Diagnosis of second-order turbulent properties of the surface layer for three-dimensional flow based on the Mellor–Yamada model

NWP models such as the Weather Research and Forecasting (WRF) Model generally use second-moment turbulent models for parameterizing the planetary boundary layer (PBL). The most common parameterizations follow Mellor-Yamada and account for the vertical turbulent mixing only; that is, standard PBL parameterizations are one-dimensional (1DPBL).

The horizontal diffusion of momentum is parameterized based on Smagorinsky's model for numerical stability. Although the combination of 1DPBL and 2D Smagorinsky parameterizations is successful at coarse grid resolutions (e.g., grid-size dx similar to 12-2 km), it does not represent well the effect of horizontal turbulence as gridcell size decreases (<1 km). To reconcile the representation of vertical and horizontal turbulent mixing, a full three-dimensional PBL scheme (3DPBL) based on the Mellor-Yamada model was implemented in WRF.