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A microwave model for remote sensing of snow based on dense media radiative transfer theory with random rough surface boundary conditions is developed. Both volume scattering and rough surface scattering effects are treated by numerical Maxwell model of 3D simulations (NMM3D). Detailedly, the volume scattering model is based on dense media radiative transfer (DMRT) theory by using Monte Carlo (MC) simulations of the three-dimensional solutions of Maxwell's equations for densely distributed sticky particles. The rough surface scattering is modeled by the numerical Maxwell model of 3D simulations (NMM3D), which is accelerated by sparse matrix canonical grid method (SMCG). The bistatic scattering coefficients and emissivity of rough surfaces are utilized as the boundary conditions for the DMRT. Full multiple scattering solutions are calculated by solving the DMRT numerically. The results for a layer of dry snow over a rough ground at 18.7 GHz and 38.5GHz are illustrated.