A statistical model for foward scattering of waves off a rough surface

Using methods of physical optics, a statistical description of the scattering of waves off a rough surface is obtained. The rough surface is assumed to consist of a large number of independent point scatterers which fluctuate randomly in vertical position and also disappear and appear at random. The surface is divided into cells so that no more than one scatterer can occupy a cell, and the events in any two different cells are independent of each other. The average scattered signal, the mean square fluctuation, and the time covariance of the fluctuating portion of the signal are computed in terms of the mean-square scatterer height, the grazing angle, the radiation wavelength, the decay time for disappearance of scatterers, the time autocorrelation of a scatterer height, and the a priori probability of finding a given cell occupied by a scatterer.