An eddy-diffusivity/mass-flux parametrization for dry and shallow cumulus convection

Recently, a new consistent way of parametrizing simultaneously local and non-local turbulent transport for the convective atmospheric boundary layer has been proposed and tested for the clear boundary layer. This approach assumes that in the convective boundary layer the subgrid-scale fluxes result from two different mixing scales: small eddies, that are parametrized by an eddy-diffusivity approach, and thermals, which are represented by a mass-flux contribution. Since the interaction between the cloud layer and the underlying sub-cloud layer predominantly takes place through strong updraughts, this approach offers an interesting avenue of establishing a unified description of the turbulent transport in the cumulus-topped boundary layer. This paper explores the possibility of such a new approach for the cumulus-topped boundary layer. In the sub-cloud and cloud layers, the mass-flux term represents the effect of strong updraughts. These are modelled by a simple entraining parcel, which determines the mean properties of the strong updraughts, the boundary-layer height, the lifting condensation level and cloud top. The residual smaller-scale turbulent transport is parametrized with an eddy-diffusivity approach that uses a turbulent kinetic energy closure. The new scheme is implemented and tested in the research model MesoNH.