Modeling the Shallow Cumulus-topped Boundary Layer at Gray Zone Resolutions

This study investigates simulated fair weather shallow cumulus-topped boundary layer (SCTBL) on kilometer and sub-kilometer scale horizontal resolutions, also known as the numerical gray zone of boundary layer turbulence. Based on a priori analysis of a simulated classic SCTBL with large-eddy simulation, its gray zone scale is determined. The dominant length scale of the cloud layer (CL) is found to be the effective cloud diameter, while that of the underlying mixed layer (ML) is the size of organized convection. The two scales are linked by a simple geometric argument based on vertically coherent updrafts, and are quantified through spectral analysis. Comparison to a simulated dry convective boundary layer (CBL) further reveals that the ML gray zone scale does not differentiate between clear and cloudy conditions with the same bulk stability. A posteriori simulations are then performed over a range of resolutions to evaluate the performance of a recently developed scale-adaptive planetary boundary layer (PBL) scheme. Simulation results suggest indifferences to the scale-adaptive capability. Detailed analyses of flux partition reveal that, in the absence of a shallow cumulus scheme, overly-energetic resolved fluxes develop in the CL at gray zone and coarse resolutions, and are responsible for over-predicted resolved convection in the ML. These results suggest that modifications are needed for scale-adaptive PBL schemes under shallow cumulus-topped conditions.