Electromagnetic power of lightning superbolts from Earth to space

Lightning superbolts are the most powerful and rare lightning events with intense optical emission, first identified from space. Superbolt events occurred in 2010-2018 could be localized by extracting the high energy tail of the lightning stroke signals measured by the very low frequency ground stations of the World-Wide Lightning Location Network. Here, we report electromagnetic observations of superbolts from space using Van Allen Probes satellite measurements, and ground measurements, and with two events measured both from ground and space. From burst-triggered measurements, we compute electric and magnetic power spectral density for very low frequency waves driven by superbolts, both on Earth and transmitted into space, demonstrating that superbolts transmit 10-1000 times more powerful very low frequency waves into space than typical strokes and revealing that their extreme nature is observed in space. We find several properties of superbolts that notably differ from most lightning flashes; a more symmetric first ground-wave peak due to a longer rise time, larger peak current, weaker decay of electromagnetic power density in space with distance, and a power mostly confined in the very low frequency range. Their signal is absent in space during day times and is received with a long-time delay on the Van Allen Probes. These results have implications for our understanding of lightning and superbolts, for ionosphere-magnetosphere wave transmission, wave propagation in space, and remote sensing of extreme events.


On the ground
Each ECLAIR station is equipped with a vertical electric field antenna mounted on a mast, and a computer used for data digitalization and archiving 1,2 . The dipole antenna was designed and manufactured by CEA. Its pass-band is from 500 Hz to 5 MHz. The response inside this band is flat and was calibrated. The acquisition is achieved by comparison of the signal with a threshold of 1 V/m. The sampling frequency is 12.5 MHz, with a time window of 30 ms (including a pre-triggering time of 6 ms), a dynamic range of 14 bits, an idle time of less than 0.5 ms (between 2 triggering). Timing accuracy is ± 50 ns with GPS time-stamping. The spectrograms of ground data in Figure 2, Figure 3, and Supplementary Figure 6 were produced using 8172-point Fourier transforms with 95% overlap and a Hanning window.

In space
The twin Van Allen Probes spacecraft have an orbital perigee near 620 km altitude and an apogee near 5.8 Earth radii 3 . They are in near-equatorial orbits, sampling +/-20 degrees magnetic latitude. Their orbital period is ~9 hours and their orbits precess through all local times every ~2 years. The spacecraft spin with a period of ~11 seconds. This work uses survey and burst observations of VLF plasma waves from the EFW instrument 4 and the EMFISIS instrument suite 5 on the Van Allen Probes spacecraft. Both EFW and EMFISIS use the same sensors for data-collection -six voltage probes to measure electric fields and a three-axis search coil magnetometer (SCM) to measure wave magnetic fields. The EMFISIS survey data used here consist of power spectral densities (PSD) calculated on-board the spacecraft using Fourier transforms of time-series E-field and B-field data. The survey data sample the first 0.5 seconds of each 6 seconds, and they consist of -65 pseudo -logarithmically spaced frequency bins between ~2 Hz and ~11 kHz. In this analysis, the PSDs from all three axes of the SCM are summed, and the PSDs from the two spin-plane electric field components are summed. The axial electric field component is not considered due to spacecraft noise concerns. The EFW and EMFISIS burst data both consist of electric field signals on two orthogonal axes (in the spin plane) and three orthogonal axes of SCM data. The EFW burst data are sampled at 16,384 samples/s for ~5.5 second intervals, with a bandpass from ~100 Hz to ~8 kHz. The EMFISIS burst data are sampled at 35,000 sample/s for 6 second intervals with a bandpass from ~10 Hz to ~11 kHz. Some aliasing is observed when strong signals exist out of band (e.g. Figure 2d), creating vertical features in the burst spectrograms. The short intervals of EFW and EMFISIS burst data used here are selected on-board via triggering algorithms that search for intervals of high signal to noise. On the order of 70 burst intervals are collected, each, by EFW and by EMFISIS on a typical day. A fraction of these are collected at low L-shell (L < 3). The spectrograms of Van Allen Probes burst data in Figure 2 In the section Simultaneous ground-based and space measurement of a superbolt of the main text, we calculate the wave Poynting flux direction by first rotating the burst timeseries data into magnetic field-aligned coordinates. In this case, all three components of the search coil data are used, but only the two spacecraft spin-plane components of the electric field. This produces reasonable results because the ambient magnetic field is nearly in the spacecraft spin plane. Windowed fast Fourier transforms are performed, and the Poynting flux vector is calculated in the frequency domain such that, S, in each spectral bin, f, is S(f) = 1/µ0(E(f) x B * (f)), with µ0 the vacuum permeability, B * is the complex conjugate of the Fourier transform of B, and E Fourier transform of E. The angle between the Poynting flux vector direction and the background magnetic field is calculated for each spectral bin to determine whether the VLF waves are moving along or against the local ambient magnetic field direction.

Supplementary Method 2. Influence of the WWLLN station number and residual time on superbolt statistics
This supplementary section discusses the difference between the number of WWLLN superbolts used in this article (10,724) and the number of WWLLN superbolts in the definitive WWLLN superbolt article 6 . There are two limiting criteria that most likely account for these different numbers: WWLLN residual value (goodness of fit) and the minimum number of WWLLN stations detecting a stroke. Both values are given in Supplementary Table 5 and 6 for each of the 66 superbolts. The 'WWLLN residual' is the residual value in μs from the best fit minimization of timeof-group-arrivals (TOGAs) from all stations recording an event. This article used events with residuals < 30 μs. The work in 6 does not mention the residual value used to limit the data. We hypothesize, based on results shown below, that residuals < 25 μs were used in 6 . Increasing the residual time limit in this article increases tolerance and probability to measure a given event at the expense of location accuracy. However, the loss in location accuracy of less than 9 km for a 30 µs criteria is not significant in our study when those ground locations are mapped to the magnetosphere. The mean value of the WWLLN residual value of all superbolts in Supplementary Table 5 and 6 is 18.7 µs.
The minimum number of WWLLN stations detecting an event was set to eight for this article, while the minimum number required in 6 was seven. Increasing the minimum number of stations to eight in this paper adds confidence in the accuracy of the stroke energy determination 6 , and minimally affects the total number of superbolts received. The mean value of the WWLLN station number of all superbolts in Supplementary Table 5 and 6 is 10. Supplementary Table 8 shows the effect of minimum number of WWLLN receivers detecting the event and the WWLLN residual time on the total number of superbolts. These numbers are plotted in Supplementary Figure 10, showing the statistics of the number of superbolts in 2010-2019 for various residual times and its comparison with the statistics of 6 (their figure 9) referred in the main article. Values of the two studies agree within 10% on average, with 9290 superbols versus 10,724. In addition, we verify in Supplementary Table 9 that the number of superbolts we identify in space from the Van Allen Probes is not strongly dependent upon a WWLLN residual time of 25 versus 30 μs. Supplementary Table 9 shows that using a residual time of <25 µs instead of <30 µs would reduce the number of superbolts by 10% from 66 to 59 events.

Supplementary Tables
Supplementary Table 1 Supplementary Table 2: Superbolts general information. Information relative to the superbolts presented in Figure 2, Figure 3, and discussed in the text. See also Supplementary Table 3. Unavailable data is listed with a "-".
Supplementary Table 3: Superbolts electromagnetic power. Information relative to the superbolts presented in Figure 2, Figure 3, and discussed in the text. See also Supplementary Table 2. Unavailable data is listed with a "-".   System (C/NOFS) satellite orbiting at an altitude of ~700 km. E 2 (mV 2 /m 2 ) is a median of the C/NOFS squared amplitude, with error bars of ~1 order of magnitude for distances below than 7000 km and larger above. E 2 (mV 2 /m 2 ) is produced by the integration of the PSD in the VLF range, from 6 to 16 kHz, therefore a slightly different range than in this study. Worldwide WWLLN detection efficiency is about 10% on average, but rises to 50-70% of strong lightning 9,10 , which are the events focused on in this superbolt study.   Table 7: Superbolt transmission factors. Transmission factors of the two superbolts observed simultaneously on Earth and in space. Transmission factor computed at a given frequency from the ratio of the space PSD (averaged over 1 s) with the ground PSD (averaged over 1.5 ms) both in mV 2 /m 2 /Hz scaled at 300 km (using laws of Figure 4) for both superbolts, which are observed synchronously on Earth and in space on the 2013/01/23 (cf. Figure 3 and Supplementary Figure 6 and Supplementary Table 2) and on the 2012/12/05. On the 2013/01/23, both survey and burst time windows turned out to be perfectly synchronized (cf. Figure 2c in the main text). This allows to use safely the survey data and to verify that both methods, which are very different from each other (survey PSD are directly computed on board, as explained in Supplementary Method 1, while burst PSD are computed by the authors as explained in the text), lead to similar PSD and, thus, transmission factors. Last line reports the PSD integrated over the written frequency range, in mV 2 /m 2 , and the associated transmission factor.    7  10  1425  1091  334  7  15  5343  4293  1050  7  20  10258  8432  1826  7  25  14067  11613  2454  7  30  16647  13722  2925  8  10  573  444  129  8  15  2819  2318  501  8  20  6240  5253  987  8   We display the Van Allen Probes burst mode measurements of (a) the electric field power spectral density (PSD in in mV 2 /m 2 /Hz) with (b) its time-average spectrum, (c) the squared electric field, (d) the electric field waveform, (e) the magnetic field PSD in pT 2 /Hz with (f) its spectrum, (g) the squared magnetic field, (h) the magnetic field waveform, (i) the survey electric and magnetic field time-integrated power spectral density (within the black window). The electromagnetic field PSD has a characteristic descending tone shape (between t~0.4-0.6 s) but shows a second wave at t=0.6s that is the reflection of a secondary wave of the superbolt. The superbolt frequency reaches 400 Hz (deep in the whistler-mode hiss wave band) after 2s (e). The sharp rising tone just prior to the main whistler profile in (a) is an anti-aliasing filter effect with a fold over of the power above the top frequency. This effect is a classic measurement feature also visible in Figure 2a Table 3). The superbolt PSD at t=0.5s in Supplementary Figure 6(a,e) is not perturbed by another strong lightning (cf. intensity reported in Supplementary  Figure 6c). The first peak on the ground is symmetric (a,e). The map itself is made with ©Matlab Mapping Toolbox.