A Two-Energies Turbulence Scheme

A new turbulence scheme with prognostic equations for two turbulence energies is presented. The scheme is an extension of a Turbulence Kinetic Energy (TKE) scheme with an additional prognostic energy, which represents the effects of temperature and moisture variances in compact form. The extension is inspired by the ideas of Zilitinkevich et al. (2013), but the two-energies turbulence scheme is valid for the whole stability range and includes the influence of moisture. The additional turbulence prognostic energy is used only for the calculation of the stability parameter. Thus the two-energies scheme is similar to a standard TKE scheme in that the turbulent fluxes are down-gradient and proportional to the local gradients of the diffused variables. However, the energy-dependent stability parameter is not anymore strictly local and obtains a prognostic character. These characteristics enable the scheme to model both turbulence and clouds in the planetary boundary layer.

In order to treat boundary layer clouds and turbulent mixing consistently the Assumed Probability Density Function (APDF) method is used for computation of the buoyancy flux and the cloud fraction. The higher order moments, which are required to determine the shape of the trivariate probability density function, are diagnosed from the turbulent fluxes and the two prognostic energies.

We implemented the turbulent core of the Cloud Layers Unified By Binormals (CLUBB) model and the two-energies scheme into the ICOsahedral Non-hydrostatic (ICON) Single Column Model (SCM). We will present results of the coupled ICON-CLUBB SCM and the ICON-Two-Energies SCM for selected idealized cases.