A Turbulence Scheme with Two Prognostic Turbulence Energies

A new turbulence scheme with two prognostic energies is presented. The scheme is an extension of a turbulence kinetic energy (TKE) scheme following the ideas of Zilitinkevich et al. but valid for the whole stability range and including the influence of moisture. The second turbulence prognostic energy is used only for a modification of the stability parameter. Thus, the scheme is downgradient, and the turbulent fluxes are proportional to the local gradients of the diffused variables. However, the stability parameter and consequently the turbulent exchange coefficients are not strictly local anymore and have a prognostic character. The authors believe that these characteristics enable the scheme to model both turbulence and clouds in the planetary boundary layer. The two-energy scheme was tested in three idealized single-column model (SCM) simulations, two in the convective boundary layer and one in the stable boundary layer. Overall, the scheme performs better than the standard TKE schemes. Compared to the TKE schemes, the two-energy scheme shows a more continuous behavior in time and space and mixes deeper in accordance with the LES results. A drawback of the scheme is that the modeled thermals tend to be too intense and too infrequent. This is due to the particular cutoff formulation of the chosen length-scale parameterization. Long-term three-dimensional global simulations show that the turbulence scheme behaves reasonable well in a full atmospheric model. In agreement with the SCM simulations, the scheme tends to overestimate cloud cover, especially at low levels.