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Large‐scale weather forecasting and climate models are beginning to reach horizontal resolutions of kilometers, at which common assumptions made in existing parameterization schemes of subgrid‐scale turbulence and convection—such as that they adjust instantaneously to changes in resolved‐scale dynamics—cease to be justifiable. Additionally, the common practice of representing boundary‐layer turbulence, shallow convection, and deep convection by discontinuously different parameterizations schemes, each with its own set of parameters, has contributed to the proliferation of adjustable parameters in large‐scale models. Here we lay the theoretical foundations for an extended eddy‐diffusivity mass‐flux (EDMF) scheme that has explicit time‐dependence and memory of subgrid‐scale variables and is designed to represent all subgrid‐scale turbulence and convection, from boundary layer dynamics to deep convection, in a unified manner. Coherent up and downdrafts in the scheme are represented as prognostic plumes that interact with their environment and potentially with each other through entrainment and detrainment. The more isotropic turbulence in their environment is represented through diffusive fluxes, with diffusivities obtained from a turbulence kinetic energy budget that consistently partitions turbulence kinetic energy between plumes and environment. The cross‐sectional area of up and downdrafts satisfies a prognostic continuity equation, which allows the plumes to cover variable and arbitrarily large fractions of a large‐scale grid box and to have life cycles governed by their own internal dynamics. Relatively simple preliminary proposals for closure parameters are presented and are shown to lead to a successful simulation of shallow convection, including a time‐dependent life cycle.

A large-eddy simulation (LES) framework is developed for simulating the dynamics of clouds and boundary layers with closed water and entropy balances. The framework is based on the anelastic equations in a formulation that remains accurate for deep convection. As prognostic variables, it uses total water and entropy, which are conserved in adiabatic and reversible processes, including reversible phase changes of water. This has numerical advantages for modeling clouds, in which reversible phase changes of water occur frequently. The equations of motion are discretized using higher-order weighted essentially nonoscillatory (WENO) discretization schemes with strong stability preserving time stepping. Numerical tests demonstrate that the WENO schemes yield simulations superior to centered schemes, even when the WENO schemes are used at coarser resolution. The framework is implemented in a new LES code written in Python and Cython, which makes the code transparent and easy to use for a wide user group.

Stratocumulus clouds are the most common type of boundary layer cloud; their radiative effects strongly modulate climate. Large eddy simulations (LES) of stratocumulus clouds often struggle to maintain fidelity to observations because of the sharp gradients occurring at the entrainment interfacial layer at the cloud top. The challenge posed to LES by stratocumulus clouds is evident in the wide range of solutions found in the LES intercomparison based on the DYCOMS‐II field campaign, where simulated liquid water paths for identical initial and boundary conditions varied by a factor of nearly 12. Here we revisit the DYCOMS‐II RF01 case and show that the wide range of previous LES results can be realized in a single LES code by varying only the numerical treatment of the equations of motion and the nature of subgrid‐scale (SGS) closures. The simulations that maintain the greatest fidelity to DYCOMS‐II observations are identified. The results show that using weighted essentially non‐oscillatory (WENO) numerics for all resolved advective terms and no explicit SGS closure consistently produces the highest‐fidelity simulations. This suggests that the numerical dissipation inherent in WENO schemes functions as a high‐quality, implicit SGS closure for this stratocumulus case. Conversely, using oscillatory centered difference numerical schemes for momentum advection, WENO numerics for scalars, and explicitly modeled SGS fluxes consistently produces the lowest‐fidelity simulations. We attribute this to the production of anomalously large SGS fluxes near the cloud tops through the interaction of numerical error in the momentum field with the scalar SGS model.