Semi-empirical model for amplitude fluctuations by atmospheric turbulence in aircraft flyover sound

Atmospheric turbulence leads to well-audible fluctuations in the amplitude of sound propagating through the atmospheric boundary layer. However, the best currently available theoretical model is valid only for short propagation distances and low turbulence regimes. A new model for predicting the standard deviation of amplitude fluctuations was developed based on the existing theoretical model of Ostashev and Wilson and the analysis of empirical data. The dataset includes over 5000 aircraft flyover events in different meteorological conditions from March to August. The model considers an effective propagation length based on the boundary layer height, frequency-dependent saturation of amplitude fluctuations, turbulence decay time during periods of decreasing solar radiation, and turbulence production by nocturnal low-level-jets. The model adaptations have significantly reduced the mean squared error from over 10 dB in the pure theoretical model to 0.3 dB in the new model. The findings will help improving the modelling of outdoor sound propagation for elevated sound sources like aircraft and wind turbines. Modelling these fluctuations can considerably improve the realism of the listening experience in aircraft flyover auralisation. Further, it helps estimating the measurement uncertainty in measured aircraft noise, especially for maximum levels.