Generalized form of the direct and adjoint radiative transfer equations

The main goal of this paper is to give a rigorous derivation of the generalized form of the direct (also referenced as forward) and adjoint radiative transfer equations. The obtained expressions coincide with expressions derived by Ustinov [Adjoint sensitivity analysis of radiative transfer equation: temperature and gas mixing ratio weighting functions for remote sensing of scattering atmospheres in thermal IR. JQSRT 2001;68:195-211]. However, in contrast to [Ustinov EA. Adjoint sensitivity analysis of radiative transfer equation: temperature and gas mixing ratio weighting functions for remote sensing of scattering atmospheres in thermal IR. JQSRT 2001;68:195-211] we formulate the generalized form of the direct radiative transfer operator fully independent from its adjoint. To illustrate the application of the derived adjoint radiative transfer operator we consider the angular interpolation problem in the framework of the discrete ordinate method widely used to solve the radiative transfer equation. It is shown that under certain conditions the usage of the solution of the adjoint radiative transfer equation for the angular interpolation of the intensity can be computationally more efficient than the commonly used source function integration technique.