A novel methodology for radiative transfer in a planetary atmosphere |
| |
Authors: | Alain L. Fymat Robert E. Kalaba |
| |
Affiliation: | (1) Jet Propulsion Laboratory, California Institute of Technology, Pasadena, California, USA;(2) University of Southern California, Los Angeles, California, USA |
| |
Abstract: | A novel methodology for evaluating the field of anisotropically scattered radiation within a homogeneous slab atmosphere of arbitrary optical thickness is provided. It departs from the traditional radiative transfer approach in first considering that the atmosphere is illuminated by an isotropic light source. From the solution of this problem, it subsequently proceeds to that for the more conventional case of monodirectional illumination. The azimuthal dependence of the field is separated in the usual manner by an harmonic expansion, leaving a problem in four dimensions ( =optical depth, 0=thickness, , =directions of incidence and scattering) which, as is well known, is numerically extremely inconvenient. Two auxiliary radiative transfer formulations of increasing dimensionality are considered: (i) a transfer equation for the newly introduced functionbm( , , 0) with Sobolev's function m( , 0) playing the role of a source-function. Because the incident direction does not intervene, m is simply expressed as a single integral term involvingbm. For bottom illumination, an analogous equation holds for the other new functionhm( , , 0). However, simple reciprocity relations link the two functions so that it is only necessary to considerbm; (ii) a transfer equation for the other new functionam( , , , 0) with a source-function provided by Sobolev's functionDm( , , 0). For bottom illumination, another functionfm( , , , 0) is introduced; by a similar argument using reciprocity relations,fm is reduced toam rendering necessary only the consideration ofam. However, a fundamental decomposition formula is obtained which shows thatam is expressible algebraically in terms of functions of a single angular variable. The functions m andDm are shown to be the values in the horizontal plane ofbm andam, respectively. The other auxiliary functionsXm andYm are also expressed algebraically in terms ofbm. These results enable one to proceed to the final step of evaluating the radiation field for monodirectional illumination. The above reductions toalgebraic relations involving only the functionbm appear to be more advantageous than Sobolev's (1972) recent approach; they also circumvent some basic numerical difficulties in it. We believe the present approach may likewise prove to be superior to most (if not all) other methods of solution known heretofore.This paper presents the results of one phase of research carried out at the Jet Propulsion Laboratory under Contract No. NAS-7-100 sponsored by the National Aeronautics and Space Administration. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|