Lyapustin A, Knyazikhin Y
Appl Opt. 2001 Jul 20;40(21):3495-501. doi: 10.1364/ao.40.003495.
An application of the Green's function method to the one-dimensional radiative transfer problem with a non-Lambertian surface is described. This method separates atmospheric radiative transport from the lower boundary condition and allows expressing a solution analytically for an arbitrary surface reflectance. In the physical sense, the Green's function represents bidirectional atmospheric transmission for the unitary radiance source located at the bottom of the atmosphere. The boundary-value problem for the Green's function is adjoint to the problem for atmospheric path radiance, and therefore it can be solved by use of existing numerical methods by reversal of the direction of light propagation. From an analysis of an exact operator solution and extensive numerical study, we found two accelerating parameterizations for computing the surface-reflected radiance. The first one is a maximum-eigenvalue method that is comparable in accuracy with rigorous radiative transfer codes in calculations with realistic land-cover types. It requires a total of the first three orders of the surface-reflected radiance. The second one is based on the Lambertian approximation of multiple reflections. Designed for operational applications, it is much faster: Already the first-order reflected radiance ensures an average accuracy of better than 1%.
描述了格林函数方法在具有非朗伯表面的一维辐射传输问题中的应用。该方法将大气辐射传输与下边界条件分离，并允许针对任意表面反射率解析地表达解。从物理意义上讲，格林函数表示位于大气底部的单位辐射源的双向大气传输。格林函数的边值问题与大气路径辐射的问题互为共轭，因此可以通过反转光传播方向，利用现有的数值方法来求解。通过对精确算子解的分析和广泛的数值研究，我们找到了两种用于计算表面反射辐射的加速参数化方法。第一种是最大特征值方法，在使用实际土地覆盖类型进行计算时，其精度与严格的辐射传输代码相当。它总共需要表面反射辐射的前三个阶次。第二种基于多次反射的朗伯近似。专为业务应用而设计，它速度快得多：仅一阶反射辐射就能确保平均精度优于1%。
