This page reviews and organizes emerging hybrid Earth System Models (ESMs), which combine Machine Learning (ML) and physics-based components, alphabetically. Hybrid ESMs retain essential components for physical consistency (e.g., the dynamical core) while using ML to enhance parameterizations for small-scale processes (e.g., clouds). These models hold promise for improving long-term projections of Earth's physical climate and biogeochemical cycles.
If you notice any errors, omissions, or outdated information, please feel free to submit a pull request.
Author: Tom Beucler (UNIL); written in the context of AI4PEX.
- ACE
- CBRAIN
- CliMA
- ClimSim
- Corrective ML
- DLESyM
- Hybrid ARP-GEM
- Hybrid CAM
- Hybrid LSM
- Hybrid SAM
- Hybrid WRF
- ICON-ML
- LUCIE
- MOM6
- NCAM
- NeuralGCM
- Samudra
The AI2 Climate Emulator (ACE) emulates NOAA's FV3GFS atmospheric model using spherical Fourier neural operators. ACE operates with six prognostic variables, can be forced through insolation and sea surface skin temperature, diagnoses radiative and energy fluxes at the atmosphere's boundaries, and runs on a single GPU. ACE2 improves upon ACE by enforcing global conservation of dry air mass and humidity, making it a hybrid climate model and improving climate stability and surface pressure representation. ACE2, which can be coupled to a slab ocean, is trained and tested on historical climate reanalysis (1940-2020) and 100 km-resolution Unified Forecast System (UFS) simulations forced by historical sea surface temperatures and greenhouse gas concentrations.
Latest coupled simulations in Clark, S. K., Watt-Meyer, O., Kwa, A., McGibbon, J., Henn, B., Perkins, W. A., ... & Harris, L. M. (2024). ACE2-SOM: Coupling to a slab ocean and learning the sensitivity of climate to changes in CO2. arXiv:2412.04418.
- Watt-Meyer, O., Henn, B., McGibbon, J., Clark, S. K., Kwa, A., Perkins, W. A., Wu, E., Harris, L., & Bretherton, C. S. (2024). ACE2: Accurately learning subseasonal to decadal atmospheric variability and forced responses. arXiv 2411.11268
- Duncan, J. P., Wu, E., Golaz, J. C., Caldwell, P. M., Watt‐Meyer, O., Clark, S. K., ... & Bretherton, C. S. (2024). Application of the AI2 Climate Emulator to E3SMv2's global atmosphere model, with a focus on precipitation fidelity. Journal of Geophysical Research: Machine Learning and Computation, 1(3), e2024JH000136.
- Watt-Meyer, O., Dresdner, G., McGibbon, J., Clark, S. K., Henn, B., Duncan, J., ... & Bretherton, C. S. (2023). ACE: A fast, skillful learned global atmospheric model for climate prediction. arXiv preprint 2310.02074.
Cloud Brain (CBRAIN) aims to break the convective parameterization deadlock in the Community Atmosphere Model (CAM) by training neural networks to emulate the total subgrid thermodynamic time tendencies. These tendencies represent the cumulative tendencies of prognostic thermodynamic variables (temperature and specific humidity) due to subgrid-scale processes such as convection, radiation, and turbulence.
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In the aquaplanet ("ocean world") configuration, the Super-Parameterized Community Atmosphere Model v3 (SPCAM3) is used. Here, each coarse grid cell contains a two-dimensional convection-permitting model that explicitly resolves convection, providing the target tendencies for the neural networks.
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In the realistic geography configuration, the Super-Parameterized Community Atmosphere Model v5 (SPCAM5) is coupled with the Community Land Model v4 (CLM4). As in the aquaplanet configuration, each coarse grid cell includes a two-dimensional convection-permitting model that explicitly resolves convection, providing the target tendencies for the neural networks.
Latest coupled simulations in Lin, J., Yu, S., Peng, L., Beucler, T., Wong-Toi, E., Hu, Z., ... & Pritchard, M. S. (2024). Sampling Hybrid Climate Simulation at Scale to Reliably Improve Machine Learning Parameterization. arXiv preprint 2309.16177.
- Behrens, G., Beucler, T., Iglesias-Suarez, F., Yu, S., Gentine, P., Pritchard, M., ... & Eyring, V. (2024). Improving Atmospheric Processes in Earth System Models with Deep Learning Ensembles and Stochastic Parameterizations. arXiv preprint 2402.03079.
- Rasp, S., Pritchard, M. S., & Gentine, P. (2018). Deep learning to represent subgrid processes in climate models. Proceedings of the national academy of sciences, 115(39), 9684-9689.
- Iglesias‐Suarez, F., Gentine, P., Solino‐Fernandez, B., Beucler, T., Pritchard, M., Runge, J., & Eyring, V. (2024). Causally‐informed deep learning to improve climate models and projections. Journal of Geophysical Research: Atmospheres, 129(4), e2023JD039202.
- Ott, J., Pritchard, M., Best, N., Linstead, E., Curcic, M., & Baldi, P. (2020). A fortran‐keras deep learning bridge for scientific computing. Scientific Programming, 2020(1), 8888811.
- Beucler, T., Gentine, P., Yuval, J., Gupta, A., Peng, L., Lin, J., ... & Pritchard, M. (2024). Climate-invariant machine learning. Science Advances, 10(6), eadj7250.
- Mooers, G., Pritchard, M., Beucler, T., Ott, J., Yacalis, G., Baldi, P., & Gentine, P. (2021). Assessing the potential of deep learning for emulating cloud superparameterization in climate models with real‐geography boundary conditions. Journal of Advances in Modeling Earth Systems, 13(5), e2020MS002385.
- Gentine, P., Pritchard, M., Rasp, S., Reinaudi, G., & Yacalis, G. (2018). Could machine learning break the convection parameterization deadlock?. Geophysical Research Letters, 45(11), 5742-5751.
The Climate Modeling Alliance (CliMA) is "building a new Earth system model that leverages recent advances in computational and data sciences to learn directly from a wealth of Earth observations from space and the ground." Its atmospheric component adopts a generalized version of the Eddy-Diffusivity Mass-Flux framework and relies on Bayesian inference for parameter calibration and uncertainty quantification through the "Calibrate, Emulate, Sample" framework. Its oceanic component is based on the "Oceananigans" model, which is designed for the numerical simulation of incompressible, stratified, rotating fluid flows on CPUs and GPUs.
Latest coupled simulations in Christopoulos, C., Lopez-Gomez, I., Beucler, T., Cohen, Y., Kawczynski, C., Dunbar, O., & Schneider, T. (2024). Online Learning of Entrainment Closures in a Hybrid Machine Learning Parameterization. Authorea Preprints.
- Lopez‐Gomez, I., Christopoulos, C., Langeland Ervik, H. L., Dunbar, O. R., Cohen, Y., & Schneider, T. (2022). Training physics‐based machine‐learning parameterizations with gradient‐free ensemble Kalman methods. Journal of Advances in Modeling Earth Systems, 14(8), e2022MS003105.
- Lima, M., Deck, K., Dunbar, O. R., & Schneider, T. (2024). Toward Routing River Water in Land Surface Models with Recurrent Neural Networks. arXiv preprint 2404.14212.
- Charbonneau, A., Deck, K., & Schneider, T. (2023). A physics-constrained neural differential equation for data-driven seasonal snowpack forecasting. Artificial Intelligence for the Earth Systems, in review.
- Schneider, T., Lan, S., Stuart, A., & Teixeira, J. (2017). Earth system modeling 2.0: A blueprint for models that learn from observations and targeted high‐resolution simulations. Geophysical Research Letters, 44(24), 12-396.
ClimSim, the first benchmark dataset for hybrid ML-physics climate emulation, includes simulation data from the Energy Exascale Earth System Model Multi-scale Modeling Framework (E3SM-MMF). E3SM-MMF embeds GPU-accelerated cloud-resolving models within each grid cell of E3SM and uses explicit scalar momentum transport to ensure the quality of subgrid-scale fluxes. ClimSim provides billions of multivariate input/output vector pairs, capturing the aggregate effect of cloud-resolving models on E3SM's macro-scale state. ClimSim also inspired a Kaggle competition and includes an end-to-end workflow for developing hybrid ML-physics simulators.
Latest coupled simulations in Hu, Z., Subramaniam, A., Kuang, Z., Lin, J., Yu, S., Hannah, W. M., ... & Pritchard, M. S. (2024). Stable Machine-Learning Parameterization of Subgrid Processes with Real Geography and Full-physics Emulation. arXiv preprint 2407.00124.
- Yu, S., Hu, Z., Subramaniam, A., Hannah, W., Peng, L., Lin, J., Bhouri, M. A., Gupta, R., Lütjens, B., Will, J. C., Behrens, G., Busecke, J. J. M., Loose, N., Stern, C. I., Beucler, T., Harrop, B., Heuer, H., Hillman, B. R., Jenney, A., ... Pritchard, M. (2024). ClimSim-Online: A large multi-scale dataset and framework for hybrid ML-physics climate emulation. arXiv preprint 2306.08754
- Yu, S., Hannah, W., Peng, L., Lin, J., Bhouri, M. A., Gupta, R., ... & Pritchard, M. (2024). ClimSim: A large multi-scale dataset for hybrid physics-ML climate emulation. Advances in Neural Information Processing Systems, 36.
Building on early efforts to enhance subgrid-scale physics through machine learning with near-global storm-resolving aquaplanet simulations, AI2 has developed a series of data-driven solutions to improve the (thermo)dynamics of FV3-GFS, the atmospheric component of the Unified Forecast System (UFS). The latest efforts focused on learning apparent dynamic tendencies to nudge temperature and humidity toward a reference state derived from a global storm-resolving GFDL X-SHiELD simulation, informally called "Corrective ML."
Latest coupled simulations in Watt‐Meyer, O., Brenowitz, N. D., Clark, S. K., Henn, B., Kwa, A., McGibbon, J., ... & Bretherton, C. S. (2024). Neural network parameterization of subgrid‐scale physics from a realistic geography global storm‐resolving simulation. Journal of Advances in Modeling Earth Systems, 16(2), e2023MS003668.
- Kwa, A., Clark, S. K., Henn, B., Brenowitz, N. D., McGibbon, J., Watt‐Meyer, O., ... & Bretherton, C. S. (2023). Machine‐learned climate model corrections from a global storm‐resolving model: Performance across the annual cycle. Journal of Advances in Modeling Earth Systems, 15(5), e2022MS003400.
- Clark, S. K., Brenowitz, N. D., Henn, B., Kwa, A., McGibbon, J., Perkins, W. A., ... & Harris, L. M. (2022). Correcting a 200 km resolution climate model in multiple climates by machine learning from 25 km resolution simulations. Journal of Advances in Modeling Earth Systems, 14(9), e2022MS003219.
- Bretherton, C. S., Henn, B., Kwa, A., Brenowitz, N. D., Watt‐Meyer, O., McGibbon, J., ... & Harris, L. (2022). Correcting coarse‐grid weather and climate models by machine learning from global storm‐resolving simulations. Journal of Advances in Modeling Earth Systems, 14(2), e2021MS002794.
- Chen, T. C., Penny, S. G., Whitaker, J. S., Frolov, S., Pincus, R., & Tulich, S. (2022). Correcting systematic and state‐dependent errors in the NOAA FV3‐GFS using neural networks. Journal of Advances in Modeling Earth Systems, 14(11), e2022MS003309.
- Watt‐Meyer, O., Brenowitz, N. D., Clark, S. K., Henn, B., Kwa, A., McGibbon, J., ... & Bretherton, C. S. (2021). Correcting weather and climate models by machine learning nudged historical simulations. Geophysical Research Letters, 48(15), e2021GL092555.
- Sanford, C., Kwa, A., Watt‐Meyer, O., Clark, S. K., Brenowitz, N., McGibbon, J., & Bretherton, C. (2023). Improving the reliability of ML‐corrected climate models with novelty detection. Journal of Advances in Modeling Earth Systems, 15(11), e2023MS003809.
- Brenowitz, N. D., Henn, B., McGibbon, J., Clark, S. K., Kwa, A., Perkins, W. A., ... & Bretherton, C. S. (2020). Machine learning climate model dynamics: Offline versus online performance. NeurIPS 2020 CCAI workshop.
- Brenowitz, N. D., & Bretherton, C. S. (2019). Spatially extended tests of a neural network parametrization trained by coarse‐graining. Journal of Advances in Modeling Earth Systems, 11(8), 2728-2744.
- Brenowitz, N. D., & Bretherton, C. S. (2018). Prognostic validation of a neural network unified physics parameterization. Geophysical Research Letters, 45(12), 6289-6298.
Latest coupled simulations in Cresswell-Clay, N., Liu, B., Durran, D., Liu, A., Espinosa, Z. I., Moreno, R., & Karlbauer, M. (2024). A deep learning earth system model for stable and efficient simulation of the current climate. arXiv preprint 2409.16247.
Hybrid ARP-GEM1 combines the dynamical core of the new global atmospheric model ARP-GEM1 (Global, Efficient, and Multiscale version of ARPEGE version 1) with neural network-based parameterizations. It employs the Python interface of the Message Passing Interface-based “field-exchange” method OASIS3, enabling neural network integration on heterogenous High-Performance Computing (HPC) architectures. Initial prototypes emulate deep learning parameterization, and Hybrid ARP-GEM1's modular design enables the coupling of diverse data-driven parameterizations in the near term.
Latest coupled simulations in Balogh, B., Saint-Martin, D., & Geoffroy, O. (2024). Online test of a neural network deep convection parameterization in ARP-GEM1. arXiv preprint 2410.21920
Latest coupled simulations in Chapman, W. E., & Berner, J. (2024). A State-Dependent Model-Error Representation for Online Climate Model Bias Correction. Authorea Preprints.
- Gettelman, A., Gagne, D. J., Chen, C. C., Christensen, M. W., Lebo, Z. J., Morrison, H., & Gantos, G. (2021). Machine learning the warm rain process. Journal of Advances in Modeling Earth Systems, 13(2), e2020MS002268.
- Limon, G. C., & Jablonowski, C. (2023). Probing the skill of random forest emulators for physical parameterizations via a hierarchy of simple CAM6 configurations. Journal of Advances in Modeling Earth Systems, 15(6), e2022MS003395.
More coming soon.
See: Son, R., Stacke, T., Gayler, V., Nabel, J. E., Schnur, R., Alonso, L., ... & Carvalhais, N. (2024). Integration of a Deep‐Learning‐Based Fire Model Into a Global Land Surface Model. Journal of Advances in Modeling Earth Systems, 16(1), e2023MS003710.
Using the hypohydrostatic configuration of the System for Atmospheric Modeling (SAM), quasi-global aquaplanet simulations can represent convection and large-scale circulation simultaneously at horizontal resolutions as coarse as 12 km. This provides an ideal testbed for machine learning parameterization approaches, such as leveraging non-local information across grid columns to model subgrid momentum fluxes, employing reduced-precision computations, and making parameterizations scale-aware. Numerical stability is ensured through a per-process flux prediction framework and a short integration timestep, which allow the use of tailored SAM prognostic equations and precipitation diagnostics.
Latest coupled simulations in Yuval, J., & O’Gorman, P. A. (2023). Neural‐network parameterization of subgrid momentum transport in the atmosphere. Journal of Advances in Modeling Earth Systems, 15(4), e2023MS003606.
- Yuval, J., O'Gorman, P. A., & Hill, C. N. (2021). Use of neural networks for stable, accurate and physically consistent parameterization of subgrid atmospheric processes with good performance at reduced precision. Geophysical Research Letters, 48(6), e2020GL091363.
- Wang, P., Yuval, J., & O’Gorman, P. A. (2022). Non‐local parameterization of atmospheric subgrid processes with neural networks. Journal of Advances in Modeling Earth Systems, 14(10), e2022MS002984.
- Yuval, J., & O’Gorman, P. A. (2020). Stable machine-learning parameterization of subgrid processes for climate modeling at a range of resolutions. Nature communications, 11(1), 3295.
- Georgakaki, P., & Nenes, A. (2024). RaFSIP: Parameterizing ice multiplication in models using a machine learning approach. Journal of Advances in Modeling Earth Systems, 16(6), e2023MS003923.
- Zhong, X., Yu, X., & Li, H. (2024). Machine learning parameterization of the multi-scale Kain–Fritsch (MSKF) convection scheme and stable simulation coupled in the Weather Research and Forecasting (WRF) model using WRF–ML v1. 0. Geoscientific Model Development, 17(9), 3667-3685.
- Zhong, X., Ma, Z., Yao, Y., Xu, L., Wu, Y., & Wang, Z. (2023). WRF–ML v1. 0: a bridge between WRF v4. 3 and machine learning parameterizations and its application to atmospheric radiative transfer. Geoscientific Model Development, 16(1), 199-209.
Latest coupled simulations in Heuer, H., Schwabe, M., Gentine, P., Giorgetta, M. A., & Eyring, V. (2024). Interpretable multiscale machine learning-based parameterizations of convection for ICON. Journal of Advances in Modeling Earth Systems, 16, e2024MS004398.
- Grundner, A., Beucler, T., Gentine, P., & Eyring, V. (2024). Data‐driven equation discovery of a cloud cover parameterization. Journal of Advances in Modeling Earth Systems, 16(3), e2023MS003763.
- Grundner, A., Beucler, T., Gentine, P., Iglesias‐Suarez, F., Giorgetta, M. A., & Eyring, V. (2022). Deep learning based cloud cover parameterization for ICON. Journal of Advances in Modeling Earth Systems, 14(12), e2021MS002959.
Latest coupled simulations in Guan, H., Arcomano, T., Chattopadhyay, A., & Maulik, R. (2024). LUCIE: A Lightweight Uncoupled ClImate Emulator with long-term stability and physical consistency for O (1000)-member ensembles. arXiv preprint 2405.16297.
Latest coupled simulations in Gregory, W., Bushuk, M., Zhang, Y., Adcroft, A., & Zanna, L. (2024). Machine learning for online sea ice bias correction within global ice‐ocean simulations. Geophysical Research Letters, 51(3), e2023GL106776.
- Zhang, C., Perezhogin, P., Gultekin, C., Adcroft, A., Fernandez‐Granda, C., & Zanna, L. (2023). Implementation and evaluation of a machine learned mesoscale eddy parameterization into a numerical ocean circulation model. Journal of Advances in Modeling Earth Systems, 15(10), e2023MS003697.
- Perezhogin, P., Zhang, C., Adcroft, A., Fernandez-Granda, C., & Zanna, L. (2023). Implementation of a data-driven equation-discovery mesoscale parameterization into an ocean model. arXiv preprint 2311.02517.
- Sane, A., Reichl, B. G., Adcroft, A., & Zanna, L. (2023). Parameterizing vertical mixing coefficients in the ocean surface boundary layer using neural networks. Journal of Advances in Modeling Earth Systems, 15(10), e2023MS003890.
- Partee, S., Ellis, M., Rigazzi, A., Shao, A. E., Bachman, S., Marques, G., & Robbins, B. (2022). Using machine learning at scale in numerical simulations with SmartSim: An application to ocean climate modeling. Journal of Computational Science, 62, 101707.
Latest coupled simulations in Han, Y., Zhang, G. J., & Wang, Y. (2023). An ensemble of neural networks for moist physics processes, its generalizability and stable integration. Journal of Advances in Modeling Earth Systems, 15(10), e2022MS003508.
- Wang, X., Han, Y., Xue, W., Yang, G., & Zhang, G. J. (2022). Stable climate simulations using a realistic general circulation model with neural network parameterizations for atmospheric moist physics and radiation processes. Geoscientific Model Development, 15(9), 3923-3940.
- Han, Y., Zhang, G. J., Huang, X., & Wang, Y. (2020). A moist physics parameterization based on deep learning. Journal of Advances in Modeling Earth Systems, 12(9), e2020MS002076.
The Neural General Circulation Model (NeuralGCM) is based on a differentiable pseudo-spectral dynamical core implemented in JAX. Processes not represented by the core are learned in an end-to-end manner using a single-column parameterization that optimizes medium-range weather forecasting. NeuralGCM enables stable, multi-decadal simulations of climate variability under prescribed sea surface temperatures and is being updated to accurately simulate observed global precipitation fields.