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Full wave and physical optics solutions for the scattered radiation fields from rough surfaces are compared. The full wave solutions involve complete expansions of the fields and exact boundary conditions. The solutions for the radiation fields axe provided in a form that can be readily compared with earlier solutions to the problem, and they can be applied directly to engineering problems without the need to carry out any of the analytic procedures encountered in the derivations. The surface impedance concept, reciprocity, and energy conservation relationships are considered in detail, and special consideration is given to grazing incidence and excitation at the Brewster angle. This work on irregular ground effects on radio wave propagation is relevant to problems of communication, navigation, and active remote sensing.