Discrete theory of radiation transfer in the "ocean-atmosphere" system

Kurzfassung

After discretization of the scattering integral for a medium slab, the radiation transfer equation takes the form of a matrix ordinary differential equation that has an analytical solution. This solution has the form of scatterers - a matrix of the layer radiance factor, connecting the angular radiance distribution of the incident and outgoing radiations. The solutions of the boundary-value problem complement the boundary conditions for the layer to complete at each boundary, which makes it possible to use the propagator of the matrix equation to determine the field inside the slab. The solution has the property of invariance, which allows replacing two adjacent layers with one, which determines the matrix-operator method, that allows considering the vertical heterogeneity of the slab. This approach makes it possible to represent the Fresnel and diffuse reflection on the layer boundary also in the matrix form. Accordingly, all the expressions for the light field of a slab acquire a closed matrix form, which makes it possible to analytically estimate the accuracy and applicability domain of known engineering approximations