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 tau integration to be performed analytically, thus permitting accurate and rapid solutions for optically thick atmospheres. Results are shown for values of tau up to 50, and various checks indicate that the method maintains an accuracy of better than 1%. -Authors