Negative cloud-to-ground (CG) flashes typically contain 3-5 leaderreturn stroke sequences which effectively transfer net negative charge to the ground (Rakov and Uman, 2003). The processes associated with charge transfer to ground are upward connecting and unconnected leaders (e.g., Nag et al., 2021;Nag et al., 2023a), return strokes, Mcomponents, and continuing currents. Continuing currents may occur immediately following the impulsive flow of current during a CG return stroke and are usually relatively low amplitude (from a few amperes to a few kiloamperes) and long duration (several to hundreds of milliseconds) (Rakov and Uman, 2003, Ch. 4.8). Continuing currents may occur during the first and/or one or more subsequent strokes in the same flash. While we focus on negative strokes in this study, positive strokes are also associated with significant continuing currents. Continuing current is defined as "long" if its duration is longer than 40 ms (Kitagawa et al., 1962;Brook et al., 1962), as "short" if its duration is between 10 and 40 ms (Campos et al., 2007), and as "very-short" if its duration is less than 10 ms; durations shorter than 3 ms are often ignored to avoid contamination from the return stroke pulse tail (Ballarotti et al., 2005;Shindo and Uman, 1989). Long continuing currents are of particular interest to the greater community because of their ability to cause heating induced damages to ground-based infrastructure such as electric power systems/ lines (e.g., Schulz and Nag, 2020;Montanyà et al., 2022) as well as initiate forest fires (Latham and Williams, 2001;Pineda et al., 2014;Bitzer, 2017;Pérez-Invernón et al., 2023).
While it is critical to measure and characterize continuing currents in CG lightning, remotely estimating its duration and amplitude from the electromagnetic fields measured by most existing ground-based lightning locating systems (LLSs) is not possible. Continental-scale LLSs (Cummins and Murphy, 2009;Nag et al., 2015;Mallick et al., 2014) focus on the geolocation of impulsive return stroke pulses (in addition to cloud pulses) using their low frequency (LF) signature, but the sensors in these networks have difficulty measuring the long duration field changes associated with continuing currents. Generally, continuing currents do not produce strong very high frequency (VHF) emissions that can be sensed by ground-based sensors, so regional LLSs operating at VHF cannot be used for estimating their duration and amplitude. However, continuing current durations can be measured using highspeed video cameras (Boys, 1926;Winn et al., 1973;Brantley et al., 1975;Fisher et al., 1993;Ballarotti et al., 2005;Saba et al., 2006a;Campos et al., 2007;Ferro et al., 2009;Campos et al., 2014;Tran and Rakov, 2016;Bitzer, 2017;Leal and Rakov, 2024), return stroke channel-base current measurements on instrumented towers (Berger et al., 1975;Visacro et al., 2004;Visacro et al., 2010;Visacro et al., 2012;Takami and Okabe, 2007;Miki et al., 2019;Nag et al., 2021;Nag et al., 2023a;Plaisir et al., 2023), and electric field measurements with sufficiently low (fraction of a Hertz) frequency-bandwidth lower-limit (Clarence and Malan, 1957;Shindo and Uman, 1989;Brook et al., 1962;Kitagawa et al., 1962;Livingston and Krider, 1978;Nag and Rakov, 2012;Ferro et al., 2009;Fairman and Bitzer, 2022;Leal and Rakov, 2024). Additionally, current measurements on instrumented towers can also provide continuing current amplitude as a function of time. Use of lightning optical signatures, measured by space-based lightning detectors, to estimate CG continuing current characteristics has been discussed in various studies (Christian et al., 1992;Goodman et al., 2013;Bitzer, 2017;Fairman and Bitzer, 2022;Leal and Rakov, 2024;Ding et al., 2024). Fairman and Bitzer (2022) suggested a method of "predicting" continuing current in CG flashes (using measurements in Alabama), whose optical emissions were reported by the Geostationary Lightning Mapper (GLM) onboard the Geostationary Operational Environmental Satellite (GOES). Recently, Ding et al. (2024) applied that method to their dataset from Florida, Utah, and Brazil. Fairman and Bitzer (2022) showed that GLM flashes with higher probabilities of containing continuing current (continuous optical emissions) tended to cover longer distances, have higher maximum optical energies, and larger maximum areas.
In this study, we examine the responses of the GLM (onboard the GOES-16 satellite) to negative CG lightning strokes and flashes measured at ground using high-speed video cameras. We also compare continuing current durations estimated from GLM-reported flashes to those measured from high-speed video camera records as well as lightning channel-base current and electric field waveforms. Finally, for a small subset of GLM flashes, we examined the VHF source altitudes reported by a Lightning Mapping Array (LMA) time-coincident with GLMreported groups.
Our ground-truth dataset was comprised of 77 negative CG flashes containing 174 (67 first and 107 subsequent) strokes, all of which were captured on high-speed video and geolocated by the U.S. National Lightning Detection Network (NLDN) (Cummins and Murphy, 2009). It should be noted that not all the first and subsequent strokes in the 77 flashes were captured on camera due to them being outside the camera's FOV or due to a limited record length (see also section 2.5). All the flashes occurred in the Space Coast of Florida around the Melbourne Lightning Observatory (MLO) (Nag et al., 2023b) and Kennedy Space Center (KSC) between 2018 and 2023. Seven of these flashes (19 strokes) struck the instrumented KSC Industrial Area Tower (IAT) (Nag et al., 2023a); in addition to video camera records, we have channelbase current waveforms for these flashes. Additionally, for one singlestroke flash that struck the IAT, channel-base current waveforms were measured, but the flash was not captured on video. Also, for 8 flashes (19 strokes) we measured electric fields at the MLO. Finally, for 6 flashes (26 strokes) we obtained VHF lightning mapping data from the KSC LMA (Zhang and Cummins, 2020;Nag et al., 2023a).
The GLM optical sensor consists of charged-coupled device (CCD)
arrays that record continuously over the western hemisphere (Goodman et al., 2013). They detect transient optical pulses at the 777.4 nm neutral oxygen emission line triplet from lightning at any time of day throughout the field of view (FOV). The GLM uses signal processing techniques to filter out background noise from lightning optical transients and to group the recorded emissions from lightning into clusters with different "product levels" (Goodman et al., 2013;Mach, 2020). The products we consider here are events, groups, and flashes. Events represent optical emissions detected in individual pixels during an approximately 2-ms integration period, groups represent events detected in adjacent pixels during the same integration period, and flashes represent the collection of groups that fall within temporal and spatial thresholds determined by the GLM's operational sorting algorithm, called the Lightning Cluster-Filter Algorithm (LCFA). The LCFA sorts localized groups occurring within 330 ms in time and 16.5 km in space using a weighted Euclidean distance between these groups, into flashes (Goodman et al., 2013;Mach, 2020). We used the "Level 2" GLM data, which is the operational GLM dataset, for all analysis in this paper. Additionally, in section 4.1, we used "Level 0" data to examine the effect of GLM's ground-processing algorithm, which is the raw data at full instrument resolution prior to the application of GLM's groundprocessing (which includes filtering, georeferencing, and groupclustering) of data. In the following, we provide an overview of the measurement systems used to acquire the ground-truth dataset, techniques used to find matches in the GLM data, and methods to measure/ estimate continuing current durations.
The strokes in our dataset were captured using Phantom high-speed video cameras that are part of the MLO at Florida Institute of Technology and at the IAT at KSC (Khounate et al., 2021;Nag et al., 2023a). The camera frame rates ranged from 10,000 frames per second (fps) to approximately 793,650 fps (Khounate et al., 2021). Video camera frames were GPS time-stamped.
There were 5 first and 14 subsequent strokes (in 7 flashes) captured on high-speed video, that struck the IAT and for which channel-base current measurements were available. Note that one of the subsequent strokes was the second stroke in the flash in a new channel that attached to the IAT. Additionally, for a negative stroke (last stroke via new channel to ground of a four-stroke negative flash) that struck the IAT, channel-base current waveforms were measured, but the flash was not captured on video; this flash is only included in our analyses in section 3.3 where we compare GLM groups and LMA VHF sources. The current measurement system on the 91.2-m-tall IAT consists of a shunt and Rogowski coil near the base of a 6.2-m tall mast and Franklin rod at the top of tower (Nag et al., 2023a;Plaisir et al., 2023). The system was designed to measure current in four separate channels including three from the shunt and one from the Rogowski coil. This allows for broadband current measurements from less than 1 A to 350 kA. The data was transmitted via fiber optic links, digitized with a 12-bit oscilloscope with a 50 MHz sampling rate, and was GPS time-stamped.
A broadband electric field measurement system deployed at the MLO was used to record field waveforms of 7 first and 12 subsequent strokes (in 8 flashes) which were also captured on high-speed video. The MLO is located on the roof of a five-story building on the campus of Florida Institute of Technology (Khounate et al., 2021). These strokes occurred at distances ranging from 1 to 13 km from the MLO. The electric field measurement system was comprised of flat-plate antenna and associated electronics from which data were transmitted via fiber optic link to a digitizer with a sampling rate of 50 or 100 MHz. The bandwidth of the system ranged from 0.16 Hz (determined by an integrator RC decay time-constant of 0.978 s) to 15 MHz. Each electric field record was GPS timestamped.
The KSC LMA (Thomas et al., 2004;Zhang and Cummins, 2020;Nag et al., 2023a) operated between about 2015 to 2021 and provided highresolution coverage in a 100 km radius region centered on KSC, including Titusville to the northwest and Melbourne to the south. For our study period, the network was comprised of 7-8 sensors. The average distance between sensors was around 10 km, with an additional more-distant sensor near Tampa. For the six flashes in our dataset for which the KSC LMA data was available, source locations were determined by 6 or more sensors.
Our dataset only includes strokes that were geolocated by the NLDN. The NLDN stroke-time and location were used as references when identifying the responses of the GLM. The following criteria were used to select, for analysis, GLM groups associated with the flashes and strokes in our dataset.
(1) We considered all GLM-reported groups within 30 km of the NLDN-reported first-stroke location and within -1 to +2 s of the NLDN-reported stroke-time of the first stroke in a flash. (2) For individual strokes, we considered GLM-reported groups within 30 km of the stroke location and within ±4 ms of the reported NLDN stroke-time. Additionally, to examine if the 30-km spatial limit affected the GLM stroke detection efficiency, we also considered spatial criteria of 10, 12.5, 15, and 20 km.
Our spatial criterion of 30 km is roughly 3 to 3.5 times the GLM pixel length of around 8.2-8.5 km in Florida and is meant to accommodate any horizontal extent of the in-cloud portions of our cloud-to-ground flashes. The 30 km flash grouping spatial criterion was also used by Zhang and Cummins (2020) (and noted in Zhang, 2019).
We separately examined the GLM responses to first strokes, subsequent strokes in new channels to ground, and subsequent strokes in the same channel as a previous stroke. First strokes and subsequent strokes were identified using high-speed video camera records. Negative first stroke leaders display optical stepping and significant branching as the downward leader approaches ground in conjunction with relatively slow (typically of the order of 10 5 m/s) leader speed. Subsequent-stroke leaders in the same channel as the preceding one lack these (stepping and branching) characteristics and have significantly faster leader speeds (typically of the order of 10 7 m/s). In cases where these leader characteristics could not be clearly recognized in the high-speed video camera frames due to relatively large distance-to-channel and low leader-channel luminosity, the re-illumination of the leader branching (generally not present in subsequent strokes) at the start of the return stroke was used to recognize first strokes. These first and subsequent strokes were then time-matched with those reported by the NLDN within the FOV of the cameras.
We computed the duration of the continuing current from our highspeed video camera records by measuring the time-period during which the CG channel was visible following the return stroke. We defined the continuing current start-time as the time of the first frame showing the downward leader attached to the upward leader (i.e., the first frame showing the leader-channel luminosity near ground abruptly increasing compared to the previous frame). The continuing current end-time was defined as the time of the frame in which the lightning channel could no longer be distinguished from the frame's background. Fig. 1 shows five frames for a first stroke (stroke ID 20200704_17_01) in our dataset including the frames used to define the start-and end-times of the continuing current. For a few flashes, the section of the channel close to ground was not within the FOV of the camera. For such cases, the starttime was defined as when the first frame showed an increase in luminosity of the channel-section within the FOV. The minimum timeresolution was 100 μs, associated with video camera records captured at the 10,000 fps.
Table 1 summarizes the characteristics of the strokes in our dataset derived from the NLDN and high-speed video camera records. The NLDN-reported distances from camera for the 174 strokes ranged from 330 m to 30 km. The NLDN groups cloud pulses and CG strokes into flashes using a space-time grouping algorithm (e.g., Murphy and Nag, 2015). In order to calculate the first-to-last stroke and interstroke time intervals, all NLDN-reported strokes, regardless of whether they were captured on high-speed video, were used. The interstroke intervals and first-to-last stroke time-intervals ranged from 0.36 to 521 ms and 17.3 to 974 ms, respectively, with the medians being 55.6 and 252 ms, respectively. The geometric mean (GM) interstroke interval was 52 ms. This is comparable to the GM interstroke intervals in the range of 57-65 ms reported in previous studies (Shindo and Uman, 1989;Thottappillil et al., 1992;Rakov et al., 1994;Saba et al., 2006a;Ballarotti et al., 2012;Leal et al., 2021). Our median first-to-last stroke interval is comparable to negative cloud-to-ground flash durations reported by Berger et al. (1975), Diendorfer et al. (1998), Saba et al. (2006a), andBallarotti et al. (2012) in the range of 163-300 ms. When only considering flashes with continuing current producing strokes, for intervals preceding the stroke with continuing current, Shindo and Uman (1989) reported GM interstroke intervals of 53 ms (N = 16) and 28 ms (N = 22) for strokes with short and long continuing currents, respectively. In our dataset, the GM intervals were 71.8 ms (N = 10) and 84.3 ms (N = 2), respectively; our intervals are longer in comparison to those of Shindo and Uman, which can likely be attributed to our significantly smaller sample sizes. Our dataset included 10 single-stroke flashes, all reported by the NLDN and recorded on high-speed video. Additionally, 14 subsequent strokes occurred in new channels. Characteristics for single-stroke flashes, subsequent strokes in pre-existing channel, and subsequent strokes in new channels are reported separately in Table 1. The absolute NLDNestimated peak current magnitudes for all strokes in this dataset ranged from 5 to 228 kA, with the median being 26 kA. The continuing current durations for all strokes ranged from 0.28 to 685 ms, with median being 2.5 ms. 44.3 % (N = 77), 17.8 % (N = 31), and 6.9 % (N = 12) of our 174 strokes had video-camera measured continuing current durations greater than 3, 10, and 40 ms, respectively. For the 77 strokes with continuing current durations greater than 3 ms (which can be viewed as the traditionally-defined minimum value of continuing current duration), the median duration was 8 ms.
For the seven flashes (19 strokes) with channel-base current measurements, the continuing current duration was found by defining the start and end-times, respectively, as when the return stroke current waveform decayed to 10 % of its peak value and when the current waveform in the most sensitive current measurement channel decayed to within 1-3 % of the average background noise level.
We also estimated continuing current duration from our electric field measurements (at the MLO) for eight flashes (19 strokes). Continuing current that effectively transfers negative charge to ground produces electrostatic field change of the same polarity as the preceding negative return stroke. In this study, we defined the continuing current start-time as the time of the return-stroke electric radiation field peak. The stop time was defined as when the slope of the electric field change following the return stroke returned to near-zero. Note that, prior to finding the continuing current duration, we processed our electric field waveforms to improve our measurement system's decay time constant of 0.978 s by extending it to 50 s (e.g., Nag and Rakov, 2012;Rubinstein et al., 2012;Kohlmann et al., 2017).
Finally, to estimate the continuing current duration from the GLM data, we first considered the GLM groups for each stroke in our dataset occurring within the space-time criteria of 30 km and ± 4 ms of the NLDN location and stroke-time, respectively. The time of the GLM group matching this space-time criteria and closest in time to the NLDN stroketime was defined as the continuing current start-time. We then tracked all groups following this first one with the same GLM flash identification (ID) number that occurred in contiguous 2-ms time-bins, regardless of our space-time criteria; the continuing current end-time was defined as the time of the last group that was in this time-contiguous set. This method is similar to that used by Fairman and Bitzer (2022). Additionally, we also examined the GLM-estimated continuing current duration by relaxing the time-contiguous criterion to include semi-timecontiguous groups (i.e., those occurring with an inter-group interval of 2 ms or one GLM frame) with the same GLM flash ID.
Figs. 2a, b, and c show the video-camera-frame mean gray level, channel-base current waveform, and GLM group energy, respectively, for an eight-stroke CG flash (ID 20230808_71) occurring on August 08, 2023 at the KSC IAT on a 700-ms time-window. The same measurements are shown in Figs. 2d, e, and f, respectively, but only for the last stroke (stroke 8) on a 275-ms time-window. The duration of the continuing current measured from the video-camera and current waveform are shown in Figs. 2d and e, respectively. For this stroke, the GLM reported two groups occurring in two time-contiguous 2-ms time bins, one each before and after the NLDN stroke time (as shown in Fig. 2f), and there were no other groups reported with the same GLM flash ID preceding or following these matched groups within the 275 ms time-window. So, the GLM-estimated (using our method described above) continuing current duration was 2 ms, while those measured using the video camera and current waveform were 237 and 190 ms, respectively. For the eight strokes in this flash, the continuing current durations obtained from the video camera and current waveform ranged from 4.4 to 237 ms and 5.3 to 190 ms, respectively, while that estimated from the GLM groups for seven of the eight strokes was 2 ms each. Note that the GLM did not report any groups associated with the fifth stroke in this flash.
Similarly, Figs. 3a, b, and c, respectively, show the video-cameraframe mean gray level, electric field waveform, and the GLM group energy for a four-stroke flash (ID 20230615_65) that occurred on June 15, 2023, near the MLO on a 275-ms time-window. The video-camera-frame mean gray level, electric field waveform, and GLM group energy are shown on a 10-ms time-window for the second stroke in Figs. 3d, e, and f, respectively. The GLM-estimated continuing current duration for this stroke was 4 ms, while those measured using the highspeed video and electric field waveforms were 4.73 and 5.85 ms, respectively. For the four strokes shown in Figs. 3a, b, and c, the continuing current durations ranged from 0.63 to 4.73 ms and 0.99 to 7.27 ms measured from the high-speed video and the electric field waveform, respectively, while that estimated from the GLM groups for two of the four strokes were 2 ms and 4 ms. Note that the GLM did not report any groups associated with the first and last stroke in this flash. Also note that the second peak in the mean gray level in Fig. 3d is due to an M-component occurring during the falling edge of the return stroke pulse.
In section 3.2, we analyze in detail the continuing current durations measured/estimated from our high-speed video, channel-base current, and electric field measurements as well as those obtained from the GLM groups and further discuss the results in section 4.2.
The GLM detection efficiencies, using the space-time criteria discussed in section 2.5, are shown in Table 2 for the 77 flashes containing 174 strokes in our dataset. Of the 77 flashes, the GLM detected 62, with the resulting flash detection efficiency being 80.5 %. Using the spacetime criteria of within 30 km and ± 4 ms of the matched NLDN stroke, 87 of the 174 strokes were detected by the GLM resulting in a stroke detection efficiency of 50 %. For single-stroke flashes, the detection efficiency was 30 % (3 of 10). The stroke detection efficiency decreased somewhat with decreasing GLM-group-to-NLDN-stroke distance-limit, with it being 41.3 % using the criteria of within 10 km and ± 4 ms of the matched NLDN stroke. The detection efficiencies for first and subsequent strokes were 31.3 % and 61.7 %, respectively, and for subsequent strokes in new versus pre-existing channels the detection efficiencies were 50 % and 63.4 %, respectively. Fig. 4a shows the GLM detection efficiency as a function of stroke order. For all space-time criteria used, the detection efficiencies for higher order strokes, specifically second and third strokes in a flash, were greater than that for first Fig. 1. Five frames for a first stroke (stroke ID 20200704_17_01 captured on July 4, 2020) in our dataset. The first frame (Frame -3) shows the negative leader just prior to ground attachment and return stroke onset (with channel visibility just above the near-ground branching obscured by intervening clouds). The luminosity abruptly increases in the next frame (Frame -2) when the return stroke is in progress and the frame-time is defined as the continuing current (CC) start time. Frame 25 shows an example of a colour-inverted frame to increase the visibility of the channel. Frame 71 shows the last pixel with visible channel remnant and a "background noise" pixel. In the last frame (Frame 72) the channel is no longer visible and the frame-time is defined as the continuing current stop time.
strokes. It should be noted that sample sizes (shown in Fig. 4a below the horizontal axis) for higher order strokes were relatively small. Fig. 4b shows a histogram of NLDN reported peak-current magnitudes for strokes detected (dark blue bars) and not detected (light blue bars) by the GLM. For strokes with peak-current magnitudes less than versus greater than 30 kA, the GLM detection efficiencies were similar (50 % versus 50.6 %), indicating that the stroke detection efficiency was independent of the peak current. Finally, Fig. 4c shows the histogram of "ground-truth" continuing current durations (derived from the highspeed video) for strokes detected (dark blue bars) and not detected (light blue bars) by the GLM. The GLM detection efficiencies for strokes with high-speed video continuing current durations less than and greater than 3 ms were 37.5 % (36 of 97) and 64.9 % (50 of 77), respectively. Also, the detection efficiency for strokes with continuing current durations greater than 10 ms was 58.1 % (18 of 31). These findings indicate that strokes with significant (> 3 ms) continuing current durations were more likely to be detected by the GLM. See section 4.1 for further discussion.
In Fig. 5a, we show a histogram of continuing current durations for the 87 strokes reported by the GLM, estimated from the GLM groups using space-time criteria of 30 km and ± 4 ms along with semi-timecontiguous (blue bars) and time-contiguous (red bars) groups (which are the two methods described in section 2.6). As can be seen from the histogram, the continuing current durations obtained using the two methods are very similar. The semi-time-contiguous-group GLM continuing current durations are compared to those obtained from highspeed video in the scatter plot in Fig. 5b. None of the GLM continuing current durations exceeded 6 ms. Also, the GLM continuing current durations were unrelated to the "ground truth" durations obtained from video camera records.
The continuing current durations obtained from our three measurements (high-speed video camera records, channel-base current waveforms, and electric field waveforms) are compared in Fig. 6. Figs. 6a and c show, respectively, the scatter plots of continuing current durations measured from high-speed video versus channel-base current waveforms and from high-speed video versus electric field waveforms. The 19 first and subsequent strokes in Fig. 6a had accompanying channel-base current measurements. Similarly, a different group of first and subsequent strokes in Fig. 6c had accompanying electric field waveforms. The coefficients of determination (R 2 ) (shown in Figs. 6a and c) were 0.98 and 0.99 (p-values <0.001 in each case), respectively; this indicates a statistically significant correlation between continuing current durations obtained from high-speed video versus those obtained from current and electric field waveforms (which is expected). In Figs. 6b and d, we show the same scatter plots as in Figs. 6a and c, respectively, but for shorter duration (<20 and 15 ms, respectively) continuing currents. The R 2 values decreased significantly in Figs. 6b and d to 0.26 (N = 15) and 0.47 (N = 18), respectively; this is due to the increased scatter in the data when only the shorter duration continuing currents are included. In all four plots, the black dashed line indicates the slope = 1 line. It is apparent from Fig. 6d that continuing current durations were often overestimated when measured from electric field waveforms relative to those measured from high-speed video. See section 4.2 for further discussion.
For 6 flashes in our dataset, data from the KSC LMA were available. Using NLDN stroke-times and locations as reference, we identified the corresponding LMA flashes (e.g., Bruning and Thomas, 2015) comprised of their associated VHF sources. For four of these flashes, groups were reported by the GLM. Using methods described in Zhang and Cummins (2020), the flash area, flash length, and flash extent can be calculated from the LMA data using a convex hull flash object (Bruning and Macgorman, 2013;Bruning and Thomas, 2015). Using these methods, the flash area is the hull area, the flash extent is the major axis length of the convex hull, and the flash length is the total path length of connected LMA sources from the two longest non-colinear axis limits back to flash origin (Zhang and Cummins, 2020). A summary of these flash characteristics and the number of GLM detected strokes are shown in Table 3. The smallest flash area was 22.1 km 2 for a single-stroke flash (20210612_45). The GLM did not report any groups for any of our spacetime criteria for this flash. The largest LMA flash area was 356 km 2 for a 3-stroke flash (20210616_46). The GLM only reported groups for the first and third strokes of this flash using the 30 km/±4 ms stroke criteria. For two of the six flashes for which we had LMA data, all strokes (9 and strokes in flashes 20200710_31 and 20200906_37, respectively) had matching GLM groups using the 30 km/±4 ms stroke criteria. These two flashes had LMA flash area, length, and extent of 81.6 and 83.2 km 2 , 42.9 and 23.1 km, and 19.2 and 12.7 km, respectively. Finally, the remaining two (of six) flashes (20180809_72 and 20190726_73) had LMA flash areas of 42.2 and 40.8 km 2 , respectively, with the first having a The first-to-last stroke and interstroke time intervals were computed using all NLDN-reported strokes, regardless of whether they were captured on highspeed video.
b For 12 strokes (including 8 with continuing current durations >22 ms), the channel remained slightly illuminated at the end of our video camera record. These continuing current durations should be treated as underestimates.
no GLM reported groups for any of the 4 strokes and the second having matching GLM groups for all 5 subsequent strokes, but not the first return stroke. The GLM-reported flash areas were significantly (about 7 to 22 times) larger than their LMA flash areas for three of the flashes and somewhat comparable (356 km 2 for LMA versus 204 km 2 for GLM) for one flash. The GLM flash durations matched reasonably well with the Fig. 3. (a) The high-speed video-camera mean gray level per frame, (b) electric field waveform, and (c) GLM group energy for an eight-stroke CG flash (ID 20230615_65), occurring on June 15, 2023, all shown on a 275-ms time-window. (d), (e), and (f) Same as in (a), (b), and (c), respectively, but only for the second stroke, shown on a 10-ms time-window. The green and red stars represent the continuing current (CC) start-and stop-times, respectively, determined for the measurements in (a), (b), (d), and (e). The vertical dashed gray lines in all plots indicate the NLDN-reported stroke times. The durations of the continuing current measured from the video-camera, current waveform, and GLM are shown in (d), (e), and (f), respectively. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
LMA flash durations, except for flash 20210616_46 in which the GLM underestimated the flash duration by about 55 %. The number of GLMreported groups in a flash appeared to be unrelated to the number of LMA VHF sources. The GLM flash energies ranged from 20.3 to 555 fJ; interestingly the flash (20210616_46) with the longest LMA duration and largest number of LMA sources had the lowest GLM-reported energy.
In Fig. 7 we show the LMA source altitudes and the number of LMA sources in the bottom panel (Fig. 7b), as well as the GLM group energies in the top panel (Fig. 7a) plotted with respect to the NLDN first stroke time (t = 0) for a five-stroke flash (flash ID 20200906_37). In Fig. 7a, the GLM data are shown in 2-ms time-bins while in Fig. 7b, the LMA sources are grouped in 5-ms time-bins. The minimum and maximum LMAsource altitudes are represented by the ends of the whiskers on the vertical lines and the median is represented by the rhombus marker. The source altitudes ranged from 1.4 to 14.4 km with the median altitudes ranging from 2.4 to 6.7 km. GLM reported groups only during one (for strokes 1-4) or two (for stroke 5) 2-ms time-bins near the NLDN stroketimes. This is consistent with the GLM responses for the strokes shown in Figs. 2 and 3. The median LMA source altitudes at the times during which the GLM reported groups ranged from 4.1 to 4.4 km. The GLMreported group energies ranged from 8.1 to 48.1 fJ for the five strokes. Interestingly, the number of LMA sources per 5 ms increased in the later portion (after t = 125 ms or so) of this flash prior to the occurrence of the last stroke (for which GLM groups were reported during two contiguous 2-ms time-bins) at about t = 190 ms. Overall, the GLM detected 19 of the 26 strokes for which we had LMA data.
The GLM detection efficiency for the negative CG strokes in our dataset that occurred in Florida from 2018 to 2023 was 50 %. For strokes with continuing current durations longer than 10 ms, the GLM detection efficiency was 58.1 %. Our results are consistent with those of Ding et al. (2024), who reported the GLM stroke detection efficiency for one or more GLM groups (similar to the method used in this study) matched to their high-speed video camera records for 187 strokes (131 negative and 56 positive) with continuing current duration of at least 10 ms occurring in 2018-2022 in Florida, Utah, and Brazil to be 53 %. Their overall detection efficiency for negative strokes was 47 %, but it dropped to 40 % for strokes in Florida. Ding et al. (2024) found much lower stroke detection efficiency (0-4 % for negative strokes and 10 % overall) when requiring five consecutive groups to be reported by the GLM; a fact that is not surprising given that none of our reported CG strokes were associated with GLM-reported optical emissions visible from the cloud top continuously for >6 ms. On the other hand, Leal and Rakov (2024) reported a GLM stroke detection efficiency of greater than 90 % for 80 strokes (56 strokes in 15 negative flashes and 24 strokes in 15 positive flashes) in Brazil in May-June 2022. The discrepancy in the GLM stroke detection efficiency reported in this study and Ding et al. (2024) versus that reported by Leal and Rakov (2024) could be due to a combination of relatively small sample sizes and variations in GLM's detection efficiency due to geographic location and time-of-day. The GLM's flash detection efficiency can exceed 90 % during nighttime while its daytime detection efficiency is around 70 % (Zhang and Cummins, 2020). In our dataset, the flash and stroke detection efficiencies were 70.4 % (38 out Fig. 6. Scatter plot of continuing current (CC) durations measured from (a) high-speed video versus channel-base current waveforms for 19 first and subsequent strokes, and from (c) high-speed video versus electric field waveforms for 19 first and subsequent strokes. Note that the same 19 strokes are not used in (a) and (c). (b) Same as in (a), but for continuing current durations shorter than 20 ms. (d) Same as in (c), but for continuing current durations shorter than 15 ms. The dashed black line represents the slope = 1 line.
of 54 flashes) and 33.9 % (38 out of 112 strokes), respectively, for flashes occurring between 06:00 and 18:00 local time (daytime) and 100 % (16 out of 16 flashes) and 81.3 % (39 out of 48 strokes), respectively, for flashes occurring between 20:00 and 04:00 local time (nighttime).
The GLM detection efficiency was roughly the same for single-stroke flashes as for all first strokes (30 % and 31.3 %, respectively) for our dataset. The detection efficiency for first strokes was significantly lower compared to that for subsequent strokes (31.3 % versus 61.7 %). One possible reason for the higher GLM detection efficiency for subsequent strokes is that subsequent stroke channels may try to neutralize more distant pockets of charge by extending deeper inside the thundercloud and perhaps reaching higher altitudes leading to longer duration optical emissions that appear brighter from above the cloud top, making them more detectable by the GLM (Leal and Rakov, 2024). On the other hand, studies using both ground-based photographs (e.g., Jordan and Uman, 1983) and space-based observations (from Fast On-Orbit Recording of Transient Events or FORTE, Light et al., 2001) have shown first strokes to be optically brighter than subsequent strokes. Therefore, it is suspected that the lower GLM detection efficiency for single-stroke flashes and first strokes could be due to algorithmic processing techniques at ground and/or onboard the GLM (see further discussion below) rather than being related to lightning characteristics.
We found that changing the spatial criteria for matching GLM groups to NLDN strokes from 30 km to 10 km had modest effect on the GLM stroke detection efficiency (50 % versus 41.3 %, respectively), indicating that for the negative strokes in our dataset the two-dimensional locations of the GLM reported groups were relatively close to that of the NLDN strokes. The distances of the closest GLM group relative to the NLDN stroke location ranged 0.33 to 29.5 km, with the median distance being 6.9 km. Note that our time criteria (for matching GLM groups for finding GLM stroke detection efficiency) of within ±4 ms of the NLDN stroke-time results in a time-window that is four times longer than the GLM temporal resolution of 2 ms and enabled us to examine the relatively "prompt" responses the GLM may have to cloud-to-ground return strokes.
While the GLM stroke detection efficiency for our dataset was unaffected by the return stroke peak current (50 and 50.6 % for strokes with peak currents less than and greater than 30 kA), strokes with significant (> 3 ms) continuing current durations were more likely to be detected by the GLM than those without significant continuing currents (stroke detection efficiency of 37.5 % versus 64.9 % for strokes with continuing current durations shorter versus longer than 3 ms). Also, detection efficiency for strokes with continuing current durations longer than 10 ms was 58.1 %. This is likely due to longer duration currents producing somewhat brighter and more sustained optical emissions visible from the cloud top.
For 1363 strokes in Florida and New Mexico, Rakov and Uman (1990) reported that first strokes are significantly less likely to be followed by long continuing currents than subsequent strokes, especially second strokes (see their Fig. 3). Table 4 shows the percentage of strokes of different stroke order with continuing current durations longer than 3 ms and 10 ms in our relatively small dataset of 174 strokes in Florida. The percentage of strokes with significant continuing currents were similar for first and second strokes, while the GLM detection efficiency increased from 31.3 to 53.8 % (for the 30 km spatial criteria). So, the GLM detection efficiency difference between first and second strokes for our dataset cannot be attributed (at least solely) to the "natural" tendency of lightning second strokes to more frequently (than first strokes) have long continuing currents. However, GLM's bias toward detecting strokes with longer continuing currents is apparent when considering third strokes and all subsequent strokes (see Table 4): they had 1.8-2.4 times the number of strokes with continuing current durations longer than 10 ms compared to first strokes and their detection efficiencies were roughly 2-2.3 times that for first strokes.
The GLM-derived continuing current durations were unrelated to those measured using ground-based instruments, with the GLM-derived durations being severely underestimated. Our results are inconsistent with those of Fairman and Bitzer (2022), who reported that for their 152 CG strokes from April 2017 with continuing current durations (estimated from electric field records) of 10 ms or greater, the arithmetic mean (AM) and median of the maximum number of GLM-reported timecontiguous groups were 10 (i.e., 20 ms continuing current duration) and 16 (i.e., 32 ms continuing current duration), respectively (see their Table S1). In this study, the GLM-estimated continuing current durations did not exceed 6 ms (i.e., 3 time-contiguous groups) for any of the 174 (video-camera recorded) strokes in our dataset, while the continuing current durations measured from high-speed video camera records ranged from 0.28 to 685 ms (see Table 1). Ding et al. (2024) reported the AM and median ratio of the GLM-estimated to high-speed video measured continuing current durations to be 37 % and 26 %, respectively, for 18 strokes in 2018-2021 with at least five time-contiguous GLM-reported groups. In this study, the AM and median ratios were 12.9 % and 13.9 %, respectively, for 31 strokes with continuing current durations greater than 10 ms. Note that Ding et al. ( 2024) used a relaxed space-time criteria (compared to those used in this study) of within -4 ms of the stroke time to +4 ms after the end of the visibility of the continuing current in the high-speed video and within 50 km of the stroke location to find matching GLM groups.
The significant underestimation of continuing current durations by the GLM reported in this study and in Ding et al. (2024) could be due to the onboard or ground processing algorithms used by the GLM. Specifically, the GLM uses a time-varying background image as a reference for identifying rapid lightning-related changes in illumination. The background image is tied to the onboard threshold beyond which events are recorded. Changes in the onboard processing algorithms (referred to as "RTEP Settings Revision J") were made in June 2018 to make this timevarying background image adapt four-times more rapidly to sub-second changes in incident light than prior to this date (Cummins et al., 2023). This change could result in GLM events (and groups) associated with optical emissions from continuing currents being filtered out onboard and not being sent to ground. Also, it is possible that these onboard settings may result in missed/unreported first strokes and single-stroke flashes as they are "lost" in the background variations during the onboard processing. The dataset used by Fairman and Bitzer (2022) consisted of strokes that occurred in April 2017 (prior to the June 2018 algorithm change), while those in this study occurred in August 2018-September 2023 (after the algorithm change).
In order to examine the effect of the ground processing algorithm, the GLM data prior to ground processing (but after being sent to ground), called Level 0 data, were obtained for six selected flashes in our dataset. These included 18 strokes (in all six flashes) and 12 strokes (in four of the six flashes) with video-camera estimated continuing current durations shorter and longer than 10 ms, respectively. We applied the same space-time criteria described in section 2.5 with respect to the NLDN stroke location and time to both the Level 0 and Level 2 data to identify matching GLM events, followed by the time-contiguous criteria (but regardless of the flash ID, which is not available for Level 0 data) to estimate the continuing current duration. Fig. 8 shows a histogram for the number of GLM events obtained from Level 0 (blue bars) and Level (orange bars) data for the 30 strokes. The number of GLM-reported events ranged 0 to 42 (AM = 9.6) and 0 to 37 (AM = 6.9) for the Level 0 and Level 2 data, respectively. The modest reductions in the number of events in the Level 2 data are likely due to noise-filtering (Mach and Bateman, 2024) being applied in the ground processing to the Level 0 data to produce the Level 2 data. The number of reported events were greater in the Level 0 data versus the Level 2 data for (76.7 %) of the 30 strokes, with it remaining the same for seven strokes. Remarkably, while only two (of six) first strokes had any reported events in the Level 2 data, in the Level 0 data, all six first strokes had reported events. As seen from Fig. 8, for the four first strokes with zero Level events, Level 0 data had 2-14 reported events. While this analysis is for only six first strokes, the first-stroke detection efficiency increased from 33.3 % for Level 2 to 100 % for Level 0 data. This indicates that the noise-filtering being applied to the Level 0 data in the ground-processing to produce the Level 2 data may be resulting in a significant reduction in first-stroke detection efficiency. This is consistent with the findings of Mach and Bateman (2024) who reported that the filter that removes all flashes with only a single group, introduced to the ground processing algorithm in November 2017, decreases the detection efficiency while improving the false alarm rate (FAR) of the GLM. Efforts are being made to restore these filtered flashes without increasing the FAR. However, the increased event count in the Level 0 data for our dataset does not significantly affect the estimated continuing current duration which requires time-contiguous events/groups. For 8 (26.7 %) of the strokes, the continuing current durations increased (by 2 ms for 7 strokes and from 0 to 4 ms for one stroke) for the Level 0 data. The AM continuing current duration increased from 0.87 ms in the Level 2 data to 1.46 ms in the Level 0 data, both of which are significantly lower than the AM of 33 ms for the video-camera measured continuing current durations for these 30 strokes. The strokes for which the video-camera derived continuing current durations were greater than 10 ms are indicated by the broken-line rectangle in Fig. 8. No significant difference is noted in the changes between Level 0 and Level 2 datasets for strokes with continuing current durations shorter versus longer than 10 ms. In summary, it appears that the onboard processing similarly affects the Level 0 and Level 2 data such that GLM's responses to strokes with significant continuing currents are severely affected; GLM's groundprocessing does not appear to have a significant impact on this. However, the ground processing does appear to be significantly reducing the first stroke detection efficiency.
Generally speaking, the continuing current durations that we measured from the lightning channel-base current waveforms agree well with those obtained from the high-speed video camera measurements (see Figs. 4a and b). The percentage errors (Δt cc %) in the video-camerameasured continuing current durations (t CC-VC ) with respect to those measured from the current waveforms (t CC-CW ) were computed as Δt cc % = 100(t CC-VC -t CC-CW )/t CC-CW and are shown in Table 5. The percentage errors, with the corresponding duration differences (t CC-VC -t CC-CW ) shown within parentheses, ranged from -54.6 % (-3.64 ms) to 148 % (8.35 ms) for the 19 strokes with the median signed and absolute errors being -6.12 % (-0.82 ms) and 24.8 % (3.64 ms), respectively. As can be seen from Fig. 6a, for three of the four strokes with current-waveformmeasured continuing current durations >50 ms, the video-camera derived durations were significantly longer. This is likely due to sections of leader-channel well above the channel-base (see, e.g., Fig. 1, fourth panel) remaining dimly illuminated even after the channel-base current decayed to below the noise-level of the measurement channel. The current being measured at the channel-base versus the optical signature being an integration of the entire channel length within the video camera' FOV could be a contributing factor to the discrepancy between continuing current durations derived from the two measurements. To the best of our knowledge, errors in continuing current durations measured from video camera records for natural downward CG lightning are not available from any previous studies, even though some studies (e.g., Diendorfer et al., 2003;Wang et al., 2005;Zhou et al., 2011;Zhou et al., 2013;Zhou et al., 2014) have compared the luminosities from high-speed video camera records to measured current amplitude for various lightning processes, including continuing current, in upward and triggered lightning.
For 16 out of 19 strokes with associated electric field measurements, the continuing current durations derived from electric field waveforms were longer than the durations obtained via high-speed video (see the waveforms in Figs. 3d and f for an example, as well as the scatter plots in Figs. 6c and d). Note that these are not the same 19 strokes discussed in the previous paragraph. The percentage errors (Δt cc %) in continuing current durations obtained from electric field waveforms (t CC-EW ) with respect to those obtained from high-speed video records (t CC-VC ) are shown in Table 6. The percentage errors, with the corresponding duration differences (t CC-EW -t CC-VC ) shown within parentheses, ranged from -61.3 % (-1.57 ms) to 911 % (5.75 ms), with the median signed and absolute errors both being 83.7 % (0.97 and 1.2 ms, respectively). The largest percentage error (911 %) was associated with a stroke whose continuing current durations obtained from video-camera and electric field measurements were 0.63 and 6.38 ms, respectively (see Fig. 6c).
Our result indicating overestimation of continuing current durations obtained from electric field waveforms is consistent with the findings of Saba et al. (2006b), who reported an average error of 23 % for 19 strokes, with the electric field derived continuing current durations being longer with respect to those obtained from high-speed video. This is also consistent with the results of Fairman and Bitzer (2022) who reported continuing current durations derived from electric field waveforms to be longer than those from high-speed video for the majority of their 50 strokes. Note that, in our dataset of 19 strokes, the majority (82.2 %) had very short continuing current durations (<10 ms). Estimating continuing current durations from electric field waveforms for short duration currents can be error-prone due to poorer signal-tonoise ratio for the low-amplitude field changes occurring during slowly-varying continuing currents after the return stroke pulse. Also, the channel remained slightly illuminated at the end of our video camera record for one stroke (with continuing current duration of 83.7 ms, see Fig. 6c), indicating that its video camera derived continuing current duration was somewhat underestimated. This could also be true for another stroke in our dataset for which only part of the channel was captured in the camera's field of view.
The GLM detected four of the six flashes for which we had LMA data; the two undetected flashes had the lowest number of LMA VHF events of the six flashes. This is consistent with the findings of Zhang and Cummins (2020), who reported an average GLM flash detection efficiency of 73.8 % using 241,206 LMA flashes from 2018 through 2019. They reported that GLM flash detection efficiency increased with increasing LMA flash duration, increasing flash area, longer channel length, and longer flash extent. The significant discrepancies between the GLMreported flash areas versus those reported by the LMA (GLM flash areas were 7 to 22 times larger than those of the LMA for three flashes) can be attributed, at least in part, to the relative coarseness of the GLM pixel resolution. The minimum pixel size of the GLM is approximately 64 km 2 at nadir and about 66-72 km 2 in Florida near the locations of the flashes in this dataset. The discrepancies in flash durations reported by the GLM versus LMA need further investigation (with larger datasets than in this study) and can likely be attributed, in part, to phenomenological differences between the optical emissions associated with channel heating detected by the GLM versus VHF sources associated with breakdown of air and channel formation detected by the LMA. The differences in how flashes are defined in the GLM LCFA (see section 2) versus in the LMA (e.g., Bruning and Thomas, 2015) as well as the GLM not detecting relatively dim optical emissions can also contribute to differences in reported flash characteristics.
We examined the responses of the GLM (onboard the GOES-16 satellite) to 174 negative CG strokes that occurred in the Space Coast of Florida in 2018-2023 and were captured on high-speed video as well as reported by the U.S. NLDN. The GLM flash and stroke detection efficiencies were 80.5 and 50 %, respectively. The detection efficiency was lower for first strokes (31.3 %) and for single stroke flashes (30 %) than for subsequent strokes (61.7 %). The stroke detection efficiency was 2.4 times higher during nighttime than that during daytime (81.3 versus 33.9 %, respectively). The stroke detection efficiency did not appear to be dependent on the return stroke peak current with the detection efficiencies being similar (around 50 %) for strokes with peak-current magnitudes less than versus greater than 30 kA. However, strokes with longer continuing current durations were somewhat more likely to be detected by the GLM, with the detection efficiency for strokes with no significant (<3 ms duration) continuing current being 37.5 % and that for those with significant (>3 ms duration) continuing current being 64.9 %. Continuing current durations estimated from GLM groups did not exceed 6 ms for any of the 174 strokes and were unrelated to the "ground truth" continuing current durations obtained from high-speed video camera records which ranged from 0.28 to 685 ms. Our analysis indicates that the onboard processing techniques similarly affect the GLM Level 0 and Level 2 datasets such that GLM's responses to strokes with significant continuing currents are severely affected; GLM's ground-processing does not appear to have a significant impact on this. However, the ground processing does appear to be significantly reducing the first stroke detection efficiency. The continuing current durations measured from high-speed video camera records correlated well with those measured from channel-base current waveforms, and the median absolute error was 24.8 %. Continuing current durations measured from electric field waveforms tended to be overestimated compared to durations derived from video camera records. Four out of six flashes for which we had LMA data were detected by the GLM; the two undetected flashes had the lowest number of LMA VHF sources. For four flashes with both LMA data and GLM-reported groups, the number of groups in a flash appeared to be unrelated to the number of LMA VHF sources. The GLM-reported flash areas were significantly (about 7 to 22 times) larger than their LMA flash areas for three of the flashes and somewhat comparable for the fourth flash.