A comparison of local and non-local turbulence closure methods for the case of a cold air outbreak

Numerical experiments have shown that large-eddy-simulation models (LES) are able to reproduce the common features of convective boundary layers (CBL) quite well. Models which cannot resolve the convective motions due to their grid structure (1D-models or models with coarse horizontal and/or vertical resolution) have to take into account the effects of large eddies within their subgrid diffusion terms. Turbulent fluxes are frequently parameterized through first-order-closure methods (K-theory). Recently, non-local closure schemes have also been developed. In this paper we compare 1D- and 2D-models using different local and non-local first-order closure methods. The analysis is carried out for the case of an idealized cold air outbreak (CAO). One of the non-local closures is based on the so-called transilient turbulence theory. The reference states are given by a bulk-model and a 2D-model which resolves the large eddies explicitly. A comparison of the results is presented for characteristic quantities such as evolution of boundary-layer height and surface heat flux as well as mean wind and temperature profiles. It is found that simple local first-order closure does not give good agreement with the reference models. The results of the transilient turbulence model shows that a non-local closure is able to parameterize the effects of the large eddies. Comparable results are produced by a local closure where eddy diffusivities are parameterized by dimensionless gradient-functions.