Two-scale models for rough surface scattering: Comparison between the boundary perturbation method and the integral equation method

This paper presents a comparison between two models for rough surface scattering computations: the boundary perturbation method (BPM) and the integral equation method (IEM). They differ in two fundamental aspects: the method used to compute the electric and magnetic fields on the surface and the surface information required for the computation. The two approaches lead analytically to the same solution in the two asymptotic cases of very large and very small vertical displacements, with no intermediate scales. For a composite surface the solution of the BPM is expressed as the sum of two terms, while a series development up to higher orders can be formulated with the IEM. In this paper, the comparison is restricted to composite surfaces and, particularly, to the ocean surface. After presenting a method for the two-scale decomposition of a rough surface, which satisfies the constraints of the electromagnetic model for each scale, we compute the scattering by the ocean surface using both models for various instrumental configurations and surface conditions. We show that considering the accuracy of usual radar measurements and under the assumptions made for the development of the models, both methods give very similar results. Since the BPM is based on a simple physical argument and appears to be more efficient than the two-scale IEM with regard to the computation time, the BPM should be preferred for ocean-like rough surfaces.