Mixing efficiency and entrainment at an atmospheric inversion layer

The context is that of the convectively-driven atmospheric boundary layer capped by an inversion layer (i.e. a stably-stratified interface) and we focus on the regime of equilibrium entrainment, i.e. when the boundary-layer evolution is in a quasi steady state. The parameterization of the entrainment process across the interfacial layer is usually based on the entrainment ratio, namely the ratio of the negative of the heat flux at the interface to the heat flux at the ground surface. Hence the issue is to relate the entrainment ratio to measurable parameters. In this study, we rely on a formulation of convective entrainment in terms of mixing efficiency, which can be computed directly for instance from high-resolution vertical profiles of virtual potential temperature. We discuss the applicability of this parameterization for an explicit treatment of the entrainment process in classical boundary-layer parameterization schemes implemented in meso-scale models