Radiation field in an atmosphere subjected to cosine varying diffuse radiation

Abstract

The radiation field is calculated in an optically finite or semi-infinite, two- dimensional, plane-parallel, absorbing-emitting but nonscattering grey atmosphere subjected to diffuse cosine varying incident boundary radiation. We again approximate the kernel of the integral equation for the emissive power by a sum of exponents. After this approximation the integral equation can be solved exactly. The solution can be written in generalized x- and y-functions (or h- andg-functions in the semi-infinite case) which were introduced for a one- dimensional atmosphere. Since the radiation field in the case of diffuse incident radiation can be described as a superposition of solutions for the collimated case, we can find the accurate values for the source function and the radiative flux at arbitrary optical depths in the atmosphere. As in the case of collimated incident radiation, this approximation allowed of finding accurate numerical values for the source function and the radiative flux.