The Overlapping of Cloud Layers in Shortwave Radiation Parameterizations

Using the shortwave radiation scheme of Fouquart and Bonnel that accounts for scattering and absorption by gases and cloud particles, we study the effect of varying the assumption for the overlap of partially cloudy layers, and the resultant impact upon the heating rate profile, planetary albedo, net flux at the surface, and atmospheric net absorption. In this study, we consider the maximum, minimum, and random overlap assumptions and a radically simple scheme to approximate the radiative effects of a random overlapping of clouds. This simple scheme involves linear combinations of clear and cloudy reflectivities and transmissivities within a layer, and gives, respectively, fluxes and heating rates with maximum differences of 5% and 0.1 K day−1 compared to similar quantities obtained from a full calculation assuming a random overlapping of cloud layers. This former approach, however, is much more time efficient (five times faster for a 3-cloud atmosphere, three times faster in a full-size GCM). Compared to the random assumption, the maximum overlap assumption gives smaller planetary albedo and larger net flux at the ground, whereas larger planetary albedo and smaller net flux at the ground result from the minimum overlap assumption. These differences tend to smooth out for larger values of the surface reflectivity. Systematic difference in the radiative forcings of a GCM due to these different cloud overlap assumptions largely vary with the cloud generation scheme.