Evaluation of the Kinetic Energy Approach for Modeling Turbulent Fluxes in Stratocumulus

The modeling of vertical mixing by a turbulence scheme on the basis of prognostic turbulent kinetic energy (E) and a diagnostic length scale (l ) is investigated with particular emphasis on the representation of entrainment. The behavior of this E–l scheme is evaluated for a stratocumulus case observed in the Atlantic Stratocumulus Transition Experiment, and a comparison is made with the results of large eddy simulation models for the same case. It appears that the E–l model is well capable of reproducing the main features of vertical mixing and entrainment. This is the case with a high vertical grid spacing of 25 m and a short time step of 1 s, even with a relatively simple formulation for the turbulent length scale. However, the model results degenerate rapidly on coarse temporal and spatial resolution. For time steps on the order of 1 min it is shown that the process-splitting time integration scheme (in which the tendencies due to turbulent diffusion and radiation are computed independently) results in a too cold cloud top, a too large buoyancy flux, and a too high entrainment rate. For a vertical grid spacing of the order of 200 m (as commonly used in operational models) the model does not behave well either. At such resolution, entrainment appears to be predominantly related to the Eulerian (gridbox) representation of the cloud and not to the physics of the turbulence scheme. This gridbox representation of the cloud prevents the cloud from descending due to prevailing large-scale subsiding motion, and therefore generates an entrainment rate that balances the subsidence rate. An unphysical dependency of the entrainment rate on the subsidence rate results. A general conceptual model for this behavior is presented. Finally, the relevance of these results for large-scale atmospheric models is discussed