Fast 3-D Inhomogeneous Radiative Transfer Model Using a Planar-Stratified Forward Algorithm and Horizontal Perturbation Series

A horizontally inhomogeneous unified microwave radiative transfer (HI-UMRT) model is presented to study the 3-D effects of the horizontal inhomogeneous clouds on the computed microwave radiances and facilitate satellite radiance assimilation over the horizontally inhomogeneous all-weather conditions. HI-UMRT provides a coupled two-Stokes parameter numerical radiance solution of the 3-D radiative transfer (RT) equation by embedding the existing 1-D UMRT algorithm into an iterative perturbation scheme. The horizontal derivatives in the radiances of the lower perturbation order are treated as the source functions of the azimuthal harmonic perturbation RT equations that are readily solved using the planar-stratified 1-D UMRT algorithm. The horizontal radiance derivative is estimated by central differencing. A perturbation source-function analysis shows that the increase in computing time for the 3-D HI-UMRT model relative to the 1-D UMRT model is moderate, since: 1) the computationally efficient UMRT engine is applied only to the perturbation equations with nontrivial solutions and 2) the layer parameters for the 1-D solution are reused for all higher perturbation orders. Numerical simulations using HI-UMRT based on 3-D cloud profiles simulated by the Weather Research and Forecasting numerical weather model illustrate the convergence of the iterative perturbation series. An intercomparison of the top-of-atmosphere brightness temperature images for HI-UMRT versus the change planar-stratifiedslant path UMRT model illustrates the considerable impact of cloud horizontal inhomogeneities on the computed upwelling microwave radiances.