Articles | Volume 16, issue 11
https://doi.org/10.5194/gmd-16-3123-2023
© Author(s) 2023. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/gmd-16-3123-2023
© Author(s) 2023. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Review and perspective paper
| 
02 Jun 2023
Review and perspective paper |
| 02 Jun 2023
| 02 Jun 2023
Differentiable programming for Earth system modeling
Maximilian Gelbrecht
CORRESPONDING AUTHOR
Earth System Modelling, School of Engineering and Design, Technical University of Munich, Munich, Germany
Potsdam Institute for Climate Impact Research, Potsdam, Germany
Alistair White
Earth System Modelling, School of Engineering and Design, Technical University of Munich, Munich, Germany
Potsdam Institute for Climate Impact Research, Potsdam, Germany
Sebastian Bathiany
Earth System Modelling, School of Engineering and Design, Technical University of Munich, Munich, Germany
Potsdam Institute for Climate Impact Research, Potsdam, Germany
Niklas Boers
Earth System Modelling, School of Engineering and Design, Technical University of Munich, Munich, Germany
Potsdam Institute for Climate Impact Research, Potsdam, Germany
Department of Mathematics and Global Systems Institute, University of Exeter, Exeter, UK
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Cited
18 citations as recorded by crossref.
- Prediction of monthly Arctic sea ice concentration using physics-constrained U2-Net M. Liu et al. https://doi.org/10.1016/j.engappai.2026.115334
- Neural general circulation models for weather and climate D. Kochkov et al. https://doi.org/10.1038/s41586-024-07744-y
- Using Physics-Encoded GeoAI to Improve the Physical Realism of Deep Learning′s Rainfall-Runoff Responses under Climate Change H. Li et al. https://doi.org/10.1016/j.jag.2024.104101
- Deep Learning Emulator Towards Both Forward and Adjoint Modes of Atmospheric Gas-Phase Chemical Process Y. Liu et al. https://doi.org/10.3390/atmos16091109
- Arctic Sea Ice Concentration Prediction Using Spatial Attention Deep Learning H. Gu et al. https://doi.org/10.1109/JSTARS.2024.3486187
- Explainable Offline‐Online Training of Neural Networks for Parameterizations: A 1D Gravity Wave‐QBO Testbed in the Small‐Data Regime H. Pahlavan et al. https://doi.org/10.1029/2023GL106324
- Spatiotemporal response of depth‑to‑water table (ZWT) to the Three Gorges Reservoir impoundment across hydrological year types J. Feng et al. https://doi.org/10.1016/j.ejrh.2026.103344
- JCM v1.1: a differentiable, intermediate-complexity atmospheric model E. Davenport et al. https://doi.org/10.5194/gmd-19-6451-2026
- Neural Networks Under Hamiltonian Constraints: A Comprehensive Review on Structural Evolution and Applications Z. Zhang et al. https://doi.org/10.1109/ACCESS.2025.3638011
- Advancing parameter uncertainty quantification in hydrology models through integration of variational inference with a differentiable hydrology framework G. V. Nguyen et al. https://doi.org/10.1007/s00477-025-02954-w
- Targeted Calibration to Adjust Stability Biases in Complex Dynamical System Models D. Pals et al. https://doi.org/10.1103/624z-1p1s
- JAX-MPM: a learning-augmented differentiable meshfree framework for GPU-accelerated Lagrangian simulation and geophysical inverse modeling H. Du & Q. He https://doi.org/10.1007/s00366-026-02320-6
- Advances in land surface forecasting: a comparison of LSTM, gradient boosting, and feed-forward neural networks as prognostic state emulators in a case study with ecLand M. Wesselkamp et al. https://doi.org/10.5194/gmd-18-921-2025
- Reconstructing historical climate fields with deep learning N. Bochow et al. https://doi.org/10.1126/sciadv.adp0558
- Spatio-temporal consistency of cloud-microphysical parameter sensitivity in a warm-conveyor belt M. Hieronymus et al. https://doi.org/10.1016/j.jocs.2025.102614
- Constructing extreme heatwave storylines with differentiable climate models T. Whittaker & A. Di Luca https://doi.org/10.5194/wcd-7-393-2026
- Integrating multi-task learning with a differentiable physics constrained framework for hydrological forecasting Y. Yan et al. https://doi.org/10.1038/s41598-026-41277-w
- Emulating non-differentiable metrics via knowledge-guided learning: Introducing the Minkowski image loss F. Quarenghi et al. https://doi.org/10.1017/eds.2026.10048
18 citations as recorded by crossref.
- Prediction of monthly Arctic sea ice concentration using physics-constrained U2-Net M. Liu et al. https://doi.org/10.1016/j.engappai.2026.115334
- Neural general circulation models for weather and climate D. Kochkov et al. https://doi.org/10.1038/s41586-024-07744-y
- Using Physics-Encoded GeoAI to Improve the Physical Realism of Deep Learning′s Rainfall-Runoff Responses under Climate Change H. Li et al. https://doi.org/10.1016/j.jag.2024.104101
- Deep Learning Emulator Towards Both Forward and Adjoint Modes of Atmospheric Gas-Phase Chemical Process Y. Liu et al. https://doi.org/10.3390/atmos16091109
- Arctic Sea Ice Concentration Prediction Using Spatial Attention Deep Learning H. Gu et al. https://doi.org/10.1109/JSTARS.2024.3486187
- Explainable Offline‐Online Training of Neural Networks for Parameterizations: A 1D Gravity Wave‐QBO Testbed in the Small‐Data Regime H. Pahlavan et al. https://doi.org/10.1029/2023GL106324
- Spatiotemporal response of depth‑to‑water table (ZWT) to the Three Gorges Reservoir impoundment across hydrological year types J. Feng et al. https://doi.org/10.1016/j.ejrh.2026.103344
- JCM v1.1: a differentiable, intermediate-complexity atmospheric model E. Davenport et al. https://doi.org/10.5194/gmd-19-6451-2026
- Neural Networks Under Hamiltonian Constraints: A Comprehensive Review on Structural Evolution and Applications Z. Zhang et al. https://doi.org/10.1109/ACCESS.2025.3638011
- Advancing parameter uncertainty quantification in hydrology models through integration of variational inference with a differentiable hydrology framework G. V. Nguyen et al. https://doi.org/10.1007/s00477-025-02954-w
- Targeted Calibration to Adjust Stability Biases in Complex Dynamical System Models D. Pals et al. https://doi.org/10.1103/624z-1p1s
- JAX-MPM: a learning-augmented differentiable meshfree framework for GPU-accelerated Lagrangian simulation and geophysical inverse modeling H. Du & Q. He https://doi.org/10.1007/s00366-026-02320-6
- Advances in land surface forecasting: a comparison of LSTM, gradient boosting, and feed-forward neural networks as prognostic state emulators in a case study with ecLand M. Wesselkamp et al. https://doi.org/10.5194/gmd-18-921-2025
- Reconstructing historical climate fields with deep learning N. Bochow et al. https://doi.org/10.1126/sciadv.adp0558
- Spatio-temporal consistency of cloud-microphysical parameter sensitivity in a warm-conveyor belt M. Hieronymus et al. https://doi.org/10.1016/j.jocs.2025.102614
- Constructing extreme heatwave storylines with differentiable climate models T. Whittaker & A. Di Luca https://doi.org/10.5194/wcd-7-393-2026
- Integrating multi-task learning with a differentiable physics constrained framework for hydrological forecasting Y. Yan et al. https://doi.org/10.1038/s41598-026-41277-w
- Emulating non-differentiable metrics via knowledge-guided learning: Introducing the Minkowski image loss F. Quarenghi et al. https://doi.org/10.1017/eds.2026.10048
Saved (final revised paper)
Latest update: 21 Jul 2026
Editorial statement
This paper reviews the technique of differentiable programming in Earth System Modeling.
This paper reviews the technique of differentiable programming in Earth System Modeling.
Short summary
Differential programming is a technique that enables the automatic computation of derivatives of the output of models with respect to model parameters. Applying these techniques to Earth system modeling leverages the increasing availability of high-quality data to improve the models themselves. This can be done by either using calibration techniques that use gradient-based optimization or incorporating machine learning methods that can learn previously unresolved influences directly from data.
Differential programming is a technique that enables the automatic computation of derivatives of...
