An alternative method of solution to radiative transfer

Abstract

In this work, we propose an alternative method for solving a to radiative transfer equation in the four-stream approximation following the ideas of Jiménez-Aquino and Varela (2005). We use the Li and Ramaswamy (1995) proposal to establish the set of four coupled first-order differential equations associated with the radiances or radiative intensities. The method consists in transforming those four coupled differential equations into a set of four independent fourth-order differential equations associated with the quantities $M^s$ and $M^d$, which represent the sum and the difference respectively of two radiative intensities. As a consequence of this fact, the solutions for the radiative intensities are then easily calculated, and no matrix method is required.