On the relationship between clear-sky planetary and surface albedos: a parameterization for simple energy balance climate models

In simple energy balance climate models all physical and dynamical processes are parameterized in terms of the single unknown variable: the surface temperature. To simulate the ice-albedo feedback, the surface albedo is usually assumed to be a function of surface temperature. But to compute the absorbed solar radiation in such models one requires the top-of-the atmosphere albedo: the planetary albedo. In the present study, a simple linear relationship is derived between planetary albedo and surface albedo for the case of clear skies. The relationship is based upon a regression equation derived from simulations and has a standard error of estimate of 0.028. The estimation of planetary albedo from surface albedo is checked by comparing zonally averaged clear-sky planetary albedos, estimated from zonally averaged surface albedos, to satellite determinations of zonally averaged minimum albedos for monthly mean conditions. The minimum albedos are assumed to be representative of the clear-sky planetary albedos. The results show root-mean square differences of 0.05 between the estimated clear-sky planetary albedos and the minimum albedos.More accurate relationships can be obtained if one uses an additional parameter - the solar zenith angle. In this case, the standard errors of estimate are reduced to 0.017 for a zenith angle of 0°, 0.018 for a zenith angle of 60° and 0.021 for a zenith angle of 85°.