A radiation transport equation that describes the spatiotemporal evolution of the directional spectrum of underwater acoustic noise is presented and applied to ship noise. A ray-based algorithm is used to solve the transport equation and numerically simulate the evolution of the directional noise spectrum produced by a passing ship. The model described accounts for the transient and highly episodic nature of shipping noise, the strong anisotropy of the radiated shipping noise, the directional dependence of the resulting acoustic field, and the critical angle dependence of bottom-reflected energy. The model predicts time histories of sound pressure level and directional spectral energy density at distant locations if the ship track and the ship's radiated noise power are known. Simulations are shown to be in qualitatively good agreement with observations.
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