Polarization and Mueller matrix for multiple scattering by hexagonal ice crystals

The effective Mueller matrices for multiple scattering by hexagonal ice crystal particles for visible and near-infrared wavelengths are investigated by employing a rigorous radiative transfer model based on the adding-doubling method. Two specific hexagonal ice crystal geometries: hexagonal columns (with aspect ratios of 2a/L= 20μm/75μm, and 2a/L= 80μm/300μm) and a hexagonal plate (with an aspect ratio of 2a/L= 300μm/80μm), are assumed for the shapes of the scatterers in this study. The effective Mueller matrices are determined by considering four polarization states for the incident radiation. Furthermore, the errors associated with the scalar radiative transfer simulation and the first-order-scattering approximation are also investiagted. In the case of an optical thickness of τ=1, the relative errors of the intensity of radiation due to the scalar approximation in radiative transfer computation are typically between -0.4% and 0.1%. Moreover, the effect of the order of scattering on the degree of linear polarization is also investigated. It is shown that substantial errors may be introduced by the first-order-scattering approximation, and thus, the higher order scattering is critical to the polarization configuration of the radiation field.