Whereas 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.
N2 - Plain Language Summary: Clouds constitute an important element of the climate system reflecting incoming solar radiation and emitting infra‐red radiation that heats the atmosphere. The net radiative impact of clouds however depends on many factors including their size. It is thus of prime importance to characterize the size of clouds, in particular convective clouds, and understand the underlying processes controlling them. In this study, a numerical model is used to simulate two convective situations at horizontal resolutions providing a fine description of cloud processes. After identifying individual clouds and calculating their size, statistical methods are employed to characterize the cloud size distributions. Depending on the situation, cloud size distributions are found to be best represented by either power‐laws with an exponential cutoff or exponential functions. Pure power‐laws, which constitute the most popular model used to represent cloud size distributions, are generally found to yield poorer fits. Finally, it is demonstrated that power‐laws in cloud size distributions emerge when individual cloud cores, that are exponentially distributed in size, are brought closer to each other and merge as the cloud ensemble organizes. N2 - Key Points: A combination of statistical methods is used to fit cloud size distributions from two simulated convective cloud ensembles.Depending on the situation, exponential distributions and power‐laws with an exponential cutoff may constitute superior alternatives to pure power‐laws.
The merging of individual cloud cores is found to control the emergence of power‐law cloud size distributions.