An Advection-Diffusion scheme for the convective boundary layer: description and 1d-results

We present a simple integrated scheme to parameterize the convective boundary layer. The conventional approach is to parameterize the dry convective boundary layer with a K-diffusion scheme. In the cumulus boundary layer the sub-cloud layer mixing is parameterized by K-diffusion whereas the cloud layer is parameterized by the mass flux approach. A new way of unifying the parameterization of the boundary layer by combining the K-diffusion and the mass-flux approaches is proposed. The approach is based on the concept that in the convective boundary layer the main mechanisms of mixing are: "local" mixing that can be parameterized by a diffusion approach and "non-local" mixing performed by the strong thermals that can be parameterized by a mass-flux approach. The strong updrafts are modeled by a simple entraining rising parcel. This entraining rising parcel determines the boundary layer height and, if present, the lifting condensation level and cloud top. A non-dimensionalised mass flux profile is used to evaluate the non-local advective transport by this rising parcel whereas the local transport by smaller eddies is parameterized by the more conventional diffusive transport. This approach has the conceptual advantages that the whole convective boundary layer is described by one scheme that has non- local advection and local diffusion in both cloud and sub-cloud layer. The cumulus topped boundary layer and the dry convective boundary layer are unified in a simple way; in both cases the mass flux term will parameterize the non-local mixing. Also, the closure problem at cloud base is partly solved since the entraining parcel equation is integrated from the surface layer. Recent experimentation with this parameterization implemented into a 1D model has shown promising results