A framework for convection and boundary layer parameterization derived from conditional filtering

A new theoretical framework is derived for parameterization of subgrid physical processes in atmospheric models; the application to parameterization of convection and boundary layer fluxes is a particular focus. The derivation is based on conditional filtering, which uses a set of quasi-Lagrangian labels to pick out different regions of the fluid, such as convective updrafts and environment, before applying a spatial filter. This results in a set of coupled prognostic equations for the different fluid components, including subfilter-scale flux terms and entrainment/detrainment terms. The framework can accommodate different types of approaches to parameterization, such as local turbulence approaches and mass-flux approaches. It provides a natural way to distinguish between local and nonlocal transport processes, and makes a clearer conceptual link to schemes based on coherent structures such as convective plumes or thermals than the straightforward application of a filter without the quasi-Lagrangian labels. The framework should facilitate the unification of different approaches to parameterization by highlighting the different approximations made, and by helping to ensure that budgets of energy, entropy, and momentum are handled consistently and without double counting. The framework also points to various ways in which traditional parameterizations might be extended, for example by including additional prognostic variables. One possibility is to allow the large-scale dynamics of all the fluid components to be handled by the dynamical core. This has the potential to improve several aspects of convection-dynamics coupling, such as dynamical memory, the location of compensating subsidence, and the propagation of convection to neighboring grid columns