The effects of subgrid-scale (SGS) condensation and transport become more important as the grid spacings increase from those typically used in large-eddy simulation (LES) to those typically used in cloudresolving models (CRMs). Incorporation of these SGS effects can be achieved by a joint probability density function approach that utilizes higher-order moments of thermodynamic and dynamic variables. This study examines how well shallow cumulus and stratocumulus clouds are simulated by two versions of a CRM implemented with low-order (1.5-order) and third-order turbulence closures (LOC and TOC). Resolution sensitivities of the closure are studied by refining the grid spacing from control simulation (with standard CRM grids of 4 km) to simulations with much finer meshes in the horizontal.
In our simulations cumulus clouds are mostly produced through SGS transport processes while stratocumulus clouds are produced through both SGS and resolved-scale processes in the TOC version of the CRM at standard resolution. In contrast, the LOC version of the CRM requires resolved-scale circulations to produce both cumulus and stratocumulus clouds, as SGS transports within cloud layer remain small in this model. The mean profiles of thermodynamic variables, cloud fraction and liquid water content exhibit significant differences between the two versions of the CRM, with the TOC results agreeing better with the LES than the LOC results. The characteristics, temporal evolution and mean profiles of shallow cumulus and stratocumulus clouds are weakly dependent upon the horizontal grid spacing used in the TOC CRM. However, the ratio of the SGS to resolved-scale fluxes becomes smaller as the horizontal grid spacing decreases. The subcloud-layer fluxes are mostly due to the resolved scales when horizontal grid spacings approach the depth of this layer. The overall results of the TOC simulations suggest that the 1-km grid spacing is a good choice for CRM simulation of shallow cumulus and stratocumulus.