The role of consistent turbulence energetics in the representation of dry and shallow convection

Abstract

In this doctoral dissertation, the role of consistent turbulence energetics is examined in the context of sub-grid turbulence, convection, and cloud condensation parameterizations for numerical weather and climate models. The property of energetic consistency is formally defined and divided into two categories, local and non-local, and various common parameterization approaches are classified according this framework. I show theoretically that the basis of local energetic consistency is the inclusion of mean-gradient transport and buoyancy acceleration terms in the diagnostic and prognostic budget equations of all second-order statistical moments, including fluxes. Effectively, these terms account for the conversion between turbulent kinetic energy (TKE) and turbulent potential energy (TPE) under stably stratified conditions. With simple numerical experiments, I show that if local energetic consistency is not satisfied, then thermodynamic profiles cannot be correctly predicted under stably conditions, such as in the boundary layer capping inversion. I then extend the concept of energetic consistency from local turbulent mixing to non-local convective transport. I show that the popular eddy diffusivity-mass flux (EDMF) approach for unified parameterization of turbulence and convection treats the turbulent transport of turbulent energy in two parallel but inconsistent ways: advectively and diffusively. I introduce a novel parameterization approach, inspired by EDMF, that consistently partitions all second-order moments, including TKE, between convective and non-convective parts of a grid cell and show that this approach predicts significantly more realistic depths of convective boundary layers than conventional EDMF schemes. Finally, I introduce a novel method for validating this parameterization approach, based on Langragian particle tracking in large-eddy simulations.