A Detailed Comparison Between a Small-Slope Model of Acoustical Scattering From a Rough Sea Surface and Stochastic Modeling of the Coherent Surface Loss

Abstract

The accurate modeling of underwater acoustical reflection from a wind-roughened ocean surface is a challenging problem. Some complicating factors are the presence of near-surface bubbles and the potential for shadowing of acoustical energy by parts of the surface itself. One essential factor, which is the subject of this paper, is the specular reflection of coherent plane waves at an ocean-like rough surface. We tested the accuracy of one rough surface reflection model, the small-slope approximation (SSA) approach as used by Williams (J. Acoust. Soc. Amer., vol. 116, no. 4, pp. 1975-1984, Oct. 2004), for scenarios for which scattering was entirely in the vertical plane. The SSA model was used to compute values of the coherent plane wave reflection loss per bounce for wind speeds between 5 and 12.5 m/s, frequencies between 1.5 and 9 kHz, and grazing angles between about 1 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">°</sup> and 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">°</sup> . These values were compared to those obtained from a Monte Carlo approach based on the parabolic equation (PE) method, where realistic ocean surfaces were generated based on the Pierson-Moskowitz spectrum for ocean surface heights. The SSA model compared favorably with the more rigorous PE method for most of the range of parameters considered. An approximation to the SSA model was derived for application to grazing angles less than particular values, and this approximation was shown to compare well with results from PE modeling.