Geometric Structures Underlying Parameterizations in Geophysical Fluid Dynamics.
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In climate predictions, clouds are the leading source of uncertainty. This is partly because, to simulate the fluid dynamics of climate over the entire globe, a large grid spacing must be used, so clouds are a subgrid-scale parametrization rather than a resolved feature. Here, a framework is investigated with finer grid spacing of O(1) or O(10)km so that some clouds are not subgrid-scale; instead, clouds evolve on the numerical grid. This cloud evolution is achieved using stochastic modeling. Hence, the framework is idealized in the sense that the full fluid dynamics of cloud circulations is still not resolved, and simplified vertical structures are used. Nevertheless, the fluid dynamics model includes evolving clouds that interactively adjust in size, shape, lifetime, and regional coverage. In addition, different cloud types are included with different roles in the climate system, including deep convective clouds and also boundary-layer clouds such as shallow cumulus and stratocumulus clouds. Other basic aspects of the idealized climate system are planetary-scale circulations (e.g., Walker circulation) and radiation. With these ingredients (evolving clouds, planetary-scale circulations, and radiation), the framework has the potential for idealized investigations of climate change with interactive cloud–radiative feedback of individual clouds. Here, the formulation of the model equations is presented, and numerical simulations are shown to illustrate the model dynamics and climate change.
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This paper is Part II of a two‐part paper that documents the Climate Model version 4X (CM4X) hierarchy of coupled climate models developed at the Geophysical Fluid Dynamics Laboratory. Part I of this paper is presented in Griffies et al. (2025a, https://doi.org/10.1029/2024MS004861 ). Here we present a suite of case studies that examine ocean and sea ice features that are targeted for further research, which include sea level, eastern boundary upwelling, Arctic and Southern Ocean sea ice, Southern Ocean circulation, and North Atlantic circulation. The case studies are based on experiments that follow the protocol of version 6 from the Coupled Model Intercomparison Project. The analysis reveals a systematic improvement in the simulation fidelity of CM4X relative to its CM4.0 predecessor, as well as an improvement when refining the ocean/sea ice horizontal grid spacing from the 0.25° of CM4X‐p25 to the 0.125° of CM4X‐p125. Even so, there remain many outstanding biases, thus pointing to the need for further grid refinements, enhancements to numerical methods, and/or advances in parameterizations, each of which target long‐standing model biases and limitations.
We present the GFDL‐CM4X (Geophysical Fluid Dynamics Laboratory Climate Model version 4X) coupled climate model hierarchy. The primary application for CM4X is to investigate ocean and sea ice physics as part of a realistic coupled Earth climate model. CM4X utilizes an updated MOM6 (Modular Ocean Model version 6) ocean physics package relative to CM4.0, and there are two members of the hierarchy: one that uses a horizontal grid spacing of 0.25° (referred to as CM4X‐p25) and the other that uses a grid 0.125° (CM4X‐p125). CM4X also refines its atmospheric grid from the nominally 100 km (cubed sphere C96) of CM4.0–50 km (C192). Finally, CM4X simplifies the land model to allow for a more focused study of the role of ocean changes to global mean climate. CM4X‐p125 reaches a global ocean area mean heat flux imbalance of -0.02 W m -2 within $\mathcal{O}$ (150) years in a pre‐industrial simulation, and retains that thermally equilibrated state over the subsequent centuries. This 1850 thermal equilibrium is characterized by roughly 400 ZJ less ocean heat than present‐day, which corresponds to estimates for anthropogenic ocean heat uptake between 1870 and present‐day. CM4X‐p25 approaches its thermal equilibrium only after more than 1000 years, at which time its ocean has roughly 1100 ZJ more heat than its early 21st century ocean initial state. Furthermore, the root‐mean‐square sea surface temperature bias for historical simulations is roughly 20% smaller in CM4X‐p125 relative to CM4X‐p25 (and CM4.0). We offer the mesoscale dominance hypothesis for why CM4X‐p125 shows such favorable thermal equilibration properties.
We evaluate cloud simulations using satellite simulators against multiple observational data sets. These simulators have been run within the Geophysical Fluid Dynamics Laboratory's Atmosphere Model version 4.0 (AM4.0), as well as an alternative configuration where a fully two‐moment Morrison‐Gettelman cloud microphysical parameterization with prognostic precipitation (MG2) is applied, denoted as AM4‐MG2. The modeled cloud spatial distributions, vertical profiles, phase partitioning, cloud‐to‐precipitation transitions, and radiative effects compare reasonably well with satellite observations. Model biases include the under‐prediction of total and low‐level clouds, especially optically thin/intermediate clouds with cloud optical depth of less than 23, but the over‐prediction of thick clouds, indicating “too few, too bright” biases. These biases counteract each other, and give rise to reasonable estimates of cloud radiative effects. The underestimate of low‐level clouds is associated with too early and too frequent drizzle/precipitation formation. The precipitation bias is improved in AM4‐MG2, where the autoconversion scheme initiates the precipitation more realistically. There also exist discrepancies between models and observations for midlevel and high‐level clouds. Additional biases include the underestimate of liquid cloud fraction and the overestimate of ice cloud fraction.
Abstract The complexity of growing spatiotemporal resolution of climate simulations produces a variety of climate patterns under different projection scenarios. This paper proposes a new data-driven climate classification workflow via an unsupervised deep learning technique that can dimensionally reduce the vast volume of spatiotemporal numerical climate projection data into a compact representation. We aim to identify distinct zones that capture multiple climate variables as well as their future changes under different climate change scenarios. Our approach leverages convolutional autoencoders combined with k -means clustering (standard autoencoder) and online clustering based on the Sinkhorn–Knopp algorithm (clustering autoencoder) across the conterminous United States (CONUS) to capture unique climate patterns in a data-driven fashion from the Geophysical Fluid Dynamics Laboratory Earth System Model with GOLD component (GFDL-ESM2G). The developed approach compresses 70 years of GFDL-ESM2G simulation at 0.125° spatial resolution across the CONUS under multiple warming scenarios to a lower-dimensional space by a factor of 660 000 and then tested on 150 years of GFDL-ESM2G simulation data. The results show that five climate clusters capture physically reasonable and spatially stable climatological patterns matched to known climate classes defined by human experts. Results also show that using a clustering autoencoder can reduce the computational time for clustering by up to 9.2 times when compared to using a standard autoencoder. Our five unique climate patterns resulting from the deep learning–based clustering of the lower-dimensional space thereby enable us to provide insights on hydrometeorology and its spatial heterogeneity across the conterminous United States immediately without downloading large climate datasets. Significance Statement This paper presents a data-driven climate classification approach using unsupervised deep learning to dimensionally reduce climate model outputs and to identify distinct climate regions for their future changes. Our approach compresses climate information for 70 years of Geophysical Fluid Dynamics Laboratory Earth System Model data across the conterminous United States (CONUS) at 0.125° spatial resolution. The results reveal that five climate clusters capture reasonable and stable climatological patterns matched to known climate patterns. The embedded clustering process in deep learning provides ×9.2 times faster execution than the k -means clustering technique. These results give us insight about climate spatial patterns and heterogeneity of hydrological patterns across the conterminous United States without downloading large climate datasets.
Relatively strongly stratified turbulent flows tend to self-organise into a ‘layered anisotropic stratified turbulence’ (LAST) regime, characterised by relatively deep and well-mixed density ‘layers’ separated by relatively thin ‘interfaces’ of enhanced density gradient. Understanding the associated mixing dynamics is a central problem in geophysical fluid dynamics. It is challenging to study LAST mixing, as it is associated with Reynolds numbers $Re := UL/\nu \gg 1$ and Froude numbers $Fr :=(2{\rm \pi} U)/(L N) \ll 1$ ( $U$ and $L$ being characteristic velocity and length scales, $\nu$ the kinematic viscosity and $N$ the buoyancy frequency). Since a sufficiently large dynamic range (largely) unaffected by stratification and viscosity is required, it is also necessary for the buoyancy Reynolds number $Re_{b} := \epsilon /(\nu N^{2}) \gg 1$ , where $\epsilon$ is the (appropriately volume-averaged) turbulent kinetic energy dissipation rate. This requirement is exacerbated for oceanically relevant flows, as the Prandtl number $Pr := \nu /\kappa = {O}(10)$ in thermally stratified water (where $\kappa$ is the thermal diffusivity), thus leading (potentially) to even finer density field structures. We report here on four forced fully resolved direct numerical simulations of stratified turbulence at various Froude ( $Fr=0.5, 2$ ) and Prandtl ( $Pr=1, 7$ ) numbers forced so that $Re_{b}=50$ , with resolutions up to $30\,240 \times 30\,240 \times 3780$ . We find that, as $Pr$ increases, emergent ‘interfaces’ become finer and their contribution to bulk mixing characteristics decreases at the expense of the small-scale density structures populating the well-mixed ‘layers’. However, extreme mixing events (as quantified by significantly elevated local destruction rates of buoyancy variance $\chi _0$ ) are always preferentially found in the (statically stable) interfaces, irrespective of the value of $Pr$ .
Here, we highlight the differing roles of vorticity and strain in the transport of coarse-grained scalars at length scales larger than ℓ by smaller scale (subscale) turbulence. We use the first term in a multiscale gradient expansion due to which exhibits excellent correlation with the exact subscale physics when the partitioning length ℓ is any scale smaller than that of the spectral peak. We show that unlike subscale strain, which acts as an anisotropic diffusion/antidiffusion tensor, subscale vorticity's contribution is solely a conservative advection of coarse-grained quantities by an eddy-induced nondivergent velocity, v * , that is proportional to the curl of vorticity. Therefore, material (Lagrangian) advection of coarse-grained quantities is accomplished not by the coarse-grained flow velocity, u¯ ℓ , but by the effective velocity, u¯ ℓ + v * , the physics of which may improve commonly used LES models.
Generative deep learning techniques are employed in a novel framework for the construction of surrogate models capturing the spatiotemporal dynamics of 2D plasma turbulence. The proposed Generative Artificial Intelligence Turbulence (GAIT) framework enables the acceleration of turbulence simulations for long-time transport studies. GAIT leverages a convolutional variational auto-encoder and a recurrent neural network to generate new turbulence data from existing simulations, extending the time horizon of transport studies with minimal computational cost. The application of the GAIT framework to plasma turbulence using the Hasegawa–Wakatani (HW) model is presented, evaluating its performance via various analyses. Very good agreement is found between the GAIT and the HW models in the spatiotemporal Fourier and Proper Orthogonal Decomposition spectra, the flow topology characterized by the Okubo–Weiss parameter, and the time autocorrelation function of turbulent fluctuations. Excellent agreement has also been obtained in the probability distribution function of particle displacements and the effective turbulent diffusivity. In-depth analyses of the latent space of turbulent states, choice of hyperparameters and alternative deep learning models for the time prediction are presented. Our results highlight the potential of Artificial Intelligence-based surrogate models to overcome the computational challenges in turbulence simulation, which can be extended to other situations such as geophysical fluid dynamics.
Large-scale windstorms represent an important atmospheric hazard in the Northeastern US (NE) and are associated with substantial socioeconomic losses. Regional simulations performed with the Weather Research and Forecasting (WRF) model using lateral boundary conditions from three Earth System Models (ESMs: Geophysical Fluid Dynamics Laboratory (GFDL), Hadley Centre Global Environment Model (HadGEM) and Max Planck Institute (MPI)) are used to quantify possible future changes in windstorm characteristics and/or changes in the parent cyclone types responsible for windstorms. WRF nested within MPI ESM best represents important aspects of historical windstorms and the cyclone types responsible for generating windstorms compared with a reference simulation performed with the ERA-Interim reanalysis for the historical climate. The spatial scale and frequency of the largest windstorms in each simulation defined using the greatest extent of exceedance of local 99.9th percentile wind speeds (U > U999) plus 50-year return period wind speeds (U50,RP) do not exhibit secular trends. Projections of extreme wind speeds and windstorm intensity/frequency/geolocation and dominant parent cyclone type associated with windstorms vary markedly across the simulations. Only the MPI nested simulations indicate statistically significant differences in windstorm spatial scale, frequency and intensity over the NE in the future and historical periods. This model chain, which also exhibits the highest fidelity in the historical climate, yields evidence of future increases in 99.9th percentile 10 m height wind speeds, the frequency of simultaneous U > U999 over a substantial fraction (5–25%) of the NE and the frequency of maximum wind speeds above 22.5 ms−1. These geophysical changes, coupled with a projected doubling of population, leads to a projected tripling of a socioeconomic loss index, and hence risk to human systems, from future windstorms.
Understanding how turbulence enhances irreversible scalar mixing in density-stratified fluids is a central problem in geophysical fluid dynamics. While isotropic overturning regions are commonly the focus of mixing analyses, we here investigate whether significant mixing may arise in anisotropic statically stable regions of the flow. Focusing on a single forced direct numerical simulation of stratified turbulence, we analyse spatial correlations between the vertical density gradient $\partial \rho /\partial z$ and the dissipation rates of kinetic energy $\epsilon$ and scalar variance $\chi$ , the latter quantifying scalar mixing. The domain is characterized by relatively well-mixed density layers separated by sharp stable interfaces that are correlated with high vertical shear. While static instability is most prevalent within the mixed layers, much of the scalar mixing is localized to the intervening interfaces, a phenomenon not apparent if considering local static instability or $\epsilon$ alone. While the majority of the domain is characterized by the canonical flux coefficient $\varGamma \equiv \chi /\epsilon =0.2$ , often assumed in ocean mixing parametrizations, extreme values of $\chi$ within the statically stable interfaces, associated with elevated $\varGamma$ , strongly skew the bulk statistics. Our findings suggest that current parametrizations of turbulent mixing may be biased by undersampling, such that the most common, but not necessarily the most significant, mixing events are overweighted. Having focused here on a single simulation of stratified turbulence, it is hoped that our results motivate a broader investigation into the role played by stable density interfaces in mixing, across a wider range of parameters and forcing schemes representative of ocean turbulence.
Abstract Cumulus entrainment substantially regulates the earth's climate but remains poorly constrained in global climate models. Recent studies have shown that cumulus bulk entrainment (or dilution) is particularly sensitive to continentality, with the entrainment rate in simulated maritime cumuli nearly double that of continental cumuli. This study examines the impacts of such land–ocean entrainment contrasts on the current climate using 21‐year simulations with the Geophysical Fluid Dynamics Laboratory's High‐Resolution Atmospheric Model (HIRAM). In response to a 25% reduction in the HIRAM entrainment parameter c 0 over land, precipitation over tropical land regions increases by up to 40%. Along with directly facilitating enhanced convective precipitation, this c 0 reduction induces an increase in soil moisture, which may contribute to a further enhancement of convective precipitation over land. A 25% c 0 reduction over the oceans leads to more widespread modifications of convection patterns, with the strongest signal in the tropical Pacific. Deep convection shifts upstream (eastward) there, inducing enhanced large‐scale ascent over the central Pacific with compensating subsidence and reduced humidity and precipitation over the western Pacific (WP). Land–ocean variations in c 0 project onto the Pacific Walker circulation, with the 25% land reduction strengthening it by 4% and the 25% ocean reduction weakening it by 14%. These changes are driven by variations in convective and large‐scale stratiform heating over the Pacific. While reduced c 0 over land enhances diabatic heating in the Maritime Continent to strengthen the Walker circulation, reduced c 0 over the oceans decreases diabatic heating in the WP to weaken the Walker circulation.
We present a variable-resolution global chemistry-climate model (AM4VR) developed at NOAA's Geophysical Fluid Dynamics Laboratory (GFDL) for research at the nexus of US climate and air quality extremes. AM4VR has a horizontal resolution of 13 km over the US, allowing it to resolve urban-to-rural chemical regimes, mesoscale convective systems, and land-surface heterogeneity. With the resolution gradually reducing to 100 km over the Indian Ocean, we achieve multi-decadal simulations driven by observed sea surface temperatures at 50% of the computational cost for a 25-km uniform-resolution grid. In contrast with GFDL's AM4.1 contributing to the sixth Coupled Model Intercomparison Project at 100 km resolution, AM4VR features much improved US climate mean patterns and variability. In particular, AM4VR shows improved representation of: precipitation seasonal-to-diurnal cycles and extremes, notably reducing the central US dry-and-warm bias; western US snowpack and summer drought, with implications for wildfires; and the North American monsoon, affecting dust storms. AM4VR exhibits excellent representation of winter precipitation, summer drought, and air pollution meteorology in California with complex terrain, enabling skillful prediction of both extreme summer ozone pollution and winter haze events in the Central Valley. AM4VR also provides vast improvements in the process-level representations of biogenic volatile organic compound emissions, interactive dust emissions from land, and removal of air pollutants by terrestrial ecosystems. We highlight the value of increased model resolution in representing climate–air quality interactions through land-biosphere feedbacks. AM4VR offers a novel opportunity to study global dimensions to US air quality, especially the role of Earth system feedbacks in a changing climate.
Abstract Materials simulations based on direct numerical solvers are accurate but computationally expensive for predicting materials evolution across length- and time-scales, due to the complexity of the underlying evolution equations, the nature of multiscale spatiotemporal interactions, and the need to reach long-time integration. We develop a method that blends direct numerical solvers with neural operators to accelerate such simulations. This methodology is based on the integration of a community numerical solver with a U-Net neural operator, enhanced by a temporal-conditioning mechanism to enable accurate extrapolation and efficient time-to-solution predictions of the dynamics. We demonstrate the effectiveness of this hybrid framework on simulations of microstructure evolution via the phase-field method. Such simulations exhibit high spatial gradients and the co-evolution of different material phases with simultaneous slow and fast materials dynamics. We establish accurate extrapolation of the coupled solver with large speed-up compared to DNS depending on the hybrid strategy utilized. This methodology is generalizable to a broad range of materials simulations, from solid mechanics to fluid dynamics, geophysics, climate, and more.
This work develops the NSBC (non-stationary bias correction) methodology to correct temperature projection bias from E3SM. The NSBC deep learning framework consists of a three-part architecture: an auto-encoder for compressing the spatial information, an LSTM for predicting annual temperature mean, and a U-Net for capturing the residual bias in temperature. The non-stationary bias correction (NSBC) framework can correct the non-stationarity of the biases of the climate models, which significantly improves the accuracy of future temperature prediction and improves the overestimation of extreme high temperatures that many existing bias correction methods suffer from. Getting started 1. Obtain the historical climate simulation and observation data. The E3SM simulation data are available through https://aims2.llnl.gov/search/cmip6/. The pseudo observations, the Geophysical Fluid Dynamics Laboratory (GFDL)-ESM4 model (Krasting et al., 2018) are available through https://aims2.llnl.gov/search/cmip6/. The spatial resolution of E3SM and pseudo observation datasets are both regridded to a common 1° resolution grid using conservative interpolation. The regridded E3SM and pseudo observation with 1° resolution can be found throught ./data/. 2. Train the Auto-encoder model. Python 0-autoencoder.py 3. Train the LSTM Python 1-LSTM.py 4. Generate the annual mean temperature based on trained LSTM Python 2-generate_annual_mean_LSTM.py 5. Train the U-Net. Python 3-unet.py 6. Evaluation and compared with the baseline Python 4_evaluation.py Is there a deadline approaching that requires the release of yo
Abstract The frequency of atmospheric blocking has been largely underestimated by general circulation models (GCMs) participating in the Coupled Model Intercomparison Project (CMIP). Errors in the onset, persistence, barotropicity, geographical preference, seasonality, intensity, and moving speed of global blocking were diagnosed in 10 Geophysical Fluid Dynamics Laboratory (GFDL) GCMs for recent CMIP5 and CMIP6 using a detection approach that combines zonal eddies and the reversal of zonal winds. The blocking frequency, similar at 500 and 250 hPa, is underestimated by 50% in the Atlantic–Europe region during December–February but is overestimated by 60% in the Pacific–North America region during that season and by 70% in the southwest Pacific during July–August. These blocking biases at 500 hPa were investigated in the five CMIP6 models that showed improvements over the CMIP5 versions. The Atlantic–Europe underestimate corresponds to lower instantaneous blocking rates, lower persistent blocking rates, and higher persistent stationary ridge rates; the number of blocks with a duration of 4–5 days is only 40%–65% of that in observations. In contrast, the overestimate consists of excessive blocks with a duration longer than 12 days in the Pacific–North America and up to twice as many 4–6-day events in the southwest Pacific. Simulated December–February blocks up to 12 days in the Pacific–North America region tend to be stronger and to move more slowly than those in observations. Diagnostic sensitivity tests indicated that the zonal mean and zonal eddy components of the mean state play a key role, as replacing each with that of observations substantially reduced many of the outstanding biases in these GCMs.