Comparison of a Small Slope Approximation Model of Reflection Loss at the Rough Ocean Surface with Stochastic Modelling using PE

The accurate modelling of underwater acoustic 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 acoustic energy by parts of the surface itself. One essential factor, which is the subject of the present paper, is the specular reflection of coherent plane waves at an ocean-like rough surface. We tested the accuracy of the rough surface reflection model adopted by the authors, the small-slope approximation (SSA) approach as used by Williams et al. (JASA, 116, Oct. 2004). 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 and 10 degrees. 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 favourably with the more rigorous PE method for most of the range of parameters considered.