Abstract Parameterizing boundary layer turbulence in Earth System Models (ESMs) introduces a key source of uncertainty. Here, we explore the impact of implementing a prognostic formulation (PMF) for momentum flux, which permits countergradient (CG) fluxes. We implement PMF in the turbulence parameterization in the Community Atmosphere Model version 6 (CAM6). CG fluxes in PMF reduce globally‐integrated momentum flux in CAM6. A similar response in globally‐integrated momentum flux is observed when reducing a tunable diffusivity parameter in the existing diagnostic formulation for momentum flux (DMF). Both methods of reducing effective eddy diffusivity produce qualitatively similar responses in the modeled general circulation, namely an enhanced upward branch of the Hadley cell, increased equatorward low‐level flow, and strengthened meridional temperature and moisture gradients. However, the reduction in effective eddy diffusivity from CG fluxes in PMF produces a higher‐magnitude response in the general circulation compared to reducing the diffusivity parameter in DMF.

Turbulence and cloudiness in cumulus-topped marine boundary layers are studied using data from the nonprecipitating shallow cumulus clouds, spanning 141 h and encompassing 603 individual clouds. On average, the cumulus had bases at 558 m, were 99 m thick, had a chord length of 500 m, and exhibited an hourly base-layer cloudiness of 12%. Changes in cloud fraction were primarily driven by variations in cloud number not chord length. High-resolution Doppler lidar and cloud radar observations were used to estimate updraft and downdraft mass fluxes in the cumulus base layer under both clear and cloudy regions. Cloudy updrafts contributed only ;23% of the total updraft mass flux at cloud base, indicating that most upward mass flux originated from clear-air eddies. Updraft strength, rather than updraft fraction, was found to predominantly control both clear and cloudy updraft mass fluxes. Cloud-base cloudiness strongly correlated with cloudy updraft mass flux but showed negligible correlation with clear-air updraft mass flux. Clear-air downdraft mass flux exhibited a strong relationship with the ratio of surface buoyancy to inversion strength. Mesoscale analysis revealed that moist patches had greater cloudiness, updraft mass flux, and vertical velocity variance compared to dry patches. Additionally, mesoscale base-layer cloud fraction was highly and significantly correlated with cloudy updraft mass flux in both dry and moist environments. Results presented herein have implications for cumulus parameterization development along with climatological and model evaluation studies conducted at the ENA site.

The Coriolis effect can deflect turbulent momentum flux and anisotropy of turbulent kinetic energy. This Coriolis turbulent deflection is usually omitted in parameterizations of atmospheric turbulence and convection. However, previous large-eddy simulations (LES) found that the nontraditional Coriolis terms (NCTs) can enhance vertical velocity variance with easterly flow and suppress it with westerly flow. To parameterize this effect in the atmosphere, this study introduces the Coriolis terms to the Cloud Layers Unified By Binormals (CLUBB) parameterization of clouds and turbulence. We design three single-column benchmarks to test the implementation of the NCTs in CLUBB. First, assuming that all except the Coriolis terms vanish on the right-hand side of the prognostic equations of the second-order moments of velocity, we derive an analytical solution in which the anisotropy of the moments rotates back to the initial state with a certain period. Our CLUBB results match this analytic benchmark. Second, assuming dry and neutrally stratified atmosphere with constant geostrophic winds, our CLUBB and LES results suggest that the NCTs make the Ekman layer deeper with geostrophic easterlies but shallower with westerlies. Third, under realistic conditions for trade-wind shallow convection, our CLUBB results show that the cloud layer becomes shallower if we omit the NCTs or flip the geostrophic winds from easterly to westerly. These benchmarks not only validate the Coriolis terms in CLUBB but also form a model hierarchy that aids our understanding of the effects of the NCTs on turbulence and convection.

In this study, we extend the Cloud Layers Unified by Binormals (CLUBB) turbulence scheme within the GFDL atmospheric model (AM4) by implementing direct momentum-flux prognosis and a multiscale turbulent lengthscale, to improve the simulation of nocturnal precipitation and associated Low-Level Jets (LLJs) over the Great Plains (GP). Toward this aim, we set up four AM4-CLUBB configurations: diagnosed momentum flux, prognosed momentum flux, diagnosed momentum flux with a multiscale turbulent lengthscale, and prognosed momentum flux with a multiscale turbulent lengthscale. Simulations are evaluated against the AM4 control, the Integrated Multi-satellitE Retrievals for GPM (IMERG), and the Doppler wind radar profiles from the Atmospheric Radiation Measurement program. Results show that all AM4-CLUBB configurations improve the precipitation timing from the unrealistic midday peak seen in the AM4 control simulation toward the satellite-observed nocturnal maximum. The configuration that prognoses momentum flux and uses a multi-scale turbulent lengthscale, best matches the timing and intensity of GP precipitation rate. This configuration is also that which more accurately simulates the ARM-observed nocturnal LLJ wind profiles, while increasing the frequency of counter-gradient momentum fluxes near the LLJ core compared to prognosing momentum fluxes with the original AM4-CLUBB turbulent lengthscale. Momentum budget analysis attributes this increase to a nearly fivefold enhancement in the buoyancy production term when using the multiscale formulation, and leads to stronger nocturnal convective activity, as diagnosed from the greater vertical velocity skewness and plume asymmetry.

When a new, better-formulated physical parameterization is introduced into a global atmospheric model, aspects of the global model solutions are sometimes degraded. Then, in order to use the new global model to address science questions, there is an incentive to restore its accuracy. Oftentimes this restoration is achieved by tuning of model parameter values. Unfortunately, the retuning process is expensive because characterizing the parameter dependence requires numerous time-consuming global simulations. To reduce the cost of tuning, this manuscript introduces a “poor man's” model tuner, “QuadTune”. QuadTune carves the globe into regions and approximates the model parameter dependence through the use of an uncorrelated quadratic emulator (i.e., response surface). The simplicity of the emulator reduces the required number of global model simulations and aids explainability of tuner behavior. Tuning removes parametric error but leaves behind model structural error. Structural error manifests itself as regional residual biases, such as stubborn biases and tuning trade-offs. To visualize these residual biases, QuadTune's software includes a set of diagnostic plots. This paper illustrates the use of the plots for characterizing residual biases with an example tuning problem.

Skillful representation of tropical variability and diurnal cycle of precipitation has remained a challenge in global atmosphere models, and often improvements in the variability lead to degradation in the mean-state. Here, we introduce a configuration of the E3SM Atmosphere Model with a new large-scale microphysics scheme and several enhancements to the deep convective scheme that improves the variability. The new configuration improves various modes of convectively-coupled equatorial waves, with increased strength of Kelvin waves and more coherent eastward propagation of the Madden-Julian Oscillation from the Indian Ocean to the central Pacific Ocean. The same configuration also improves the phase of the diurnal cycle of precipitation, particularly over the continental United States in the boreal summer and over Tropical land regions. Previous studies have shown that, individually taken, some of the deep convective enhancements can improve certain aspects of the variability, and here we show that combining their effects can lead to robust improvements in the variability. This model configuration can form the basis for future studies to examine the response of tropical and diurnal variability under various climate states and their relationships with other modes of variability.

Vertical velocity distribution below cloud is one of the key determinants of cloud life cycle, but observations of this variable are extremely sparse in space. Doppler lidar retrievals and large-eddy simulations at the U.S. Department of Energy's Atmospheric Radiation Measurement User Facility Southern Great Plains site are used to determine whether vertical velocity statistics from temporally dense profiles at a single location can be substituted for spatial vertical velocity statistics. We show that even a small number (five) of widely distributed [O(18) latitude/longitude spacing] lidars is suffi-cient sampling to reconstruct domainwide spatial vertical velocity variance, but not higher moments of the vertical velocity distribution. Spatial and temporal vertical velocity variances in the Doppler lidar observations are nearly interchangeable as long as the spatial variance is temporally averaged and the temporal variance is averaged across lidars. This is true even though the dominant spatial scales of vertical velocity variability are 3 km, more than an order of magnitude smaller than the spacing between the lidars. In the limit where the temporal variance does not vary across a spatial domain (e.g., if the meteorological and surface forcing of the atmospheric turbulence is homogeneous across the domain) and the domain-mean vertical velocity is zero, the commonly available retrieval of temporal vertical velocity variance at one site is equivalent to the spatial variance over the domain. We use an updraft parcel model to show that substituting temporal for spatial vertical velocity statistics will have a relatively minor effect on cloud droplet number concentrations.

Recent studies reveal an anti-correlation between global cloud feedback (CF) and effective radiative forcing due to aerosol-cloud interaction (ERFaci) in Earth system models, but the physical mechanisms underlying it remain uncertain. Here we investigate how different turbulence representations contribute to this relationship over the global ocean using an ensemble of Energy Exascale Earth System Model version 2 simulations with perturbed turbulence parameters. The anti-correlation appears only in the tropical ascent regime. In the Northern Hemisphere midlatitude and high latitude regimes, there is no significant correlation, and in the tropical marine low cloud and Southern Ocean regimes, the correlation is positive. These opposite correlations are primarily driven by opposing CF responses to perturbed parameters. We find that the mean-state turbulent mixing strength affects both CF and ERFaci, enabling strong correlations in certain regimes. This study highlights the complex linkages between CF and ERFaci through turbulent processes across diverse cloud regimes.

A general formulation for the distribution problem is presented, which is applicable to frequency distributions of subgrid-scale variables and hydrometeor size distributions, as well as to probability distributions characterizing data uncertainties. The general formulation is presented based upon two well-known basic principles: the maximum-entropy principle and the Liouville equation. The maximum-entropy principle defines the most likely general distribution form if necessary constraints are specified. This paper proposes to specify these constraints as the output variables to be used in a host model. Once a general distribution form is defined, the problem of the temporal evolution of the distribution reduces to that of predicting a small number of parameters characterizing it. This paper derives prognostic equations for these parameters from the Liouville equation. The developed formulation, which is applicable to a wide range of atmospheric modeling problems, is specifically applied to the condensation growth of cloud droplets as a demonstration.

This paper describes the atmospheric component of the US Department of Energy's Energy Exascale Earth System Model (E3SM) version 3. Significant updates have been made to the atmospheric physics compared to earlier versions. Specifically, interactive gas chemistry has been implemented, along with improved representations of aerosols and dust emissions. A new stratiform cloud microphysics scheme more physically treats ice processes and aerosol-cloud interactions. The deep convection parameterization has been largely improved with sophisticated microphysics for convective clouds, making model convection sensitive to large-scale dynamics, and incorporating the dynamical and physical effects of organized mesoscale convection. Improvements in aerosol wet removal processes and parameter re-tuning of key aerosol and cloud processes have improved model aerosol radiative forcing. The model's vertical resolution has increased from 72 to 80 layers with the extra eight layers added in the lower stratosphere to better simulate the Quasi-Biennial Oscillation. These improvements have enhanced E3SM's capability to couple aerosol, chemistry, and biogeochemistry and reduced some long-standing biases in simulating tropical variability. Compared to its predecessors, the model shows a much stronger signal for the Madden-Julian Oscillation, Kelvin waves, mixed Rossby-gravity waves, and eastward inertia-gravity waves. Aerosol radiative forcing has been considerably reduced and is now better aligned with community best estimates, leading to significantly improved skill in simulating historical temperature records. Its simulated mean-state climate is largely comparable to E3SMv2, but with some notable degradation in shortwave cloud radiative effect, precipitable water, and surface wind stress, which will be addressed in future updates.

In global atmospheric models, resolving stratocumulus (Sc) in the vertical is computationally expensive. However, Sc appear only under special meteorological conditions. Therefore, there is motivation to refine the vertical grid levels adaptively. In order to facilitate the possibility of parallelization on graphical processing units, our grid adaptation method prescribes the number of vertical levels a priori. Then grid levels are relocated toward altitude ranges in need of refinement. Because the method relocates existing grid levels, rather than adding extra levels, there is a risk of creating regions with overly coarse grid spacing, that is, voids in the grid mesh. To prevent such voids from forming, a simple method is developed to impose a maximum grid spacing. To decide where to place enhanced resolution, the authors develop an empirical mesh refinement criterion. It refines grid spacing near the ground, near strong temperature gradients, and within clouds. Our grid adaptation method is implemented in a single-column model and evaluated on four test cases: decaying stratocumulus, developing shallow cumulus, a quasi-stationary stratocumulus deck, and the diurnal cycle of a dry boundary layer. In the stratocumulus cases, mesh refinement leads to improvements in both the time evolution of fields and their time averages. The other two cases show smaller differences.

AbstractThe parameterization of subgrid‐scale processes such as boundary layer (PBL) turbulence introduces uncertainty in Earth System Model (ESM) results. This uncertainty can contribute to or exacerbate existing biases in representing key physical processes. This study analyzes the influence of tunable parameters in an experimental version of the Cloud Layers Unified by Binormals (CLUBBX) scheme. CLUBB is the operational PBL parameterization in the Community Atmosphere Model version 6 (CAM6), the atmospheric component of the Community ESM version 2 (CESM2). We perform the Morris one‐at‐a‐time (MOAT) parameter sensitivity analysis using short‐term (3‐day), initialized hindcasts of CAM6‐CLUBBX with 24 unique initial conditions. Several input parameters modulating vertical momentum flux appear most influential for various regionally‐averaged quantities, namely surface stress and shortwave cloud forcing (SWCF). These parameter sensitivities have a spatial dependence, with parameters governing momentum flux most influential in regions of high vertical wind shear (e.g., the mid‐latitude storm tracks). We next evaluate several experimental 20‐year simulations of CAM6‐CLUBBX with targeted parameter perturbations. We find that parameter perturbations produce similar physical mechanisms in both short‐term and long‐term simulations, but these physical responses can be muted due to nonlinear feedbacks manifesting over time scales longer than 3 days, thus causing differences in how output metrics respond in the long‐term simulations. Analysis of turbulent fluxes in CLUBBX indicates that the influential parameters affect vertical fluxes of heat, moisture, and momentum, providing physical pathways for the sensitivities identified in this study.

Abstract The higher‐order turbulence scheme, Cloud Layers Unified by Binormals (CLUBB), is known for effectively simulating the transition from cumulus to stratocumulus clouds within leading atmospheric climate models. This study investigates an underexplored aspect of CLUBB: its capacity to simulate near‐surface winds and the Planetary Boundary Layer (PBL), with a particular focus on its coupling with surface momentum flux. Using the GFDL atmospheric climate model (AM4), we examine two distinct coupling strategies, distinguished by their handling of surface momentum flux during the CLUBB's stability‐driven substepping performed at each atmospheric time step. The static coupling maintains a constant surface momentum flux, while the dynamic coupling adjusts the surface momentum flux at each CLUBB substep based on the CLUBB‐computed zonal and meridional wind speed tendencies. Our 30‐year present‐day climate simulations (1980–2010) show that static coupling overestimates 10‐m wind speeds compared to both control AM4 simulations and reanalysis, particularly over the Southern Ocean (SO) and other midlatitude ocean regions. Conversely, dynamic coupling corrects the static coupling 10‐m winds biases in the midlatitude regions, resulting in CLUBB simulations achieving there an excellent agreement with AM4 simulations. Furthermore, analysis of PBL vertical profiles over the SO reveals that dynamic coupling reduces downward momentum transport, consistent with the found wind‐speed reductions. Instead, near the tropics, dynamic coupling results in minimal changes in near‐surface wind speeds and associated turbulent momentum transport structure. Notably, the wind turning angle serves as a valuable qualitative metric for assessing the impact of changes in surface momentum flux representation on global circulation patterns.

Abstract Land‐atmosphere interactions are central to the evolution of the atmospheric boundary layer and the subsequent formation of clouds and precipitation. Existing global climate models represent these connections with bulk approximations on coarse spatial scales, but observations suggest that small‐scale variations in surface characteristics and co‐located turbulent and momentum fluxes can significantly impact the atmosphere. Recent model development efforts have attempted to capture this phenomenon by coupling existing representations of subgrid‐scale (SGS) heterogeneity between land and atmosphere models. Such approaches are in their infancy and it is not yet clear if they can produce a realistic atmospheric response to surface heterogeneity. Here, we implement a parameterization to capture the effects of SGS heterogeneity in the Community Earth System Model (CESM2), and compare single‐column simulations against high‐resolution Weather Research and Forecasting (WRF) large‐eddy simulations (LESs), which we use as a proxy for observations. The CESM2 experiments increase the temperature and humidity variances in the lowest atmospheric levels, but the response is weaker than in WRF‐LES. In part, this is attributed to an underestimate of surface heterogeneity in the land model due to a lack of SGS meteorology, a separation between deep and shallow convection schemes in the atmosphere, and a lack of explicitly represented mesoscale secondary circulations. These results highlight the complex processes involved in capturing the effects of SGS heterogeneity and suggest the need for parameterizations that communicate their influence not only at the surface but also vertically.

Discretized numerical models of the atmosphere are usually intended to faithfully represent an underlying set of continuous equations, but this necessary condition is violated sometimes by subtle pathologies that have crept into the discretized equations. Such pathologies can introduce undesirable artifacts, such as sawtooth noise, into the model solutions. The presence of these pathologies can be detected by numerical convergence testing. This study employs convergence testing to verify the discretization of the Cloud Layers Unified By Binormals (CLUBB) model of clouds and turbulence. That convergence testing identifies two aspects of CLUBB’s equation set that contribute to undesirable noise in the solutions. First, numerical limiters (i.e. clipping) used by CLUBB introduce discontinuities or slope discontinuities in model fields. Second, nonlinear numerical diffusion employed for improving numerical stability can introduce unintended small-scale features into the solution of the model equations. Smoothing the limiters and using linear diffusion (low-order hyperdiffusion) reduces the noise and restores the expected first-order convergence in CLUBB’s solutions. These model reformulations enhance our confidence in the trustworthiness of solutions from CLUBB by eliminating the unphysical oscillations in high-resolution simulations. The improvements in the results at coarser, near-operational grid spacing and timestep are also seen in cumulus cloud and dry turbulence tests. In addition, convergence testing is proven to be a valuable tool for detecting pathologies, including unintended discontinuities and grid dependence, in the model equation set.

The Department of Energy (DOE)'s Energy Exascale Earth System Model (E3SM), including its atmosphere model (EAM), has many relatively new features. In a previous study we conducted a systematic parametric sensitivity analysis for EAM based on short, perturbed parameter ensemble (PPE) simulations, mainly focusing on global mean climate features and metrics. While parameter values in global climate models are generally invariant in space and time, model response to parameters perturbation may vary by regions and climate regimes, which motivates the need to better understand the EAM model behaviors and physics at regional scale and process level. In this study, using the same set of PPE simulations and a similar sensitivity analysis framework, we identify parameters that cause largest sensitivities over different regions and compare model responses in fast atmospheric processes to the parameters across different cloud regimes for several important cloud-related fidelity metrics. We find that cloud forcing has opposite response to some parameters over mid-latitude vs. tropical land. We also analyze how the parametric sensitivity varies as stratocumulus transitions to shallow convection and to deep convection over ocean. Low cloud forcing and shortwave cloud forcing in the subtropical eastern Pacific are most sensitive to the parameters controlling the width of the probability density function (PDF) of the subgrid vertical velocity (w') (gamma) and the damping of the w' skewness (c8) near the coast but become more sensitive to the parameter affecting the damping of the w' variance (c1) further offshore. Detailed interpretation of the spatial dependence of parametric sensitivity is provided. We also investigate how the parametric sensitivity evolves with prediction duration. This study improves our process-level understanding of cloud physics and parameterization and provides insights for developing more advanced regime-aware parameterization schemes in global climate model.

Chapter 10 Higher-Order Equations Closed by the Assumed PDF Method: Suitability for Parameterizing Cumulus Convection Vincent E. Larson, Vincent E. Larson Department of Mathematical Sciences, University of Wisconsin-Milwaukee, Milwaukee, WI, USA Pacific Northwest National Laboratory, Richland, WA, USASearch for more papers by this author Vincent E. Larson, Vincent E. Larson Department of Mathematical Sciences, University of Wisconsin-Milwaukee, Milwaukee, WI, USA Pacific Northwest National Laboratory, Richland, WA, USASearch for more papers by this author Book Editor(s):Yangang Liu, Yangang LiuSearch for more papers by this authorPavlos Kollias, Pavlos KolliasSearch for more papers by this author First published: 30 November 2023 https://doi.org/10.1002/9781119529019.ch10Book Series:Geophysical Monograph Series AboutPDFPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShareShare a linkShare onEmailFacebookTwitterLinkedInRedditWechat Summary One method for parameterizing turbulence and clouds in the Earth's atmosphere is higher-order closure. In this method, equations are formed for relevant subgrid-scale moments, such as vertical turbulent fluxes and vertical velocity variance. These equations contain unclosed terms. 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This paper provides a comprehensive derivation of the total energy equations for the atmospheric components of Earth System Models (ESMs). The assumptions and approximations made in this derivation are motivated and discussed. In particular, it is emphasized that closing the energy budget is conceptually challenging and hard to achieve in practice without resorting to ad hoc fixers. As a concrete example, the energy budget terms are diagnosed in a realistic climate simulation using a global atmosphere model. The largest total energy errors in this example are spurious dynamical core energy dissipation, thermodynamic inconsistencies (e.g., coupling parameterizations with the host model) and missing processes/terms associated with falling precipitation and evaporation (e.g., enthalpy flux between components). The latter two errors are not, in general, reduced by increasing horizontal resolution. They are due to incomplete thermodynamic and dynamic formulations. Future research directions are proposed to reconcile and improve thermodynamics formulations and conservation principles.