A Unified Microwave Radiative Transfer Model for General Planar Stratified Media: Slab Formulation

A unified microwave radiative transfer (UMRT) model is presented for computing the thermal radiation emitted from any geophysical medium composed of planar layers of either densely or tenuously distributed moderately sized spherical scatterers. UMRT employs the discrete-ordinate eigenanalysis (DOE) method with layer adding to solve the differential radiative transfer equation for such multilayer structures. UMRT inherits the symmetrization and analytical diagonalization and factorization techniques of symmetric and positive definite matrices from the discrete-ordinate tangent linear radiative transfer (DOTLRT) model presented by Voronovich These techniques ensure accuracy, numerical stability, and rapid computation for all matrix operations required for DOE along with a fast Jacobian calculation for radiance assimilation purposes. UMRT extends the applicability of DOTLRT by including both the Mie theory and the dense media radiative transfer (DMRT) theory. Other nontrivial extensions within UMRT are the following: 1) The vertical and horizontal radiation intensities are coupled within each layer by applying the reduced Mie or DMRT phase matrices, and 2) the physical temperature profile of a layer is allowed to be linear in height. The symmetry properties of both the reduced Mie and DMRT phase matrices are proved, and the associated scattering and absorption coefficients are compared and discussed. The UMRT slab formulation is validated by imposing energy conservation, and the numerical results for some nominal cases are produced and discussed.