Approximate Solutions for Surface Reflection Loss Inclusive of a Practical Model of Refraction in the Wind-Driven Bubbly Layer

The authors previously prepared a model of coherent acoustic reflection loss at the ocean surface by combining a model of surface roughness loss with determination of surface incidence angle that accounted for the refractive effects of a uniformly stratified distribution of wind-driven bubbles. Originally, the surface roughness loss was based on a second-order small-slope approximation and the surface incidence angle was obtained using an exact solution for propagation of the incident acoustic plane wave in a layer of particular sound-speed variation. In this paper, the previous solution for surface incidence angle is simplified with the assumption that the grazing angle at the bottom of the layer is small. An approximate solution for the surface grazing angle is found in terms of grazing angle below the layer and a polynomial series in a derived parameter, which in turn is a function of wind speed and acoustic frequency. This determination of surface angle is combined with a simplified model of surface roughness loss to produce a complete model suitable for use with ray-type transmission calculations or hand calculations. The resulting model permits the prediction of the coherent surface reflection loss with only wind speed and frequency as input parameters. Results from the use of this approximated model with a Gaussian beam acoustic propagation code are compared with predictions based on Monte Carlo parabolic equation transmission calculations for surface ducted scenarios including various levels of roughness. The zones of validity of the model are considered at length.