Analysis of Pressure Forcings for the Vertical Turbulent Fluxes in the Convective Boundary Layer at Gray Zone Resolutions

At kilometer and sub-kilometer resolutions, known as the numerical gray zone for boundary layer turbulence, the atmospheric boundary layer turbulence becomes partially resolved and partially subgrid-scale (SGS) in a numerical model, thus requiring scale-adaptive turbulence schemes. Such schemes are often built by modifying the existing parameterizations, either the planetary boundary layer (PBL) schemes or the large-eddy simulation (LES) closures, to produce the right SGS turbulent fluxes at gray zone resolutions. However, the underlying forcings responsible for the changes in the vertical turbulent fluxes are largely ignored in these approaches. This study follows the original approach of Wyngaard (2004) and analyzes the turbulent buoyancy and momentum flux budgets, to gain a better understanding of the variations of flux forcings at gray zone resolutions. The investigation focuses on the pressure covariance term, which is one of the most dominant terms in the budget equations. By using the coarse-grained LES of a dry convective boundary layer (CBL) case as reference, two widely-used pressure covariance models are evaluated and optimized across the gray zone resolution range. The optimized linear model is further evaluated a priori against another dry CBL case with a different bulk stability, and a shallow-cumulus-topped boundary layer case. The model applies well to both cases, and notably shows good performance for the cloud layer. Based on the analysis of the flux forcings and the optimized pressure model, a scale-adaptive turbulence model for the gray zone is derived from the steady-state flux budgets.