Sei Alain
Northrop Grumman SpaceTechnology, 1 Space Park, Redondo Beach, California 90278, USA.
Appl Opt. 2007 May 1;46(13):2471-80. doi: 10.1364/ao.46.002471.
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 nonhomogeneous Lambertian surface in a plane-parallel atmosphere, an extension of this formula was proposed in the 1980s and has been implemented recently in the 6S algorithm. To analyze this extension, the rigorous formula of the top of the atmosphere signal in a plane-parallel atmosphere bounded by a nonhomogeneous Lambertian surface is derived. Then the 6S algorithm extension is compared to the exact formula and approximations and their validity is 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 Green's function.
经典的钱德拉塞卡公式将地表反照率与大气顶层辐射率联系起来，该公式严格适用于均匀朗伯面。对于平面平行大气中的非均匀朗伯面，20世纪80年代提出了该公式的一种扩展形式，并且最近已在6S算法中得以实现。为了分析这种扩展形式，推导了由非均匀朗伯面界定的平面平行大气中大气顶层信号的精确公式。然后将6S算法扩展形式与精确公式及近似公式进行比较，并检验它们的有效性。精确公式的推导基于将辐射场分离为直接分量和漫射分量、引入问题的格林函数以及利用格林函数对辐射场的边界值进行积分。
