Developing a parameterization schame for the gray zone of the atmospheric boundary layer

Abstract:

There is an intermediate model resolution in which neither the Reynolds Averaged Navier-Stokes Simulation (RANS) nor the Large-Eddy Simulation (LES) is applicable in the atmospheric boundary layer. This model resolution is termed "terra incognita" by Wyngaard (2004) or, more generally, "gray zone" in the atmospheric boundary layer, and it corresponds to several hundred meters for a typical convective boundary layer (Honnert et al. 2011). Developing a turbulence scheme applicable to the gray zone is required practically because a numerical weather prediction (NWP) model with such the resolution will be achieved in the near future.
To explore a parameterization scheme for the gray zone, we focus on the length scales associated with the TKE dissipation and the eddy viscosity. First, dependence of these length scales on the horizontal grid size is investigated for a mixed layer through a priori analysis. The obtained length scales are highly anisotropic even though the aspect ratio between the horizontal and vertical grid sizes is close to unity.
Furthermore, the length scales as the functions of the horizontal and vertical grid sizes are empirically determined from the results obtained from the a priori analysis, and are incorporated into the Deardorff model. The numerical experiments with the new model are performed for an ideal unstable boundary layer, and are compared with those with the original Deardorff model, which employs the isotropic length scale. The new model is capable of appropriately representing the resolved convection and the heat flux even for a model resolution corresponding to the gray zone, whereas the original Deardorff model underestimates the effect of the subgrid scale motions and artificial convections become dominant as the model resolution is coarser.