Variations of Subgrid-Scale Turbulent Fluxes in the Dry Convective Boundary Layer at Gray Zone Resolutions

In the numerical gray zone of the convective boundary layer (CBL), the horizontal resolution is comparable to the size of organized convective circulation. As turbulence becomes partially resolved, gridscale variations of the subgrid-scale (SGS) turbulent fluxes become significant compared to the mean. Previously, such variations have often been ignored in scale-adaptive planetary boundary layer (PBL) schemes developed for the gray zone. This study investigates these variations with respect to height and resolution based on large-eddy simulations. It is found that SGS fluxes exhibit maximum variability at the center of the gray zone, where the resolved and the SGS mean fluxes are approximately equal. A simple analytical model is used to associate such characteristic variations to the nonlinear interactions of the dominant energy-containing mode of CBL turbulence. Examination of the horizontal distribution of the SGS fluxes reveals their preferential location over the updraft edges surrounding the core. A priori analysis further suggests the ability of a scale-similarity closure to reproduce the unique spatial patterns of the SGS fluxes at gray zone resolutions. Four scale-adaptive PBL schemes are evaluated focusing on their representations of the modeled SGS flux variability. Their shared shortcomings as a result of their gradient diffusion-based formulation are exposed. This study suggests that a mixed model consisting of a scale-adaptive PBL scheme to represent the mean, and a scale-similarity component to account for gridscale variability to be advantageous for the gray zone. Significance StatementAs Gresho and Lee's famous quote on numerical schemes goes, "Don't suppress the wiggles. They're telling you something!" In the numerical gray zone, where the grid spacing is comparable to the characteristic length scale of the flow, turbulence is partially resolved. The "wiggles" (or gridscale variability) reflecting the resolved heterogeneity of turbulent fluxes is an outstanding feature of the gray zone. However, they are often overlooked as error bars to the mean. This study uncovers the significance of these error bars, and characterizes and explains their variations with height and grid spacing. A suitable model that captures such variations is investigated to help build better planetary boundary layer schemes.