Numerics and subgrid-scale modeling in large eddy simulations of stratocumulus clouds

Are general circulation models obsolete?

Traditional general circulation models, or GCMs-that is, three-dimensional dynamical models with unresolved terms represented in equations with tunable parameters-have been a mainstay of climate research for several decades, and some of the pioneering studies have recently been recognized by a Nobel prize in Physics. Yet, there is considerable debate around their continuing role in the future. Frequently mentioned as limitations of GCMs are the structural error and uncertainty across models with different representations of unresolved scales and the fact that the models are tuned to reproduce certain aspects of the observed Earth. We consider these shortcomings in the context of a future generation of models that may address these issues through substantially higher resolution and detail, or through the use of machine learning techniques to match them better to observations, theory, and process models. It is our contention that calibration, far from being a weakness of models, is an essential element in the simulation of complex systems, and contributes to our understanding of their inner workings. Models can be calibrated to reveal both fine-scale detail and the global response to external perturbations. New methods enable us to articulate and improve the connections between the different levels of abstract representation of climate processes, and our understanding resides in an entire hierarchy of models where GCMs will continue to play a central role for the foreseeable future.

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

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 Budget-Based Turbulence Length Scale Diagnostic

The most frequently used boundary-layer turbulence parameterization in numerical weather prediction (NWP) models are turbulence kinetic energy (TKE) based-based schemes. However, these parameterizations suffer from a potential weakness, namely the strong dependence on an ad-hoc quantity, the so-called turbulence length scale. The physical interpretation of the turbulence length scale is difficult and hence it cannot be directly related to measurements or large eddy simulation (LES) data. Consequently, formulations for the turbulence length scale in basically all TKE schemes are based on simplified assumptions and are model-dependent. A good reference for the independent evaluation of the turbulence length scale expression for NWP modeling is missing. Here we propose a new turbulence length scale diagnostic which can be used in the gray zone of turbulence without modifying the underlying TKE turbulence scheme. The new diagnostic is based on the TKE budget: The core idea is to encapsulate the sum of the molecular dissipation and the cross-scale TKE transfer into an effective dissipation, and associate it with the new turbulence length scale. This effective dissipation can then be calculated as a residuum in the TKE budget equation (for horizontal sub-domains of different sizes) using LES data. Estimation of the scale dependence of the diagnosed turbulence length scale using this novel method is presented for several idealized cases.

Turbulence Structure in a Stratocumulus Cloud

The growth of computing power combined with advances in modeling methods can yield high-fidelity simulations establishing numerical simulation as a key tool for discovery in the atmospheric sciences. A fine-scale large-eddy simulation (LES) utilizing 1.25 m grid resolution and 5.12 × 5.12 km 2 horizontal domain is used to investigate the turbulence and liquid water structure in a stratocumulus cloud. The simulations capture the observed cloud morphology, including elongated regions of low liquid water path, cloud holes, and pockets of clear air within the cloud. The cloud can be partitioned into two broad layers with respect to the maximum mean liquid. The lower layer resembles convective turbulent structure with classical inertial range scaling of the velocity and scalar energy spectra. The top and shallower layer is directly influenced by the cloud top radiative cooling and the entrainment process. Near the cloud top, the liquid water spectra become shallower and transition to a k − 1 power law for scales smaller than about 1 km .

An Extended Eddy-Diffusivity Mass-Flux Scheme for Unified Representation of Subgrid-Scale Turbulence and Convection

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.