Scale-dependent instabilities in the model gray zone

Atmospheric processes such as convection and boundary layer turbulence are modeled differently at the large and small scales. Convection, for example, is often represented with mass flux parameterizations in mesoscale or general circulation models (GCMs), but is resolved in cloud-resolving models (CRMs) or large-eddy simulations (LES). As resolution for these models improves, previously parameterized processes become partially resolved on the grid. At these grid spacings, neither the parameterization nor the LES closure is appropriate. In light of the modeling difficulties, the model “gray zone” is named to describe the region where the grid resolution is similar to the dominant length scale of an atmospheric process. 

One of the difficulties of gray zone modeling is flow instabilities. We examine thermal and shear instability mechanisms in their respective model gray zone. The former represents daytime boundary layer convection, and the latter is typical for triggering nighttime turbulent events. The nature of both marginal instability states suggests that in the gray zone, the onset of vigorous turbulent mixing as well as the most unstable modes are grid-dependent. While first order mean profiles of LES, mesoscale, and gray zone simulations converge, higher order statistics such as variance and skewness from the gray zone simulations may diverge from physically realistic values. Linear instability theories are used to explain the observed unphysical behavior of gray zone results. Such dynamical difficulties must be considered when building scale-aware parameterizations for high-resolution mesoscale or GCMs, or subgrid-scale closures for coarse resolution CRMs or LES.