Electromagnetic wave propagation and scattering in dense, discrete random media with application to remote sensing of snow

Abstract

This dissertation investigates wave propagation and scattering in dense, discrete random media using Monte Carlo simulations and analytic dense media theory. The Monte Carlo simulations use an exact numerical formulation based on the Foldy-Lax multiple scattering equations that allow computation of the incoherent field arising from scattering and absorption in systems of up to 5000 spheres with 40% fractional volume. The extinction coefficient obtained by simulation is compared to that obtained under classical methods and with dense media theory such. as quasi-crystalline approximation (QCA) and quasi-crystalline approximation with coherent potential (QCA-CP). For dense media, the independent scattering approximation overestimates the amount of scattering while scattering calculated under QCA-CP agrees well with both simulation and carefully controlled experiment. At high fractional volumes the simulations predict a slightly larger extinction than QCA-CP Monte Carlo simulations also predict the presence of absorption enhancement where the absorption coefficient exceeds that predicted under the independent absorption assumption.The application of remote sensing of snow utilizes dense media radiative transfer (DMRT) theory to predict the redistribution of radiant energy. Monte Carlo simulations provide a means to accurately determine the quantities necessary for DMRT, namely the extinction coefficient, absorption coefficient, phase matrix and effective permittivity. The phase matrix thus obtained differs from the classical assumption by containing non-zero off-diagonal elements while the effective permittivity agrees well with mixing formulae. A second order iterative solution to DMRT produces bi-static scattering levels that are comparable to those seen in actual snow data.The effect of the scatterer placement on the electromagnetic wave is investigated by modeling the adhesive character of the particles that causes them to clump together with a sticky-particle pair distribution function. The adhesive character may provide a more accurate depiction of particles that exist in clusters (for example snow grains). The effect of the sticky-particles on the electromagnetic wave is calculated analytically using QCA and numerically with Monte Carlo simulations with both predicting much stronger scattering due to the larger particles. Snow sections prepared stereologically are analyzed to determine a family of pair distribution functions that can be used to calculate the scattering from a log-normal distribution of particle sizes.