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Proceedings Paper

Extension of Chandrasekhar's formula to non-homogeneous Lambertian surfaces and comparison with the 6S formulation
Author(s): Alain Sei
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Paper Abstract

The classical Chandrasekhar's formula, which relates the surface albedo to the top of the atmosphere radiance, rigorously applies to a homogeneous Lambertian surface. For a non-homogeneous Lambertian surface in a plane parallel atmosphere, an extension of this formula proposed in the eighties has been implemented recently in the 6S algorithm. To analyze this extension, this paper derives the rigorous formula of the top of the atmosphere signal in a plane parallel atmosphere bounded by a non-homogeneous Lambertian surface. Then the 6S algorithm extension is compared to the exact formula and approximations and their validity are examined. The derivation of the exact formula is based on the separation of the radiation fields into direct and diffuse components, on the introduction of the Green's function of the problem and on integrations of boundary values of the radiation fields with the Green's function.

Paper Details

Date Published: 30 October 2007
PDF: 10 pages
Proc. SPIE 6745, Remote Sensing of Clouds and the Atmosphere XII, 674519 (30 October 2007); doi: 10.1117/12.736078
Show Author Affiliations
Alain Sei, Northrop Grumman Space Technology (United States)

Published in SPIE Proceedings Vol. 6745:
Remote Sensing of Clouds and the Atmosphere XII
Adolfo Comerón; Richard H. Picard; Klaus Schäfer; James R. Slusser; Aldo Amodeo, Editor(s)

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