Surface roughness, a fundamental characteristic of atmospheric ice particles, is essential for defining an appropriate particle morphology model to simulate optical properties of atmospheric particles. This dissertation presents a dynamic stochastic parameterization approach based on combining the discrete differential geometry and stochastic partial differential equations to generate particle overall shapes and the degree of surface roughness. The scattering of light by particles modeled as Gaussian spheroids with size parameters up to 300 is simulated with the Invariant Imbedding T-Matrix (II-TM) method to investigate the effect of particle surface roughness on the single-scattering properties, including the phase matrix, single-scattering albedo, and extinction efficiency. It is shown that high-frequency oscillations of the phase matrix with respect to scattering angle are gradually suppressed as the degree of roughness increases. The dissertation presents a more thorough method of roughened particles in light scattering computation than various ad hoc methods reported in the literature. We discuss how surface roughness influences the Muller matrix patterns of ice particles. These results also enable better understanding of microphysics on ice surface and more accurate parameterization of atmospheric ice particles. We show that surface irregularity changes the phase matrix elements dramatically. An analysis of optical modeling of mineral dust aerosols as Gaussian spheroids is presented. The modeling results are compared with experimental measurements of feldspar to validate the applicability of roughened model particles. The Gaussian spheroids shows better data fitting than smooth spheroids. Furthermore, we analyze population density and shape distributions of Gaussian spheroid for different mineral dust species. In addition to the scattering study, we propose a new Monte Carlo method for radiative transfer based on the Metropolis algorithm.
