Power-Law Scaling in the Internal Variability of Cumulus Cloud Size Distributions due to Subsampling and Spatial Organization

Abstract

In this study, the spatial structure of cumulus cloud populations is investigated using three-dimensional snapshots from large-domain LES experiments. The aim is to understand and quantify the internal variability in cloud size distributions due to subsampling effects and spatial organization. A set of idealized shallow cumulus cases is selected with varying degrees of spatial organization, including a slowly organizing marine precipitating case and five more quickly organizing diurnal cases over land. A subdomain analysis is applied, yielding cloud number distributions at sample sizes ranging from severely undersampled to nearly complete. A strong power-law scaling is found in the relation between cloud number variability and subdomain size, reflecting an inverse linear relation. Scaling subdomain size by cloud size yields a data collapse across time points and cases, highlighting the role played by cloud spacing in controlling the stochastic variability. Spatial organization acts on top of this baseline model by increasing the maximum cloud size and by enhancing the variability in the number of smallest clouds. This reflects that the smaller clouds start to live on top of larger-scale thermodynamic structures, such as cold pools, which favor or inhibit their formation. Compositing all continental cumulus cases suggests the existence of a prototype diurnal time dependence in the spatial organization. A simple stochastic expression for cloud number variability is proposed that is formulated in terms of two dimensionless groups, which allows objective estimation of the degree of spatial organization in simulated and observed cumulus cloud populations.

Impact of resolution on large-eddy simulation of midlatitude summertime convection

“…Our study confirms this hypothesis, with the addition that tracking objects in time can give valuable information on the tendency of convection to form clusters. Another possible improvement could be new indices that take into account both ends of the size distribution function separately: Neggers et al (2019) have shown that spatial organization affects both ends of the cloud size PDF, but in different ways: while the number of large clouds increases, there is an enhanced variability in the number of small clouds, especially shallow cumulus clouds below the 1 km scale. However, in our study, we are mainly concerned with deep precipitating convection where such small cloud sizes are neglected.…”

“…Unlike SCAI and COP, which mainly quantify the degree of clustering, the NN-based organization index I org (Tompkins and Semie, 2017) is able to distinguish between three types of spatial distribution: clustered, regular, and random. In this approach, we treat objects as discs (similar to Nair et al, 1998), and we compute the cumulative distribution function of the NN edge-to-edge distances (NNCDF) and compare it to the NNCDF of theoretical randomly distributed objects over the same domain. The theoretical NNCDF is approximated by bootstrapping, in which a random number of objects with the observed size distribution are randomly placed over the domain (Weger et al, 1992;Nair et al, 1998).…”

“…In this approach, we treat objects as discs (similar to Nair et al, 1998), and we compute the cumulative distribution function of the NN edge-to-edge distances (NNCDF) and compare it to the NNCDF of theoretical randomly distributed objects over the same domain. The theoretical NNCDF is approximated by bootstrapping, in which a random number of objects with the observed size distribution are randomly placed over the domain (Weger et al, 1992;Nair et al, 1998). We perform 100 simulations and compare the observed NNCDF to the 100 theoretical NNCDFs in a graph.…”

“…Analyses of climate change projections have indicated that while the thermodynamic contribution to the intensification of extreme precipitation is expected to be relatively homogeneous globally, there may be strong regional differences in the dynamic contribution due to changes in circulation patterns (Emori and Brown, 2005;Pfahl et al, 2017;Norris et al, 2019). CRMs should therefore also be able to simulate the time evolution of convective precipitation events and their interaction and organization among each other in a realistic way, to correctly represent their sensitivity to 2 m air temperature.…”

Responses to referee comments, Atmos. Chem. Phys. Discuss. acp-2020-336

“…Satellite observations (e.g., Zhao and Di Girolamo, 2007) and LES studies (e.g., Neggers et al, 2003) have shown that in shallow-cumulus cloud fields, the vast majority of clouds are small, and larger clouds are few and far-between. The cloud-size distribution has been variously characterized by lognormal, exponential, or power-law functions (e.g., Neggers et al, 2019). The R eff distributions at the cloud-layer midpoints for the layer-depth sensitivity experiments of Sect.…”