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

Abstract

We demonstrate that an extended eddy‐diffusivity mass‐flux (EDMF) scheme can be used as a unified parameterization of subgrid‐scale turbulence and convection across a range of dynamical regimes, from dry convective boundary layers, through shallow convection, to deep convection. Central to achieving this unified representation of subgrid‐scale motions are entrainment and detrainment closures. We model entrainment and detrainment rates as a combination of turbulent and dynamical processes. Turbulent entrainment/detrainment is represented as downgradient diffusion between plumes and their environment. Dynamical entrainment/detrainment is proportional to a ratio of a relative buoyancy of a plume and a vertical velocity scale, that is modulated by heuristic nondimensional functions which represent their relative magnitudes and the enhanced detrainment due to evaporation from clouds in drier environment. We first evaluate the closures off‐line against entrainment and detrainment rates diagnosed from large eddy simulations (LESs) in which tracers are used to identify plumes, their turbulent environment, and mass and tracer exchanges between them. The LES are of canonical test cases of a dry convective boundary layer, shallow convection, and deep convection, thus spanning a broad rangeof regimes. We then compare the LES with the full EDMF scheme, including the new closures, in a single‐column model (SCM). The results show good agreement between the SCM and LES in quantities that are key for climate models, including thermodynamic profiles, cloud liquid water profiles, and profiles of higher moments of turbulent statistics. The SCM also captures well the diurnal cycle of convection and the onset of precipitation.

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

“…The subdomain-mean terms can be explicitly solved for by introducing n prognostic subdomain equations for each variable and an additional equation for each plume area fraction a i , which may be diagnostic or prognostic. Cohen et al (2020) derive the subdomain equations used in the EDMF framework, starting from the Navier-Stokes equations. The use of prognostic subdomain equations means that convective fluxes such as w * i ψ * i in (2) are explicitly solved for, while turbulent fluxes like w ′ i ψ ′ i must be modeled.…”

“…The prognostic equation for environmental TKE can be written in non-conservative form as (Cohen et al, 2020) ∂ē…”

“…For the simulations reported in the next section, the parameter space used is shown in Table 1. The rest of parameters used in the EDMF scheme, which do not appear explicitly in the formulation of the mixing length closure, are reported in Cohen et al (2020).…”

“…Cohen et al. (2020) derive the subdomain equations used in the EDMF framework, starting from the Navier‐Stokes equations. The use of prognostic subdomain equations means that convective fluxes such as in () are explicitly solved for, while turbulent fluxes like must be modeled.…”

“…Section 4 illustrates the performance of the EDMF scheme with the turbulent mixing closure in boundary layer regimes where vertical transport is strongly dependent on the turbulence closure used: the stable boundary layer (SBL), the stratocumulus‐topped boundary layer (STBL), and dry convection. The performance of the extended EDMF scheme with this closure in moist convective cases is demonstrated in a companion paper (Cohen et al., 2020). Finally, section 5 summarizes the results and conclusions.…”