Theoretical development of Monte Carlo codes for modeling cumulus cloud fields

Reflected fluxes are calculated for stratocumulus cloud fields as a function of skycover, cloud aspect ratio, and cloud shape. Cloud liquid water volume is held invariant as cloud shape is varied so that the results can be utilized more effectively by general circulation models and climate models. On the basis of required accuracy in the Earth Radiation Budget Experiment program, an order of magnitude value of 10 W/sq m is used to estimate significant differences between plane parallel and broken cloudiness. This limit is exceeded for cloud covers between 10% and 90%, indicating that plane paralel calculations are not satisfactory at most values of cloud cover. The choice of cloud shape also leads to large differences in reflected fluxes. These differences are traced to the anisotropic intensity pattern out the cloud sides, to the size and shape of the holes between clouds, and to variations in cloud area as viewed from the solar direction. An empirical relationship for effective cloud cover is given at solar zenith angle of theta = 60 deg. This relationship allows for the relatively accurate (delta F = 10 - 15 W/sq m.) computation of broken cloud field reflected fluxes from plane parallel calculations.