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\begin{document}

\title{Unified Entrainment and Detrainment Closures for Extended
Eddy-Diffusivity Mass-Flux Schemes}



\author[1]{Yair Cohen}%
\author[1]{Ignacio Lopez-Gomez}%
\author[2]{Anna Jaruga}%
\author[1]{Jia He}%
\author[3]{Colleen Kaul}%
\author[2]{Tapio Schneider}%
\affil[1]{California Institute of Technology}%
\affil[2]{Jet Propulsion Laboratory, California Institute of Technology}%
\affil[3]{Pacific Northwest National Laboratory}%


\vspace{-1em}



  
  \date{May 26, 2024}


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\begin{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, over 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 are proportional to a ratio of buoyancy
difference and vertical velocity scale, partitioned based on buoyancy
sorting approaches and modulated by a function of relative humidity
difference in cloud layer to represent buoyancy loss owing to
evaporation in mixing. We first evaluate the closures offline against
entrainment and detrainment rates diagnosed from large-eddy simulations
(LES) 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 range of 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.%
\end{abstract}%



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