Numerical prediction of shadowing in EM scattering from a rough ocean wave at grazing incidence

A hybrid moment method/geometrical theory of diffraction numerical model has been implemented to investigate the effects of shadowing in the EM scattering from a two-scale rough surface at large incidence angles. The large-scale surface consists of a single cycle (crest-to-crest) of a Stokes ocean wave. The front face of the front crest of the Stokes wave and the back face of the back crest are extended to infinity at an angle of 30° to horizontal. A random small-scale roughness is superimposed on the surface between the wave crests. Moment method basis functions approximating the current profile predicted by GTD are used to represent the current on the infinitely long faces, while pulse basis functions are used on the Stokes wave section of the surface. Because the surface is extended to infinity, no artificial illumination weighting function is needed to avoid non-physical edge effects, thereby allowing the technique to be directly applied at the extremely large incident angles (60° to 90°) where shadowing occurs. The crests of the Stokes wave were rounded off to control diffraction contributions to the calculated scattering. Calculations show that the two-scale scattering model, corrected for large-scale scattering, accurately predicts the scattering at either polarization when the incident angle is small enough that at least about five Bragg resonant wavelengths along the large-scale surface are directly illuminated. As the angle of incidence increases and shadowing becomes more severe, the two-scale model over-predicts the scattering until the incident angle approaches 90°. Then the entire small-scale surface becomes shadowed, and the two-scale model predicts only backscatter resulting from the cylindrical surface diffraction at the rounded crests. However, the numerically-calculated scattering is significantly higher, indicating that creeping wave diffraction over the crest into the shadowed region significantly affects the backscatter. This effect is more pronounced at vertical polarization than at horizontal polarization.