Scale-Similarity Subgrid-Scale Turbulence Closure for Supercell Simulations at Kilometer-Scale Resolutions: Comparison Against a Large Eddy Simulation

In numerical simulations of deep convection at kilometer-scale horizontal resolutions, in-cloud subgrid-scale (SGS) turbulence plays an important role in the transport of heat, moisture and other scalars. By coarse-graining a 50 m high-resolution large-eddy simulation (LES) of an idealized supercell storm to kilometer-scale grid spacings ranging from 250 m to 4 km, the SGS fluxes of heat, moisture, cloud and precipitating water contents are diagnosed a priori. The kilometer-scale simulations are shown to be within the “gray zone” as in-cloud SGS turbulent fluxes are comparable in magnitude to the resolved fluxes at 4 km spacing, and do not become negligible until ~500 m spacing. Vertical and horizontal SGS fluxes are of comparable magnitudes, both exhibit non-local characteristics associated with deep convection as opposed to local gradient-diffusion type of turbulent mixing. As such, they are poorly parameterized by eddy-diffusivity-based closures. To improve the SGS representation of turbulent fluxes in deep convective storms, a scale-similarity LES closure is adapted to kilometer-scale simulations. The model exhibits good correlations with LES-diagnosed SGS fluxes, and is capable of representing counter-gradient fluxes. In a posteriori tests, supercell storms simulated with the refined similarity closure model at kilometer-scale resolutions show better agreement with the LES benchmark in terms of SGS fluxes than those with a turbulent-kinetic-energy-based gradient-diffusion scheme. However, it underestimates the strength of updraft, which is suggested to be a consequence of the model effective resolution being lower than the native grid resolution.