RESEARCH ARTICLE
10.1029/2019JD030783
Key Points:• Positive leader velocities inhundreds of IC and −CG ﬂashes arein a small range of 1 to 3 × 104 m/s• Positive leader velocities in IC
ﬂashes tend to decrease as leader
propagation altitudes increase• Positive leaders in IC and −CG
ﬂashes propagate with a stablevelocity

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

Citation:
Wu, T., Wang, D., & Takagi, N. (2019).
Velocities of positive leaders inintracloud and negative cloud‐to‐ground lightning ﬂashes. Journal ofGeophysical Research: Atmospheres,
124, 9983–9995. https://doi.org/
10.1029/2019JD030783

Received 8 APR 2019
Accepted 23 AUG 2019
Accepted article online 29 AUG 2019
Published online 13 SEP 2019

Velocities of Positive Leaders in Intracloud and Negative
Cloud‐to‐Ground Lightning Flashes
Ting Wu1, Daohong Wang1, and Nobuyuki Takagi1

1

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

Abstract We have performed a statistical study on velocities of positive leaders in 553 intracloud (IC) and
220 negative cloud‐to‐ground (−CG) ﬂashes. It is found that velocities of positive leaders in IC and −CG
ﬂashes have very similar distributions, with the vast majority in the range of 1 to 3 × 104 m/s. Averagevelocities are 1.64 and 1.55 × 104 m/s, respectively, for positive leaders in IC and −CG ﬂashes. Velocitiesof positive leaders in IC ﬂashes show a clear negative correlation with initiation altitudes and leader
propagation altitudes, similar to negative leaders in IC ﬂashes. The negative correlation also exists for
positive leaders in −CG ﬂashes but is relatively weak. We also found that positive leaders in both IC and−CG ﬂashes propagate with a stable velocity, contrary to downward positive leaders in +CG ﬂashes
and upward positive leaders in negative upward and triggered ﬂashes, which were usually found toaccelerate during propagations. These results suggest that positive leaders in IC and −CG ﬂashes andthose in +CG, upward and triggered ﬂashes propagate with essentially different velocities. The differences
and possible reasons are discussed.

Plain Language Summary Positive leaders in lightning ﬂashes are much less well known thannegative leaders. It has long been thought that positive leaders are an order of magnitude slower thannegative leaders, but recent observations of positive leaders in positive cloud‐to‐ground (+CG), upward
and rocket‐triggered lightning suggest that positive leaders can be as fast as, or even faster than, negative
leaders. In this study, velocities of positive leaders in 553 intracloud (IC) and 220 −CG ﬂashes are analyzed,
and it is found that positive leaders in IC and −CG ﬂashes are indeed an order of magnitude slower thannegative leaders. The results also suggest that positive leaders in IC and −CG ﬂashes are different from thosein +CG, upward and triggered ﬂashes in many respects. The differences and possible reasons are discussed.

1. Introduction
It is widely accepted that natural lightning ﬂashes start with bidirectional leaders with positive and negativeends propagating in opposite directions (Kasemir, 1960; Mazur & Ruhnke, 1993; Montanyà et al., 2015; Tran
& Rakov, 2016; van der Velde & Montanyà, 2013). Compared with negative leaders, positive leaders aremuch less well studied. Unlike negative leaders in negative cloud‐to‐ground (−CG) ﬂashes that ultimately
propagate out of clouds and can be readily observed by high‐speed video cameras, positive leaders in both
−CG and IC ﬂashes primarily develop inside clouds. Although positive leaders in positive cloud‐to‐ground(+CG) ﬂashes propagate out of clouds before connecting to the ground, +CG ﬂashes are usually much rarer
than −CG and IC ﬂashes and the chance of capturing them with high‐speed video cameras is rather low(Kong et al., 2008; Saba et al., 2008; Wang & Takagi, 2011). Furthermore, although in‐cloud negative leaders
can be imaged by very high frequency and low‐frequency (LF) lightning mapping systems (e.g., Lyu et al.,2016; Rison et al., 1999; Shao & Krehbiel, 1996; Wu et al., 2015), positive leaders usually radiate much more
weakly in radio frequencies and are essentially masked by the radiation from the simultaneous negative leaders (Shao et al., 1999). As a result, most studies on positive leaders are based on observations of upward
positive leaders from high structures (Lu et al., 2009; Shi et al., 2018; Wang et al., 2016; Wang & Takagi,2012) or in rocket‐triggered lightning (Biagi et al., 2009; Biagi et al., 2011; Edens et al., 2012; Hill et al.,2012; Jiang et al., 2013; Kito et al., 1985; Kotovsky et al., 2019; Sun et al., 2014; Yoshida et al., 2010).

©2019. American Geophysical Union.
All Rights Reserved.

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A key property of positive leaders is the velocity of their propagations. It has long been thought that velocitiesof positive leaders are an order of magnitude smaller than those of negative leaders (Les Renardieres
Group, 1977; Mazur et al., 1998; Williams, 2006). However, many recent observations of positive leaders
in +CG lightning, upward lightning, and rocket‐triggered lightning show that positive leaders can be as
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fast as, or even faster than, negative leaders (Chen et al., 2015; Saba et al., 2008; Wang & Takagi, 2011,2012; Yoshida et al., 2010).
Relatively slow positive leaders (~2 × 104 m/s) have also been reported by a few studies but were observed in−CG and IC ﬂashes (Lapierre et al., 2014; Proctor et al., 1988; Shao & Krehbiel, 1996; van der Velde &Montanyà, 2013). Their velocities were inferred by the extension of recoil leaders traversing positive
leader channels. These results indicate that velocities of positive leaders in −CG and IC ﬂashes may befundamentally different from downward positive leaders in +CG and upward positive leaders in negative
upward and rocket‐triggered ﬂashes. However, only a handful of cases have been reported in the literature,and it is not clear whether a systematic velocity difference exists for positive leaders in different types oflightning ﬂashes. In this study, we will analyze positive leader velocities in 220 −CG ﬂashes and 533 IC
ﬂashes. With such a large sample, we will be able to investigate the systematic differences between positive
leader velocities in different types of lightning ﬂashes as well as possible reasons for the differences.
For simplicity, downward positive leaders connecting to the ground in +CG ﬂashes and initial upward
positive leaders in negative upward and triggered lightning ﬂashes will be referred to as “positive leaders
in +CG, upward and triggered ﬂashes” throughout this paper.

2. Data
Data in this study were obtained during the summer of 2017 in Gifu, Japan, with an LF lightning mapping
system called Fast Antenna Lightning Mapping Array (FALMA). FALMA can reconstruct three‐dimensional (3‐D) structures of lightning ﬂashes with great detail, and, with the help of electric ﬁeld change
waveforms recorded at multiple sites, allows us to unambiguously determine types of lightning discharges.
More details and examples of lightning ﬂashes imaged by FALMA can be found in Wu et al. (2018a).
During the summer of 2017, thousands of IC and −CG ﬂashes were recorded. For the study of positive leaders, 966 IC ﬂashes and 336 −CG ﬂashes with clear positive leader channels were selected. A simple method
described in section 3.1 was used to estimate overall velocities of positive leaders. For some lightning ﬂashes,
estimations with this method had relatively large errors and were excluded for the analysis. Ultimately, 533
IC ﬂashes and 220 −CG ﬂashes were used for the calculation.
As evidence for the discussion (section 5), overall velocities of downward positive leaders in +CG ﬂashes arealso brieﬂy analyzed. As reported by Wu et al. (2018b), 46 +CG ﬂashes were observed inside or near the
network of the FALMA during the summer of 2017. Positive leader velocities were roughly estimated by
dividing the 3‐D distance by the time difference between the ﬁrst source of a ﬂash and the ﬁrst return stroke.
Only ﬂashes with the horizontal distance between the ﬁrst source and the ﬁrst return stroke smaller than 5
km were selected. With this criterion, 27 out of 46 +CG ﬂashes were selected for this calculation.

3. Methodology
3.1. Rough Estimation of Overall Velocities
Positive leaders in IC and −CG ﬂashes usually cannot be directly detected due to their weak radiation inradio frequencies. However, as the positive leader develops, the so‐called recoil leader (or K change, K
process) repeatedly develops either at or close to the tip of the positive leader (e.g., Saba et al., 2008;
Warner et al., 2012) back toward the origin of the ﬂash and sometimes into the negative leader channel.
These recoil leaders carry negative charges and have strong radiation and can be well resolved by the
FALMA. From the initiation locations of recoil leaders, the development of positive leaders can be inferred.
Figure 1 shows the 3‐D mapping result of an IC ﬂash with the typical bilevel structure. The initiation point of
this ﬂash is shown as a triangle, which connects negative leader channels shown in blue and positive leader
channels shown in red. Similarly, Figure 2 shows the 3‐D mapping result of a −CG ﬂash. This ﬂash had 11
return strokes with three different terminations. Positive leaders in both IC and −CG ﬂashes mainly
propagate horizontally in the main negative charge region.
From these two examples, we can see that positive leaders in IC and −CG ﬂashes have many branches, but mostof the branches do not show well‐deﬁned channel structures; this is due to the fact that the radiation sources arefrom recoil leaders which occur intermittently. Therefore, it would be impractical to identify each channel and
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Figure 1. The 3‐D mapping result of an intracloud ﬂash. (a) Height‐time view. (b) Height‐distance (from west to east)
view. (c) Plan view. (d) Distance (from south to north)‐height view. (e) Source distribution along the height. The triangle represents the ﬁrst source of this ﬂash. Blue dots represent negative leaders and red dots represent positive leaders.

calculate the 3‐D velocity for each branch. In this study, we use a simple method similar to that used by van der
Velde and Montanyà (2013) and Schultz et al. (2018), who estimated positive and negative leader velocities with
the Lightning Mapping Array data, to roughly estimate the overall velocity of positive leaders. All sources of
positive leader channels (red sources in Figures 1 and 2) are selected and the 3‐D distance and timedifference between each source and the ﬁrst source (the triangles in Figures 1 and 2) are calculated. The
distance‐time relations for positive leaders in the two ﬂashes in Figures 1 and 2 are shown in Figure 3.
For the selected positive leader sources (red dots in Figure 3), an automated process is developed to estimate theleader velocity. First, each ﬂash is divided into multiple 20‐ms windows, and in each window the positive leader
source with the maximum distance from the origin is selected, shown as black and yellow dots in Figure 3. Second,from these black and yellow dots, possible outliers (yellow dots) are identiﬁed and excluded. These outliers are
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Figure 2. The same as Figure 1 but for a negative cloud‐to‐ground (−CG) ﬂash. Cross signs represent return strokes (different colors indicate different striking points).

identiﬁed as those points with distances smaller than the previous two points or larger than the following two
points. Finally, for the remaining points with maximum distances (black dots), a linear regression is madeand the slope is determined as the overall velocity. For the IC ﬂash in Figure 1 and the −CG ﬂash in
Figure 2, overall velocities of positive leaders are estimated to be 2.4 and 1.5 × 104 m/s, respectively.
This method is relatively accurate for positive leaders mainly developing outward in the radial direction but
inaccurate for those developing in the tangential direction. Therefore, only lightning ﬂashes with positive
leaders mainly developing in the radial direction are selected for the estimation of velocities. As described in
section 2, from 966 IC ﬂashes and 336 −CG ﬂashes with relatively good location results, 533 IC ﬂashes and220 −CG ﬂashes have been selected for this analysis.
3.2. Estimation of 3‐D Velocities
For some positive leader branches that are well located, we can estimate 3‐D velocities in a more accurate
way. Figure 4a shows the plan view of positive leader sources in the −CG ﬂash in Figure 2. A branch
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Figure 3. Estimation of positive leader velocities for (a) the intracloud (IC) ﬂash in Figure 1 and (b) the negative cloud‐to‐ground (−CG) ﬂash in Figure 2. Red dots are positive leader sources. Black and yellow dots are sources with the maximum
distance in 20‐ms windows. Yellow dots are determined as outliers. Black lines are the linear regression lines for black
dots. Slopes of the regression lines are the estimated velocities. See section 3.1 for more details.

whose structure can be clearly recognized are shown in red. In order to divide the channel into multiple linear
segments, four nodes labeled as “1” to “4” are chosen and are shown as blue circles in Figure 4a. Channel
segments between successive nodes can be roughly considered as straight lines. Distances of the branchsources (red dots) are calculated relative to these four nodes. Speciﬁcally, sources between Nodes 1 and 2
are calculated relative to the location of Node 1, and sources between Nodes 2 and 3 are calculated relative
to the location of Node 2, with the addition of the distance between Nodes 1 and 2, and so on. Finally,sources after the node 4 are calculated relative to the location of Node 4, with the addition of the cumulative
distance from Node 1 to Node 4. In this way, inﬂuences from the variation of propagation directions can be
minimized. Source altitudes are also considered in these calculations, so the estimated results are 3‐Dvelocities. Further, time differences are calculated relative to the earliest source between Nodes 1 and 2.
Figure 4b shows the distance‐time scatterplot of the selected sources in Figure 4a. The same automatedprocess described in section 3.1 is used to identify the black dots, which indicate the general location of
the positive leader tip. We can see that the black dots show a clear linear distance‐time relationship,
indicating that the positive leader does not show evident velocity variations during its propagation. The velocity is estimated to be 1.6 × 104 m/s, very close to the overall velocity of 1.5 × 104 m/s estimated in section 3.1.
Positive leaders in this ﬂash mainly propagated in the radial direction, so it is expected that the result
estimated using the simple method described in section 3.1 is similar to the 3‐D result estimated here.

4. Results
4.1. Distributions of Positive Leader Velocities
With the method described in section 3.1, velocities of positive leaders in 552 IC ﬂashes and 220 −CG ﬂashes arecalculated, and their distributions are shown in Figure 5. Positive leader velocities in IC and −CG ﬂashes show
very similar distributions, both having peaks around 1.5 × 104 m/s. Velocities for positive leaders in IC ﬂashes
have an average value of 1.64 × 104 m/s with a maximum of 3.2 × 104 m/s and a minimum of 1.0 × 104 m/s, andvelocities for positive leaders in −CG ﬂashes have an average value of 1.55 × 104 m/s with a maximum of 3.0 ×
104 m/s and a minimum of 0.92 × 104 m/s. An overwhelming majority (532 of 533 IC ﬂashes and 218 of 220
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Figure 4. Illustration of the method to calculate the 3‐D velocity of a positive leader branch in the negative cloud‐to‐ground ﬂash in Figure 2. (a) Plan view of positive leader sources. Red dots represent the selected positive leader branch.
Four blue circles represent four nodes to divide the channel into four segments. (b) Distance‐time view of the selectedsources (red dots in Figure 4a). The same method in Figure 3 is used to determine the linear regression line and estimate
the velocity. See section 3.2 for more details.

−CG ﬂashes) is in the range of 1 to 3 × 104 m/s. Therefore, positive leaders in IC and −CG ﬂashes are indeed oneorder of magnitude slower than negative leaders (Les Renardieres Group, 1977; Williams, 2006).
From the above results, it is interesting to note that the range of positive leader velocities in IC and −CG
ﬂashes is very small, from 0.92 to 3.2 × 104 m/s, the maximum being only about 3.5 times as large as theminimum. In contrast, Wu et al. (2015) reported that negative leader velocities in 662 IC ﬂashes ranged from
0.5 to 17.8 × 105 m/s, the maximum being about 35 times as large as the minimum. Positive leader velocities
in +CG, upward and triggered ﬂashes seem to have even larger differences in different observations, large
velocities being 2 orders of magnitude larger than small velocities (e.g., Edens et al., 2012; Saba et al.,2010; Wang & Takagi, 2011; Yoshida et al., 2010).
In spite of the very small range (0.92 to 3.2 × 104 m/s), previous reports of positive leader velocities of IC and−CG ﬂashes in different regions all fall within this range (Lapierre et al., 2014; Shao & Krehbiel, 1996; van
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Figure 5. Distributions of positive leader velocities in (a) intracloud (IC) and (b) negative cloud‐to‐ground (−CG) ﬂashes.

der Velde & Montanyà, 2013), indicating that velocities of positive leaders in IC and −CG ﬂashes do not havelarge variations in different lightning ﬂashes or different thunderstorms.
4.2. Relationship Between Positive Leader Velocity and Altitude
Wu et al. (2015) demonstrated that velocities of initial negative leaders in IC ﬂashes decreased as
initiation altitudes increased. Proctor (1997) also found that lightning ﬂashes initiating at higher altitudes

Figure 6. Relationships between positive leader velocities and initiation altitudes and mean propagation altitudes for (aand b) intracloud (IC) ﬂashes and (c and d) negative cloud‐to‐ground (−CG) ﬂashes. Red dots represent average velocities for every 20 consecutive black dots. Values of r represent correlation coefﬁcients.

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had relatively slow negative leaders. In this section, we will investigate whether positive leaders have thesimilar feature.
Velocities of all positive leaders in IC and −CG ﬂashes calculated in section 4.1 are plotted against initiation
altitudes of lightning ﬂashes and mean propagation altitudes of positive leaders as shown in Figure 6.
The value of r indicates the correlation coefﬁcient between velocities and initiation altitudes or mean
propagation altitudes. The initiation altitude is calculated as the altitude of the ﬁrst source in a ﬂash,
assuming initial positive and negative leaders start from the same point. The mean propagation altitude iscalculated as the median altitude of all positive leader sources in a ﬂash. Further, average velocities for every
20 consecutive events are calculated and are shown as red dots in Figure 6.
From Figure 6, we can see that for positive leaders in IC ﬂashes, velocities show a clear decreasing trend withincreasing initiation altitudes and mean propagation altitudes. Correlation coefﬁcients are −0.44 and −0.41,
respectively, for initiation altitudes and mean propagation altitudes. This result is similar to the negative
correlation between initiation altitudes and initial negative leader velocities in IC ﬂashes (Wu et al., 2015).
For positive leaders in −CG ﬂashes, no correlation can be recognized between velocities and initiation
altitudes (the correlation coefﬁcient is −0.08). However, a weak negative correlation exists between
velocities and mean propagation altitudes (the correlation coefﬁcient is −0.26). It seems that positive leader
velocities in −CG ﬂashes are also inﬂuenced by leader propagation altitudes but compared to positive
leaders in IC ﬂashes, other factors may have larger inﬂuences.
Edens et al. (2012) reported velocities in the range of 1 to 3 × 104 m/s for a positive leader in a triggered ﬂash in
New Mexico. They noted that positive leaders in triggered lightning appeared to propagate more slowly in New
Mexico than in other regions, but the reason was not clear. It is possible that the negative correlation between
positive leader velocity and the altitude is also applicable to triggered lightning, and the high altitude (3.2 km
above sea level) of the lightning triggering facility in New Mexico contributed to the low velocity.
It should also be noted that although altitudes of positive leaders in −CG ﬂashes are generally lower
than those in IC ﬂashes, velocities of positive leaders in −CG ﬂashes are essentially the same as thosein IC ﬂashes. Therefore, positive leaders in IC and −CG ﬂashes as a whole do not preserve the altitude‐
velocity correlation.

4.3. Velocity Variations During Leader Propagations
Many observations have shown that both downward positive leaders in +CG ﬂashes and upward positive
leaders in upward and rocket‐triggered lightning ﬂashes accelerate as they propagate (Biagi et al., 2011;
Campos et al., 2014; Jiang et al., 2013; Kito et al., 1985; Kong et al., 2008, 2015; Saba et al., 2008, 2010;
Wang & Takagi, 2011). In this section, we will investigate whether positive leaders in IC and −CG ﬂashes
have the similar behavior.
Overall velocities estimated by the method described in section 3.1 are inﬂuenced by propagation directions of leaders and cannot accurately indicate variations during leader propagations. Therefore, themethod described in section 3.2 is used and 3‐D velocities of positive leaders with clear channels in 10
IC ﬂashes and 10 −CG ﬂashes are calculated. Figures 7 and 8 show results for IC and −CG ﬂashes,
respectively. For each ﬂash, the estimated 3‐D velocity is shown above the regression line, with the overall velocity estimated using the method described in section 3.1 shown in parentheses, both in the unit of
104 m/s.
From Figures 7 and 8, it seems that although in some cases, the velocities show certain slight variations(Figures 7c, 7e, and 8i), in most cases, velocities of positive leaders in both IC and −CG ﬂashes do not show
evident variations as the leaders propagate. Previous studies of positive leader velocities in +CG, upward andtriggered ﬂashes usually reported large increases as leaders propagated. For example, Kong et al. (2008)
showed that the velocity of a positive leader in a +CG ﬂash increased from 0.1 to 3.8 × 105 m/s as it
approached the ground. Biagi et al. (2011) reported that the velocity of an upward positive leader in a
rocket‐triggered lightning ﬂash increased from 5.5 × 104 m/s between heights of 123 and 134 m to 2.1 ×
105 m/s at a height of 350 m. Such large increases clearly do not exist in Figures 7 and 8. Propagation
distances of the positive leaders shown in Figures 7 and 8 are generally larger than 10 km, longer than those

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Figure 7. Velocity estimation in 3‐D for positive leaders in 10 intracloud (IC) ﬂashes. Numbers above regression lines
4
4
indicate 3‐D velocities (×10 m/s; section 3.2), and those in parentheses indicate overall velocities (×10 m/s; section 3.1).

observed in +CG, upward and triggered ﬂashes, indicating that positive leaders in both IC and −CG ﬂashes
propagate with a stable velocity over a large distance.
These results also demonstrate that overall velocities estimated with the method described in section 3.1 do
not have large differences with 3‐D velocities. Most of the cases analyzed here have a difference smaller than
20%. The selection of positive leaders that mainly propagate in the radial direction accounts for this small
difference (section 3.1).

5. Discussion
From the results of this study, we can see that there are several major differences between velocities of
positive leaders in IC and −CG ﬂashes and those in +CG, upward and triggered ﬂashes. First, positive
leaders in +CG, upward and triggered ﬂashes are generally faster than those in IC and −CG ﬂashes.
Velocities of positive leaders in +CG, upward and triggered ﬂashes are mainly above 3 × 104 m/s(Biagi et al., 2009, 2011; Hill et al., 2012; Kong et al., 2015; Saba et al., 2010; Wang & Takagi, 2011, 2012;
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Figure 8. The same as Figure 7 but for 10 negative cloud‐to‐ground (−CG) ﬂashes.

Yoshida et al., 2010), which is virtually the upper end of positive leader velocities in IC and −CG ﬂashes.
Second, positive leaders in +CG, upward and triggered ﬂashes are frequently observed to accelerate
during propagations (Biagi et al., 2011; Campos et al., 2014; Jiang et al., 2013; Kito et al., 1985; Kong et al.,2008, 2015; Saba et al., 2008, 2010; Wang & Takagi, 2011), while those in IC and −CG ﬂashes do not show
clear variations in velocity as they propagate. Third, velocities of positive leaders in +CG, upward andtriggered ﬂashes observed in different studies span a very wide range, from 104 to 106 m/s, but those in IC
and −CG ﬂashes concentrate in a small range of 1 to 3 × 104 m/s. We discuss the possible reasons forthese differences in following sections.
5.1. Why Positive Leaders in +CG, Upward and Triggered Flashes Accelerate While Those in IC
and −CG Flashes Do Not
Positive leaders in +CG, upward and triggered ﬂashes reported in previous studies essentially
propagated vertically between charge regions in thunderclouds and the ground or high objects on the
ground (wire‐trailing rockets in the case of triggered lightning) where the electric ﬁeld‐height proﬁle is
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Figure 9. Distribution of positive leader velocities in positive cloud‐to‐ground (+CG) ﬂashes.

strongly inﬂuenced by the effect of electrostatic induction of the ground and high objects. For example, inthe case of positive leaders in +CG ﬂashes, they propagate from charge regions in thunderclouds toward
the ground, and as they approach the ground, the electric ﬁeld between the tip of positive leaders and theground increases, which may be the reason for increased velocities.
As for positive leaders in IC and −CG ﬂashes, they propagate mainly horizontally inside negative charge
regions. As charged particles are distributed approximately uniformly in the horizontal direction, thebackground electric ﬁeld in the horizontal direction is not as signiﬁcant as that in the vertical direction.
Therefore, propagations of positive leaders in IC and −CG ﬂashes are barely affected by the backgroundelectric ﬁeld and the velocities are stable.
There have also been high‐speed video observations of positive leaders propagating in largely horizontal
directions near cloud bases, and unlike vertical positive leaders in +CG, upward and triggered ﬂashes,these horizontal positive leaders seem to propagate with relatively stable velocities. For example, Saba
et al. (2008) observed that one horizontal positive leader segment between altitudes of 2,200 and 2,700m showed no increase in the velocity. Similar observations can also be found in Montanyà et al.
(2015) and Yuan et al. (2019). These observations support the above explanation that the increase in velocity for positive leaders in +CG, upward and triggered ﬂashes is due to the vertical propagation andapproach to a virtual electrode.
5.2. Why Positive Leaders in +CG, Upward and Triggered Flashes Have Very Different Velocities
in Different Observations While Those in IC and −CG Flashes Do Not
As discussed above, the background electric ﬁeld in the horizontal direction is relatively weak in negative
charge regions in which positive leaders of IC and −CG ﬂashes propagate, so positive leaders of IC and−CG ﬂashes observed in different studies essentially propagate in similar background electric ﬁelds. As aresult, velocities of positive leaders in IC and −CG ﬂashes have a very small range, even in different thunderstorms and different regions. On the other hand, the ambient electric ﬁeld for positive leaders in +CG,
upward and triggered ﬂashes is inﬂuenced by the induction effect of the ground and high objects on the
ground, with the height proﬁle dependent on the altitude and shape of grounded objects, the topography,
the charge amount in thunderclouds, the altitude of charge regions, and so on. As a result, positive leaders
in +CG, upward and triggered ﬂashes present signiﬁcantly different velocities in different observations.
5.3. Why Positive Leaders in +CG, Upward and Triggered Flashes Are Generally Observed to be
Faster Than Those in IC and −CG Flashes
The reasons for +CG ﬂashes and upward and triggered ﬂashes may be different. For positive leaders in +CG
ﬂashes, they were observed by high‐speed video cameras when they had propagated out of thunderclouds
and approached the ground, so the “average velocity” of positive leaders in +CG ﬂashes reported by previous
studies was the average velocity for approximately the ﬁnal 2,000 m or less before the leaders connected to
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the ground (Campos et al., 2014; Saba et al., 2008; Wang & Takagi, 2011). Considering the observation that
positive leaders in +CG ﬂashes usually accelerate as they approach the ground (e.g., Biagi et al., 2011;
Campos et al., 2014; Wang & Takagi, 2011), the initial velocity when the leaders are inside thunderclouds
is likely much lower than the reported values on the order of 105 or even 106 m/s.
As described in section 2, overall velocities of positive leaders in 27 +CG ﬂashes observed in thecurrent study have also been calculated. These velocities were roughly estimated from the 3‐D
distance and the time difference between the ﬁrst source of a +CG ﬂash and the ﬁrst return stroke. The
distribution of velocities is shown in Figure 9. Only ﬂashes with the horizontal distance between the ﬁrst
source and the ﬁrst return stroke smaller than 5 km were selected for this calculation, so we believe theseresults are relatively accurate. From Figure 9 we can see that the majority of velocities are on the order of
104 m/s, and more than half are below 6 × 104 m/s. Initial velocities of positive leaders when they are inside
thunderclouds should be lower than these values, and it is possible that they are actually similar to thevelocities of positive leaders in IC and −CG ﬂashes reported in this study.
High velocities of positive leaders in upward and triggered ﬂashes are likely due to the existence of tallobjects, which signiﬁcantly increases the local electric ﬁeld. According to Wang and Takagi (2012), initial
velocities of positive leaders from a tower of 330 m above the sea level were about 1 to 2 × 106 m/s, while
those from a tower of 145 m above the sea level were about 1 to 2 × 105 m/s, indicating the effect of highobjects in increasing positive leader velocities.

6. Conclusions
Velocities of positive leaders in 533 IC ﬂashes and 220 −CG ﬂashes are analyzed. It is found that velocities ofthe majority of positive leaders in both IC and −CG ﬂashes are in a small range of 1 to 3 × 104 m/s. Averagevelocities are very close, 1.64 and 1.55 × 104 m/s, respectively, for positive leaders in IC and −CG ﬂashes.
Velocities of positive leaders in IC and −CG ﬂashes are generally lower than those in +CG, upward and triggered ﬂashes reported in previous studies. It seems possible that positive leader velocities in IC and −CG
ﬂashes in different thunderstorms and different regions mostly fall in the small range of 1 to 3 × 104
m/s. It is also found that positive leaders in IC and −CG ﬂashes propagate with a stable velocity, contrary
to those in +CG, upward and triggered ﬂashes, which were usually found to accelerate during propagations. Differences between positive leader velocities in IC and −CG ﬂashes and those in +CG, upward
and triggered ﬂashes are likely due to different environments in which positive leaders propagate.
Positive leaders in IC and −CG ﬂashes mainly propagate horizontally in the main negative charge region
while those in +CG, upward and triggered ﬂashes mainly propagate vertically outside thunderstorms, andthe different ambient electric ﬁeld may be the primary reason for the different velocities.
Similar to negative leaders in IC ﬂashes, positive leaders in IC ﬂashes also tend to have smaller velocities athigher altitudes. The negative correlation between velocities and propagation altitudes also exists for
positive leaders in −CG ﬂashes but is relatively weak, suggesting that factors other than the altitude havelarger inﬂuences on velocities of positive leaders in −CG ﬂashes.
Acknowledgments
This work was supported by the
Ministry of Education, Culture, Sports,
Science, and Technology of Japan(Grants 15H02597, 16H04315, and
18K13618). Data analyzed in this paper
can be downloaded from the website(http://doi.org/10.5281/
zenodo.2633348).

WU ET AL.

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