Stationary solutions for the rough surface radar backscatter cross sections based on a two scale full wave approach

Using a full wave approach, the rough surface radar backscatter cross sections are expressed as weighted sums of two cross sections. The radar cross sections associated with the larger scale surface are reduced by a factor equal to the square of the characteristic function of the smaller scale surface (that rides upon the larger scale surface). The Bragg scatter contributions from the small scale surface are modulated by the slopes of the large scale surface. The backscatter cross sections are obtained by regarding the rough surface as an ensemble of patches of random rough surfaces with arbitrary orientations. It is shown that the full wave solutions are stationary over a wide range of patch sizes. The patches are characterized by the spectral wavenumber that separates the large scale surface from the small scale surface. The mean square heights and slopes of the large (and small) scale surfaces depend on the choice of patch sizes.