Twenty-seven natural flashes of three thunderstorms which occurred during October 2012 in Southern France are acoustically reconstructed and analyzed in the [0.1 − 180]-Hz frequency bandwidth and the [0.3−20]-km distance range. A 50-m triangular array of four recalibrated microphones sampled at 500 Hz has been used for the recording. A novel method of separation of return strokes from intracloud discharges within the acoustical signal is detailed and systematically applied. It shows the possibility to separate nearby cloud-to-ground (CG) events or nearby and distant CGs of the same flash. The separation method yields a total of 36 return stroke signals and spectra, along with some intracloud signals. The combination of reconstruction, separation, and frequency analysis provides new insights on the origin of thunder infrasound, showing unambiguously that thunder infrasound originate dominantly from return strokes. Apart from the higher amplitude of CGs, no clear difference between intracloud and CG spectra is observed. No sharp frequency peaks can be put into evidence. The spectral variability with distance is highlighted, especially for the total acoustic energy and the center frequency and bandwidth. A link between acoustic energy and impulse charge moment change is also found, though only by a small number of data.The description of these two mechanisms explaining the infrasonic and audible acoustic content of thunder has been summarized by Few (1995). Regarding the audible content, the sudden core heating (25,000-30,000 K) just after the electric discharge produces a chain of strong shock waves along the lightning channel. The time dependence of pressure within the lightning channel was estimated by Orville (1968a) from the first measured time resolved optical spectra (Orville, 1968b), with peak overpressure exceeding 80 kPa. Based on a radiation thermodynamical model, Hill (1971) could simulate such values, with even higher shock amplitudes for shorter times (see his Figure 5). The different steps to switch from strong shock waves to weak shock waves and finally to acoustic waves are developed by Few (1969). Theory for self similar strong shock wave was proposed by Taylor (1950) for point sources and Lin (1954) for line sources and then numerically extended to transition and weak shock regimes by Brode (1955) for spherically symmetric shocks. The cylindrical symmetry was described by Plooster (1970). An empirical match between strong and weak shock theories has been applied to lightning by Jones et al. (1968) assuming a rectilinear channel. However, lightning channel tortuosity has been observed optically by Hill (1968), who proposed a mean value of 16 ∘ deflection of one segment to the next. Synthesizing these previous studies, Few et al. (1967) andFew (1969) assumed that the transition between strong and weak shocks takes place approximately in the same range of distances as the transition between cylindrical and spherical divergence. This distance is called relaxation radius. Indeed,

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.

Thunder produces complex signals with a rich infrasonic and audible frequency spectrum. These signals depend both on the source and the propagation to the observer. However, there is no mutual agreement on the link between the observed spectral content and the generation mechanisms. The objectives of this study is to provide additional experimental and theoretical investigations, especially on the return stroke, based on a database of several thousands of acoustic and electromagnetic signals recorded in Southern France during autumn 2012 (HyMeX campaign). It contains a sufficient number of events close to the source (<1 km) to minimize propagation effects and to focus on the source effects. Source localization and lightning acoustical reconstruction indicate that infrasonic and low frequency audible part (1-40 Hz) of the spectrum show no clear differences between the return stroke and the intracloud discharges. These observations are compatible with a source mechanism due to the thermal expansion associated to the sudden heating of the air in the lightning channel. An original model inspired by Few's string pearl theory has been developed. It shows that the tortuous channel geometry explains at least partly the low frequency content of observed thunder spectrum.

Infrasound and low frequency sounds are discussed as a method to characterize lightning flashes in a complementary way to electromagnetic (EM) observations. Thunder and EM data result mainly from a 2-months long observation campaign in Southern France, dedicated to monitor atmospheric electricity as part of the hydrological cycle in Mediterranean (HyMeX program). Possibilities and limitations to follow storms by sound or infrasound (in the 1 to 40 Hz frequency range) at various distances are outlined. The influence of distance, wind, and ambient noise is examined. Several examples of individual lightning flashes acoustical reconstruction are compared to EM reconstruction by means of a Lightning Mapping Array. Both Intra-Cloud or Cloud-to-Ground (CG) discharges are investigated. Special emphasis is brought to the lower part of CGs, as many acoustic signals are localized inside the lightning CG channel. A statistical comparison between the acoustical versus EM approaches is performed, thanks to a significant number of recorded discharges in a single storm. Performances of acoustical reconstruction are detailed as function of observation range. Detailed signal analysis compared to a theoretical model shows that the tortuous channel geometry explains at least partly the low frequency content of our observations of thunder spectra.

Thunder from 27 natural lightning flashes of three thunderstorms has been recorded in 2012 in Southern France in the 0.1–180 Hz frequency bandwidth, using a 50 m-wide triangular array of 4 recalibrated microphones in the 0.3–20 km distance range from lightning. Source reconstruction allows to separate, within the acoustical signal, Cloud-to-Ground (CG) from Intra-Cloud (IC) parts of the discharge. The possibility to separate nearby CG events is shown. A total of 36 CG signals and associated spectra is obtained, along with some IC signals. The combination of reconstruction, separation, and frequency analysis provides new insights on the origin of thunder. Thunder infrasound is shown unambiguously to originate dominantly from return strokes. Spectra of CGs and ICs are similar, but of higher amplitude for CGs. No sharp frequency peaks can be clearly evidenced. The influence of distance, therefore of propagation effects, is pointed out. Best fits of energy and frequency gravity center dependence with distance are in agreement with a nonlinear line source propagation. A link between acoustic energy and impulse Charge Moment Change (iCMC) is also indicated. Lightning is modeled as a randomly tortuous line source, and the resulting spectra are compared to observations.

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