The scattering of waves by random rough surfaces has important applications in remote sensing of
oceans and land. The problem of developing a model for rough surfaces is very difficult since, at best,
the scattering coefficient σ0 is dependent upon (at least) radar frequency, geometrical and
physical parameters, incident and observation angles, and polarization. The problem of electromagnetic
scattering from a random rough surface is analyzed using the Kirchhoff approximation (stationary phase,
scalar approximation), the small perturbation model and the two-scale model. The first major new
consideration in this paper is the polarimetric signature calculation as a function of the transmitter
location and receiver location for a bistatic radio- link. We calculate the like- and cross-polarized
received power directly using the scattering coefficients, without calculating the Mueller matrix. Next,
the study of the regions of validity of the Kirchhoff and small-perturbation rough surface scattering
models (in the bistatic case) is presented. Comparisons between the numerical calculations and the models
are made for various of the surface height rms and correlation length both normalized to the incident
wave number (denoted by σ and L, respectively). By using these two parameters to form a
two-dimensional space, the approximate regions of validity are then established. The second major new
consideration is the development of a theoretical two-scale model describing bistatic reflectivity as
well as the numerical results computed for the bistatic radar cross-section from rough surfaces especially
from the sea and snow-covered surfaces. The results are used to show the Brewster angle effect on
near-grazing angle scattering.