The computational tools available for prediction of sound propagation through the atmosphere have increased dramatically during the past decade. The numerical techniques include analytical solutions for selected index of refraction profiles, ray trace techniques which include interaction with a complex impedance boundary, a Gaussian beam ray trace algorithm, and more sophisticated approximate solutions to the full wave equation; the fast field program (FFP) and the parabolic equation (PE) solutions. This large array of computational approaches raises questions concerning under what conditions the various approaches are reliable and concerns about possible errors in specific implementations. This paper presents comparisons of predictions from the several models assuming a complex impedance ground and four atmospheric conditions. For the cases studied, it was found that the FFP and PE algorithms agree to within numerical accuracy over the full range of conditions and agree with the analytical solutions where available. Comparisons to ray solutions define regimes where ray approaches can be used. There is no attempt to compare calculated transmission losses to measurements.

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The Gaussian beam approach solves the wave equation in the neighborhood of the conventional rays using the parabolic approximation. The solution associates with each ray a beam having a Gaussian amplitude profile normal to the ray. The approximate overall solution for a given source is then constructed by a superposition of Gaussian beams along nearby rays. The solution removes ray-tracing artifacts such as perfect shadows and infinite energy at caustics without the computational difficulties of numerical solutions to the wave equation. In this paper, the Gaussian beam approach is applied to atmospheric sound propagation in the presence of refraction above a ground surface. A brief overview of the method is presented. Calculations obtained from Gaussian beam tracing are compared to those obtained from the fast field program (FFP) and to experimental measurements. The experiments were made above a concave surface indoors that simulates propagation under downward refraction (inversion or downwind) in the cases of a hard and finite impedance surface. These experiments include measurements in the presence of a barrier. Measurements were also made in a wind tunnel in the presence of wind and temperature gradients. The results suggest that beam tracing can be applied to complex atmospheric sound propagation problems with advantages over conventional ray tracing and full-wave solutions.

A new boundary-element method for predicting outdoor sound propagation over uneven ground is presented. This allows the sound field around complex boundaries (various absorptive properties and shapes) and in the presence of refraction to be calculated accurately. The total sound pressure is expressed as the sum of the incident pressure and the pressure scattered by the obstacles in the propagation medium, involving layer potentials. The Green’s function used in this formulation takes meteorological and ground effects into account and relies on recent models for propagation in inhomogeneous media, such as normal modes, residue series, the parabolic equation, or the fast-field program. In this paper, this new method, called Meteo-BEM, is derived, based on both boundary-element methods (BEM) in a quiescent medium, and propagation models in inhomogeneous media. The hypothetical case of a rigid, thin noise barrier on a flat ground, under a known sound-speed gradient condition, is studied. Comparison of numerical simulations with experimental results shows that this new method is a powerful tool for outdoor sound propagation prediction, which gives rise to many applications and developments.