From the analytical theory of rough surface Green's function based on the extension of the diagram method of Bass, Fuks and Itô, with the smoothing approximation, numerical results are presented for Gaussian and sea spectra and compared with a benchmark method by considering a one-dimensional perfectly conducting Gaussian rough surface. The effects of multiple scattering due to the surface roughness are incorporated systematically into the solutions through an effective surface impedance, which can be iterated up to the second-order. In addition, comparisons of the bistatic scattering coefficients are presented with the first- and second- orders conventional small perturbation method. This study will be useful for remote sensing of the ocean surface, especially when the transmitter is close to the surface.
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