A Semi-Analytic Technique to Integrate the Radiative Transfer Equation over Optical Depth

Abstract

A method of fitting polynomials to the intensity distribution as a function of optical depth is described for use with the Gauss-Seidel iterative technique for solving the equation of radiative transfer. This technique enables the τ integration to he performed analytically, thus permitting accurate and rapid solutions for optically thick atmospheres. Results are shown for values of τ up to 50, and various cheeks indicate that the method maintains an accuracy of better than 1%.