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

The paper examines how well an Eddington approximation can reproduce brightness temperatures obtained from a more complete, N-stream discrete ordinate solution in the microwave regime. Radiation propagation through a plane parallel medium is considered. 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 found to be 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.