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

Alain Sei

doi:10.1117/12.736082

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

Alain Sei

Author Affiliations +

Proceedings Volume 6745, Remote Sensing of Clouds and the Atmosphere XII; 67451E (2007) https://doi.org/10.1117/12.736082
Event: SPIE Remote Sensing, 2007, Florence, Italy

Abstract

The classical Chandrasekhar's formula relating the surface reflectance to the top of the atmosphere radiance rigorously applies to a Lambertian surface. For a homogeneous non Lambertian surface in a plane parallel atmosphere, an extension of this formula has been proposed in the work of Tanre and has been implemented 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 an homogeneous non Lambertian surface. Then this formula is compared to the 6S algorithm extension and approximations used and their validity are pointed out. The methods used for this rigorous derivation are classical. They are based on the systematic separation of direct and diffuse components of the radiation fields, on the introduction of the Green's function of the problem and on convolutions of boundary values of the radiation fields with the Green's function.

Citation Download Citation

Alain Sei "Extension of Chandrasekhar's formula to a homogeneous non-Lambertian surface and comparison with the 6S formulation", Proc. SPIE 6745, Remote Sensing of Clouds and the Atmosphere XII, 67451E (17 October 2007); https://doi.org/10.1117/12.736082

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