On the accuracy of the Eddington approximation for radiative transfer in the microwave frequencies

Radiative transfer calculations in the presence of clouds and precipitation simplify as the wavelengths of the radiation approach the Rayleigh scattering regime. In particular, the transfer of microwave radiation is often simpler than the equivalent calculations at shorter wavelengths because the order of quadrature and moments of the phase function needed for the treatment of scattering decrease as the wavelength increases. The purpose of this paper is to examine how well an Eddington approximation can reproduce brightness temperatures obtained from a more complete, N ‐stream discrete ordinate solution in the microwave regime. Radiation propagating through a plane parallel medium will be considered in this discussion. Although model discrepancies are complicated functions of the cloud constituents, the differences between an eight‐stream discrete ordinate solution and an analytical Eddington solution were generally small, ranging from 0 to 6°K when only one uniform layer of hydrometeors was considered. When realistic, multilayered cloud hydrometeor profiles were used, the differences between these two models never exceeded 3°K over the entire range of microwave frequencies considered (6.6–183 GHz). The models agreed to within 0.2°K in the absence of scattering constituents.