This monograph deals with the statistical properties of the scattered field of an electromagnetic wave propagating over a (perfectly conducting) rough surface at low grazing angles. Two different approaches, one based on the parabolic equation techniques and the other based on an exact full wave integral equation, are investigated. For the parabolic equation modeling of the forward scattering over a rough surface, only the mean field is considered. Efficient Fourier split-step solutions are carried out and results are compared to the experimental data. Meanwhile a recently published analytical approach, the mean Green's function technique for computing the mean scattered field, is numerically evaluated through direct comparisons with other methods. In the second method, the surface is assumed to be periodic resulting in a surface integral equation over only one single period. The new integral equation is discretized using the method of moments and is solved using the generalized conjugate residue algorithm with the help of the fast multipole method. Both the mean and the second moment of the scattered field are studied.

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