Introduction

There are basically three modes of charge transfer to ground in the main channel of cloud-to-ground lightning discharges: leader/return-stroke sequence, continuing current, and M-component (Rakov et al.1), where the M-component is defined as a transient, guided/bouncing-wave process excited in a grounded lightning channel carrying a steady current of some tens to hundreds of amperes. M-components can be identified in optical, current, and radiofrequency field records of lightning. All three modes are well studied for -CGs (negative cloud-to-ground flashes), while for +CGs (positive cloud-to-ground flashes) there are still many questions that remain to be answered. Specifically, to the best of our knowledge, there is only one study (Campos et al.2) in which M-components in +CGs were recorded with high-speed framing cameras, and those records do not reveal the M-component mechanism in this type of lightning. Romero et al.3, who studied upward positive lightning initiated from the Santis tower (Switzerland), reported that current pulses characteristic of M-components come in either polarity, but no optical records were obtained in that study. Thus, the question remains if the bouncing-wave process known to occur in M-components in -CGs also occurs in +CGs. With this question in mind, we examined in detail three +CGs recorded at the Lightning Observatory in Gainesville (LOG), Florida, using high-speed framing cameras and radiofrequency field measuring systems. The results turned out to be surprising.

Specifically, besides the evidence of bouncing waves expected for classical M-components occurring in -CGs, two very unusual phenomena were observed. One M-component in a +CG appeared to be fed, via an inferred transient in-cloud link, by the charge transfer in another grounded lightning channel 11 km away, not by an in-cloud process as expected. Also, some charge-feeding events in +CGs caused the main-channel luminosity to temporarily decrease, which is opposite to what is expected for classical M-components. The inferred mechanisms of the observed phenomena are the main focus of this study.

In the following, we present our results on unexpected transient phenomena in positive lightning leading to the following two discoveries: (a) the ability of +CG to talk to a concurrent -CG many kilometers away and (b) the existence of both surges and dips in the luminosity of +CG channel to ground, as this channel is energized by recoil leaders. Our findings have implications for understanding of basic mechanisms of +CGs that are more hazardous and more difficult to protect against than -CGs.

Results

In this paper, we will present three positive cloud-to-ground lightning flashes (+CGs), Flash 1906, Flash 2014, and Flash 1830 that occurred on July 9th, 2019 at 20:42:21.3276299 UTC, on August 21st, 2020 at 01:00:57.3608563 UTC, and on July 17th, 2018 at 17:37:40.3336513 UTC, respectively. Flash 1906 will be used to introduce (in two separate subsections) the two main discoveries of this study, (1) a transient luminosity increase (M-component) in the +CG main channel that was apparently caused by a transient (stroke) in a tower-terminated -CG 11 km away and (2) a charge-feeding process (associated with recoil leader) in +CG, which resulted in a luminosity dip, instead of luminosity surge, in the +CG main channel. Flash 2014, as well as an additional event, positive Flash 1830, presented in Supplementary Note 1, will be used to contrast the transient luminosity enhancements and luminosity dips, both occurring in the same +CG. Additionally included in Supplementary Note 1 is negative Flash 1863 which is used to illustrate the similarity of M-components in +CGs and –CGs.

Individual high-speed camera frames, luminosity profiles, and electric field records will be presented for each of the three +CGs. Flashes 1906 and 2014 were optically imaged in the visible range, while Flash 1830 was imaged in the medium-to-far infrared (3–5 µm) range.

Data for Flash 1906 are presented in Figs. 1–5. Additional information on this flash is found in Figs. S4 and S5 of Supplementary Notes 3 and 4. According to the U.S. National Lightning Detection Network (NLDN), Flash 1906 occurred at a relatively large distance of 13 km from the Lightning Observatory in Gainesville (LOG), Florida, and contained a single stroke (leader/return-stroke sequence) with a peak current of 95 kA. The optically imaged downward positive leader was preceded by an in-cloud negative leader, the latter being detected via its scattered light (see a head-to-tail sequence of small arrows in Fig. 2a) and its electric field signature. The in-cloud leader extended at an apparent 2D speed of 5 × 105 m/s and exhibited stepping. The +CG return stroke (RS) was followed by a continuing current (CC) of about 50 ms in duration, estimated from both optical (see Fig. 2b, c) and electric field (see inset in Fig. 1c) records. Flash 1906 triggered (or was concurrent with) a seven-stroke -CG terminated on the 257-m tall tower (located 8.8 km from LOG; see Fig. 1a) and exhibited below-cloud branches that were created during the leader stage, discharged (or oppositely charged) during the RS/early CC stage, decayed, and then reactivated by recoil leaders during the late CC stage, as seen in Fig. 2a–c. The distance between the ground connections of this flash (+CG) and the -CG terminated on the tower was 11 km (see Fig. 1a). One of the strokes of the tower-terminated –CG occurred essentially simultaneously with an M-component (transient luminosity enhancement) in the CC-carrying +CG channel, while recoil leaders reactivating the +CG below-cloud branches each caused a luminosity (and by inference current) dip in the +CG main channel. The +CG and all seven strokes of the -CG are labeled in Fig. 1b. Note that the first two negative strokes (Strokes 1 and 2 of the -CG) occurred concurrently with the CC stage of the +CG (compare Fig. 1b, c). The -CG channel was outside the field of view of the cameras installed at LOG, and its termination on the 257-m tower was established using NLDN data and the previously identified (Zhu et al.4,5) characteristic RS E-field waveforms (showing early zero-crossing and oscillatory tail; see inset in Fig. 3c and Fig. S5 in Supplementary Note 4), based on observations with the same instrumentation and for the same tower. Both the M-component (marked M) that was essentially simultaneous with Stroke 1 of the -CG terminated on the tower and the luminosity dips (marked R1 to R4) in the +CG main channel caused by recoil leaders in below-cloud branches are seen in Fig. 3a (the corresponding electric field records are shown in Fig. 3b, c). We will discuss the M-component and the luminosity dips in Flash 1906 in the next two subsections. Then, in the last subsection, we will compare M-components and luminosity dips based on data for Flashes 2014 and 1830.

Fig. 1: Single-stroke positive Flash 1906.
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a NLDN data (the diamond representing +CG and seven overlapping circles representing seven return strokes (RS) of the tower-terminated -CG) superimposed on a radar reflectivity map. The thin broken line represents the line of sight of high-speed cameras installed at the Lightning Observatory in Gainesville (LOG) (the square in the lower-right corner of the map). b, c High-gain (τ = 440 µs) and low-gain (τ = 10 ms) electric field waveforms, respectively, displayed on a 240-ms time scale. The inset in c shows the low-gain E-field waveforms (from 0 to 50 ms) before (black) and after (red) compensation for instrumental decay.

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Fig. 2: Single-stroke positive Flash 1906.
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a Composite image of the leader stage (1000 50-µs frames), b selected continuing current (CC) stage frame between M-component (M) and luminosity dip R1 with all leader branches decayed, and c the CC stage (900 50-µs frames) showing leader branches reactivated by recoil leaders RL1 to RL4. Extrapolation of camera’s field of view in a is based on the known locations of both the +CG termination point and the 257-m tower (see Fig. 1a). Two overlapping red and blue dotted-line boxes in a show the regions for which individual frames are presented. Two channel cross-sections, for which luminosity variations as a function of time are analyzed, are marked “Upper” and “Lower” in a. Four branches reactivated by recoil leaders during the CC stage are marked, in the order of their occurrence, in c. Also marked in c is the main channel, the point at which each of the four recoil leaders attached to the main channel, and branch cross-sections for which luminosity variations as a function of time are shown in Supplementary Note 3.

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Fig. 3: Single-stroke positive Flash 1906.
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a Luminosity variations in the Upper (blue) and Lower (red) cross-sections of the +CG main channel, including M-component labeled M and four luminosity dips labeled R1 to R4. b, c Low-gain and high-gain electric field waveforms, respectively, aligned (with ± 12.5-µs uncertainty) with the luminosity variations shown in a. Inset in c shows the integrated dE/dt waveform for the RS of Stroke 1 of the -CG (see also Fig. S5 in Supplementary Note 4, where the same waveform along with the other six RS waveforms of the tower-terminated -CG are presented without saturation). Downward deflection of RS electric field waveforms corresponds to the motion of negative charge to ground (or positive charge out of the ground). The –CG RS onset signifies the movement of positive charge from the ground to the cloud at the position of the tower, occurring at the same time as the positive charge moves to the ground in the form of M-component at the position of +CG channel. Region 1 (except for the middle panel) is shown on an expanded time scale in d and e, with f showing our hypothetical scenario leading to establishment of a transient in-cloud link between the +CG and the tower-terminated –CG. A more complete version of this scenario is found in Supplementary Note 5.

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Fig. 4: Single-stroke positive Flash 1906.
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a, b “Region 2” of Fig. 3a, c shown on an expanded time scale. Microsecond-scale E-field pulses associated with collisions of recoil leaders RL1 and RL2 with the main channel are marked in b and shown expanded in two panels between a, b. R1 and R2 in a are luminosity dips with their onset times corresponding to the microsecond-scale pulses marked in b. c Selected individual frames showing the evolution of RL1. Bidirectional extension of RL1 is seen in Frames 25.05 ms to 25.15 ms. Connection to the main channel is established in Frame 25.2 ms (AP stands for attachment point), and in Frame 25.8 ms this connection is almost completely decayed (essentially lost). Luminosity of the main channel decreased as a result of connection of RL1 to the main channel and started increasing (recovering) when the connection decayed.

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Fig. 5: Single-stroke positive Flash 1906.
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a and b “Region 3” of Fig. 3a, c shown on an expanded time scale. Microsecond-scale E-field pulses associated with collisions of RL3 and RL4 with the main channel are marked in b and shown expanded in two panels between a and b. R3 and R4 in a are luminosity dips with their onset times corresponding to the microsecond-scale pulses marked in b. c Selected Individual frames showing the evolution of RL3. Bidirectional extension of RL3 is seen in Frames 34.5 ms to 34.7 ms. Connection to the main channel is established in Frame 34.75 ms (AP stands for attachment point), and starting with Frame 35.5 ms the branch reactivated by RL3 gradually decayed. Luminosity of the main channel decreased (see the leading edge of luminosity dip R3 in a) as a result of connection of RL3 to the main channel and partially recovered after the branch reactivated by RL3 started to decay. No recovery is seen in a for RL4 due to significant overall luminosity decay.

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Flash 1906: M-component in +CG occurs concurrently with Stroke 1 of -CG 11 km away

The M-component (marked M in Fig. 3a, d), occurred in the main channel of Flash 1906, about 22 ms after the positive RS onset, during the 50-ms long CC following the RS. The M-component luminosity waveshape was more or less symmetrical and its duration was about 800 µs. Both the occurrence context and luminosity waveshape characteristics are similar to those of M-components in -CGs, suggesting that “classical” M-components can occur in both -CGs and +CGs. At the time of the M-component, NLDN (also the Earth Networks Total Lightning Network, ENTLN) reported a negative stroke terminated on the 257-m tower, which was outside of the field of view of the cameras operating at LOG and 11 km away from the +CG channel seen in Fig. 2. This negative stroke (the first stroke of the seven-stroke tower-terminated -CG) apparently caused the M-component labeled M in Fig. 3a, d. The two essentially simultaneous transients, one in the +CG main channel and the other in the tower-terminated –CG channel, were associated with a brief scattered-light illumination of the cloud within the field of view of the camera. The in-cloud negative leader channel, shown by the head-to-tail sequence of small arrows in Fig. 2a, decayed about 55 ms before the emergence of the downward positive leader from the cloud, but was re-illuminated and further extended to the left (see thick green line in Fig. 2a) by the +CG return stroke. That channel could have helped in establishing an in-cloud link between the +CG and -CG channels to ground, facilitating the transient electric coupling between the -CG stroke and the +CG M-component. This hypothesis is supported by the following observational facts: (1) it is consistent with the slope of the green-line in-cloud channel in Fig. 2a and the relative positions of the LOG, tower, and +CG channel (see Fig. 1a) and (2) the green-line in-cloud channel, although not optically detectable at the time of the M-component onset (at about 21 ms; see Fig. 3d), remained connected to the ground via the +CG main channel for about 50 ms, as evidenced by the presence of CC in the +CG channel (see inset in Figs. 1c and 2b). There were no M-components in the +CG main channel associated with the other six return strokes of the tower-terminated -CG, which suggests that the inferred coupling between the tower and the +CG channel was brief. As noted above, the electric field waveform of the first RS of the –CG (see inset in Fig. 3c) exhibited the features (early zero-crossing and oscillatory tail) previously found to be characteristic of negative strokes terminated on that same tower by Zhu et al.4,5. Thus, we conclude that the time coincidence of the M-component in the main channel of the +CG (labeled M in Fig. 3d) and the electric field signature characteristic of negative RS terminated on the 257-m tower (see Fig. 3e and inset in Fig. 3c) constitutes evidence of the interaction of two concurrent flashes, one +CG and the other -CG, such that the electric charge was in effect transferred, via an inferred transient in-cloud link, between the two points on the ground separated by 11 km. The inferred in-cloud link must have existed before the -CG RS onset in order to explain the observations described above; in the absence of such link, there would have been an appreciable delay between the M-component and RS waveforms (an in-cloud leader propagating at a speed of 106 m/s would need 11 ms to cover the 11-km distance separating the tower and the +CG channel), not seen in Fig. 3d, e. Further, it appears that the M-component in the +CG channel begins about 250 µs (±12.5 µs which is our alignment uncertainty) prior to the -CG RS onset (M-component and RS onset times are marked by vertical dotted lines in Fig. 3d, e), which implies that the inferred in-cloud link between the -CG and +CG channels to ground was established during the leader stage of Stroke 1 of the -CG. In other words, the downward negative leader above the tower was draining (at least in part) negative charge from the ground via the +CG channel 11 km away and the inferred in-cloud link. It is worth noting that the distances from LOG to the +CG main channel and to the tower are different, 13 and 8.8 km, respectively. This difference in distances corresponds a difference in propagation times of electromagnetic signals in air of 14 µs. Accounting for this difference in propagation times to LOG, would lead to a larger delay of the RS onset in the -CG relative to the M-component onset in the +CG, which further supports our inference that electrical connection between the +CG and -CG was established during the leader stage of Stroke 1 of the -CG.

The NLDN-reported first RS current peak at the tower was 20 kA (see Figure S5a), which is considerably higher than the expected leader current. However, RS current peaks (dominated by higher frequency components) are strongly attenuated within the first kilometer of the channel they traverse (e.g. Zhu et al.5); this is why the contributions of the leader and RS of the –CG to the +CG M-component (see Fig. 3d) appear to be comparable.

The tower-terminated -CG was likely an upward flash (other hypothetical scenarios are considered in the Discussion section), in which case all its strokes were of subsequent type. An upward flash initiated from the same tower was previously observed at LOG by Zhu et al.4, who used both a high-speed framing camera and an electric field measuring system. They presented optical evidence that all strokes (a total of six) in that flash were initiated by bidirectional (negative end extending downward) leaders with durations of the order of 1 ms. The RS electric field waveforms in that flash were, as noted above, very similar to their counterparts in the tower-terminated -CG presented in this paper (see Figure S5).

Flash 1906: Reactivated branches cause luminosity dips in +CG main channel

Figure 2a shows a composite image of the leader stage showing multiple below-cloud branches that all decayed within about 4 ms after the RS onset (see Fig. 2b) and later were reactivated by recoil leaders (see Fig. 2c). Four recoil leaders, marked RL1 to RL4 in Fig. 2c are discussed in detail below. Two overlapping dotted boxes in Fig. 2a indicate the regions for which individual frames are shown in Figs. 4c and 5c to illustrate the evolution of RL1 and RL3, respectively. Luminosity variations vs. time were examined in the main-channel cross-sections marked “Upper” and “Lower” in Fig. 2a and in the selected cross-sections (marked in Fig. 2c) of branches reactivated by the recoil leaders. All four recoil leaders appeared to attach to the main channel at the same point (marked in Fig. 2c), located very close to the cloud boundary.

Luminosity variations in the +CG main channel and the corresponding electric field changes are shown in Fig. 3, with expansions of Regions 2 and 3 being presented in Figs. 4a, b and 5a, b, respectively. Additionally, luminosity variations in the reactivated branches are compared to the main-channel luminosity variations in Fig. S4 in Supplementary Note 3.

Selected individual frames (25.05–25.25 ms, 25.75 ms, and 25.8 ms) showing the evolution of recoil leader RL1 are presented in Fig. 4c. The overall morphology of RL1 is seen in Fig. 2c. RL1 was first detected in Frame 25 ms and showed bidirectional extension in the following Frames 25.05 ms - 25.15 ms. In Frame 25.2 ms, it made connection to the main channel at the attachment point labeled AP. As a result of this connection, luminosity of the main channel decreased (see the leading edge of luminosity dip labeled R1 in Fig. 4a). In Frame 25.8 ms (see Fig. 4c), connection of RL1 to the main channel has decayed (is essentially lost), resulting in an increase (recovery) of the main-channel luminosity seen in Fig. 4a (the trailing edge of luminosity dip labeled R1). The effect of RL2 (see Fig. 2c) on the luminosity of the main channel (see luminosity dip R2 in Fig. 4a) is similar to (but smaller than) that of RL1.

Expansions of relatively small microsecond-scale pulses associated (coincident) with the collisions of RL1 and RL2 with the main channel are shown between panels (a) and (b) in Fig. 4b. The origin of the relatively large positive, millisecond-scale K-change-type waveform (see Rakov and Uman; Section 4.106) in Fig. 4b, whose onset time is about 26 ms, is unclear, with one possibility being a transient process in the in-cloud source resulting in an additional positive charge transfer to the CC-carrying channel. This pulse occurred at the time when RL1 decayed or essentially lost its connection with the main channel and the main-channel luminosity started recovering after its preceding decrease (see Fig. 4a). It is possible that the K-change-type event contributed to the luminosity recovery in the main channel. However, since no similar millisecond-scale electric field waveform is seen at the time when RL2 lost its connection with the main channel (see Fig. 4a, b), the K-change-type waveform is unlikely to be a signature of the process leading to disconnection of RLs from the main channel.

Evolution of recoil leader RL3 is shown in Fig. 5c, with the luminosity vs. time profiles and electric field waveforms for both RL3 and RL4 being presented in Fig. 5a, b, respectively. Events R3 and R4 in Fig. 5a are generally similar to (although less pronounced than) events R1 and R2 shown in Fig. 4a. The most significant difference is that R4 did not show the main-channel luminosity recovery (after its preceding decrease); both the reactivated branch and the main channel just continued to decay to the end of the CC, which became undetectable around 50 ms. Note that the leading edge (downward deflection) of luminosity dip R3 was associated with heavy branching (labeled “Fountain” in Frames 35.05 ms and 35.1 ms shown in Fig. 5c; see also Fig. 2c) at the far end of the RL3 channel. The abrupt decrease in the main-channel luminosity seen in Fig. 5a is accompanied by the intensification of the side branch (see Frames 35.05 ms and 35.1 ms in Fig. 5c). This is apparently indicative of the transfer of positive charge from the in-cloud source over many kilometers to the far end of RL3, at the expense of transporting that charge to ground along the main channel. The fountain may be also indicative of the presence of dominant negative charge in the cloud just above the fountain. Note that the morphology of the fountain was significantly different in 5 consecutive 50-µs frames (varied from frame to frame), in which the fountain was imaged.

Flashes 2014 and 1830: M-components versus luminosity dips

Flash 2014 had two positive strokes that developed in channels of drastically different shape (see Fig. 6a, b) and terminated at different locations (1.5 km apart). In the optical records (50-µs frame exposure time), the first-RS onset frame and 10 frames following it are saturated, and for the second stroke 28 frames are saturated. The interstroke interval was 66 ms, as seen in the electric field record shown in Fig. 6c. The first and second strokes terminated on the ground 2.8 km and 1.6 km from LOG, respectively. The corresponding NLDN-reported peak currents were 95 and 20 kA. The first return stroke was followed by continuing current (CC) 7 ms in duration with no significant variations in channel luminosity. In this paper, we will only examine the second stroke, which contained CC over 400 ms in duration, inferred from the continuing channel luminosity in the optical record, which exhibited variations resembling M-components and a luminosity dip. In Figs. 7 and 8, we show the luminosity vs. time variations for three cross-sections marked “Upper”, “Middle”, and “Lower” in Fig. 6b, and the corresponding electric field waveforms, with the alignment uncertainty (estimated as described by Zhu et al.7) being ±24 µs.

Fig. 6: Two-stroke positive Flash 2014.
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a 50-µs frame of the leader stage just before the first return-stroke (RS1) onset. b A single 50-µs frame of the continuing current following RS2. Three channel cross-sections for which luminosity variations as a function of time are shown in Figs. 7 and 8 are color-coded and marked “Upper”, “Middle”, and “Lower”. c Low-gain electric field waveform of the entire flash. RS2 occurred 66 ms after RS1. Continuing current (CC) is marked in c. The total CC duration based on the optical record is over 400 ms (electric field signature of CC is distorted by the instrumental decay, τ = 10 ms).

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Fig. 7: Two-stroke positive Flash 2014, Stroke 2.
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a Luminosity variation during the second return stroke (RS2) followed by continuing current. b, c Low-gain and high-gain electric field waveforms, respectively, aligned (with ± 24-µs uncertainty) with the luminosity variation shown in a. Full time scale is 52.5 ms. M stands for M-components (events causing channel luminosity enhancements) and R is used to mark an event causing channel luminosity dip seen around 125 ms in a.

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Fig. 8: Two-stroke positive Flash 2014, Stroke 2.
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a–c Expansion of Region 1 labeled in Fig. 7, showing M-components M1 to M7. M1 occurred about 0.5 ms after the RS onset. d–f are the same as a–c, respectively, but shown on an expanded (1.3 ms) time scale, to magnify M-component M3. g–i Expansion of Region 2 labeled in Fig. 7, showing event R1 (luminosity dip).

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Figure 7 shows luminosity variations and electric field changes on a 52.5-ms time scale, including the RS (clipped in the luminosity panel), seven events, labeled M1 to M7, which are similar to M-components in –CGs (M1 is clipped in the luminosity panel), and one event, labeled R1, which constitutes a transient luminosity decrease (dip), as opposed to luminosity enhancement associated with classical M-components. Two regions, which are marked Region 1 and Region 2 in Fig. 7 are shown on expanded time scales in Fig. 8.

As seen in Fig. 8a, M1 occurred about 0.5 ms after the RS onset and is saturated. We have subjectively reconstructed (extrapolated) the missing part of the M1 luminosity pulse by black dotted line. This pulse is accompanied by a hook-shaped electric field signature in Fig. 8b, which is characteristic of M-components in -CGs. For comparison, we present in Figure S3 in Supplementary Note 2 an M-component in a negative stroke, which is very similar (including the characteristic time shift between the luminosity (and by inference current) and close electric field peaks) to M1 shown in Fig. 8a. Luminosity variations M3 to M7 in Fig. 8a, occurring 7 to 12 ms after the RS onset, are accompanied by electric field variations seen in Fig. 8c. Luminosity and electric field signatures of M3 are shown on an expanded (1.3 ms) time scale in Fig. 8d-f. Clearly, the negative electric (essentially electrostatic, since the distance was as small as 1.6 km) downward-deflecting field peak in (f) (even after compensation for instrumental decay) occurs before the luminosity peak in (d), which also applies to M4 to M7, a feature that is characteristic of M-components (Rakov et al.1 Qie et al.8 Jiang et al.9 Zhou et al.10). Note that the sequence of M4 to M7 looks like a damped oscillation in Fig. 8a, c with a period of about 1 ms and the corresponding frequency of about 1 kHz.

The electric field waveforms shown in Fig. 8h, i are indicative of K-changes, and the corresponding luminosity signature in Fig. 8g is a dip, labeled R1 (see also Fig. 7a–c). Neither NLDN nor ENTLN reported this event (even though it produced a pronounced microsecond-scale electric field pulse, see inset in Fig. 8i). Event R1 occurred 31 ms after the RS onset; that is, during the CC whose duration was over 400 ms. Note that we also observed luminosity dips at the later stage of CC of positive Flash 1906, with elapsed times (since the RS onset) of a few tens of milliseconds (see R1 to R4 in Fig. 3a) and in another +CG presented in Supplementary Note 1 (see R1 to R4 in Fig. S2), with elapsed times being 17–31 ms.

We described the mechanism behind the luminosity dips in the previous section of the paper using our data for positive Flash 1906, for which the causative processes were optically imaged. Those dips appear to be similar to classical M-components in that they are also transients occurring in grounded channels carrying steady currents, but, instead of enhancing the background steady current flowing to ground in the main channel, they temporarily reduce that current. In Flash 1906, we observed this unexpected phenomenon to involve decayed branches that were reactivated by recoil leaders (see Figs. 4c and 5c), with these reactivated branches appearing to compete with the main channel for the access to the cloud charge source. No branches were imaged in Flash 2014 and, as a result, we cannot be certain about the mechanism behind the luminosity dip labeled R1 in Fig. 8g. Event R1 in Flash 2014, along with other luminosity dips observed in this study, is further discussed in Supplementary Note 6.

Discussion

In this study, we observed luminosity variations in the grounded channels of three +CGs (Flashes 1906, 2014, and 1830, the latter one presented in Figs. S1 and S2 of Supplementary Note 1) during the late stage of the RS process (0.5 to 2 ms after the RS onset) and during the CC stage (5 to 35 ms after the RS onset). Luminosity variations observed during the late RS stage in positive Flashes 2014 and 1830 are similar to M-components observed in the same context in -CGs. Also similar (except for the polarity) are the associated hook-shaped electric field signatures, characteristic of M-components in -CGs observed at distances of a few kilometers from the lightning channel (see Figure S3). More importantly, we found that the electric field peak precedes the luminosity peak (and by inference current peak), which is a characteristic feature of M-components in –CGs. Based on the above, we infer that the M-component process in +CGs is essentially the same as the classical M-component well studied in –CGs (Rakov and Uman; Section 4.96), except for the polarity. Indeed, in either case, additional charge is injected into the upper part of the main channel, with this charge injection resulting in a downward current wave followed by a ground-reflected upward current wave, as described by, for example, Rakov et al.1 and Tran and Rakov11.

We now discuss the processes that lead to the initiation of M-component proper in the main channel to ground. Yoshida et al.12, who used a pair of VHF broadband interferometers to study initial continuous current (ICC) pulses in negative rocket-and-wire triggered lightning in Florida, found that the ICC pulses can be initiated by either recoil leaders in decayed in-cloud branches or via interception of separate in-cloud leaders by a grounded current-carrying channel. ICC pulses are thought to be of the same nature as M-components (at least in –CGs). In-cloud events giving rise to M-components in grounded channels of –CGs were also studied by Shao et al.13, Pilkey et al.14, Jiang et al.15, and Kotovsky et al.16 among others. Here, we documented an M-component (labeled M in Fig. 3d) that apparently resulted from the interaction of two concurrent CGs of opposite polarity at known locations with ground termination points being separated by 11 km. The –CG (inferred to be an upward flash) initiated from the 257-m tower and contained seven RSs. The first RS effectively transported positive charge from the ground at the position of the tower to the cloud and then, via an inferred transient in-cloud link, to the grounded, CC-carrying channel of the +CG, causing a transient luminosity enhancement (M-component) in that channel.

Our detailed hypothetical scenario of electric coupling between the +CG and the tower-terminated –CG is illustrated in Fig. S6 in Supplementary Note 5. In this scenario, the negative in-cloud leader associated with the +CG CC propagated toward the tower and triggered an upward positive leader (UPL) from the tower (e.g., Schumann et al.17 Zhu et al.7) and then the UPL transitioned to the ICC, as seen in panels (c) and (d) of Fig. S6. Normally, in upward flashes, there is a no-current interval of a few tens of milliseconds between the end of the ICC and the first RS (e.g., Rakov and Uman6), which requires the interruption/termination of the ICC. In this case, as well in the case the tower-terminated -CG being actually a downward flash, the in-cloud link between the +CG and -CG channels would have to be established by the interaction of the in-cloud negative leader associated with the +CG CC and the bidirectional leader above the tower preceding the first RS (bidirectional leaders above the same tower producing RSs were previously documented by Zhu et al.7). The latter scenario is illustrated in panel (e) of Fig. S6 and in Fig. 3f, where the upper (positive) end of the bidirectional leader above the tower is just about to make connection to the in-cloud negative leader associated with CC in the +CG channel. Note that Stroke 2 (which was necessarily preceded by an essentially no-current interval and which was smaller than Stroke 1; see Fig. S5 in Supplementary Note 4) of the tower-terminated -CG did not produce an M-component in the +CG channel, which is consistent with the transient nature of the inferred in-cloud link.

Clearly, the available data do not allow us to be certain about the scenario leading to formation of the in-cloud link between the +CG and –CG channels. Additional observations are needed, but, regardless of that scenario, the observational fact is that the concurrent +CG and -CG, separated by 11 km, were briefly coupled, so that positive charge was drawn from the ground at the position of -CG (by Stroke 1) and injected into the ground at the position of +CG (by the M-component), and that was happening at essentially the same time (see Fig. 3d, e). In other words, our main findings are not materially influenced by the uncertainty in the process(es) involved in the creation of the in-cloud link.

Transient lightning processes concurrently transporting to the ground charges of opposite polarity have never been reported before. However, Stolzenburg et al.18 observed two grounded channels, 3.3 km apart, one of which hosted an M-component and the other a dart leader followed by a return stroke. They suggested that both the M-component and the dart leader could be initiated by the same in-cloud event. Similar to our case, there were two transient processes, one in a hot channel (M-component) and the other in a decayed channel (dart leader), and there was electric coupling between those two channels, but, in contrast with our case, both of those processes transported to the ground charges of the same (negative) polarity.

Another unexpected phenomenon we have discovered in +CGs is the transient luminosity decrease (dip) at the time of a recoil leader colliding with the CC-carrying channel. The luminosity decrease in the main channel was associated with a luminosity increase in the branch reactivated by the recoil leader (see Fig. S4 in Supplementary Note 3), as if the branch were robbing the main channel of current.

Direction of luminosity change (surge of dip) depends on whether the current magnitude of the CC channel is forced to increases or decreases, which, in turn, depends on the polarity of charge injected into the grounded CC channel. If the CC current in a +CG is defined as negative (positive charge is moving downward), then a negative-charge wave traveling downward along that channel will constitute a negative-current wave, reducing the background positive CC. In this case, the channel luminosity will exhibit a temporary decrease (dip). Conversely, when a positive-charge wave travels downward along the same channel to ground, the associated current wave will be positive (same polarity as that of the background CC), and the channel luminosity will temporarily increase. In this latter case, we will have a classical M-component (Rakov and Uman; Section 4.96). It remains to be seen if luminosity dips can occur in -CGs. In this study, it has been established that in +CGs both types of perturbations in the CC channel, transient luminosity enhancements and luminosity dips, are possible. Furthermore, luminosity dips in +CGs appear to be common: all three +CGs presented in this paper exhibited CC channel luminosity dips. The only criterion for selecting +CGs for this study was their proximity to LOG.

In order to inject a downward negative charge wave into the +CG CC channel (as marked in Frame 25.2 ms in Fig. 4c), the polarity of the near end of the RL making connection to the CC channel transferring positive charge to the ground must be negative (as marked in Frame 25.1 ms in Fig. 4c). This is consistent with the observations of Saba et al.19 who reported RLs in decayed, below-cloud positive-leader branches, whose negative ends extended toward (and made contact with) the +CG main channel and produced a negative RS. There was, however, a difference: in Saba et al.‘s19 study, RLs connected to the main channel after its decay (when it was non-luminous), while in our case the main channel was carrying CC. Still, in both cases negative charge was moving downward along the +CG channel, resulting in either a negative RS or a CC luminosity dip.

Methods

All data presented in this paper were acquired at the Lightning Observatory in Gainesville (LOG), Florida, which is equipped with multiple high-speed framing cameras, wideband electric and magnetic field measuring systems, and X-ray/gamma-ray detectors. The LOG instrumentation (GPS-synchronized) was set to trigger on electric field changes produced by close lightning (within about 6 km of LOG). NLDN (U.S. National Lightning Detection Network) and ENTLN (Earth Networks Total Lightning Network) data were used to determine the distances to lightning channels and obtain estimates of return-stroke peak currents.

The high-speed framing cameras used in this study included Phantom V310 (visible range; 0.4–0.8 µm) and FLIR X6900sc (medium-to-far infrared range; 3.0–5.0 µm). The Phantom camera had resolution of 288 × 512 pixels and was operated at 20,000 fps (frames per second) with 47.39 µs exposure time and 2.61 µs dead time. The FLIR camera was operated at 1004 fps with 0.8 ms exposure time and 196 µs dead time. Its resolution was 640 × 512 pixels. In this paper, we refer to FLIR and Phantom frames as 1-ms and 50-µs frames, respectively. Positive Flashes 1906 and 2014, presented in the main paper, as well as negative Flash 1863 presented in Supplementary Note 1, were recorded by the Phantom (visible-range) camera. Positive Flash 1830, presented in Supplementary Note 1, was recorded by the FLIR (infrared) camera. All distances and channel extension speeds estimated using high-speed framing camera data are 2D.

Three types of electric field records were used in this study: low-gain E-field records with an instrumental decay time constant of 10 ms, high-gain E-field records with an instrumental decay time constant of 440 µs, and dE/dt records. We integrated the dE/dt records to show microsecond-scale return-stroke E-field waveforms that were either unresolved or saturated in E-field records. The upper frequency response (−3 dB) for both the low-gain and high-gain systems was 12.5 MHz. In all the electric field waveforms shown in this paper, the positive return-stroke (RS) electric field change deflects upward and for negative RSs it deflects downward, except for Fig. S3 where the negative RS electric field change deflects upward.

The luminosity variation measurements presented in this paper are based on the high-speed camera images. The procedure was as follows. The cross-sections are selected to be perpendicular to the lightning channel section of interest. The luminosity of the cross-section is calculated as the mean value of all pixels above certain threshold that are intersected by the cross-section line. The luminosity threshold was determined by examining the background luminosity of the frame in question and set to the maximum value of the mean values found for several regions of the frame away from the lightning image area. The background luminosity was subtracted from the luminosity of the cross-section.

More detailed information on LOG and its instrumentation can be found in the review papers by Rakov et al.20,21,22 and Ding and Rakov23.