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

• Published in: Geophysical research letters 2019-10, Vol.46 (20), p.11479-11489
• Main Authors: Lacroix, Arthur, Coulouvrat, François, Marchiano, Régis, Farges, Thomas, Ripoll, Jean‐Francois
• Format: Article
• Language: English
• Subjects: Acoustic absorption; Acoustic models; Acoustic propagation; Acoustics; Agreements; Atmosphere; Computational fluid dynamics; Computer simulation; Discharge; Elastic waves; Elongation; Energy; Energy measurement; Engineering Sciences; Fluid flow; Frequency dependence; Frequency response; Hydrodynamics; Infrasound; Lightning; Lightning channels; Lightning discharges; Mathematical models; Microphones; modeling; Ocean, Atmosphere; Optical observations; Pressure; Pressure waves; Process parameters; Radiation; Return strokes (lightning); Sciences of the Universe; Sound; Sound absorption; Sound propagation; Sound transmission; Statistical models; thunder; Tortuosity; Wave propagation
• ISSN: 0094-8276; 1944-8007
• DOI: 10.1029/2019GL085369

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 Summary Thunder 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. Key Points Novel statistical model of thunder with tortuous channel and radiation‐hydrodynamics simulated source is presented Good agreement found between modeled and measured acoustic energy over a distance range is shown