Equivalent impedance of a large rough surface at low grazing angles

The parabolic equation technique has been widely used in the study of wave propagation over smooth earth and inhomogeneous atmosphere. To properly account for surface roughness in the parabolic equation formulation has been the goal of many propagation researchers lately. The behavior of average equivalent impedance at low grazing angles is investigated here for a large rough surface. We numerically solve a Volterra integral equation of the second kind to predict fields over a rough surface through a spectral acceleration algorithm. The equivalent impedance (or admittance) of the rough surface is then calculated by comparing the resulting normalized field to the field of a two-ray model over a constant impedance plane.