A Systematic Study of the Lowest Order Small Slope Approximation for a Pierson–Moskowitz Spectrum

In an earlier work, a model for calculating scattering from rough surfaces at very low grazing angles was presented. The utility of this model depends on the lowest order small slope approximation (SSA1). In order to ascertain when this new model, called the SSA+, is applicable, we present a systematic study of the accuracy of the SSA1 bistatic scattering cross section for 1-D surfaces for a Pierson-Moskowitz roughness spectrum and the Dirichlet boundary condition. Different frequencies, angles of incidence, and wind speeds are combined to examine 112 different cases. The ranges of scattering angles for which the SSA1 is accurate are given, and an analysis of when the SSA+ can be used is presented. All data and plots are available online.