Acoustical Energy of Return Strokes: A Comparison Between a Statistical Model and Measurements

Abstract

This letter proposes a new statistical model of thunder. The tortuous geometry of the emitting return stroke is randomly generated to fit observations of negative cloud-to-ground discharges. Pressure waves are initialized by radiation-hydrodynamics simulations and linearly propagated into an isothermal atmosphere incorporating standardized sound absorption. The thunder pressure frequency signal is defined as the product of the input pressure governed by a deposited energy with the stochastic frequency response of the elongated discharge. We find the low-frequency content of thunder is mostly due to stroke elongation originating from tortuosity. Acoustic energy per stroke length and spectrum slope are statistically compared to measurements, with good agreement found. We show both a near-and far-field regime of the acoustical energy over distance described by two different power laws. The correlation found between the lightning energy and the acoustic energy paves the way for using thunder measurement to estimate deposited energy. Plain Language SummaryThunder is the remote acoustic signature of lightning. It covers a wide range of frequencies, from infrasound below 20 Hz to higher audible sounds. To what extent the recording of thunder can provide useful information about lightning? As an attempt to answer this question, a new thunder model is proposed and compared with measurements made in Southern France in Fall 2012. The model relies on three key ingredients. The first one is the geometry of the lightning channel from cloud to ground, modeled as a random process whose parameters are chosen to fit well-known optical observations. The second component is the acoustical pressure wave near the discharge that originates from the hot air expanding from the lightning discharge, obtained from radiation-hydrodynamic simulations. The third aspect is propagation, assuming simply a homogeneous but sound absorbing atmosphere. Acoustic model predictions are compared at different distances with measured data with good agreements. Comparison shows, for the first time to our knowledge, that the easily measured overall acoustic energy at one distant microphone can inform us about the order of magnitude of deposited energy within the lightning channel.

Infrasound Thunder Detections across 15 Years over Ivory Coast: Localization, Propagation, and Link with the Stratospheric Semi-Annual Oscillation

“…Studies about thunder, since the 1960s, have been dedicated to the theoretical interpretation of thunder generation (whether in the audible or infrasonic domain) and to the possibility of reconstructing the acoustic sources of thunder in three dimensions. Lacroix et al [3] have pointed out that arrays having an aperture in the kilometer range prevent precise 3D reconstruction; furthermore, Farges et al [4] showed that beyond 20 km it is not possible to reconstruct in 3D the lightning channels.…”

“…The acoustic sources are co-localized with the discharges located using the electromagnetic measurements of a lightning mapping array (LMA). Very recently, Lacroix et al [3] suggested a new model based on Few's [9] development, which also takes into account the interference of the waves emanating from the multiple sources distributed along the flash channel. The authors showed that the amplitude level of the infrasonic part of the signal is thus comparable with or even higher than the audible one.…”

Locating Thunder Source Using a Large-Aperture Micro-Barometer Array

“…It should be, however, noted in this respect that the analysis was limited on the localization of the region (point) from which the highest infrasound power was generated to different directions because only time instants of the most distinct pressure fluctuations were used for the calculations of source positions. As mentioned previously, the pressure fluctuations at different microbarometer sites were not sufficiently correlated to imagine the whole lightning channel as was done by Lacroix et al (2019) who used the small-scale array. Nevertheless, the localizations of the highest infrasound source power mostly to altitudes 3-5 km in this study are consistent with some previous studies that used small scale arrays and focused on the analysis of distinct short infrasound pulses (Chum et al, 2013;Arechiga et al, 2014).…”

“…One of the not fully explained phenomena is also the generation of acoustic pulses in the infrasound frequency range that are observed in addition to the audible thunderclap. According to recent works, the source of infrasound is fast adiabatic expansion of the hot lightning channel as it is generally accepted for audible frequency range (Few, 1969;Assink et al, 2008;Lacroix et al, 2019). Another mechanism could be the pressure change caused by ohmic air heating by currents flowing from the charged area into the lightning channel (Few, 1985).…”

Acoustical reconstruction and thunder energy localisation in lightning flashes measured over Corsica during EXAEDRE field campaign

“…Co-localisation of acoustic sources with in-cloud detections provided by SAETTA high-frequency (60-66 MHz) electromagnetic lightning locating system, and with ground impacts provided by Meteorage, ensures the efficiency and precision of the method. This one was already used successfully in a previous field campaign (HyMeX-SOP1) in Cévennes in 2012 [2,3,4]. The detection algorithm PMCC also provides the various recorded signal intensities.…”