Theoretical model for scattering of radar signals in Ku- and C-bands from a rough sea surface with breaking waves

A small-slope approximation (SSA) is used for numerical calculations of a radar backscattering cross section of the ocean surface for both K-u- and C-bands for various wind speeds and incident angles. Both the lowest order of the SSA and the one that includes the next-order correction to it are considered. The calculations were made by assuming the surface-height spectrum of Elfouhaily et al for fully developed seas. Empirical scattering models CMOD2-I3 and SASS-II are used for comparison. Theoretical calculations are in good overall agreement with the experimental data represented by the empirical models, with the exception of HH-polarization in the upwind direction. It was assumed that steep breaking waves are responsible for this effect, and the probability density function of large slopes was calculated based on this assumption. The logarithm of this function in the upwind direction can be approximated by a linear combination of wind speed and the appropriate slope. The resulting backscattering cross section for upwind, downwind and cross-wind directions, for winds ranging between 5 and 15 m s(-1), and for both polarizations in both wave bands corresponds to experimental results within 1-2 dB accuracy.