A new look at decoupling of atmospheric radiative transfer and anisotropic surface reflection

- We found a general expression separating atmosphere and surface radiative transfer.
- Separation is based on a new surface resolving kernel approach.
- The surface resolving kernel is defined with an integral equation of the Fredholm type.
- The equation's kernel and source are defined with solutions of the standard problems.
- The approach allows for variation of the surface condition for remote sensing.

This paper presents a new approach for separating atmospheric radiative transport from the lower boundary condition in the case of one-dimensional problem. The approach allows for an exact analytical expression of the solution for an arbitrary surface reflectance. The solution has the form of linear combination of the standard problem solutions with illumination from both top and bottom of the atmosphere. The problem with illumination from below can be solved with existing radiative transfer codes by reversing the order of the atmospheric layers. The solutions for illumination from below are weighted with a surface resolving kernel that is specific for every lower boundary condition. The surface resolving kernel is defined by an integral equation of the Fredholm type. The solution for the Lambertian surface is also obtained in the framework of this approach. Different methods of solution for the surface resolving kernel are considered. The successive iterations of the integral equation for the surface resolving kernel are equivalent to the decomposition of the surface reflected radiance by the orders of reflection. Recipes for the cases when standard problems are solved with the methods of discrete ordinates and spherical harmonics are also considered.