Problem of refraction inclusion in the radiative transfer equation for the atmosphere-ocean spherical system

A new method of inclusion of refraction in the radiative transfer equation (RTE) for the atmosphere-ocean spherical system (AOS) is propozed. It is based on deformation of the spherical coordinate system according to spatial distribution of refraction index of light. It is shown that in the coordinate system deformed thus, the differential and integral operators of the RTE take a simpler form free of refraction members and corresponding to rectilinear propagation of light if the refraction is taken into account. Reflection, transmission and refraction of light at the interface in the AOS model is defined by optical parameters of an elementary volume of medium in the RTE. These parameters are introduced with the use of notions of the generalized functions theory and the Fermat principle. They are defined in Sobolev-Shvarz sense and expressed through the linear continuous functionals.