Unifying Vertical Turbulent Mixing and Horizontal Diffusion into a Three Dimensional Planetary Boundary Layer Parameterization

Numerical weather prediction models do not provide a consistent representation of turbulent mixing. The effects of vertical turbulent mixing are represented by one dimensional (1D) planetary boundary layer parameterizations (PBLs). The horizontal mixing is represented based on different physical principles by the diffusion parameterizations. This splitting is adequate at grid spacing of O(~10 km) and coarser. However, at finer resolutions, including the sub-kilometer scale, the assumption of horizontal homogeneity that supports 1D PBL representations no longer holds. We therefore propose to unify the representation of horizontal and vertical mixing, based on first principles, into one single three-dimensional (3D) PBL parameterization. The 3D PBL scheme will ensure consistency in the representation of turbulent effects.

The 3D PBL parameterization is based on the turbulence model of Mellor and Yamada. Our implementation in the Weather Research and Forecasting model uses an algebraical model (Level 2) to diagnose the turbulent fluxes. The divergence of these fluxes provides the tendencies related to 3D turbulent mixing of the resolved variables.

An idealized numerical experiment has been designed to quantify the benefits of the 3D representation. The case prescribes a surface heat flux heterogeneity in the North to South direction and initial meridional winds. Under this set up, the solution should be homogeneous in the North to South direction. Three simulations are performed. The first one uses a standard 1D PBL parameterization in conjunction with horizontal diffusion. The second experiment uses our 3D PBL parameterization. The two experiments use a grid spacing of 200 m. To complement the previous simulations, the third experiment consists of 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.