A Scale-Aware Treatment of Subgrid Mixing in the WRF Model for Renewable Energy Applications

We present a blending turbulence kinetic energy (BTKE) scheme to improve the representation of subgrid mixing at model grid spacing between 2000 and 200 m in the Weather Research and Forecasting (WRF) model. The BTKE scheme is derived from the three-dimensional subgrid turbulent kinetic energy (TKE) equation. It includes two governing equations for subgrid TKE on two scales: one is the generalized three-dimensional subgrid TKE equation suitable for large-eddy simulation (LES) and the other is the one-dimensional subgrid TKE equation suitable for describing vertical subgrid mixing on the vertical scales ranging from the atmospheric boundary layer (ABL) scale to the model vertical grid scale. The use of two TKE equations working at different scales allows us, in principle, to improve the fidelity of the parameterized turbulent mixing across spatial scales where typical approximations associated with either type of parameterization break down. This means that when the size of the horizontal grid spacing is so great that the subgrid mixing is dominant in the vertical direction, the large eddies on the conventional ABL scale, as simulated by the one-dimensional TKE equation, will do most of the subgrid mixing. On the other hand, as the horizontal grid-spacing approaches LES scales, the ABL-scale eddies are resolved and hence only the small eddies on the order of the LES grid spacing remain subgrid and responsible for the subgrid mixing. The outcome from the two TKE equations contribute differently to subgrid mixing throughout the ABL at both the mesoscale grid spacing for numerical weather prediction (NWP) and the LES grid spacing.