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Idealized large-eddy simulations of shallow convection often utilize horizontally periodic computational domains. The development of precipitation in shallow cumulus convection changes the spatial structure of convection and creates large-scale organization. However, the limited periodic domain constrains the horizontal variability of the atmospheric boundary layer. Small computational domains cannot capture the mesoscale boundary layer organization and artificially constrain the horizontal convection structure. The effects of the horizontal domain size on large-eddy simulations of shallow precipitating cumulus convection are investigated using four computational domains, ranging from 40×40km2 to 320×320km2 and fine grid resolution (40 m). The horizontal variability of the boundary layer is captured in computational domains of 160×160km2. Small LES domains (≤40 km) cannot reproduce the mesoscale flow features, which are about 100km long, but the boundary layer mean profiles are similar to those of the larger domains. Turbulent fluxes, temperature and moisture variances, and horizontal length scales are converged with respect to domain size for domains equal to or larger than 160×160km2. Vertical velocity flow statistics, such as variance and spectra, are essentially identical in all domains and show minor dependence on domain size. Characteristic horizontal length scales (i.e., those relating to the mesoscale organization) of horizontal wind components, temperature and moisture reach an equilibrium after about hour 30. 

While GCM horizontal resolution has received the majority of scale improvements in recent years, ample evidence suggests that a model’s vertical resolution exerts a strong control on its ability to accurately simulate the physics of the marine boundary layer. Here we show that, regardless of parameter tuning, the ability of a single-column model (SCM) to simulate the subtropical marine boundary layer improves when its vertical resolution is improved. We introduce a novel objective tuning technique to optimize the parameters of an SCM against profiles of temperature and moisture and their turbulent fluxes, horizontal winds, cloud water, and rainwater from large-eddy simulations (LES). We use this method to identify optimal parameters for simulating marine stratocumulus and shallow cumulus. The novel tuning method utilizes an objective performance metric that accounts for the uncertainty in the LES output, including the covariability between model variables. Optimization is performed independently for different vertical grid spacings and value of time step, ranging from coarse scales often used in current global models (120 m, 180 s) to fine scales often used in parameterization development and large-eddy simulations (10 m, 15 s). Uncertainty-weighted disagreement between the SCM and LES decreases by a factor of ∼5 when vertical grid spacing is improved from 120 to 10 m, with time step reductions being of secondary importance. Model performance is shown to converge at a vertical grid spacing of 20 m, with further refinements to 10 m leading to little further improvement.

In successive generations of computer models that simulate Earth’s atmosphere, improvements have been mainly accomplished by reducing the horizontal sizes of discretized grid boxes, while the vertical grid spacing has seen comparatively lesser refinements. Here we advocate for additional attention to be paid to the number of vertical layers in these models, especially in the model layers closest to Earth’s surface where climatologically important marine stratocumulus and shallow cumulus clouds reside. Our experiments show that the ability of a one-dimensional model to represent physical processes important to these clouds is strongly dependent on the model’s vertical grid spacing.

 

Coarse-gridded atmospheric models often account for subgrid-scale variability by specifying probability distribution functions (PDFs) of process rate inputs such as cloud and rainwater mixing ratios (q_candq_r, respectively). PDF parameters can be obtained from numerous sources: in situ observations, ground- or space-based remote sensing, or fine-scale modeling such as large-eddy simulation (LES). LES is appealing to constrain PDFs because it generates large sample sizes, can simulate a variety of cloud regimes/case studies, and is not subject to the ambiguities of observations. However, despite the appeal of using model output for parameterization development, it has not been demonstrated that LES satisfactorily reproduces the observed spatial structure of microphysical fields. In this study, the structure of observed and modeled microphysical fields are compared by applying bifractal analysis, an approach that quantifies variability across spatial scales, to simulations of a drizzling stratocumulus field that span a range of domain sizes, drop concentrations (a proxy for mesoscale organization), and microphysics schemes (bulk and bin). Simulatedq_cclosely matches observed estimates of bifractal parameters that measure smoothness and intermittency. There are major discrepancies between observed and simulatedq_rproperties, though, with bulk simulatedq_rconsistently displaying the bifractal properties of observed clouds (smooth, minimally intermittent) rather than rain while bin simulations produceq_rthat is appropriately intermittent but too smooth. These results suggest fundamental limitations of bulk and bin schemes to realistically represent higher-order statistics of the observed rain structure.

 

A new version of the stochastic multiplume Jet Propulsion Laboratory Eddy‐Diffusivity/Mass‐Flux (JPL‐EDMF) parameterization which consistently couples the simplified Khairoutdinov and Kogan (2000),https://doi.org/10.1175/1520-0493(2000)128<0229:ANCPPI>2.0.CO;2, warm phase cloud microphysical parameterization with the parameterization of cloud macrophysical and subgrid scale dynamical processes is described. The new parameterization combines the EDMF approach with an assumed shape of a joint probability density function of thermodynamic and kinematic variables which provide the basis for the computation of all parameterized processes. As far as we are aware this is the first attempt to consistently couple all of these parameterized processes in the EDMF framework. This paper is part one of a two paper series. Here, the JPL‐EDMF parameterization is described and benchmark simulations of precipitating stratocumulus and cumulus convection are performed in a single‐column‐model framework. The parameterization results compare favorably to the reference large‐eddy‐simulation results. In the second part (Smalley et al., 2022,https://doi.org/10.1029/2021MS002729) the JPL‐EDMF parameterization is validated for a wide range of observation‐based scenarios covering the continuous transition from subtropical stratocumulus to cumulus convection derived from global reanalysis, and parameterization uncertainties are studied in detail.