Abstract: A retrieval algorithm for calculating surface bi-directional reflectance from satellite measurements is developed with the matrix operator method. In method is applied in the matrix operator method, which makes the mathematical derivation of the explicit expression simple and straightforward by exactly decoupling the surface reflection term from the radiance and the atmospheric terms. It is shown that the explicit expression is very stable mathematically. Sensitivity test show that the mean random error of 10 percent in the aerosol profile has little effect on the retrieval of the surface bi-directional reflectance. The retrieval error can reach about 2 percent on average when maximum random error of 5 percent is introduced in the satellite measurements. The present method is limited to the clear-sky case. An application is carried out based on the field of radiance, which were made with the Earth radiation budget (ERB) instruments on the satellite Nimbus 7. The retrieved bi-directional reflectance from the ERB measurements for desert surface, land surface, and snow surface show the anisotropic behaviors of the surface reflection. They all have the large anisotropy for large viewing angles. The snow surface has a strong anisotropy of reflection in the forward direction, indicating somehow mirror reflection. !19
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