Dependence of Microwave Brightness Temperature on Bistatic Surface Scattering: Model Functions and Application to AMSU-A

For significant surface reflection, the brightness temperature above planetary surfaces depends not only on surface temperature, emissivity, and atmospheric emission, but also on the type of bistatic scattering. For a plane-parallel atmosphere, this dependence can be specified by an effective incidence angle thetas_eff from zenith of downwelling radiation. We obtained analytic expressions for the reflectivity and thetas_eff for typical scattering functions such as Lambert, Lommel-Seeliger, multiple isotropic scattering (Chandrasekhar), and Peake's grass model. In all cases, thetas_eff decreases with increasing zenith opacity (considered range: 0 to 1), and in most cases, the dependence on observation direction is small. These results are in contrast to specular reflection, where the effective incidence angle is given by the observation angle, which is, of course, independent of opacity. The dependence of terrestrial polar-region brightness temperatures on the type of bistatic scattering was studied for the advanced microwave sounding unit-A (AMSU-A). The difference between upwelling brightness temperatures calculated with diffuse and specular surface scattering is greatest for the zenith direction and for zenith opacities in the range of 0.3 to 0.6, and it decreases with increasing emissivity. A potential exists to infer a parameter A_L describing the relative contributions of Lambertian (A_L = 1) and specular (A_L = 0) scattering. Some non-Lambertian scattering functions give values of A_L > 1. For example, Lommel-Seeliger surfaces that are observed near vertical give A_L values of about 1.2, and still larger values (1.6) are obtained with the model of Peake. The angle dependence of AMSU-A measurements from the vicinity of Dome C, Antarctica, agrees with the Lambert model.