Evaluation of the COSMO-SC turbulence scheme in a shear-driven stable boundary layer

The performance of the COSMOsingle column turbulence scheme (a TKE scheme with a 1.5 order turbulence closure at the hierarchy level 2.5 following Mellor and Yamada) is investigated in the framework of the first GABLS intercomparison case. This is an idealized shear-driven stable boundary layer case with no advection. Overall the COSMO model performs reasonably well compared to the other participating models and the reference Large Eddy Simulations. However, the modification of some model parameters, together with the prescribed high vertical resolution, reveals a problem of numerical stability in the turbulence scheme: for the investigated shear-driven stable boundary layer the vertical diffusivities show unrealistic oscillations. This model deficiency, which has previously been described in literature, is explored in quite substantial detail and possible solutions are evaluated. It is found that under the given conditions the numerical description of the vertical wind gradients is crucial for the stability of the turbulence scheme. It is shown that for the determination of vertical gradients information from grid points beyond the immediately neighboring model levels must be incorporated - as it is common practice in the treatment of horizontal gradients - in order to obtain a numerically stable turbulence scheme. As a first approach vertical wind gradients are filtered using a 5-point filter prior to the evaluation of the stability functions. This approach yields to the overall best performance among all those tested and found in literature. The simulations additionally show that the use of a too high minimum diffusion coefficient (which is introduced in the model in order to avoid too low mixing) leads to losing important structures of the planetary boundary layer, such as the low level jet or a near-surface temperature inversion.