The reflected radiance and polarization are calculated for clouds with optical thicknesses from 10 to 100. The results are presented for both the haze C and nimbostratus model. The peak in the single scattered polarization at 140° for the nimbostratus model persists even with all the multiple scattering events that occur for the largest optical thicknesses considered here. The calculations are made by a Monte Carlo technique, which includes the effect of multiple scattering through all orders and a realistic anisotropic phase function for single scattering appropriate for the distribution of particle sizes in the cloud. The effect of the surface albedo is included in the calculations for the optical thickness of 10. The variation of the radiance and polarization with both the nadir and azimuthal angle is given for several solar zenith angles.
G. W. Kattawar and G. N. Plass, "Radiance and Polarization of Light Reflected from Optically Thick Clouds," Appl. Opt. 10, 74-80 (1971)