Small-angle modification of the radiative transfer equation for a pseudo-spherical atmosphere

The conventional pseudo-spherical technique relies on the separation of the total radiance into the direct solar beam and the diffuse radiance; the direct solar radiance is treated in a spherical geometry, while the diffuse radiance is computed in a plane-parallel geometry. In the small-angle modification of the radiative transfer equation, the total radiance is separated into an anisotropic part and a regular part. In this paper, we pOresent two formulations of the small-angle modification of the radiative transfer equation for a pseudo-spherical atmosphere. In the first formulation, we solve the radiative transfer equation for the diffuse radiance in a pseudo-spherical atmosphere with an additional anisotropic source term computed in a plane-parallel atmosphere, while in the second formulation we solve the radiative transfer equation for the regular solution in a plane-parallel atmosphere with an additional pseudo-spherical correction term. The numerical analysis revealed that the accuracy of the small-angle models is acceptable. (C) 2012 Elsevier Ltd. All rights reserved.