A Three Dimensional Planetary Boundary Layer Parameterization to Unify the Representation of Vertical and Horizontal Turbulent Mixing

Numerical weather prediction models do not provide a consistent representation of turbulent mixing. The vertical turbulent mixing is represented with one dimensional (1D) planetary boundary layer parameterizations (PBL). The representation of the horizontal mixing is based on different physical principles than the PBL parameterization and it is accounted for by the diffusion parameterization. The splitting is adequate for grid spacing of up to O(~10 km). However, at finer resolutions the assumption of horizontal homogeneity that supports 1D PBL representations progressively deteriorates. This is a limitation for simulations over mountainous regions since the large topographic heterogeneity requires fine grid spacing. Hence, we propose to unify the representation of horizontal and vertical mixing into one single three-dimensional (3D) PBL parameterization. The 3D PBL will ensure consistency in the representation of turbulent mixing.

The 3D PBL scheme is based on the level 2 turbulence model of Mellor and Yamada. The level 2 is based on algebraic relations to diagnose the turbulent fluxes. The divergence of these fluxes provides the tendencies associated with 3D turbulent mixing. The 3D PBL has been implemented in the Weather Research and Forecasting model.

An idealized numerical experiment has been designed to quantify the benefits of the 3D PBL. The idealized case prescribes a surface heat flux heterogeneity in the North to South direction and initial meridional winds. Under this set up, the solution is homogeneous in the North to South direction. Three simulations have been performed. The first one uses a standard 1D PBL parameterization in conjunction with horizontal diffusion whereas the second ones uses the 3D PBL parameterization. The two experiments use a grid spacing of 200 m. To complement these experiments, the third experiment is an ensemble of large-eddy simulations using 40 m grid cell size. It will be shown that accounting for the horizontal turbulent fluxes in the 3D PBL parameterization is necessary to ensure the homogeneous North-to-South solution. These results suggest that is possible to remove current inconsistencies in the treatment of vertical and horizontal mixing with a 3D PBL parameterization.