Backscatter cross sections of composite random rough surfaces based on the selection of variational parameters to decompose the surface height spectral density function

Scattering from composite two scale models of rough sea surfaces is analyzed. Unlike the conventional hybrid perturbation-physical optics solutions, the unified full wave approach used here is not restricted by the small Rayleigh roughness parameter nor are the two cross sections added in an ad hoc manner. The total surface height spectral density function is decomposed in a continuous smooth manner, into of a larger and a smaller scale surface height spectral density function. The variational parameter, proportional to the ratio of the mean square height (or slopes) of the larger scale surface and the mean square height (or slope) of the total surface, is increased from zero to unity. Thus, in the limit, the unified full wave solutions for the scatter cross sections reduce to the physical optics solution and the small slope, original full wave solution. It is shown that the unified full wave solutions for the scatter cross sections are stationary over a very wide range of values of the variational parameter. The slope modulation tends to significantly increase the backscatter cross sections for the horizontally polarized waves