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フルテキストURL2007020196.pdf ( 145.7KB ) 公開日 2010-04-16
タイトルIntegration of Chandrasekhar's integral equation
作成者Tanaka, Tasuku
作成者ヨミタナカ, タスク
作成者別表記田中, 佐
作成者所属山口大学大学院理工学研究科(工学)
内容記述(抄録等)We solve Chandrasekhar's integration equation for radiative transfer in the plane-parallel atmosphere by iterative integration. The primary thrust in radiative transfer has been to solve the forward problem, i.e., to evaluate the radiance, given the optical thickness and the scattering phase function. In the area of satellite remote sensing, our problem is the inverse problem: to retrieve the surface reflectance and the optical thickness of the atmosphere from the radiance measured by satellites. In order to retrieve the optical thickness and the surface reflectance from the radiance at the top-of-the atmosphere (TOA), we should express the radiance at TOA “explicitly” in the optical thickness and the surface reflectance. Chandrasekhar formalized radiative transfer in the plane-parallel atmosphere in a simultaneous integral equation, and he obtained the second approximation. Since then no higher approximation has been reported. In this paper, we obtain the third approximation of the scattering function. We integrate functions derived from the second approximation in the integral interval from 1 to ∞ of the inverse of the cos of zenith angles. We can obtain the indefinite integral rather easily in the form of a series expansion. However, the integrals at the upper limit, ∞, are not yet known to us. We can assess the converged values of those series expansions at ∞ through calculus. For integration, we choose coupling pairs to avoid unnecessary terms in the outcome of integral and discover that the simultaneous integral equation can be deduced to the mere integral equation. Through algebraic calculation, we obtain the third approximation as a polynomial of the third degree in the atmospheric optical thickness.
本文言語eng
資料タイプtext
ファイル形式application/pdf
出版者Elsevier
NII資料タイプ学術雑誌論文
査読の有無査読あり
ISSN0022-4073
NCIDAA0070576X
掲載誌名Journal of quantitative spectroscopy and radiative transfer
76
2
開始ページ121
終了ページ144
発行日2003-01
DOIinfo:doi/10.1016/S0022-4073(02)00050-X
関連情報URL(IsPartOf)http://www.sciencedirect.com/science/journal/00224073
権利関係Copyright c2002 Elsevier Science Ltd. All rights reserved.
著者版/出版社版著者版
リポジトリID2007020196
地域区分山口大学
URIhttp://www.lib.yamaguchi-u.ac.jp/yunoca/handle/2007020196