Analytical approaches to the delta-Eddington model of the radiative transfer through vertically inhomogeneous optical depths

Abstract

Analytical approaches have been developed for one-dimensional monochromatic delta-Eddington radiative transfer equation through a vertically inhomogeneous medium. They are based on the solution of the Riccati equation that arises from the decoupling of the two-stream radiances, and seek to approximate the exponent functions in the solution as opposed to finding the solution as a whole. Depending on the case, Green-Liouville approximation or other techniques presented in this paper are utilized for finding these exponents. Though developed for atmospheric radiative transfer problems applicable to the global climate change modelling, and for non-invasive medical applications on tissue-light interactions, the techniques considered here are quiet general in nature. Hence, they can also be useful in other boundary value problems of the diffusion type that involve linear second order ordinary differential equations with variable coefficients.