Higher order perturbation theory applied to radiative transfer in non-plane-parallel media

• Published in: Journal of quantitative spectroscopy & radiative transfer Vol. 78; no. 1; pp. 105 - 118
• Main Authors: Box, Michael A., Polonsky, Igor N., Davis, Anthony B.
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 15.04.2003
• ISSN: 0022-4073; 1879-1352
• DOI: 10.1016/S0022-4073(02)00188-7

Radiative transfer in non-plane-parallel media is a very challenging problem, which is currently the subject of concerted efforts to develop computational techniques which may be used to tackle different tasks. In this paper we develop the full formalism for another technique, based on radiative perturbation theory. With this approach, one starts with a plane-parallel ‘base model’, for which many solution techniques exist, and treat the horizontal variability as a perturbation. We show that under the most logical assumption as to the base model, the first-order perturbation term is zero for domain-average radiation quantities, so that it is necessary to go to higher order terms. This requires the computation of the Green's function. While this task is by no means simple, once the various pieces have been assembled they may be re-used for any number of perturbations—that is, any horizontal variations.