Analytic forms of bidirectional reflectance functions for application to Earth radiation budget studies

Abstract

Analytic expressions for the bidirectional reflectance functions are formulated and fit to the Earth Radiation Budget Experiment (ERBE) operational models, which were developed using Nimbus 7 ERB data. The analytic bidirectional reflectance distribution functions (BRDFs) are based on theoretical considerations and are functions of viewing geometry and scene type. The models consist of a Rayleigh scattering term and a term for scattering due to clouds and surface. The darkness of the ocean permits the empirical determination of the Rayleigh component of scattering from the atmosphere. The models have the advantage that they are smooth in terms of view and solar zenith angles and relative solar azimuth angle and satisfy reciprocity. Results are presented for the ERBE scene types. The analytic functions closely model the reflectances in the forward scatter direction, but in the backscatter direction, the analytic models are slightly more limb brightened than the ERBE operational models. The model was also fit to the Dlhopolsky/Cess BRDF for clear ocean, which provides a finer angular resolution than the ERBE BRDFs. The results of this study provide a set of BRDFs for ERBE scene types in terms of a set of simple equations and few coefficients for each scene type. These models can be used for mission planning and interpretation of data from future Earth radiation budget missions such as the Clouds and Earth's Radiant Energy System (CERES).