Mathematical model of solar radiation reflection by underlying surface

摘要

The model of a plane-parallel slab of a turbid medium is accepted, where there are particles of the spherical form scattering light separately from each other. Mathematically the problem is reduced to the solution of a boundary-value problem of a radiative transfer equation in turbid media with strong anisotropic scattering. In this case the computation of a backscattering is mathematically an ill-conditioned problem by using any numerical method of the solution. In the suggested method the backscattering radiance is determined by a SH method as a difference between the exact solution and SAA that essentially reduces the order of a system and smoothes the solution at any degree of an anisotropy scattering. As SAA the small angle modification of spherical harmonics method is chosen, which has a form of series of spherical harmonics that also enables to present a backscattering analytically. The calculation of medium parameters in model is made according to the Mie theory in the form of series of spherical harmonics, that allows to take into account the effect of physical properties of the medium on the radiation reflection.