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

A pragmatic scale-adaptive turbulent kinetic energy (TKE) closure is proposed to simulate the dry convective boundary layer for a variety of horizontal grid resolutions: from 50 m, typical of large-eddy simulation models that use three-dimensional turbulence parameterizations/closures, up to 100 km, typical of climate models that use one-dimensional turbulence and convection parameterizations/closures. Since parameterizations/closures using the TKE approach have been frequently used in these two asymptotic limits, a simple method is proposed to merge them with a mixing-length-scale formulation for intermediate resolutions. This new scale-adaptive mixing length naturally increases with increasing grid length until it saturates as the grid length reaches mesoscale-model resolution. The results obtained using this new approach for dry convective boundary layers are promising. The mean vertical profiles of potential temperature and heat flux remain in good agreement for different resolutions. A continuous transition (in terms of resolution) across the gray zone is illustrated through the partitioning between the model-resolved and the subgrid-scale transports as well as by documenting the transition of the subgrid-scale TKE source/sink terms. In summary, a natural and continuous transition across resolutions (from 50 m to 100 km) is obtained, for dry convection, using exactly the same atmospheric model for all resolutions with a simple scale-adaptive mixing-length formulation.