Fitting Cumulus Cloud Size Distributions From Idealized Cloud Resolving Model Simulations

Abstract

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.

Spatial Dispersion and Statistical Description of Organized Cumulus Cloud Ensembles in Radiative Convective Equilibrium

“…In particular, as the system of points distributed along the Voronoi cell edges approaches a critical threshold, the cluster size distribution is expected to develop a power‐law tail. This analogy, may provide a credible explanation for the fact that power‐law cloud size distributions have often been found in convective cloud ensembles (Benner & Curry, 1998; Heus & Seifert, 2013; Neggers et al., 2003; Savre & Craig, 2023a; van Laar et al., 2019; Welch et al., 1988), even when the cloud fraction is much smaller than the typical 2D continuum percolation threshold (∼0.676 for disks). This idea is in particular supported by the recent results presented by Savre and Craig (2023a), in which power‐law cloud size distributions were shown to emerge in cumulus cloud ensembles when individual cloud cores start to cluster and eventually merge to form bigger clouds.…”

The Role of Passive Cloud Volumes in the Transition From Shallow to Deep Atmospheric Convection

“…As can be seen in Figures 2g and 2h, interaction with a large passive cloud can lead to deep convection even for the very small plumes, whereas the increase in CAPE does not seems to be very important. Note that while the red curve in Figure 2 depends on the choice of mixing length L , the black line is not dependent on this choice, but this situation is conditioned by the increase in the passive clouds dimensions, which has been shown to occur during the transition (Savre & Craig, 2023).…”

“…However, if this is the case, and the interaction only leads to a non‐precipitating shallow cumulus cloud, then the interaction might also lead to a passive cloud with a larger radius at a later time, as schematically presented in Figure 2i. Savre and Craig (2023) analyzed the clouds horizontal dimensions for the Large–scale Biosphere–Atmosphere (LBA) transition case (Grabowski et al., 2006), showing that, indeed, the radii of the clouds—identified based on a threshold for the condensed water path—does increase by nearly an order of magnitude during the transition, while the radii of the active plumes—clouds identified based on the updraft criteria—only show a slight increase (see Figure 2 of their study). The increase of the cloud horizontal dimension could be attributed to a process of merging between the clouds.…”