Analysis of Albedo versus Cloud Fraction Relationships in Liquid Water Clouds Using Heuristic Models and Large-Eddy Simulation

Description

The relationship between the albedo of a cloudy scene and the cloud fraction has been shown to be a useful framework for understanding the various factors that influence the cloud radiative effect. Here we study this relationship 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 exponential. 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 cloud fraction (e.g., in solid stratocumulus) the relationship between scene albedo and cloud fraction is linear. When clouds widen as they deepen, as in cumulus cloud fields, the relationship is approximately exponential. A simple heuristic model of a cumulus cloud field with a power law size distribution shows that the exponential scene albedo versus cloud fraction 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 negative 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 parameters of the power law fits to the cloud size distributions 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.