{'fraction_non_alphanumeric': 0.01634320735444331, 'fraction_numerical': 0.0020429009193054137, 'mean_word_length': 5.32258064516129, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Ray tracing in a stratified moving atmosphere: Azimuthal deviation in sound propagation.

Ray tracing based on a closed-form expression for the sound propagation path in a stratified moving medium such as a stratified atmosphere is suggested. The approach involves a one-dimensional (1D) integration over the vertical coordinate and can complement existing ray tracing codes based on a set of differential equations. It can also be used as a benchmark solution, because 1D integration is usually computationally simpler than these codes. Using this approach, a closed-form expression for the azimuthal deviation between the true and apparent source location is obtained. The result enables estimation of the azimuthal deviation given a crosswind or remote sensing of the crosswind provided the azimuthal deviation is measured. Based on these formulations, sound propagation in the atmospheric surface layer characterized by the friction velocity and surface heat flux is studied.