Evaluation of Statistical Distributions for the Parametrization of Subgrid Boundary-Layer Clouds

In numerical weather prediction and climate models, planetary boundary-layer (PBL) clouds are linked to subgrid-scale processes such as shallow convection. A comprehensive statistical analysis of large-eddy simulations (LES), obtained for warm PBL cloud cases, is carried out in order to characterize the distributions of the horizontal subgrid cloud variability. The production of subgrid clouds is mainly associated with the variability of the total water content. Nevertheless, in the case of PBL clouds, the temperature variability cannot be completely discarded and the saturation deficit, which summarizes both temperature and total water fluctuations, provides a better representation of the cloud variability than the total water content. The probability density functions (PDFs) of LES saturation deficit generally have the shape of a main asymmetric bell-shaped curve with a more or less distinct secondary maximum specific to each type of PBL clouds. Unimodal theoretical PDFs, even those with a flexible skewness, are not sufficient to correctly fit the LES distributions, especially the long tail that appears for cumulus clouds. They do not provide a unified approach for all cloud types. The cloud fraction and the mean cloud water content, diagnosed from these unimodal PDFs, are largely underestimated. The use of a double Gaussian distribution allows correction of these errors on cloud fields and provides a better estimation of the cloud-base and cloud-top heights. Eventually, insights for the design of a subgrid statistical cloud scheme are provided, in particular a new formulation for the weight of the two Gaussian distributions and for the standard deviation of the convective distribution.