Fitting Cumulus Cloud Size Distributions From Idealized Cloud Resolving Model Simulations

Abstract

AbstractWhereas it is now widely accepted that cumulus cloud sizes are power‐law distributed, characteristic exponents reported in the literature vary greatly, generally taking values between 1 and >3. Although these differences might be explained by variations in environmental conditions or physical processes organizing the cloud ensembles, the use of improper fitting methods may also introduce large biases. To address this issue, we propose to use a combination of maximum likelihood estimation and goodness‐of‐fit tests to provide more robust power‐law fits while systematically identifying the size range over which these fits are valid. The procedure is applied to cloud size distributions extracted from two idealized high‐resolution simulations displaying different organization characteristics. Overall, power‐laws are found to be outperformed by alternative distributions in almost all situations. When clouds are identified based on a condensed water path threshold, using power‐laws with an exponential cutoff yields the best results as it provides superior fits in the tail of the cloud size distributions. For clouds identified using a combination of water content and updraft velocity thresholds in the free troposphere, no substantial improvement over pure power‐laws can be found when considering more complex two‐parameter distributions. In this context however, exponential distributions provide results that are as good as, if not better than power‐laws. Finally, it is demonstrated that the emergence of scale free behaviors in cloud size distributions is related to exponentially distributed cloud cores merging as they are brought closer to each other by underlying organizing mechanisms.