents have a clear positive correlation withpeak currents of associated RSs. Particularly, strong positive pulses—for example, those with peak currents larger
than 10 kA—are mostly associated with strong RSs with peak currents larger than 100 kA. Similarly, very strong
RSs—for example, those with peak currents larger than 200 kA—are rarely associated with weak pulses.
Pulses right before positive RSs are thought to be produced by downward positive leaders or upward negative
connecting leaders. Both situations would produce positive pulses, corresponding to type-1 pulses in Figure 6.
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Figure 5. E-change waveforms of (a) a positive RS preceded by positive pulses and (b) a positive RS preceded by negative
pulses. In each case, waveforms recorded by two sites with different distances are shown. The left part shows overall
waveforms and the right part shows waveforms of preceding pulses.

And in both situations, the leader is quite close to the ground, so the pulse amplitude should be closely relatedwith the strength of the electric field near the ground. Therefore, the correlation in Figure 6 indicates that thepeak current of positive RSs is positively correlated with the electric field strength near the ground. This result
agrees with the finding by Shi et al. (2019) that the peak current of negative RSs is positively correlated with thevelocity of stepped leaders.
By comparing Figures 6a and 6b, we can see that correlations for positive strokes on land and on the sea havesome differences, especially for type-1 pulses. It is clear that the positive correlation for type-1 pulses are muchstronger when strokes are on the sea. This may be due to the fact that the sea surface is usually flat while theland surface is much more complicated, with various objects of different heights and shapes. The difference inFigures 6a and 6b may indicate that type-1 preceding pulses are mostly produced by upward negative connecting
leaders rather than downward positive leaders, because upward connecting leaders are initiated from the groundand their characteristics are more likely to be influenced by grounded objects.
It is not clear why in some cases negative pulses occurred before positive RSs. As they only account for a verysmall percentage of recorded positive RSs, they may be produced in some special conditions. For example, theupward negative connecting leader may be highly tortuous and have a short period of downward propagation
before connecting with the positive leader, or they may be produced by in-cloud negative leaders. It is also not
clear why most negative pulses, including type-2 pulses and negative type-3 pulses, are associated with positive
strokes on the sea as can be seen in Figure 6b.

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Figure 6. Relationship between peak currents of positive RSs and peak currents of preceding leader pulses within 0.5 ms
before the RS for RSs (a) on land and (b) on the sea. Preceding pulses are classified into positive pulses (red circles), negative
pulses (blue circles) and no identifiable pulses or pulses with mixed polarities (black circles).

3.5. Strong Positive Return Strokes and Comparison With Negative Ones
Wu, Wang, Huang, and Takagi (2021) analyzed strong negative RSs with peak currents larger than 150 kA in
winter and found that their E-change waveforms are largely different from those of normal RSs. In this analysis,
we will look at strong positive RSs with peak currents larger than 150 kA and compare them with negative ones.
Strong negative RSs analyzed by Wu, Wang, Huang, and Takagi (2021) are reanalyzed here. Note that Wu, Wang,
Huang, and Takagi (2021) analyzed negative RSs in a region of 300 × 300 km 2, but positive RSs analyzed in thisstudy are in a region of 200 × 200 km 2. Therefore, strong negative RSs reanalyzed in this study are also confinedin the same 200 × 200 km 2 region as positive ones. There are 59 strong negative RSs in this region as shownin Figure 7a. Six of them saturated all observation sites as represented by red crosses, and the maximum peakcurrent is 310 kA. By contrast, there are 104 strong positive RSs as shown in Figure 7b. Ten of them saturated allobservation sites, and the maximum peak current is 476 kA. This result indicates that in winter thunderstorms inthe Hokuriku region, strong positive RSs are much more frequent than negative ones, and they are more likely tocarry extremely large peak currents.
Another difference that can be seen from Figure 7 is that compared with strong negative RSs, positive RSs are
more likely to occur on the sea. In order to quantitatively analyze this feature, Figure 7c shows distributionsof elevations (meters above sea level) at locations of different types of lightning discharges, including strong
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Figure 7. Locations of (a) strong negative RSs and (b) strong positive RSs with peak currents larger than 150 kA. Red crosses
represent RSs saturating all observation sites. (c) Distributions of elevations at locations of strong negative RSs (blue bars),strong positive RSs (red bars) and all located discharge sources (black bars). Bars left of zero represent events on the sea.

negative RSs (those in Figure 7a), strong positive RSs (those in Figure 7b) and located sources of all lightning
discharges in the same region. As winter thunderstorms usually develop from the Sea of Japan, move toward theland and dissipate soon after moving ashore and colliding with mountains, most lightning discharges in winternaturally occur on the sea as demonstrated by black bars in Figure 7c. Strong positive RSs (red bars) show a similar distribution, with the majority on the sea. This result likely indicates that strong positive RSs can be produced
at any stage of thunderstorms in winter and their occurrences are not related with the topography. On the contrary,strong negative RSs have a much lower percentage on the sea, and percentages of RSs occurring at locations
with elevations up to 500 m are consistently high, indicating that strong negative RSs tend to occur at areas withmoderate elevations of a few hundred meters. In other words, moderate elevations of a few hundred meters arelikely conducive to the production of strong negative RSs.
One interesting feature of strong negative RSs analyzed by Wu, Wang, Huang, and Takagi (2021) is that theirE-change waveforms are largely different from those of normal negative RSs, leading to the consequence thatsome strong negative RSs were not recognized by nationwide lightning location systems. Here we will briefly
look at E-change waveforms of strong positive RSs. Figure 8 shows E-change waveforms of the strongest 10 positive RSs analyzed in this paper. Generally speaking, waveforms of these RSs do not have any obvious differencewith those of normal positive RSs. One clear tendency of these cases is that the time difference between the peakof the RS and the initiation of the flash (Δt in Figure 8) is relatively small; in eight of these cases, Δt is smaller
than 10 ms. However, these time differences are still about one order of magnitude larger than those in strong
negative strokes and can be hardly called abnormal. Another possible special common feature is that in many ofthese cases, some fine structures can be seen on the rising portion of RS pulses, which may have contributed to
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Figure 8. E-change waveforms of the 10 strongest positive strokes. IRS is the peak current of the positive RS. IPB is the peakcurrent of the PB (not shown). Δt is the time difference between the initiation of the flash and the peak of the RS. d is the
distance of the RS to the site recording the plotted waveform.

large rise times for strong positive RSs as demonstrated in Figure 2b. Apart from these features, these waveforms
are fairly typical positive RS waveforms and should be readily recognized by lightning location systems. We
can also see from the relationships between RS waveform parameters and peak currents shown in Figure 2 thatwaveform characteristics of strong positive RSs do not have systematic differences with those of positive RSs
with normal peak currents.

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4. Conditions Favorable to the Production of Strong Positive Strokes
Based on the results described above, we can get some idea about the general characteristics of strong positive
strokes and conditions favorable to their production. The most prominent feature of strong positive strokes isthat the time difference between the initiation of the lightning flash and the RS is very short as demonstrated in
Figure 3a. In other words, strong positive RSs usually occur very shortly after the initiation of the flash. Thisfeature is also true for strong negative strokes in winter (Wu, Wang, Huang, & Takagi, 2021) as well as in summer(Nag & Cummins, 2017; Shi et al., 2019; Zhu et al., 2015, 2016). It is likely that the positive leader connecting
to the ground is initiated at or shortly after the initiation of the flash and progresses with a high speed down to
the ground.
In order to further analyze leader activities preceding strong positive RSs, Figure 9 shows scatterplots of the
distance versus time for sources before and after some of the strongest positive RSs. Six of the ten cases in
Figure 8 with relatively good location results are selected. The distance and the time are calculated relative to the
RS represented by a black cross sign at (0, 0), and the first source of the flash is represented by a red diamondsign. Blue and red dashed lines represent velocities of 10 5 and 10 6 m/s, respectively. Located sources are generally produced by negative leaders. We can see that a common feature in these cases is a negative leader propagating away from the location of the RS with a high speed on the order of 10 6 m/s. RSs usually occur only a few
milliseconds after the lightning initiation and usually have a small horizontal distance of a few kilometers. We
can roughly estimate the speed of the positive leader connecting to the ground with some assumptions. First, we
assume the positive leader is initiated at the very beginning of the flash. Second, we assume the positive leader
propagates in a straight line to the RS location. Third, we neglect the initiation height. All these assumptions
will result in underestimations of the estimated speed. With these assumptions, the speed of the positive leader
would be equal to the slope of the line connecting the initiation source (red diamond) and the RS (black cross)in Figure 9, and we can see from Figure 9 that in most of these cases the speed is very close to 1 × 10 6 m/s.
Considering the assumptions, the actual speed may be well larger than 1 × 10 6 m/s. Downward positive leaderswith speeds on the order of 10 6 m/s have been reported before (Chen et al., 2015; Li et al., 2020; Pu et al., 2021;
Wang & Takagi, 2011), but it seems that those with speeds well smaller than 10 6 m/s are much more common(Saba et al., 2010). Furthermore, these previous observations correspond to the final stage of downward positive
leaders right before connecting to the ground, so their overall speeds including in-cloud propagations are likely
much smaller. Therefore, our estimation indicates that these strongest positive RSs are preceded by very fast
positive leaders, and we can infer that before very strong positive RSs, there is usually a positive leader initiatedat or shortly after the flash initiation and propagating downward to the ground with a large speed on the orderof 10 6 m/s. There is likely a fast negative leader as well with a speed on the order of 10 6 m/s which continued
propagating for a large distance after the positive RS. It should be noted that as we cannot estimate leader speeds
for all positive strokes, especially those with large time differences from lightning initiations, we cannot exclude
the possibility that downward positive leaders with speeds on the order of 10 6 m/s are actually very common in
winter.
Of the 10 strongest positive strokes shown in Figure 8, seven are preceded by positive PB pulses. Although peakcurrents of positive RSs associated with positive and negative PB pulses have very similar distributions as shownin Figure 3f, it seems positive RSs associated with positive PB pulses are more like to be extremely strong as canalso be seen in Figure 3c. It is well understood that positive PB pulses are produced by upward negative leadersand negative PB pulses by downward negative leaders (Wu et al., 2018b). In the case of positive PB pulses, theinitial negative leader propagates upward and the initial positive leader, though undetected, likely propagates
downward. On the other hand, in the case of negative PB pulses, the initial negative leader always starts with adownward propagation, usually followed by an upward propagation (Wu et al., 2018b). The initial positive leader
likely starts with an upward propagation, followed by a downward propagation toward the ground. Therefore,
positive RSs associated with positive PB pulses are more likely to occur in a very short time after the lightning
initiation as was demonstrated in Figure 3c, and they are apparently more likely to be associated with very strong
downward electric fields.
Another feature of strong positive strokes is that they are usually associated with strong positive leader pulses
right before RSs as demonstrated in Figure 6. As analyzed in Section 3.4, positive pulses preceding positive RSs
are likely produced by upward negative connecting leaders, and strong positive pulses likely indicate a strong
downward electric field near the ground.
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Figure 9. Scatterplots of the distance versus time for sources before and after some strong positive RSs. The distance and the time are calculated relative to the RS
shown at (0, 0). The red diamond sign is the first source of +CG flashes. Blue and red dashed lines represent velocities of 10 5 and 10 6 m/s, respectively. IRS is the peakcurrent of positive RSs. IPB is the peak current of the PB pulses before positive RSs.

Based on the above analyses, we can see that a strong downward electric field below the thundercloud, particularly near the ground, is the most essential factor in the production of strong positive strokes. Such a strong
downward electric field can be produced by a positive charge region in the lower region of a thundercloud. The
positive charge region likely has a fairly large horizontal extent as indicated by the large propagation distancesof negative leaders shown in Figure 9. In the cases of strong positive strokes starting with positive PB pulses, theWU ET AL.

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Figure 10. Illustrations of possible charge structures for strong positive strokes starting with (a) positive PB and (b) negative
PB. Blue and red arrows represent negative and positive leaders, respectively.

initial positive leader propagates downward, so it is likely that there is a small negative “pocket” charge region
below the positive charge region. The negative charge region is likely very small as it would reduce the downward
electric field. A possible charge structure is shown in Figure 10a. Note that there may also be a main negative
charge region above the positive charge region, forming an inverted tripolar charge structure. As the data in thisstudy cannot show much information about the main negative charge region, it is shown as a dashed-line ellipse
in Figure 10. Wang et al. (2021) also reported that most positive CG flashes in winter are associated with inverted
charge structures, different from the traditional explanation that positive CG flashes in winter are associated witha normal charge structure in which the upper positive charge region is horizontally displaced from the negative
charge region due to the strong wind shear (Brook et al., 1982).
For strong positive strokes starting with negative PB pulses, however, the initial positive leader needs to first
propagate upward and soon turn downward. Such complicated behavior indicates a complicated charge structure.
However, it is well known that charge structures in winter thunderstorms are usually very complicated (Wanget al., 2018; Zheng et al., 2019), which is likely the reason that positive CG flashes starting with positive andnegative PB pulses are equally common in winter. A possible charge structure is proposed in Figure 10b, whichshows a small negative charge region surrounded by a large positive charge region. The initiation location is at
the lower side of the negative charge region, below which there are also some positive charges, so the initial
negative leader starts with a downward propagation, producing negative PB pulses. The initial positive leader
first propagates upward in the small negative charge region. Soon it gets out of the negative charge region, andunder the strong downward electric field caused by the large positive charge region above, it turns downward to
the ground with a fast speed.
It is easy to explain why positive RSs occurring a long time after the lightning initiation can rarely be very strongas can be seen in Figure 3a. Positive leaders initiating these RSs are more likely to develop from a negative leader
channel after the negative leader propagated for a long time (Velde et al., 2014) and are thus far away from thelocation of the lightning initiation, where the electric field is supposed to be the strongest, and a relatively weakelectric field results in a relatively weak RS. An alternative explanation suggested by Wang et al. (2021) is thatafter a negative leader propagates for some time, it may transform to a positive leader under the so-called leader
polarity reversal mechanism (Shi et al., 2018), and the later the polarity reversal occurs, the smaller the positive
charges are left for the positive leader, and the weaker the resultant RS is.
It has long been reported that positive RSs are often preceded by extensive intracloud discharges (Fuquay, 1982;
Kong et al., 2008; Saba et al., 2009). From the results of this study, we can infer that such positive RSs areunlikely very strong.
The same is true for subsequent RSs in positive CG flashes. Subsequent RSs in positive CG flashes rarely occur
in the same channel as the first RS, but still they are usually much weaker than the first RS (Wu et al., 2020). One
reason is that subsequent RSs in positive CG flashes are usually associated with positive leaders developing fromWU ET AL.

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negative leader channels (Wu et al., 2020; Yuan et al., 2020), so they also tend to occur at a location far away fromthe lightning initiation location, similar to positive first RSs occurring a long time after the lightning initiation.

5. Conclusion
In this paper, we analyzed peak currents of first RSs in about 700 positive CG flashes observed by the FALMA
in one winter season in the Hokuriku region of Japan. We focused on investigating relationships between peakcurrents of positive RSs and their waveform characteristics and other discharge processes. The major findings are
summarized as follows.
Peak currents of positive RSs are positively correlated with E-change waveform parameters of RS pulses, including pulse width, rise time, fall time and half-peak width, with the rise time having the strongest correlation.
Positive RSs associated with positive and negative PB pulses are equally common, and peak currents of these
two types of RSs have overall similar distributions. However, the strongest positive RSs are more likely to be
associated with positive PB pulses (the same polarity as positive RSs). Peak currents of positive RSs do not haveclear correlation with amplitudes of PB pulses.
Peak currents of positive RSs are closely related with the time difference between the lightning initiation and thefirst RS. Strong positive RSs are usually associated with small time differences, which is true for RSs associatedwith both polarities of PB pulses.
Peak currents of positive RSs are also related with amplitudes of preceding leader pulses. Out of 674 positive
RSs, 232 are preceded by positive pulses, and only 15 are preceded by negative pulses. In the remaining 427
cases, there are no clear pulses or the pulses have mixed polarities. For positive RSs preceded by positive pulses,
amplitudes of preceding pulses are positively correlated with peak currents of positive RSs. Comparison ofpreceding pulses on land and on the sea indicates that preceding pulses are more likely to be produced by upward
negative connecting leaders.
Strong positive RSs with peak currents larger than 150 kA are analyzed and are compared with strong negative
RSs. It has been reported that strong negative RSs produce abnormal E-change waveforms, making them difficult to be identified by lightning location systems, but waveforms of strong positive RSs do not have abnormalfeatures. Compared with strong negative RSs, strong positive RSs are more common and are more likely to carryextremely large currents. Strong positive RSs tend to occur more frequently on the sea, just like normal winterlightning, while strong negative RSs are more likely to occur on land.
If we look at a few of the strongest positive RSs, we can see that they usually have very small time differences(smaller than 10 ms) with the lightning initiation. In other words, the strongest positive RSs usually occur in avery short period after the lightning initiation. The strongest positive RSs are also more likely to be associatedwith positive PB pulses. We can also infer that these strongest positive RSs are usually preceded by a fast downward positive leader with a speed on the order of 10 6 m/s.
Based on the above results, we suggest that a strong downward electric field is essential for producing strong
positive RSs. A large positive charge region is always necessary for such a downward electric field. For strong
positive strokes starting with positive PB pulses, a small negative charge region may exist below the large positive
charge region, and the initial positive leader starts from a location between the two charge regions, propagating
directly downward to the ground. For strong positive strokes starting with negative PB pulses, the charge structure
is more complicated; a small negative charge region surrounded by a large positive charge region is proposed, andthe initial positive leader starts from the lower edge of the negative charge region, first propagating upward andthen downward to the ground.

Data Availability Statement
Data related with this paper can be found at https://doi.org/10.5281/zenodo.6629850.

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Acknowledgments
This study was supported by the Ministryof Education, Culture, Sports, Science,
and Technology of Japan (Grants
20H02129 and 21K03681).

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References
Brook, M., Nakano, M., Krehbiel, P., & Takeuti, T. (1982). The electrical structure of the Hokuriku winter thunderstorms. Journal of GeophysicalResearch, 87(C2), 1207. https://doi.org/10.1029/jc087ic02p01207
Chen, L., Lu, W., Zhang, Y., & Wang, D. (2015). Optical progression characteristics of an interesting natural downward bipolar lightning flash.
Journal of Geophysical Research: Atmospheres, 120(2), 708–715. https://doi.org/10.1002/2014jd022463
Chronis, T., Koshak, W., & McCaul, E. (2016). Why do oceanic negative cloud-to-ground lightning exhibit larger peak current values? Journalof Geophysical Research: Atmospheres, 121(8), 4049–4068. https://doi.org/10.1002/2015jd024129
Cummins, K. L., & Murphy, M. J. (2009). An overview of lightning locating systems: History, techniques, and data uses, with an in-depth look at
the u.s. NLDN. IEEE Transactions on Electromagnetic Compatibility, 51(3), 499–518. https://doi.org/10.1109/temc.2009.2023450
Fuquay, D. M. (1982). Positive cloud-to-ground lightning in summer thunderstorms. Journal of Geophysical Research, 87(C9), 7131. https://doi.
org/10.1029/jc087ic09p07131
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(5), L05816. https://doi.org/10.1029/2007gl032764
Li, S., Qiu, S., Shi, L., & Li, Y. (2020). Broadband VHF observations of two natural positive cloud-to-ground lightning flashes. GeophysicalResearch Letters, 47(11), e2019GL086915. https://doi.org/10.1029/2019GL086915
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
Marshall, T., Stolzenburg, M., Karunarathna, N., & Karunarathne, S. (2014). Electromagnetic activity before initial breakdown pulses of lightning. Journal of Geophysical Research: Atmospheres, 119(22), 12558–12574. https://doi.org/10.1002/2014JD022155
Matsui, M., Michishita, K., & Yokoyama, S. (2019). Characteristics of negative flashes with multiple ground strike points located by theJapanese lightning detection network. IEEE Transactions on Electromagnetic Compatibility, 61(3), 751–758. https://doi.org/10.1109/
TEMC.2019.2913661
Nag, A., & Cummins, K. L. (2017). Negative first stroke leader characteristics in cloud-to-ground lightning over land and ocean. GeophysicalResearch Letters, 44(4), 1973–1980. https://doi.org/10.1002/2016GL072270
Nag, A., & Cummins, K. L. (2018). Magnetic field risetimes of negative lightning first return strokes over land and ocean. Geophysical Research
Letters, 45(23), 13133–13141. https://doi.org/10.1029/2018GL080038
Nag, A., & Rakov, V. A. (2012). Positive lightning: An overview, new observations, and inferences. Journal of Geophysical Research, 117(D8).
https://doi.org/10.1029/2012jd017545
Nag, A., & Rakov, V. A. (2014). Parameters of electric field waveforms produced by positive lightning return strokes. IEEE Transactions on
Electromagnetic Compatibility, 56(4), 932–939. https://doi.org/10.1109/TEMC.2013.2293628
Orville, R. E., & Huffines, G. R. (2001). Cloud-to-ground lightning in the United States: NLDN results in the first decade, 1989–98. Monthly
Weather Review, 129(5), 1179–1193. https://doi.org/10.1175/1520-0493(2001)129<1179:ctglit>2.0.co;2
Orville, R. E., Huffines, G. R., Burrows, W. R., & Cummins, K. L. (2011). The North American lightning detection network (NALDN)—Analysis
of flash data: 2001–09. Monthly Weather Review, 139(5), 1305–1322. https://doi.org/10.1175/2010mwr3452.1
Peterson, M., & Lay, E. (2020). GLM observations of the brightest lightning in the americas. Journal of Geophysical Research: Atmospheres,125(23). https://doi.org/10.1029/2020jd033378
Pu, Y., Cummer, S. A., & Liu, N. (2021). VHF radio spectrum of a positive leader and implications for electric fields. Geophysical Research
Letters, 48(11), e2021GL093145. https://doi.org/10.1029/2021GL093145
Qie, X., Wang, Z., Wang, D., & Liu, M. (2013). Characteristics of positive cloud-to-ground lightning in da hinggan ling forest region at relatively highlatitude, northeastern China. Journal of Geophysical Research: Atmospheres, 118(24), 13393–13404. https://doi.org/10.1002/2013JD020093
Rison, W., Thomas, R. J., Krehbiel, P. R., Hamlin, T., & Harlin, J. (1999). A gps-based three-dimensional lightning mapping system: Initial observations in central new Mexico. Geophysical Research Letters, 26(23), 3573–3576. https://doi.org/10.1029/1999GL010856
Rudlosky, S. D., & Fuelberg, H. E. (2010). Pre- and postupgrade distributions of NLDN reported cloud-to-ground lightning characteristics in thecontiguous United States. Monthly Weather Review, 138(9), 3623–3633. https://doi.org/10.1175/2010mwr3283.1
Saba, M. M. F., Campos, L. Z. S., Krider, E. P., & Pinto, O. (2009). High-speed video observations of positive ground flashes produced by intracloud lightning. Geophysical Research Letters, 36(12), 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 of positive
lightning flashes to ground. Journal of Geophysical Research, 115(D24). https://doi.org/10.1029/2010jd014330
Schumann, C., Saba, M. M. F., da Silva, R. B. G., & Schulz, W. (2013). Electric fields changes produced by positives cloud-to-ground lightning
flashes. Journal of Atmospheric and Solar-Terrestrial Physics, 92, 37–42. https://doi.org/10.1016/j.jastp.2012.09.008
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(15), 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 of three
upward bipolar lightning flashes. Journal of Geophysical Research: Atmospheres, 123(17), 9430–9442. https://doi.org/10.1029/2018jd028637
Ushio, T., Kawasaki, Z.-I., Matsuura, K., & Wang, D. (1998). Electric fields of initial breakdown in positive ground flash. Journal of GeophysicalResearch, 103(D12), 14135–14139. https://doi.org/10.1029/97jd01975
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(22).
https://doi.org/10.1002/2013jd021291
Wacker, R. S., & Orville, R. E. (1999). Changes in measured lightning flash count and return stroke peak current after the 1994 u.s. national lightning
detection network upgrade: 1. Observations. Journal of Geophysical Research, 104(D2), 2151–2157. https://doi.org/10.1029/1998jd200060
Wang, D., & Takagi, N. (2011). A downward positive leader that radiated optical pulses like a negative stepped leader. Journal of GeophysicalResearch, 116(D10), D10205. https://doi.org/10.1029/2010jd015391
Wang, D., Wu, T., & Takagi, N. (2018). Charge structure of winter thunderstorm in Japan: A review and an update. IEEJ Transactions on Powerand Energy, 138(5), 310–314. https://doi.org/10.1541/ieejpes.138.310
Wang, D., Zheng, D., Wu, T., & Takagi, N. (2021). Winter positive cloud-to-ground lightning flashes observed by lma in Japan. IEEJ Transactions on Electrical and Electronic Engineering, 16(3), 402–411. https://doi.org/10.1002/tee.23310
Wu, T., Takayanagi, Y., Funaki, T., Yoshida, S., Ushio, T., Kawasaki, Z.-I., et al. (2013). Preliminary breakdown pulses of cloud-to-ground lightning
in winter thunderstorms in Japan. Journal of Atmospheric and Solar-Terrestrial Physics, 102, 91–98. https://doi.org/10.1016/j.jastp.2013.05.014
Wu, T., Wang, D., Huang, H., & Takagi, N. (2021). The strongest negative lightning strokes in winter thunderstorms in Japan. GeophysicalResearch Letters, 48(21). https://doi.org/10.1029/2021gl095525

17 of 18

Journal of Geophysical Research: Atmospheres

10.1029/2022JD037282

Wu, T., Wang, D., & Takagi, N. (2018a). Lightning mapping with an array of fast antennas. Geophysical Research Letters, 45(8), 3698–3705.
https://doi.org/10.1002/2018GL077628
Wu, T., Wang, D., & Takagi, N. (2018b). Locating preliminary breakdown pulses in positive cloud-to-ground lightning. Journal of GeophysicalResearch: Atmospheres. https://doi.org/10.1029/2018jd028716
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(20), e2020JD033039. https://doi.org/10.1029/2020JD033039
Wu, T., Wang, D., & Takagi, N. (2021). Compact lightning strokes in winter thunderstorms. Journal of Geophysical Research: Atmospheres,126(15), e2021JD034932. https://doi.org/10.1029/2021JD034932
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(15). https://doi.
org/10.1029/2019jd032098
Zhang, Y., Zhang, Y., Lu, W., & Zheng, D. (2013). Analysis and comparison of initial breakdown pulses for positive cloud-to-ground flashes
observed in Beijing and Guangzhou. Atmospheric Research, 129–130, 34–41. https://doi.org/10.1016/j.atmosres.2013.03.006
Zheng, D., Wang, D., Zhang, Y., Wu, T., & Takagi, N. (2019). Charge regions indicated by LMA lightning flashes in Hokuriku's winter thunderstorms. Journal of Geophysical Research: Atmospheres, 124, 7179–7206. https://doi.org/10.1029/2018jd030060
Zhu, Y., Rakov, V., & Tran, M. (2016). A study of preliminary breakdown and return stroke processes in high-intensity negative lightning
discharges. Atmosphere, 7(10), 130. https://doi.org/10.3390/atmos7100130
Zhu, Y., Rakov, V. A., Mallick, S., & Tran, M. D. (2015). Characterization of negative cloud-to-ground lightning in Florida. Journal of Atmospheric and Solar-Terrestrial Physics, 136, 8–15. https://doi.org/10.1016/j.jastp.2015.08.006

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