Extension of Chandrasekhar's formula to non-homogeneous Lambertian surfaces and comparison with the 6S formulation

Alain Sei

doi:10.1117/12.736078

30 October 2007 Extension of Chandrasekhar's formula to non-homogeneous Lambertian surfaces and comparison with the 6S formulation

Alain Sei

Author Affiliations +

Proceedings Volume 6745, Remote Sensing of Clouds and the Atmosphere XII; 674519 (2007) https://doi.org/10.1117/12.736078
Event: SPIE Remote Sensing, 2007, Florence, Italy

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.

Citation Download Citation

Alain Sei "Extension of Chandrasekhar's formula to non-homogeneous Lambertian surfaces and comparison with the 6S formulation", Proc. SPIE 6745, Remote Sensing of Clouds and the Atmosphere XII, 674519 (30 October 2007); https://doi.org/10.1117/12.736078

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