Effective probability density function of rough surface slopes when strong shadowing is present

Abstract

It is shown that at low grazing angles, the slope probability density function (PDF) of the nonshadowed part of a rough surface can differ significantly from the slope PDF of the overall surface, if surface heights and slopes are functionally dependent. If the surface steepness has a tendency to increase with height, the effective slopes of the illuminated part of the surface can be significantly steeper than the average slope of the surface as a whole. This fact can play a crucial role in any theoretical interpretation of experimental results concerning radar scattering by the sea surface at low grazing angles.