A Framework for Convection and Boundary Layer Parameterization Derived from Conditional Filtering

Abstract

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.

A two‐fluid single‐column model of the dry, shear‐free, convective boundary layer

“…The governing equations are based on the conditionally filtered compressible Euler equations, as given by Thuburn et al . (). They are restricted to a single column, so that the horizontal velocity vanishes and the solution is independent of the horizonal coordinates.…”

“…Under suitable approximations the multi‐fluid governing equations reduce to those for a typical mass flux convection scheme (Thuburn et al . ). They also include subfilter‐scale terms that could account for local turbulent transports such as those commonly modelled by a downgradient eddy diffusion in the boundary layer.…”

“…), Thuburn et al . () recently proposed an approach in which a full set of prognostic equations for density, momentum, potential temperature, and moisture is used for the resolved‐scale average dynamics of convective updaughts, as well as for their environment. (Downdraughts and multiple classes of convective updraught can also be included with their own prognostic equations.)…”

“…Thuburn et al . () provide a detailed derivation of the conditionally filtered equations and discuss the relationship between relabelling and entrainment/detrainment. Thuburn and Vallis () have documented the conservation properties of the multi‐fluid equations and shown that they possess physically reasonable normal modes, thus giving some confidence that the multi‐fluid equations do provide a physically sound basis on which to model convective flows.…”

The coupling of deep convection with the resolved flow via the divergence of mass flux in the IFS

“…() and Thuburn et al . () have experimented with including the convective motions and mass exchanges in the dynamical equations and have proposed a numerical framework, albeit still experimental, that can be reduced to the traditional mass flux approach.…”