William Gregory, Mitchell Bushuk, Alistair Adcroft, Yongfei Zhang, Laure Zanna
Data assimilation is often viewed as a framework for correcting short-term error growth in dynamical climate model forecasts. When viewed on the time scales of climate however, these short-term corrections, or analysis increments, can closely mirror the systematic bias patterns of the dynamical model. In this study, we use convolutional neural networks (CNNs) to learn a mapping from model state variables to analysis increments, in order to showcase the feasibility of a data-driven model parameterization which can predict state-dependent model errors. We undertake this problem using an ice-ocean data assimilation system within the Seamless system for Prediction and EArth system Research (SPEAR) model, developed at the Geophysical Fluid Dynamics Laboratory, which assimilates satellite observations of sea ice concentration every 5 days between 1982--2017. The CNN then takes inputs of data assimilation forecast states and tendencies, and makes predictions of the corresponding sea ice concentration increments. Specifically, the inputs are states and tendencies of sea ice concentration, sea-surface temperature, ice velocities, ice thickness, net shortwave radiation, ice-surface skin temperature, sea-surface salinity, as well as a land-sea mask. We find the CNN is able to make skillful predictions of the increments in both the Arctic and Antarctic and across all seasons, with skill that consistently exceeds that of a climatological increment prediction. This suggests that the CNN could be used to reduce sea ice biases in free-running SPEAR simulations, either as a sea ice parameterization or an online bias correction tool for numerical sea ice forecasts.
Aakash Sane, Brandon G. Reichl, Alistair Adcroft, Laure Zanna
Vertical mixing parameterizations in ocean models are formulated on the basis of the physical principles that govern turbulent mixing. However, many parameterizations include ad hoc components that are not well constrained by theory or data. One such component is the eddy diffusivity model, where vertical turbulent fluxes of a quantity are parameterized from a variable eddy diffusion coefficient and the mean vertical gradient of the quantity. In this work, we improve a parameterization of vertical mixing in the ocean surface boundary layer by enhancing its eddy diffusivity model using data-driven methods, specifically neural networks. The neural networks are designed to take extrinsic and intrinsic forcing parameters as input to predict the eddy diffusivity profile and are trained using output data from a second moment closure turbulent mixing scheme. The modified vertical mixing scheme predicts the eddy diffusivity profile through online inference of neural networks and maintains the conservation principles of the standard ocean model equations, which is particularly important for its targeted use in climate simulations. We describe the development and stable implementation of neural networks in an ocean general circulation model and demonstrate that the enhanced scheme outperforms its predecessor by reducing biases in the mixed-layer depth and upper ocean stratification. Our results demonstrate the potential for data-driven physics-aware parameterizations to improve global climate models.
Cheng Zhang, Pavel Perezhogin, Alistair Adcroft, Laure Zanna
This study addresses the boundary artifacts in machine-learned (ML) parameterizations for ocean subgrid mesoscale momentum forcing, as identified in the online ML implementation from a previous study (Zhang et al., 2023). We focus on the boundary condition (BC) treatment within the existing convolutional neural network (CNN) models and aim to mitigate the "out-of-sample" errors observed near complex coastal regions without developing new, complex network architectures. Our approach leverages two established strategies for placing BCs in CNN models, namely zero and replicate padding. Offline evaluations revealed that these padding strategies significantly reduce root mean squared error (RMSE) in coastal regions by limiting the dependence on random initialization of weights and restricting the range of out-of-sample predictions. Further online evaluations suggest that replicate padding consistently reduces boundary artifacts across various retrained CNN models. In contrast, zero padding sometimes intensifies artifacts in certain retrained models despite both strategies performing similarly in offline evaluations. This study underscores the need for BC treatments in CNN models trained on open water data when predicting near-coastal subgrid forces in ML parameterizations. The application of replicate padding, in particular, offers a robust strategy to minimize the propagation of extreme values that can contaminate computational models or cause simulations to fail. Our findings provide insights for enhancing the accuracy and stability of ML parameterizations in the online implementation of ocean circulation models with coastlines.
Surya Dheeshjith, Adam Subel, Alistair Adcroft, Julius Busecke, Carlos Fernandez-Granda, Shubham Gupta, Laure Zanna
AI emulators for forecasting have emerged as powerful tools that can outperform conventional numerical predictions. The next frontier is to build emulators for long climate simulations with skill across a range of spatiotemporal scales, a particularly important goal for the ocean. Our work builds a skillful global emulator of the ocean component of a state-of-the-art climate model. We emulate key ocean variables, sea surface height, horizontal velocities, temperature, and salinity, across their full depth. We use a modified ConvNeXt UNet architecture trained on multi-depth levels of ocean data. We show that the ocean emulator - Samudra - which exhibits no drift relative to the truth, can reproduce the depth structure of ocean variables and their interannual variability. Samudra is stable for centuries and 150 times faster than the original ocean model. Samudra struggles to capture the correct magnitude of the forcing trends and simultaneously remain stable, requiring further work.
Pavel Perezhogin, Cheng Zhang, Alistair Adcroft, Carlos Fernandez-Granda, Laure Zanna
Ocean mesoscale eddies are often poorly represented in climate models, and therefore, their effects on the large scale circulation must be parameterized. Traditional parameterizations, which represent the bulk effect of the unresolved eddies, can be improved with new subgrid models learned directly from data. Zanna and Bolton 2020 (ZB20) applied an equation-discovery algorithm to reveal an interpretable expression parameterizing the subgrid momentum fluxes by mesoscale eddies through the components of the velocity-gradient tensor. In this work, we implement the ZB20 parameterization into the primitive-equation GFDL MOM6 ocean model and test it in two idealized configurations with significantly different dynamical regimes and topography. The original parameterization was found to generate excessive numerical noise near the grid scale. We propose two filtering approaches to avoid the numerical issues and additionally enhance the strength of large-scale energy backscatter. The filtered ZB20 parameterizations led to improved climatological mean state and energy distributions, compared to the current state-of-the-art energy backscatter parameterizations. The filtered ZB20 parameterizations are scale-aware and, consequently, can be used with a single value of the non-dimensional scaling coefficient for a range of resolutions. The successful application of the filtered ZB20 parameterizations to parameterize mesoscale eddies in two idealized configurations offers a promising opportunity to reduce long-standing biases in global ocean simulations in future studies.
Laure Zanna, William Gregory, Pavel Perezhogin, Aakash Sane, Cheng Zhang, Alistair Adcroft, Mitch Bushuk, Carlos Fernandez-Granda, Brandon Reichl, Dhruv Balwada, Julius Busecke, William Chapman, Alex Connolly, Danni Du, Kelsey Everard, Fabrizio Falasca, Renaud Falga, David Kamm, Etienne Meunier, Qi Liu, Antoine Nasser, Matthew Pudig, Andrew Shao, Julia L. Simpson, Linus Vogt, Jiarong Wu
Climate simulations, at all grid resolutions, rely on approximations that encapsulate the forcing due to unresolved processes on resolved variables, known as parameterizations. Parameterizations often lead to inaccuracies in climate models, with significant biases in the physics of key climate phenomena. Advances in artificial intelligence (AI) are now directly enabling the learning of unresolved processes from data to improve the physics of climate simulations. Here, we introduce a flexible framework for developing and implementing physics- and scale-aware machine learning parameterizations within climate models. We focus on the ocean and sea-ice components of a state-of-the-art climate model by implementing a spectrum of data-driven parameterizations, ranging from complex deep learning models to more interpretable equation-based models. Our results showcase the viability of AI-driven parameterizations in operational models, advancing the capabilities of a new generation of hybrid simulations, and include prototypes of fully coupled atmosphere-ocean-sea-ice hybrid simulations. The tools developed are open source, accessible, and available to all.
Jia-Rui Shi, Pavel Perezhogin, Laure Zanna, Alistair Adcroft
Mesoscale eddies remain poorly represented in most climate models, motivating the use of parameterizations to account for their dynamical effects on the coupled system. In this study, we implement a data-driven eddy parameterization based on Zanna and Bolton (2020; ZB20) in an idealized, fully coupled CESM configuration and assess its influence on the mean climate state. When applied within an eddy-permitting ocean model (MOM6) embedded in the coupled configuration, the ZB20 eddy momentum parameterization, which features upgradient (backscatter) momentum flux, energizes mesoscale eddies and strengthens poleward ocean heat transport. The response is particularly strong in the Southern Hemisphere, where the open circumpolar channel sustains vigorous eddy activity and is sensitive to the parameterization, further leading to a marked hemispheric asymmetry. The oceanic meridional overturning circulation also intensifies around 60°S. The resulting ocean adjustments produce a coherent dipolar temperature pattern, with cooling in mid-latitudes and warming at high latitudes, driven primarily by anomalous meridional heat transport rather than local surface fluxes, shown using a regional heat-budget analysis. The atmosphere, in turn, exhibits a compensating reduction in meridional heat transport and an equatorward shift of the mid-latitude jet, associated with the mid-latitude surface cooling and changes in the meridional temperature gradient. Together, these results highlight how a data-driven eddy momentum parameterization can affect large-scale circulation and the mean climate state, providing a reference for understanding its impacts in more comprehensive climate models.
Jia-Rui Shi, Laure Zanna, Alistair Adcroft
We investigate the temporal evolution of ocean heat uptake efficiency (OHUE) using observations and large ensemble model simulations. OHUE, defined as the ratio of the rate in ocean heat uptake to changes in global mean surface temperature anomalies, has exhibited significant variability over recent decades. We found a relatively low OHUE in the late 1980s, a peak around 2000, and a subsequent decline. A key finding is the significant influence of natural external forcing, mainly volcanic eruptions, which causes an abrupt decline in OHUE followed by a gradual recovery. The 1991 Mount Pinatubo eruption, a major volcanic event of the 20th century, had a lasting impact on OHUE. This study emphasizes the contribution of mid-latitudes to global OHUE changes. Our findings underscore the importance of considering natural external forcing in understanding climate dynamics and suggest conducting idealized experiments to quantify the potential effects of future volcanic eruptions on OHUE.
William Gregory, Mitchell Bushuk, Yongfei Zhang, Alistair Adcroft, Laure Zanna
In this study we perform online sea ice bias correction within a GFDL global ice-ocean model. For this, we use a convolutional neural network (CNN) which was developed in a previous study (Gregory et al., 2023) for the purpose of predicting sea ice concentration (SIC) data assimilation (DA) increments. An initial implementation of the CNN shows systematic improvements in SIC biases relative to the free-running model, however large summertime errors remain. We show that these residual errors can be significantly improved with a data augmentation approach, in which sequential CNN and DA corrections are applied to a new simulation over the training period. This then provides a new training data set with which to refine the weights of the initial network. We propose that this machine-learned correction scheme could be utilized for generating improved initial conditions, and also for real-time sea ice bias correction within seasonal-to-subseasonal sea ice forecasts.
Venkatramani Balaji, Alistair Adcroft, Zhi Liang
The comparative analysis of output from multiple models, and against observational data analysis archives, has become a key methodology in reducing uncertainty in climate projections, and in improving forecast skill of medium- and long-term forecasts. There is considerable momentum toward simplifying such analyses by applying comprehensive community-standard metadata to observational and model output data archives. The representation of gridded data is a critical element in describing the contents of model output. We seek here to propose a standard for describing the grids on which such data are discretized. The standard is drafted specifically for inclusion within the Climate and Forecasting (CF) metadata conventions. The contents of this paper have been in the "grey literature" since 2007: it has been posted to arXiv to be citable. To preserve its integrity, the contents have not been updated.
Surya Dheeshjith, Adam Subel, Shubham Gupta, Alistair Adcroft, Carlos Fernandez-Granda, Julius Busecke, Laure Zanna
With the success of machine learning (ML) applied to climate reaching further every day, emulators have begun to show promise not only for weather but for multi-year time scales in the atmosphere. Similar work for the ocean remains nascent, with state-of-the-art limited to models running for shorter time scales or only for regions of the globe. In this work, we demonstrate high-skill global emulation for surface ocean fields over 5-8 years of model rollout, accurately representing modes of variability for two different ML architectures (ConvNext and Transformers). In addition, we address the outstanding question of generalization, an essential consideration if the end-use of emulation is to model warming scenarios outside of the model training data. We show that 1) generalization is not an intrinsic feature of a data-driven emulator, 2) fine-tuning the emulator on only small amounts of additional data from a distribution similar to the test set can enable the emulator to perform well in a warmed climate, and 3) the forced emulators are robust to noise in the forcing.
William Gregory, Mitchell Bushuk, Yong-Fei Zhang, Alistair Adcroft, Laure Zanna, Colleen McHugh, Liwei Jia
We showcase a hybrid modeling framework which embeds machine learning (ML) inference into the GFDL SPEAR climate model, for online sea ice bias correction during a set of global fully-coupled 1-year retrospective forecasts. We compare two hybrid versions of SPEAR to understand the importance of exposing ML models to coupled ice-atmosphere-ocean feedbacks before implementation into fully-coupled simulations: Hybrid_CPL (with feedbacks) and Hybrid_IO (without feedbacks). Relative to SPEAR, Hybrid_CPL systematically reduces seasonal forecast errors in the Arctic and significantly reduces Antarctic errors for target months May-December, with >2x error reduction in 4-6-month lead forecasts of Antarctic winter sea ice extent. Meanwhile, Hybrid_IO suffers from out-of-sample behavior which can trigger a chain of Southern Ocean feedbacks, leading to ice-free Antarctic summers. Our results demonstrate that ML can significantly improve numerical sea ice prediction capabilities and that exposing ML models to coupled ice-atmosphere-ocean processes is essential for generalization in fully-coupled simulations.
Pavel Perezhogin, Alistair Adcroft, Laure Zanna
Data-driven methods have become popular to parameterize the effects of mesoscale eddies in ocean models. However, they perform poorly in generalization tasks and may require retuning if the grid resolution or ocean configuration changes. We address the generalization problem by enforcing physics constraints on a neural network parameterization of mesoscale eddy fluxes. We found that the local scaling of input and output features helps to generalize to unseen grid resolutions and depths offline in the global ocean. The scaling is based on dimensional analysis and incorporates grid spacing as a length scale. We formulate our findings as a general algorithm that can be used to enforce data-driven parameterizations with dimensional scaling. The new parameterization improves the representation of kinetic and potential energy in online simulations with idealized and global ocean models. Comparison to baseline parameterizations and impact on global ocean biases are discussed.
James P. C. Duncan, Elynn Wu, Surya Dheeshjith, Adam Subel, Troy Arcomano, Spencer K. Clark, Brian Henn, Anna Kwa, Jeremy McGibbon, W. Andre Perkins, William Gregory, Carlos Fernandez-Granda, Julius Busecke, Oliver Watt-Meyer, William J. Hurlin, Alistair Adcroft, Laure Zanna, Christopher Bretherton
Traditional numerical global climate models simulate the full Earth system by exchanging boundary conditions between separate simulators of the atmosphere, ocean, sea ice, land surface, and other geophysical processes. This paradigm allows for distributed development of individual components within a common framework, unified by a coupler that handles translation between realms via spatial or temporal alignment and flux exchange. Following a similar approach adapted for machine learning-based emulators, we present SamudrACE: a coupled global climate model emulator which produces centuries-long simulations at 1-degree horizontal, 6-hourly atmospheric, and 5-daily oceanic resolution, with 145 2D fields spanning 8 atmospheric and 19 oceanic vertical levels, plus sea ice, surface, and top-of-atmosphere variables. SamudrACE is highly stable and has low climate biases comparable to those of its components with prescribed boundary forcing, with realistic variability in coupled climate phenomena such as ENSO that is not possible to simulate in uncoupled mode.
Cheng Zhang, Pavel Perezhogin, Cem Gultekin, Alistair Adcroft, Carlos Fernandez-Granda, Laure Zanna
We address the question of how to use a machine learned parameterization in a general circulation model, and assess its performance both computationally and physically. We take one particular machine learned parameterization \cite{Guillaumin1&Zanna-JAMES21} and evaluate the online performance in a different model from which it was previously tested. This parameterization is a deep convolutional network that predicts parameters for a stochastic model of subgrid momentum forcing by mesoscale eddies. We treat the parameterization as we would a conventional parameterization once implemented in the numerical model. This includes trying the parameterization in a different flow regime from that in which it was trained, at different spatial resolutions, and with other differences, all to test generalization. We assess whether tuning is possible, which is a common practice in general circulation model development. We find the parameterization, without modification or special treatment, to be stable and that the action of the parameterization to be diminishing as spatial resolution is refined. We also find some limitations of the machine learning model in implementation: 1) tuning of the outputs from the parameterization at various depths is necessary; 2) the forcing near boundaries is not predicted as well as in the open ocean; 3) the cost of the parameterization is prohibitively high on CPUs. We discuss these limitations, present some solutions to problems, and conclude that this particular ML parameterization does inject energy, and improve backscatter, as intended but it might need further refinement before we can use it in production mode in contemporary climate models.
Benjamin A. Storer, Mehrnoush Kharghani, Alistair Adcroft, Hussein Aluie
Treatment of fields near domain boundaries is a long-standing problem in signal processing that has come into renewed focus following recent efforts in convolution-based multiscale coarse-graining and in machine-learned parameterizations due to ocean boundary artifacts. Here, we propose a general method for extending fields beyond the domain boundaries by solving a Laplace boundary-value problem. Construction of the harmonic extension is well-posed, including uniqueness, and is consistent with the boundary conditions by design. The formulation applies to irregular boundaries such as discretized coastlines. The harmonic extension is physically desirable since it has minimum spatial variability among all admissible extensions satisfying the boundary conditions. The method is simple to implement using well-established numerical approaches, and is broadly applicable to extending oceanic variables over land boundaries. Other applications include machine learning parametrization and subgrid modeling of wall-bounded flows and multiphase flows. We demonstrate the method by extending sea-surface temperature (SST) over land using fixed temperature (Dirichlet) and no-flux (Neumann) boundary conditions: the land-filled solution is smooth with SST values between the coastal minimum and maximum.
Cem Gultekin, Adam Subel, Cheng Zhang, Matan Leibovich, Pavel Perezhogin, Alistair Adcroft, Carlos Fernandez-Granda, Laure Zanna
Due to computational constraints, climate simulations cannot resolve a range of small-scale physical processes, which have a significant impact on the large-scale evolution of the climate system. Parameterization is an approach to capture the effect of these processes, without resolving them explicitly. In recent years, data-driven parameterizations based on convolutional neural networks have obtained promising results. In this work, we provide an in-depth analysis of these parameterizations developed using data from ocean simulations. The parametrizations account for the effect of mesoscale eddies toward improving simulations of momentum, heat, and mass exchange in the ocean. Our results provide several insights into the properties of data-driven parameterizations based on neural networks. First, their performance can be substantially improved by increasing the geographic extent of the training data. Second, they learn nonlinear structure, since they are able to outperform a linear baseline. Third, they generalize robustly across different CO2 forcings, but not necessarily across different ocean depths. Fourth, they exploit a relatively small region of their input to generate their output. Our results will guide the further development of ocean mesoscale eddy parameterizations, and multiscale modeling more generally.
Pavel Perezhogin, Alistair Adcroft, Laure Zanna
Global ocean models exhibit biases in the mean state and variability, particularly at coarse resolution, where mesoscale eddies are unresolved. To address these biases, parameterization coefficients are typically tuned ad hoc. Here, we formulate parameter tuning as a calibration problem using Ensemble Kalman Inversion (EKI). We optimize parameters of a neural network parameterization of mesoscale eddies in two idealized ocean models at coarse resolution. The calibrated parameterization reduces errors in the time-averaged fluid interfaces and their variability by approximately a factor of two compared to the unparameterized model or the offline-trained parameterization. The EKI method is robust to noise in time-averaged statistics arising from chaotic ocean dynamics. Furthermore, we propose an efficient calibration protocol that bypasses integration to statistical equilibrium by carefully choosing an initial condition. These results demonstrate that systematic calibration can substantially improve coarse-resolution ocean simulations and provide a practical pathway for reducing biases in global ocean models.
William Gregory, Mitchell Bushuk, James Duncan, Elynn Wu, Adam Subel, Spencer K. Clark, Bill Hurlin, Oliver Watt-Meyer, Alistair Adcroft, Chris Bretherton, Laure Zanna
We introduce FloeNet, a machine-learning emulator trained on the Geophysical Fluid Dynamics Laboratory global sea ice model, SIS2. FloeNet is a mass-conserving model, emulating 6-hour mass and area budget tendencies related to sea ice and snow-on-sea-ice growth, melt, and advection. We train FloeNet using simulated data from a reanalysis-forced ice-ocean simulation and test its ability to generalize to pre-industrial control and 1% CO2 climates. FloeNet outperforms a non-conservative model at reproducing sea ice and snow-on-sea-ice mean state, trends, and inter-annual variability, with volume anomaly correlations above 0.96 in the Antarctic and 0.76 in the Arctic, across all forcings. FloeNet also produces the correct thermodynamic vs dynamic response to forcing, enabling physical interpretability of emulator output. Finally, we show that FloeNet outputs high-fidelity coupling-related variables, including ice-surface skin temperature, ice-to-ocean salt flux, and melting energy fluxes. We hypothesize that FloeNet will improve polar climate processes within existing atmosphere and ocean emulators.
Luke P Van Roekel, Alistair J. Adcroft, Gokhan Danabasoglu, Stephen M. Griffies, Brian Kauffman, William Large, Michael Levy, Brandon Reichl, Todd Ringler, Martin Schmidt
We evaluate the Community ocean Vertical Mixing (CVMix) project version of the K-profile parameterization (KPP). For this purpose, one-dimensional KPP simulations are compared across a suite of oceanographically relevant regimes against large eddy simulations (LES). The LES is forced with horizontally uniform boundary fluxes and has horizontally uniform initial conditions, allowing its horizontal average to be compared to one-dimensional KPP tests. We find the standard configuration of KPP consistent with LES across many forcing regimes, supporting the physical basis of KPP. Our evaluation motivates recommendations for "best practices" for using KPP within ocean circulation models, and identifies areas where further research is warranted. Further, our test suite can be used as a baseline for evaluation of a broad suite of boundary layer models. The original treatment of KPP recommends the matching of interior diffusivities and their gradients to the KPP predicted values computed in the ocean surface boundary layer (OSBL). However, we find that difficulties in representing derivatives of rapidly changing diffusivities near the base of the OSBL can lead to loss of simulation fidelity. We propose two alternative approaches. We find the KPP entrainment buoyancy flux to be sensitive to vertical grid resolution and details of how to diagnose the KPP boundary layer depth. We modify the KPP turbulent shear velocity parameterization to reduce resolution dependence. Additionally, our results show that the KPP parameterized non-local tracer flux is incomplete due to the assumption that it solely redistributes the surface tracer flux. However, examination of the LES vertical turbulent scalar flux budgets show that non-local fluxes can exist in the absence of surface tracer fluxes. This result motivates further studies of the non-local flux parameterization.