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

Accurate representation of heterogeneous surface layer processes is essential for numerical weather prediction (NWP) with sub-kilometer grid spacing. 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. The 3DPBL uses the horizontal and vertical turbulent fluxes diagnosed from the flow gradients to handle the turbulent mixing. These gradients cannot be directly calculated near the surface. Therefore, the 3DPBL parameterization is coupled herein to a second-order diagnostic model of the three-dimensional turbulent fluxes in the surface layer. Several adjustments to the original Mellor-Yamada model, including a modified length scale, were introduced to capture flow anisotropy and dependence on stability conditions. The results are compared against data from the Wind Forecast Improvement Project 2 (WFIP2) for different weather regimes and using different grid resolutions to examine stability and scale dependency.