Scattering properties of dense media from Monte Carlo simulations with application to active remote sensing of snow

Monte Carlo simulations are used to derive the phase matrix, effective permittivity, and scattering coefficient for a random medium consisting of densely packed spheres up to 5000 in number. The results include correlated scattering and coherent wave interaction among the scatterers. The Monte Carlo simulations are based on a multiple-scattering formulation of the Foldy-Lax equations. It is shown that the derived phase matrix is in good agreement with dense media radiative transfer theory for copolarized scattering. The depolarization, however, can be substantially larger than conventional theory. Two methods are used to analyze the behavior of the coherent wave to obtain the real part of the effective permittivity. For the small particle case both methods yield values of permittivity that agree with the results of mixing formulas such as the Clausius-Mossoti mixing formula. The phase matrix and scattering coefficient obtained by simulation are used in a second-order radiative transfer model to predict the amount of backscatter from a layer of snow. It is also shown that sticky spheres, which can be used to model metamorphosed snow, produce high levels of copolarized and depolarized backscatter that can exceed the independent scattering model.