A Scale-Adaptive Turbulent Kinetic Energy Closure for the Dry Convective Boundary Layer

Turbulence parameterizations in current state-of-the-art atmospheric models are typically limited to a certain range of horizontal resolutions. Fine-scale fluid flow models employ a 3D scheme, while coarse-resolution weather and climate models rely on a 1D approach. This poses many physical and numerical challenges, as there are no established solutions for dealing with the so-called parameterization "gray zone". In this work, we propose a scale-adaptive turbulent kinetic energy closure that can be effectively used across a wide range of scales. Our approach utilizes a universal mixing length scale that naturally increases with horizontal grid size and saturates at the boundary layer height-scale. We test the new approach for grid lengths commonly used by different types of atmospheric models: from 50 m (for small-scale models that resolve most of the 3D flow), through the turbulent gray zone, up to 100 km (for large-scale models with essentially 1D subgrid-scale transport in the vertical). The results obtained for a set of idealized dry convective scenarios prove good scale-adaptivity of the proposed parameterization. The mean profiles of temperature and total vertical heat flux, as well as the entrainment velocity, all remain in good agreement across different scales. The transition across the gray zone is demonstrated through the partitioning between the model-resolved and the subgrid-scale transports as well as by documenting scale-dependence of the subgrid-scale turbulence source terms. We also address some remaining weaknesses of the scheme, in particular in the representation of the turbulent kinetic energy and its vertical distribution.