A LES Based Parameterization Scheme for the Terra Incognita in a Planetary Boundary Layer

In numerical weather prediction (NWP) models, a planetary boundary layer (PBL) parameterization based on the Reynolds-Averaged Navier Stokes (RANS) model is widely employed. High resolution NWP models which are able to partly resolve each convection in the PBL have been practically used due to increasing computational power, whereas the assumption in a RANS scheme that all the turbulence motions are parameterized would not be appropriate for reproducing fluctuations corresponding to such the high resolution NWP model. Meanwhile, a large-eddy simulation (LES) approach cannot be also applied to the model because it is required that most of the turbulent motion can be explicitly resolved for the LES. This intermediate resolution where neither the RANS nor the LES is applicable is termed the terra incognita in the PBL (Wyngaard 2004). While some turbulence schemes for the terra incognita range have been proposed (e.g. Boutle et al. 2014; Shin and Hong 2015; Ito et al. 2015), all of these schemes are based on an extension of a RANS parameterization.

In the present study, we attempt to develop a LES based parameterization scheme applicable to the terra incognita by modifying the Deardorff model (Deardorff 1980). In this approach, anisotropy of the turbulent transport between the horizontal and vertical directions is taken into account in contrast to a traditional LES scheme. The dependence of the turbulence length scales on the horizontal grid size is empirically identified from the a priori analysis and incorporated into the Deardorff model. We examine the numerical experiments for a convective PBL and compare the modified Deardorff model to the original one. The modified Deardorff model is capable of appropriately representing the resolved convection and the heat flux even for the terra incognita range, whereas the original model underestimates the effect of the subgrid scale motions as the model resolution is coarser.