Electromagnetic power of lightning superbolts from Earth to space

Superbolts are extreme lightning strokes originally identified by optical measurements from satellites (Vela), with inferred radiated power per stroke of 10^11–10^13 W. Such large power implies core channel temperatures that may exceed the commonly accepted ~3 × 10^5 K for lightning return strokes, raising questions about lightning energy balance. More recently, radio-frequency superbolts have been localized using the high-energy tail (>1 MJ) of stroke energies measured by WWLLN VLF ground stations. Their occurrence differs from ordinary lightning: superbolts are more frequent over oceans and seas, often in winter, with high wintertime occurrence in the North Atlantic and the Mediterranean. Like other cloud-to-ground flashes, superbolts emit VLF radiation that propagates in the Earth–ionosphere waveguide and can escape into the magnetosphere as whistler-mode waves. This study aims to quantify superbolt electromagnetic power density from ground to space, characterize their VLF electric and magnetic wave properties in both domains, compute ground-to-space transmission, and assess how their properties differ from ordinary lightning to improve understanding of lightning electrodynamics and wave coupling from the atmosphere to space.

Prior work identified superbolts from optical satellite data (Vela) and from WWLLN radio measurements by selecting strokes with energy >1 MJ. These studies reported nonuniform spatial and seasonal occurrence (oceanic and wintertime biases). Whistler-mode propagation of lightning-generated waves through the ionosphere and plasmasphere is well established. Statistical maps and models have estimated lightning-generated wave power at satellite footprints using WWLLN. Attenuation of sferics in the Earth–ionosphere waveguide and ionosphere has been quantified, and prior satellite observations at low altitudes have reported power–distance scaling laws for typical lightning. However, detailed electromagnetic properties of superbolts in space and simultaneous ground–space characterization had not been reported prior to this work.

• Event identification: Superbolts were identified from WWLLN as strokes with radiated energy >1 MJ (2012–2018). European events were cross-referenced with ground electric field measurements from the CEA ECLAIR campaign and detections from the Météorage (MTRG) network.
• Space instrumentation: Electric and magnetic fields were measured by the Van Allen Probes using EMFISIS and EFW instruments in both burst (high-resolution) and survey (lower-resolution) modes, near the magnetic equator (±20° magnetic latitude).
• Ground instrumentation: ECLAIR stations used vertical dipole whip antennas sampling at ~12.5 MHz, measuring electric fields from a few hundred Hz to 5 MHz; MTRG provided peak current estimates and detections.
• Selection criteria for space events: From 10,724 WWLLN superbolts, 1,143 coincided with any burst capture; 212 occurred at L < 3. After screening for clear whistler-mode triggers without contamination, uninterrupted waveforms, absence of masking by other lightning with comparable estimated power, and distance from stroke to nearest magnetic footprint (MFP) d < 8000 km (some >8000 km added by hand if clear), 66 high-quality burst events were retained (38 EFW, 28 EMFISIS; 1 observed by both). Two events were observed simultaneously on ground and in space.
• Signal processing: Waveforms were Fourier-transformed to compute electric and magnetic power spectral densities (PSD). Wave power (E^2 in V^2/m^2, B^2 in pT^2) was computed by integrating PSD over VLF bands (space: ~2–10 kHz; ground: ~2 kHz–5 MHz). Poynting flux was computed for specific events. Median squared electric fields at the spacecraft were empirically estimated from WWLLN stroke energy and event distance for comparison to observed burst powers.
• Attenuation analysis: Mean-squared fields were averaged over 1.5 ms (ground) and 1 s (space), scaled by WWLLN stroke energy, and regressed versus distance from source (to ground station or nearest MFP) to obtain power–distance scaling laws.
• Transmission factor: Using empirical power–distance laws, ground PSDs were forward-propagated and space PSDs back-propagated to a common altitude (300 km) to estimate a frequency-dependent ground-to-space transmission factor in the VLF band.
• Statistics: Ground-based statistics used 368 high-resolution ECLAIR superbolt waveforms (with 86 also detected by MTRG) and 3349 ordinary lightning strokes from the same period for comparison. Space statistics used 66 burst-mode superbolts and 431 survey-mode captures, compared with global lightning-generated wave statistics.

• Superbolts in space: Burst-mode spectrograms show characteristic whistler-mode descending tones lasting ~seconds, with PSD spanning ~0.1–10 kHz and most power above 2 kHz within the first second. Space reception is delayed 0.1–0.4 s (and up to 0.8 s in statistics) relative to WWLLN time due to propagation in the waveguide and magnetosphere.
• Discrimination from other lightning: Empirical estimates of median squared E at the spacecraft for non-superbolt lightning are >3 orders of magnitude lower than for the superbolt in the same window, confirming attribution of burst signals to the superbolt.
• Simultaneous ground–space case (1.2 MJ): At 1388 km ground distance, peak E^2 ≈ 20 (V/m)^2; mean over 1.5 ms ≈ 4 (V/m)^2 (~400× normal CG). At 3193 km from the nearest magnetic footprint in space, peak E^2 ≈ 6 × 10^-7 (V/m)^2; mean over 1 s ≈ 8.5 × 10^-8 (V/m)^2 (~200× normal lightning). Magnetic rms amplitude ≈ 19 pT (~19× normal). Two space-observed waves separated by ~0.2 s exhibit a Poynting flux sign change, consistent with bounce reflection from the conjugate hemisphere and/or multiple entry latitudes.
• Attenuation laws: Ground mean EM power decays ~d^-2 with distance, consistent with far-field behavior. In space near the equator, superbolt EM power decays ~d^-1.6 with distance to the nearest MFP; variability of 1–2 orders of magnitude is observed for similar energy and distance due to environmental and geometric factors.
• Ground-to-space transmission: Frequency-dependent transmission factor in the VLF band is ~10^-8 at ~300 km altitude for the two synchronous events (lower bound of recent model estimates), with the more distant event showing a smaller transmission due to increased path length.
• Ground statistics (superbolts vs normal lightning): Median peak current ≈ 363 kA (~10× normal). Positive CG fraction 15% (vs 28% for all triggered lightning). Rise time (50–90%) 5–6 µs (up to 15 µs) vs 1–2 µs (up to 5 µs) for normal. Decay time 10–20 µs vs 50–90 µs for normal, yielding a more symmetric first ground-wave peak. Median ground electric field at 100 km ≈ +240 V/m vs ±20 V/m for normal. Median ground E^2 over 1.5 ms ≈ 2.6 (V/m)^2 (~100× normal). Fraction of total 2 kHz–5 MHz power in VLF (2–12 kHz): ~68% for superbolts vs ~38% for normal strokes, increasing with lightning power.
• Space statistics: Superbolt EM signals are rarely observed during daytime in space (5/66 events between ~09:00–17:00 LT), consistent with day-side ionospheric attenuation. Median satellite L ≈ 1.6; mean [median] source-to-nearest MFP distance ≈ 5924 km [5023 km]. Time delay scales with L: Δt ≈ 0.277 L − 0.225 s (R^2 = 0.70). Burst-mode mean rms amplitudes across 66 superbolts: magnetic ≈ 83 pT; electric ≈ 873 µV/m. Corresponding mean [median] B^2 ≈ 3598 pT^2 [80 pT^2] and E^2 ≈ 0.40 mV^2/m^2 [0.015 mV^2/m^2]. Compared to global lightning-generated wave survey statistics, superbolt burst-mode mean powers are ~10–1000× larger. Three strongest events reached ~250 pT magnetic rms and ~6 mV/m electric rms.
• Peak vs mean: Peak burst-mode powers exceed mean by factors ~10 (magnetic) and ~13 (electric); mean peak magnetic amplitude ≈ 0.2 nT; mean peak electric amplitude ≈ 1.9 mV^2/m^2 (reported).

The observations demonstrate that superbolts transmit exceptionally powerful VLF whistler-mode waves into the magnetosphere, far exceeding typical lightning by 10–1000× in space. Their distinctive ground waveform symmetry (longer rise and shorter decay) and larger peak currents suggest physical differences from ordinary CG discharges. Daytime suppression of space-detected signals indicates strong ionospheric control over ground-to-space coupling. The weaker-than-free-space power decay in space (~d^-1.6) compared with ground (~d^-2) reflects complex propagation effects along geomagnetic field lines and through the plasma environment. The large event-to-event variability underscores the influence of L-shell, longitude, local time, and season. Because extreme events contribute disproportionately to global rms wave amplitudes at low L, accurately capturing the high-power tail requires burst-mode measurements; survey-mode underestimates total power due to temporal truncation. The extreme amplitudes imply that quasi-linear approximations for wave–particle interactions in radiation belt models may break down, motivating nonlinear treatments for accurate scattering and acceleration predictions. The two synchronous ground–space cases provide rare benchmarks for validating ray-tracing and full-wave models of VLF transmission through the atmosphere–ionosphere into space.

This work provides the first comprehensive electromagnetic characterization of lightning superbolts from ground to space, including simultaneous observations linking source waveforms to spaceborne whistler-mode waves. Key contributions include quantifying power–distance scaling on ground and in space, demonstrating 10–1000× greater spaceborne VLF power than typical lightning, establishing a ground-to-space transmission factor (~10^-8) in the VLF band, and revealing distinct ground waveform properties (higher peak currents, longer rise and shorter decay, more symmetric peaks) and space propagation features (L-dependent delays, daytime suppression). These results inform models of lightning electrodynamics, ionosphere–magnetosphere coupling, and radiation belt wave–particle interactions. Future work should include coordinated optical and electromagnetic observations, expanded simultaneous ground–space campaigns, detailed ray-tracing and full-wave modeling to resolve ducted vs unducted propagation, and comparative studies with other natural wave modes (e.g., hiss, chorus, EMIC) to contextualize superbolt-driven wave impacts.

Superbolts are rare (≈3.5 per day worldwide; ~7 per million CG strokes), making simultaneous ground–space observations unlikely; only two synchronous cases were obtained. Burst-mode captures are limited by satellite position and triggering; of 1,143 coincident burst windows only 66 clean events met strict criteria. Survey-mode records truncate signals, biasing power low. The empirical power–distance regressions exhibit 1–2 orders of magnitude variability due to environmental and geometric factors (L-shell, local time, season), limiting their predictive precision and underscoring the need for full modeling. Space detections are strongly reduced during daytime due to ionospheric attenuation, introducing local-time biases. Determination of propagation mode (ducted vs unducted) remains unresolved without dedicated ray-tracing constrained by in situ density structures.