A Generalized Mixing Length Closure for Eddy‐Diffusivity Mass‐Flux Schemes of Turbulence and Convection

Abstract

Because of their limited spatial resolution, numerical weather prediction and climate models 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 build on an eddy-diffusivity 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 (TKE) provides one ingredient for the diffusive local mixing closure, leaving a mixing length to be parameterized. Here, we propose a new mixing length formulation, based on constraints derived from the TKE balance. It expresses local mixing in terms of the same physical processes in all regimes of boundary layer flow. The formulation is tested at a range of resolutions and across a wide range of boundary layer regimes, including a stably stratified boundary layer, a stratocumulus-topped marine boundary layer, and dry convection. Comparison with large eddy simulations (LES) shows that the EDMF scheme with this diffusive mixing parameterization accurately captures the structure of the boundary layer and clouds in all cases considered. Plain Language Summary Turbulence and convection transport heat and moisture in the atmosphere and are ultimately responsible for the formation of clouds. However, they act on scales far too small to be resolved in current global atmosphere models. Instead, parameterizations have to be used to approximate their average effect on the finite volumes that are resolved in a global model. These parameterizations are often tailored to specific atmospheric conditions and fail when those conditions are not met. Here we propose a parameterization that aims to reproduce the average effect of turbulent heat and moisture transport under all atmospheric conditions. Numerical simulations demonstrate the accuracy of the parameterization in simulating turbulence in atmospheric boundary layers under stable and convective conditions, including the simulation of stratocumulus clouds.

Unified Entrainment and Detrainment Closures for Extended Eddy‐Diffusivity Mass‐Flux Schemes

“…All SCM simulations use a uniform vertical resolution of 50 m, with results from a resolution sensitivity test at 100 and 150 m shown for the first three moments in the grid. Other implementation details, such as how cloud properties are computed via numerical quadrature over implied SGS distributions, are described in Lopez-Gomez et al (2020).…”

An Improved Perturbation Pressure Closure for Eddy-Diffusivity Mass-Flux Schemes

“…The exchange of mass is represented by dynamical entrainment, E ij , dynamical detrainment, ∆ ij , and turbulent entrainment,Ê ij ; see Cohen et al (2020) for details. Vertical turbulent fluxes are represented by the downgradient eddy diffusivity K w,i (Lopez-Gomez et al, 2020).…”

“…It also results in a proliferation of correlated parameters (e.g., separate entrainment rates for shallow and deep convection), which complicates the calibration of climate models. Considerable efforts have been made to develop a unified parameteriza-tion that synthesizes the SGS turbulence and convection processes into one single scheme without artificial switches between different regimes (Lappen & Randall, 2001a, 2001c, 2001bLarson & Golaz, 2005;Golaz et al, 2002bGolaz et al, , 2002aSoares et al, 2004;Siebesma et al, 2007;Park, 2014aPark, , 2014bTan et al, 2018;Thuburn et al, 2018Thuburn et al, , 2019Weller & McIntyre, 2019;Cohen et al, 2020;Lopez-Gomez et al, 2020). A challenge in the development of such a unified scheme is closing the representation of various physical processes that emerge in the development of the scheme.…”

“…The closure explicitly recognizes the roles of the perturbation pressure as a vertical momentum source and sink and in TKE redistribution. The extended EDMF framework and its entrainment and detrainment closures are presented in Cohen et al (2020), and the eddy diffusivity and mixing length closures are discussed in Lopez-Gomez et al (2020). Together with the perturbation pressure closure, these closures make the extended EDMF a unified framework that successfully simulates a wide range of turbulent and convective regimes, from stable boundary layers to deep convection, without altering any of the equation components nor parameter values.…”

“…with TKE dissipation denoted byD e,0 . Closure schemes for the shear production, entrainment and detrainment, turbulent transport, buoyancy production, and dissipation are discussed in Cohen et al (2020) and Lopez-Gomez et al (2020).…”