A Three Dimensional PBL Parameterization for Simulations of the Flow over Complex Terrain: Implementation and Validation over the Big Southern Butte using the Weather Research and Forecasting Model

Advances in computational resources make possible the use of numerical weather predication models at high horizontal resolutions O[~100 m]. However, turbulence parameterizations implemented in current planetary boundary layer (PBL) schemes are based on the assumption that turbulent motions are statistically homogeneous in horizontal planes over a grid cell. Hence, current PBL parameterizations only account for one-dimensional (1D) mixing resulting from vertical gradients in turbulent fluxes. Although the assumption of horizontal homogeneity can be argued to be valid at grid spacing higher than several kilometers, it breaks down for grid cells of smaller dimension limiting the potential benefit of fine grid spacing over complex terrain regions, for instance. We therefore propose developing a fully three-dimensional (3D) PBL scheme that accounts for horizontal and vertical gradients in turbulent fluxes.

The proposed 3D PBL scheme is based on the algebraic turbulence model developed by Mellor and Yamada (1982). The development proceeds in steps from an algebraic model that includes an equation to diagnose the turbulent kinetic energy (TKE) to a higher level model with a prognostic equation for TKE and potential temperature variance. At each step of development we compare the performance of the 3D PBL scheme to existing 1D PBL parameterizations implemented in WRF as well as large-eddy simulations (LES). The validation uses data from a field study in Idaho carried out in 2010 and centered over an isolated mountain, the Big Southern Butte. Nested mesoscale simulations are carried out using the innermost nest with grid spacing of 111 m with both 1D and 3D PBL schemes while nested WRF-LES are carried with grid spacing of ~50 m. The results of this analysis are used to assess the performance of the new 3D PBL schemes in complex terrain where the assumption of horizontal homogeneity is violated.