Combining non-local scalings with a TKE closure for mixing in boundary layer clouds

Many NWP models use 1.5 order (or TKE) turbulence closures to parametrize transports in boundary layer clouds. These tend to work well only for boundary layers where the thermodynamic probability distributions can be considered Gaussian (eg. stratocumulus) and have traditionally (eg. Bechtold et al, 1992) had problems representing the observed boundary layer structure when the distribution is skewed (as in shallow cumulus). One approach to extend the validity of TKE closures to the cumulus regime was proposed by Bechtold et al (1995). They modelled the non-Gaussian part of the distribution through an enhancement of the Gaussian in-cloud buoyancy flux when the grid box mean thermodynamic state was weakly subsaturated. However, large-eddy simulation results will be presented that show this enhancement factor varies strongly through the cumulus cloud layer while the saturation deficit remains reasonably constant. Furthermore, a simulation of cumulus rising into stratocumulus is found to require a large enhancement just below the stratiform cloud base where the Bechtold et al parametrization gives very low values.

Instead, a new approach will be described that combines a traditional Gaussian TKE closure with non-local functions to represent explicitly that part of the distribution arising from the cumulus elements. The non-local functions are scaled using the parameters developed for shallow cumulus convection by Grant and Brown (1999). Results will be presented to demonstrate the validity of the approach from single column model simulations ranging from stratocumulus to shallow cumulus, including boundary layers where both are present.