Parameterization of Fractional Cloud Amounts in Climatic Models: The Importance of Modeling Multiple Reflections

Abstract

The neglect of multiple reflections between clouds and the earth's surface leads to an underestimate of the downward flux of solar radiation reaching the earth's surface. This underestimate is most pronounced in regions of persistent cloud cover and high surface albedos?the snow- and ice-covered regions of the high latitude zone, for example. Since the rate of snow melt (and thus snow albedo) depends upon the downward flux, neglect of multiple reflection is most serious in climatic models that predict snow and ice cover. Two simple algebraic expressions to account for multiple reflections in climate models are given and are shown to be limiting cases of a more general formula. Since this more general formula depends on the spatial distribution of subgrid-scale cloud cover amounts, an unambiguous definition of cloud amount over a GCM-scale grid square cannot be given, even if perfect knowledge of the optical properties of the subgrid-scale clouds were in hand. However, the uncertainties in downward solar flux at the earth's surface (or the albedo of the combined cloudiness-surface system) introduced by lack of knowledge of the two-dimensional geometric distribution of fractional cloud cover are shown to be generally less than 10%, most likely less than the errors in predicting cloud cover amounts or from the neglect of three-dimensional effects of finite-sized clouds.