The Reflected Light Polarization Account at the Satellite Remote Sensing of the Cloud Cover

The mathematical modelling of the polarized radiation transfer (RT) at the satellite remote sensing (SRS) of the strongly anisotropic cloudy atmosphere needs an efficient well-conditioned algorithm with accelerated solution convergence to be developed. The accelerated convergence can be achieved by the small angle approximation (SAA) subtracting from the general solution of the vectorial (polarization) RT equation (VRTE). The reminder, being a smooth function, is computed rapidly. In the current paper the SAA is determined in the frame of reference (FoR) containing the arbitrary directed sunlight rays. In contrast to the FoR containing the vertical direction of the slab the system for the coefficients of the radiation field with the coupled mutual azimuthally Fourierexpansion amplitudes is obtained. On the assumption of the continuous dependence of the angular generalized spherical function (GSF) expansion of the radiation field we use the Taylor series for the above mentioned coefficients with only two first terms left with respect to the strong anisotropy the vectorial modified SAA of the spherical harmonics method (MSH). Some computational results are given in comparison with the single scattering approximation for thin slabs, the Monte-Carlo simulation for general case scattering and the total intensity of the polarized light beam is compared with the scalar spherical harmonics method (SHM). The algorithm for back scattered radiation computation for the SRS is given as well. * Corresponding author.