A Generalized Mixing Length for Eddy-Diffusivity Mass-Flux Models of Boundary Layer Turbulence and Convection

Because of the limited spatial resolution of numerical weather prediction and climate models, they have to rely on parameterizations to represent atmospheric turbulence and convection. Historically, largely independent approaches have been used to represent boundary layer turbulence and convection, neglecting important interactions at the subgrid scale. Here we further develop an eddy diffusion/ mass flux (EDMF) scheme that represents all subgrid-scale mixing in a unified manner, partitioning subgrid-scale fluctuations into contributions from local diffusive mixing and coherent advective structures and allowing them to interact within a single framework. The EDMF scheme requires closures for the interaction between the turbulent environment and the plumes and for local mixing. A second-order equation for turbulence kinetic energy provides one ingredient for the diffusive local mixing closure, leaving a mixing length to be parameterized. A new mixing length formulation is proposed, expressing local mixing in terms of the same physical processes in all regimes of boundary layer flow, from stable to convective boundary layers. The formulation is tested across a wide range of boundary layer regimes, including a stably stratified boundary layer, shallow cumulus convection, and the stratocumulus-topped marine boundary layer. Comparison with large eddy simulations (LES) shows that the EDMF scheme with this diffusive mixing par ameterization accurately captures the structure of the boundary layer in all the cases considered .