Near-grazing illumination and shadowing of rough surfaces

A simple and computationally efficient methodology is demonstrated for treating the interaction of radio waves near grazing above rough surfaces. We apply it to the sea from HF through the microwave. Results using actual finite seawater conductivity depart significantly from those of a perfectly conducting profile for vertical polarization; for horizontal polarization there is essentially no difference. Shadowing behind wave crests is surprisingly shallow for vertical polarization even when the occluded depth is tens of wavelengths. This methodology gives expressions for the effective surface impedance at grazing as modified by the roughness when height scales greatly exceed the radio wavelength, augmenting prior expressions valid at HF for the sea obtained from perturbation theory. These effective impedances can then be used in formulations for radiation and surface wave propagation/diffraction at and below the horizon.