An Iteration Method for Solving the Asymptotic Equation of Optically Thick Layers

For optically thick plane-parallel homogeneous layers, the reflection may be approximated by using so-called asymptotic expressions, which involve the reflection properties of the corresponding semi-infinite layer and the leading eigensolution of the equation of radiative transfer. In this paper, equations are derived for computing the escape function, diffusion pattern, diffusion exponent, and the reflection of semi-infinite clouds by using an iteration method. This method is suitable for numerical computations and is valid throughout the full range of single scattering albedos. The present formulations are validated by comparing them with established methods of radiative transfer.