Key Elements of Turbulence Closures for Simulating Deep Convection at Kilometer‐Scale Resolution

Abstract

Kilometer‐scale grid spacing is increasingly being used in regional numerical weather prediction and climate simulation. 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‐Väisälä frequency ( Nm2). With this formulation in cloudy regions, eddy diffusivity can be excessively increased in “unstable” regions, which produce downward (downgradient) heat flux in a conditionally unstable environment leading to destabilization and further amplification of eddy diffusivities. A more appropriate criterion based on saturation mixing ratio helps eliminate this problem. However, shallow clouds cannot be simulated well in any case at 1‐km resolution with the traditional models, whereas DRM allows for countergradient heat flux for both shallow and deep convection and predicts the distribution of clouds and fluxes satisfactorily. This is because DRM employs an eddy diffusivity model that is dynamically adjusted and a reconstruction approach that allows countergradient fluxes.

Evaluation of turbulence parametrizations in convective clouds and their environment based on a large‐eddy simulation

“…() and Shi et al . () have shown that thermodynamical countergradient areas also exist within convective clouds in simulations at kilometre‐scale resolutions and cannot be represented by traditional eddy‐diffusivity schemes.…”

“…These areas, referred to as "countergradient areas", are due to nonlocal turbulence effects. Verrelle et al (2017) and Shi et al (2019) have shown that thermodynamical countergradient areas also exist within convective clouds in simulations at kilometre-scale resolutions and cannot be represented by traditional eddy-diffusivity schemes.…”

Crossing Multiple Gray Zones in the Transition from Mesoscale to Microscale Simulation over Complex Terrain

“…The DRM [82] is a more recent LES closure with different design, which has been applied to simulations of clouds in the terra incognita [60,83]. It employs explicit filtering and reconstruction, recognizing the different effects of the explicit LES filter and grid discretization.…”

“…where the tilde denotes the effect of discretization, the overline denotes the explicit filter, and star denotes reconstructed variables. The SGS component still has an eddy-diffusivity based form, but a dynamic eddy diffusivity model [84] is used and an anisotropic version has been developed [83]. One advantage of the dynamic model is that it allows the eddy diffusivity for scalars to be independent of the eddy viscosity.…”

“…The DRM was tested over Askervein Hill and was able to reproduce mean profiles and intermittent recirculation in the lee of the hill, which was not captured by traditional models [85]. Shi et al [60,83] examined the role of DRM in producing backscatter in shallow and deep clouds and found improved simulation results at gray zone resolutions. The mixed model tested by Moeng et al [86], which is a simplified version of the zero-order DRM, was applied to simulations of deep convection in the terra incognita and also showed good performance [59].…”