This paper presents a noise propagation approach based on the Gaussian beam tracing (GBT) method that accounts for multiple reflections over three-dimensional terrain topology and atmospheric refraction due to horizontal and vertical variability in wind velocity. A semi-empirical formulation is derived to reduce truncation error in the beam summation for receivers on the terrain surfaces. The reliability of the present GBT approach is assessed with an acoustic solver based on the finite element method (FEM) solutions of the convected wave equation. The predicted wavefields with the two methods are compared for different source-receiver geometries, urban settings, and wind conditions. When the beam summation is performed without the empirical formulation, the maximum difference is more than 40 dB; it drops below 8 dB with the empirical formulation. In the presence of wind, the direct and reflected waves can have different ray paths than those in a quiescent atmosphere, which results in less apparent diffraction patterns. A 17-fold reduction in computation time is achieved compared to the FEM solver. The results suggest that the present GBT acoustic propagation model can be applied to high-frequency noise propagation in urban environments with acceptable accuracy and better computational efficiency than full-wave solutions.
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