Quantifying and improving sub-grid diffusion in the boundary-layer grey zone

Abstract

Operational high-resolution numerical weather prediction models are now able to partially resolve turbulent motions due to increased computing power. The partitioning of resolved and parametrized fluxes becomes important in the representation of turbulent transfer that determines the state of the atmospheric boundary layer. In this study, successive simulations of a convective boundary layer using the Met Office Large Eddy Model from the large-eddy simulation to the mesoscale limit are compared with the corresponding coarse-grained fields to examine model behaviour over the grey zone. The differences in the turbulent kinetic energy partitioning between coarse-grained (reference) and actual fields are identified and used to quantify sub-grid diffusion in the grey zone under different atmospheric forcings and surface heat flux. It is shown that the excessive mixing due to the large values of mixing length at coarse resolutions results in the cut-off of resolved turbulence in the grey zone. The damping of resolved motions comes earlier for wind shear runs. In contrast, coarse-grained fields exhibit a smooth transition of the resolved turbulent kinetic energy across the scales. Decreasing numerical dissipation through the sub-grid scheme leads to the increase of resolved turbulence, but fails to reproduce the reference transition pattern that imposes some physical limitations to the partially resolved turbulence simulations. Pragmatic blending of mixing length values maintains a more realistic turbulent kinetic energy transition from fine to coarse resolutions and potential temperature profiles in the grey zone. Bounding vertical diffusion to its effective values, an approach based on maintaining inherent properties of the flow across the scales, is able to match the coarse-grained fields from the highly resolved to the almost unresolved state, regardless of the forcing. Finally, the complexity of modelling in the grey zone is exhibited in the dependence of turbulence onset on time and vertical resolution.