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Tanaka Tasuku

Affiliate Master Yamaguchi University

A solution of radiative transfer in isotropic plane-parallel atmosphere by integrating Milne equation

Journal of quantitative spectroscopy and radiative transfer Volume 95 Issue 1 Page 71-91
published_at 2005-09
2007020198.pdf
[fulltext] 169 KB
Title
A solution of radiative transfer in isotropic plane-parallel atmosphere by integrating Milne equation
Creators Tanaka Tasuku
Creator Keywords
Radiative transfer Milne integral equation Chandrasekhar's integral equation Iterative integration
In this paper we solve the inversion problem of the radiative transfer process in the isotropic plane-parallel atmosphere by iterative integrations of the Milne integral equation. As a result, we obtain the scattering function in the form of a cubic polynomial in optical thickness. The author has already solved the same problem by iterative integrations of Chandrasekhar's integral equation. In the Milne integral equation, both the cosines of the viewing angles and the optical thickness are integral variables, while in Chandrasekhar's integral equation the cosines of the viewing angles are variables but the optical thickness is not. We derive several series of exponential-like functions as intermediate derivations. Their convergences are evaluated by the author's previous work in the solution of Chandrasekhar's integral equation. The truncated scattering function up to the third order in optical thickness thus obtained is identical to that obtained from Chandrasekhar's integral equation, though their apparent forms are different. Chandrasekhar pointed out that the solution of Chandrasekhar's integral equation does not have a uniqueness of solution. The Milne equation, in contrast, has been proven to have a unique solution. We discuss the uniqueness of the solution by these two methods.
Languages eng
Resource Type journal article
Publishers Elsevier
Date Issued 2005-09
Rights
Copyright c2004 Elsevier Ltd All rights reserved.()
File Version Author’s Original
Access Rights open access
Relations
[ISSN]0022-4073
[NCID]AA0070576X
info:doi/10.1016/j.jqsrt.2004.09.035
[isVersionOf] [URI]http://www.sciencedirect.com/science/journal/00224073
Schools 大学院理工学研究科(工学)