Coupling diffuse sky radiation and surface albedo

New satellite instruments have been delivering a wealth of information regarding land surface albedo. This basic quantity describes what fraction of solar radiation is reflected from the earth's surface. However, its concept and measurements have some ambiguity resulting from its dependence on the incidence angles of both the direct and diffuse solar radiation. At any time of day, a surface receives direct radiation in the direction of the sun, and diffuse radiation from the various other directions in which it may have been scattered by air molecules, aerosols, and cloud droplets. This contribution proposes a complete description of the distribution of incident radiation with angles, and the implications in terms of surface albedo are given in a mathematical form, which is suitable for climate models that require evaluating surface albedo many times. The different definitions of observed albedos are explained in terms of the coupling between surface and atmospheric scattering properties. The analytical development in this paper relates the various quantities that are retrieved from orbiting platforms to what is needed by an atmospheric model. It provides a physically simple and practical approach to evaluation of land surface albedo values at any condition of sun illumination irrespective of the current range of surface anisotropic conditions and atmospheric aerosol load. The numerical differences between the various definitions of albedo for a set of typical atmospheric and surface scattering conditions are illustrated through numerical computation.