Analysis of albedo versus cloud fraction relationships in liquid water clouds using heuristicmodels and large eddy simulation

The relationship between the albedo of a cloudy scene A and cloud fraction f_c is studied with the aid of heuristic models of stratocumulus and cumulus clouds. Existing work has shown that scene albedo increases monotonically with increasing cloud fraction but that the relationship varies from linear to superlinear. The reasons for these differences in functional dependence are traced to the relationship between cloud deepening and cloud widening. When clouds deepen with no significant increase in f_c (e.g., in solid stratocumulus), the relationship between A and f_c is linear.When clouds widen as they deepen, as in cumulus cloud fields, the relationship is superlinear. A simple heuristic model of a cumulus cloud field with a power law size distribution shows that the superlinear A-f_c behavior is traced out either through random variation in cloud size distribution parameters or as the cloud field oscillates between a relative abundance of small clouds (steep slopes on a log-log plot) and a relative abundance of large clouds (flat slopes). Oscillations of this kind manifest in large eddy simulation of trade wind cumulus where the slope and intercept of the power law fit to the cloud size distribution are highly correlated. Further analysis of the large eddy model-generated cloud fields suggests that cumulus clouds grow larger and deeper as their underlying plumes aggregate; this is followed by breakup of large plumes and a tendency to smaller clouds. The cloud and thermal size distributions oscillate back and forth approximately in unison.