Effective computational method of the light fields in 3D medium with anisotropic scattering

Abstract

The peculiarities of the light fields forming in the clouds are their complicated geometrical three-dimensional shape and strongly anisotropic light scattering. In these conditions the solution of the radiative transfer equation becomes mathematically ill-conditioned. The problem has a fundamental character and is concerned with a physical model of the radiation transfer-ray approximation, which determines the presence of the angular singularities in the solution. For the elimination of this problem S.Chandrasekhar has offered to subtract nonscattered radiation from the solution and to state the equations for the rest smooth part. However in the conditions of the strong anisotropic scattering the similar approach loses its efficiency. The most optimal approach in the solution of this problem is the determination of the analytically simple approximate solution including all the angular singularities of the exact solution. An example of such an approach is a small-angle approximation in the Goudsmit-Saunderson form, which however is obtained only for the flat medium geometry at an almost normal incident of the solar radiation.