Noise propagation over non-rigid sloping terrain is one of the usually encountered problems in reality as well as the most difficult problem to be handled by numerical models. A new parabolic equation is developed to solve such problems. The locally reacting boundary condition is applied along the sloping ground surfaces to derive the new marching algorithms for the parabolic equation method. The new model is compared with Chien-Soroka model [J. Sound Vib. 69, 340-343 (1980)] in a flat-ground case, and then is applied to model an outdoor sound propagation measurement that involves sloping terrain. The model shows a potential that it could serve as a useful tool for solving general and complex outdoor propagation problems.
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