Key elements of turbulence closures for simulating deep convection at kilometer-scale resolution

This resolution range is in the terra incognita, where energetic eddies are partially resolved and turbulence parameterization is a challenge. The Smagorinsky and turbulence kinetic energy 1.5-order models are commonly used at this resolution range, but, as traditional eddy-diffusivity models, they can only represent forward-scattering turbulence (downgradient fluxes), whereas the dynamic reconstruction model (DRM), based on explicit filtering, permits countergradient fluxes.

Here we perform large-eddy simulation of deep convection with 100-m horizontal grid spacing and use these results to evaluate the performance of turbulence schemes at 1-km horizontal resolution. The Smagorinsky and turbulence kinetic energy 1.5 schemes produce large-amplitude errors at 1-km resolution, due to excessively large eddy diffusivities attributable to the formulation of the squared moist Brunt-Vaisala frequency (N-m(2)).