Abstract
Convection parameterizations such as eddy-diffusivity mass-flux (EDMF)
schemes require a consistent closure formulation for the perturbation
pressure, which arises in the equations for vertical momentum and
turbulence kinetic energy (TKE). Here we derive an expression for the
perturbation pressure from approximate analytical solutions for 2D and
3D rising thermal bubbles. The new closure combines a modified pressure
drag and virtual mass effects with a new momentum advection term. This
momentum advection is an important source in the lower half of the
thermal bubble and at cloud base levels in convective systems. It
represents the essential physics of the perturbation pressure, that is,
to ensure the 3D non-divergent properties of the flow. Moreover, the new
formulation modifies the pressure drag to be inversely proportional to
updraft depth. This is found to significantly improve simulations of the
diurnal cycle of deep convection, without compromising simulations of
shallow convection. It is thus a key step toward a unified scheme for a
range of convective motions. By assuming that the pressure only
redistributes TKE between plumes and the environment, rather than
vertically, a closure for the velocity pressure-gradient correlation is
obtained from the perturbation pressure closure. This novel pressure
closure is implemented in an extended EDMF scheme and is shown to
successfully simulate a rising bubble test case as well as shallow and
deep convection cases in a single column model.