A Unified Microwave Radiative Transfer Model with Jacobian for General Stratified Media

A unified microwave radiative transfer (UMRT) model is developed for rapid, stable and accurate level-centric calculation of the thermal radiation emitted from any geophysical medium comprised of planar layers of either densely or tenuously distributed, moderately sized spherical scatterers. The formulation includes rapid calculation of the tangent linear relationship (i.e., Jacobian) between the observed brightness temperature and any relevant radiative and geophysical layer parameters, such as the scattering and absorption coefficients, temperature, temperature lapse rate, and medium layer thickness.;UMRT employs a rapid multistream scattering-based discrete ordinate eigenanalysis solution with a layer-adding algorithm stabilized by incorporating symmetrization of the discretized differential radiative transfer equations and analytical diagonalization and factorization of the resulting symmetric and positive definite matrices. It is based on the discrete ordinate tangent linear radiative transfer model of Voronovich et al. (2004), but extended to include both Mie and dense media scattering theories and employ refractive layers.;Other nontrivial extensions are: 1) exact modeling of linearized temperature profiles and resulting radiation streams across medium layers, 2) compensation for refracted radiation streams using Snell's law, the Fresnel reflectivity and transmissivity coefficients, and a cubic spline interpolation matrix, and 3) seamless calculation of associated Jacobians for both sparse and dense medium parameters.;Details of the UMRT Jacobian formulation are presented. The entire formulation has been programmed in Matlab and validated through both energy conservation and numerical Jacobian intercomparisons. Comparisons of the upwelling brightness temperatures over dry snow and ice from simulations and field measurements are presented and discussed.