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フルテキストURL 2007020196.pdf ( 145.7KB ) 公開日 2010-04-16 Integration of Chandrasekhar's integral equation Tanaka, Tasuku タナカ, タスク 田中, 佐 山口大学大学院理工学研究科（工学） 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. eng text application/pdf Elsevier 学術雑誌論文 査読あり 0022-4073 AA0070576X Journal of quantitative spectroscopy and radiative transfer 76 2 121 144 2003-01 info:doi/10.1016/S0022-4073(02)00050-X http://www.sciencedirect.com/science/journal/00224073 Copyright c2002 Elsevier Science Ltd. All rights reserved. 著者版 2007020196 山口大学 http://www.lib.yamaguchi-u.ac.jp/yunoca/handle/2007020196