Toward a simple mathematical model for microwave backscatter from the sea surface at near-vertical incidence

A mathematical model for microwave backscatter from the sea at near-vertical incidence is presented. The model, which is formulated in terms of Huygens principle, expresses the backscatter in terms of an "expected transfer function" of the round-trip path between the antenna and the surface of the sea. In its present form, the model is restricted to describing the case in which the microwave-illuminated area of the sea is large enough for the distribution of illuminated sea-surface area in elevation to be accurately known. It differs from other models in that it does not make the assumption that the incident electromagnetic field is plane or that the antenna is located in the Fraunhofer zone of the scattering surface. The analysis is carried out in terms of a general probability-density function of sea-surface elevation. However, an approximately Gaussian probability-density function is assumed for the purpose of working out a detailed example. The most interesting feature of the model is that it indicates that values of average radar cross sections per unit area of the sea (
\sigma \deg
), when measured at near-vertical incidence, cease to be independent of range and of antenna gain. Needed extensions of the model should treat the case in which the illuminated area size is small, and the problem of mathematically describing the boundaries between the large and small illuminated area cases. A number of experiments are recommended for verifying predictions of the model.