Polarization and effective Mueller matrix for multiple scattering of light by nonspherical ice crystals

We investigated the errors associated with the scalar approximation (i.e., an approach that neglects polarization effects) for simulating the intensity of the radiation reflected by an ice cloud. In a case for an optical thickness of tau=1, the relative errors of the scalar approximation are typically between -0.5% and 0.1%. We also investigated the effect of the order of scattering on the degree of linear polarization. It is shown that substantial errors can be introduced by the first-order scattering approximation, and thus, the multiple-scattering effect is essential to an accurate simulation of the polarization configuration of a radiation field. Furthermore, we investigate the effective Mueller matrix pertaining to multiple scattering of light by ice clouds. The effective Mueller matrix is a 4x4 matrix that relates the incident and scattered Stokes parameters. This matrix implicitly contains the effects of all orders of scattering and absorbing events in the entire radiation transfer process. The sensitivity of the (2,1) and (3,1) elements of the effective Mueller matrix to ice crystal shape and size indicates that polarimetric information may be useful for inferring the microphysical properties of ice crystals within ice clouds.