Small-slope expansion for thermal and reflected radiation from a rough surface

Small-perturbation and small-slope expansions are applied and compared for calculation of thermal emission from a rough sea surface and reflected sky radiation. The comparison shows that the expansions are identical. This permits us to use the small-perturbation expansion to calculate microwave thermal radiation from the ocean instead of the two-scale model and the small-slope expansion. At grazing observation angles multiple scattering and shadowing become crucial and high-order terms of the expansion must be taken into account. This imposes a limitation on the applicability of the small-slope approximation.