A stochastic, multiscale model of microwave backscatter from the ocean

Abstract

The conventional view of microwave backscatter from the ocean is based on composite surface and quasi‐specular theories. In this view, backscatter at intermediate incidence angles is due to Bragg scattering from freely propagating short surface waves that are advected and modulated by longer waves. At small incidence angles the scattering process becomes quasi‐specular, coming from small facets aligned normal to the incident waves. The transition between these two processes is said to occur at incidence angles of about 10° to 20°. In this paper we demonstrate that advances in scattering theory and in computing speed make it possible to improve this view. We show that recent scattering theories agree on the form of the backscatter for incidence angles below that where multiple scattering must be considered, i.e., below about 80°. This form involves the Kirchhoff integral multiplied by a coefficient dependent on dielectric constant and incidence angle. We avoid the higher‐order calculations necessary in these theories to include the variable local incidence angle caused by surface wave slopes by applying them over restricted regions of the surface. We successively break the surface into regions from which the scatter comes from small‐, intermediate‐, and large‐scale waves. We show that in this picture, scattering from small‐scale waves is classic Bragg scattering and is very common while from large‐scale waves it is classic quasi‐specular scattering and is rarely important. For intermediate‐scale waves we evaluate the Kirchhoff integral numerically; this type of scattering becomes increasingly important with increasing wind speed. For all scales but the large one we correct the incidence angle for the slopes of all longer waves as required by composite surface theory. On this picture the transition from Bragg scattering to Kirchhoff scattering occurs gradually in a manner that is dependent on incidence angle, azimuth angle, wind speed, and the surface wave spectrum. The model indicates that Bragg scattering is often viable to surprisingly low incidence angles at low wind speeds. The model is sensitive to the wave height variance spectrum over a wide range of wave numbers. We use two recently published forms of this spectrum to compare the predictions of the model to various data that have been collected over the incidence angles range from 0° to 50°. At 0° this model produces a better fit to Ku band data from the TOPEX altimeter than does quasi‐specular theory and does so with no artificial “effective reflection coefficient.” As the incidence angle increases, the model continues to show good agreement with data without an artificial division into “quasi‐specular” and “Bragg” scattering. The advantage of this formulation over a quasi‐specular one is demonstrated by comparing the two models with data on received power taken at 36 GHz for incidence angles between nadir and 30°.