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

Abstract

The representation of deep convective clouds by convection‐permitting models could be improved by parametrizing the subgrid turbulent fluxes better. Following the work of Verrelle et al., a large‐eddy simulation (LES) of a population of convective clouds at 50‐m grid spacing was explored during the cloud life cycle to characterize the second‐order moment turbulent fluxes. The reference turbulence fields were deduced by coarse‐graining the LES outputs at horizontal grid resolutions of 500 m and 1 and 2 km. The ability of three parametrizations—the traditional K‐gradient model of Cuxart et al. (CBR), the Smagorinsky formulation, and the Moeng approach (MOENG) based on the horizontal gradients of the resolved variables—to reproduce the thermodynamical and dynamical fluxes was assessed in an offline configuration via a comparison with the reference fields. MOENG was the most appropriate scheme to represent the vertical and horizontal heat fluxes at all grid spacings in the clouds and their environment over the entire cloud life cycle, including the appropriate representation of countergradient areas. It also represented the vertical and horizontal moisture fluxes at 1‐km and 500‐m grid spacings best, while its advantage was reduced at a grid spacing of 2 km, as CBR performed slightly better for the statistical scores. MOENG was also able to represent the dynamical covariances well at grid spacings of 1 km and 500 m, even though the statistical scores were not as good as those obtained for the thermodynamical fluxes. The dynamical variances were well represented by CBR; however, for this offline evaluation, the subgrid turbulent kinetic energy, present in CBR formulations, is computed directly from the LES outputs, giving CBR an advantage over the two other diagnosed parametrizations. Also, the reference fluxes revealed an anisotropic deformation of turbulence throughout the troposphere, which was only captured by MOENG.