Comparison of power probability density functions for vertical sound propagation

Abstract

When sound travels through the atmosphere, fluctuations in the wind velocity and temperature generate fluctuations in the sound amplitude and phase, which makes source detection, localization, and identification more difficult. While there are several parametric probability density functions for the signal power, the previous literature has not shown which model performs best in a wide variety of environments. This paper compares the noncentral Erlang, gamma, compound gamma, generalized gamma, and log exponentially modified Gaussian distributions' ability to approximate the signal power distributions collected at the National Wind Technology Center (Colorado, United States) in 2018. This weeklong experimental campaign measured the vertical and slanted sound propagation of a non-moving, sinusoidal source (600-3500 Hz) on the ground using microphones mounted to a meteorological tower up to 130 m high. The dataset included several different atmospheric conditions, which were recorded by the meteorological tower and resulted in a wide range of scattering regimes in the measured acoustic data. When evaluated using the Kullback-Leibler divergence, the gamma distribution was the best two-parameter model, and the log exponentially modified Gaussian distribution was the best three-parameter model.