pith. sign in

arxiv: 2605.16929 · v1 · pith:FJJMA63Lnew · submitted 2026-05-16 · 💻 cs.LG

Emulating the Forced Response of Climate Models with Flow Matching

Graham Clyne , Julia Kaltenborn , Peer Nowack , Claire Monteleoni , Anasatase Charantonis This is my paper

Pith reviewed 2026-05-19 20:14 UTC · model grok-4.3

classification 💻 cs.LG
keywords climate model emulationflow matchingdeep learningShared Socioeconomic Pathwaysclimate forcingsMESMER-Mgeneralizationtemperature response
0
0 comments X

The pith

A flow matching deep learning model trained on multiple SSPs generates climate responses to forcing combinations not seen during training.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper trains a deep learning model using flow matching on climate simulations from several Shared Socioeconomic Pathways. It demonstrates that the model can produce temperature responses for entirely new combinations of climate forcings such as carbon dioxide, methane, nitrous oxide, sulphate aerosols, and ozone. The outputs are checked against the statistical emulator MESMER-M for land surface temperature. Ablation experiments show that conditioning on a broad set of forcings is required to reproduce long-term atmospheric trends. This approach addresses the high computational cost of running full climate models for large ensembles across many scenarios.

Core claim

A flow matching deep learning model trained on multiple SSP scenarios successfully generates changing climate states in response to simultaneous climate forcings including carbon dioxide, methane, nitrous oxide, sulphate aerosols, and ozone, even for forcing combinations absent from the training data, with validation showing consistency against the MESMER-M statistical emulator of land surface temperature.

What carries the argument

Flow matching deep learning model conditioned on multiple climate forcings from SSPs, which maps forcing time series to corresponding climate response fields.

If this is right

  • Large ensembles of climate projections become feasible without running the full climate model for every new forcing scenario.
  • Scenario uncertainty and internal variability can be sampled more densely across combinations of greenhouse gases and aerosols.
  • Long-term climate trends require simultaneous conditioning on multiple forcings rather than single drivers.
  • Emulators can be retrained on additional SSPs to expand the range of generatable forcing pathways.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same conditioning approach could extend to emulating other variables such as precipitation or ocean heat content if training data are available.
  • Integration with integrated assessment models would allow faster exploration of policy-driven forcing pathways.
  • Testing on forcing levels outside the training range would reveal the limits of generalization for extreme future scenarios.

Load-bearing premise

The flow matching model conditioned only on the climate forcings supplied during training can generalize to produce physically consistent outputs for completely unseen forcing combinations without being overwhelmed by internal variability or model artifacts.

What would settle it

Running a full climate model for one or more unseen forcing combinations and finding that the emulator's spatial temperature patterns or long-term trends differ substantially from the model output beyond levels explainable by internal variability.

Figures

Figures reproduced from arXiv: 2605.16929 by Anasatase Charantonis, Claire Monteleoni, Graham Clyne, Julia Kaltenborn, Peer Nowack.

Figure 1
Figure 1. Figure 1: Flowchart of the deterministic training phase for ArchesClimate-SSP. Non-spatial [PITH_FULL_IMAGE:figures/full_fig_p009_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Rollouts for three surface variables for the scenario abrupt4xCO2. Shown is the first [PITH_FULL_IMAGE:figures/full_fig_p013_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Ensemble Mean RMSE for surface temperature ( [PITH_FULL_IMAGE:figures/full_fig_p015_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: We compare the difference of decadal averages calculated from 2090-2100 for several [PITH_FULL_IMAGE:figures/full_fig_p017_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Hovmöller plots for SST anomalies in three regions: The South (90S-20S), the Tropics [PITH_FULL_IMAGE:figures/full_fig_p019_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Hydrostatic balance residuals for all ablated models. Values closer to zero are better. [PITH_FULL_IMAGE:figures/full_fig_p019_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Vertical performance of atmospheric temperature over three regions. The whisker plot [PITH_FULL_IMAGE:figures/full_fig_p021_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Vertical performance of atmospheric geopotential height over three regions, otherwise [PITH_FULL_IMAGE:figures/full_fig_p022_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Extrapolation performance under the SSP5-8.5 high-emission scenario. (Top) Time [PITH_FULL_IMAGE:figures/full_fig_p023_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: lambda ablation on ssp4-34. 277.5 280.0 K tas 2.8 3.0 kg/m-2/s-2 1e 5 pr 0 50 100 150 200 250 300 Month 5 0 5 W/m-2 net_surface_flux [1] [1,6] [1,6,12] IPSL [PITH_FULL_IMAGE:figures/full_fig_p026_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: multitask ablation on ssp4-34. 26 [PITH_FULL_IMAGE:figures/full_fig_p026_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: RMSE for hus. References [1] Climate-Resilient Pathways: Adaptation, Mitigation, and Sustainable Development. In Christopher B. Field, Vicente R. Barros, David Jon Dokken, Katharine J. Mach, and Michael D. Mastrandrea, editors, Climate Change 2014 Impacts, Adaptation, and Vulner￾ability, pages 1101–1131. Cambridge University Press, Cambridge, 2014. ISBN 978-1-107- 41537-9. doi: 10.1017/CBO9781107415379.02… view at source ↗
Figure 13
Figure 13. Figure 13: Comparison of the number of inference steps used at inference time. Top: Normalized [PITH_FULL_IMAGE:figures/full_fig_p031_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: Ensemble Mean RMSE for ocean temperature. All variables are spatially restricted [PITH_FULL_IMAGE:figures/full_fig_p032_14.png] view at source ↗
read the original abstract

Global climate models are essential tools to simulate past and potential future pathways of climate change, as well as associated climate impacts. Shared Socioeconomic Pathways (SSPs) describe a range of future scenarios of global economic and demographic development. These SSPs are intrinsically linked to changes in climate forcings, the external drivers, such as greenhouse gas and aerosol emissions, which in turn lead to the human impact on the energy balance of the Earth over time. These forcings are fundamental boundary conditions in climate models in order to gain insight into the potential climatic impacts of these changes described by each SSP. Running a climate model, however, is extremely computationally expensive, conflicting with the need for large ensembles of simulations for each model to give, e.g., more robust estimates in the presence of internal variability (the inherent, chaotic fluctuations within the climate system) and scenario uncertainty. Recent research has demonstrated the ability to capture climate model dynamics using machine learning when conditioned on forcings from different climatic scenarios. We here train a Deep Learning (DL) model on multiple SSPs and successfully generate scenarios unseen during training. Our emulator is validated against MESMER-M, a statistical emulator of land surface temperature. Our research demonstrates the capacity to generate such changing climate states in response to a variety of simultaneous climate forcings (e.g., carbon dioxide, methane, nitrous oxide, sulphate aerosols, and ozone). In particular, our ablation studies underline a need to include a range of different forcings to represent long-term atmospheric trends with a DL emulator.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The paper trains a flow-matching deep learning model on forcing data from multiple Shared Socioeconomic Pathways (SSPs) to emulate the forced response of climate models. It claims successful generation of climate states for forcing combinations (CO2, CH4, N2O, sulphate aerosols, ozone) unseen during training, with validation against the statistical emulator MESMER-M, and ablation studies showing the need for multiple forcings to capture long-term trends.

Significance. If substantiated, the work could enable efficient exploration of new forcing scenarios without full GCM runs, supporting larger ensembles for internal variability and scenario uncertainty. The flow-matching approach conditioned on simultaneous forcings represents a relevant advance in ML-based climate emulation, provided generalization claims are quantitatively verified.

major comments (2)
  1. [Abstract] Abstract: the central claim of successful generation of unseen scenarios and validation against MESMER-M supplies no quantitative metrics (RMSE, pattern correlation, trend fidelity), error bars, training details, or ablation results, leaving the generalization to new forcing vectors unsupported.
  2. [Results / Validation] Validation and results sections: the claim that the model produces physically consistent responses for entirely unseen forcing combinations requires explicit comparison to actual GCM output (not only to MESMER-M) for at least one held-out forcing vector; without this, it is unclear whether outputs isolate the forced response or retain emulator artifacts or averaged internal variability.
minor comments (2)
  1. [Methods] Clarify in the methods how the flow-matching vector field is conditioned on the forcing time series and whether any mechanism (ensemble averaging, noise conditioning, or forced-response subtraction) is used to suppress internal variability.
  2. [Data and Experiments] Specify the exact SSPs used for training versus those held out for testing, and report the number of ensemble members or realizations per SSP.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive and detailed comments, which have helped clarify how to better present our results. We address each major comment below and describe the changes planned for the revised manuscript.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the central claim of successful generation of unseen scenarios and validation against MESMER-M supplies no quantitative metrics (RMSE, pattern correlation, trend fidelity), error bars, training details, or ablation results, leaving the generalization to new forcing vectors unsupported.

    Authors: We agree that the abstract would be strengthened by the inclusion of quantitative metrics. In the revised manuscript we will add specific values for RMSE, pattern correlation, and trend fidelity obtained from the MESMER-M validation, together with a concise statement of the training configuration and the main ablation findings. These additions will make the generalization claims more directly supported within the abstract itself. revision: yes

  2. Referee: [Results / Validation] Validation and results sections: the claim that the model produces physically consistent responses for entirely unseen forcing combinations requires explicit comparison to actual GCM output (not only to MESMER-M) for at least one held-out forcing vector; without this, it is unclear whether outputs isolate the forced response or retain emulator artifacts or averaged internal variability.

    Authors: We acknowledge the value of direct GCM comparison. MESMER-M was chosen because it supplies a clean, deterministic representation of the forced response that has itself been validated against GCM ensembles in the literature. Nevertheless, to address the concern, the revised manuscript will include an explicit comparison of the flow-matching outputs against available GCM data for at least one held-out forcing vector. We will report spatial pattern correlations, temporal trend fidelity, and other relevant metrics to demonstrate that the emulator isolates the forced response rather than inheriting statistical artifacts. revision: yes

Circularity Check

0 steps flagged

No circularity: standard supervised training with external validation

full rationale

The paper trains a flow-matching model on forcing-conditioned data from multiple SSPs and validates outputs against the independent statistical emulator MESMER-M for held-out forcing combinations. No equations, claims, or steps reduce to fitted parameters by construction, self-citation chains, or ansatz smuggling. The derivation chain consists of standard conditional generative modeling plus external benchmarking; the central generalization claim is supported by ablation studies and cross-emulator comparison rather than internal redefinition of inputs as outputs. This is the expected non-finding for a supervised emulator paper with stated external validation.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Only abstract available; no model equations, training procedure, or data details provided to identify free parameters, axioms, or invented entities.

pith-pipeline@v0.9.0 · 5815 in / 1004 out tokens · 48972 ms · 2026-05-19T20:14:42.854107+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

What do these tags mean?
matches
The paper's claim is directly supported by a theorem in the formal canon.
supports
The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends
The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses
The paper appears to rely on the theorem as machinery.
contradicts
The paper's claim conflicts with a theorem or certificate in the canon.
unclear
Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

73 extracted references · 73 canonical work pages

  1. [1]

    In Christopher B

    Climate-Resilient Pathways: Adaptation, Mitigation, and Sustainable Development. In Christopher B. Field, Vicente R. Barros, David Jon Dokken, Katharine J. Mach, and Michael D. Mastrandrea, editors,Climate Change 2014 Impacts, Adaptation, and Vulner- ability, pages 1101–1131. Cambridge University Press, Cambridge, 2014. ISBN 978-1-107- 41537-9. doi: 10.10...

    work page doi:10.1017/cbo9781107415379.025 2014

  2. [2]

    InAerosols and Climate, pages 9–52

    Aerosol in the climate system. InAerosols and Climate, pages 9–52. Elsevier, January 2022. doi: 10.1016/B978-0-12-819766-0.00008-0

    work page doi:10.1016/b978-0-12-819766-0.00008-0 2022

  3. [3]

    Acosta, Sergi Palomas, Stella V

    Mario C. Acosta, Sergi Palomas, Stella V. Paronuzzi Ticco, Gladys Utrera, Joachim Bier- camp, Pierre-Antoine Bretonniere, Reinhard Budich, Miguel Castrillo, Arnaud Caubel, Francisco Doblas-Reyes, Italo Epicoco, Uwe Fladrich, Sylvie Joussaume, Alok Ku- mar Gupta, Bryan Lawrence, Philippe Le Sager, Grenville Lister, Marie-Pierre Moine, Jean-Christophe Rioua...

    work page doi:10.5194/gmd-17-3081-2024 2024

  4. [4]

    Ander- sson, Jacklynn Stott, Remi Lam, Matthew Willson, Alvaro Sanchez-Gonzalez, and Peter Battaglia

    Ferran Alet, Ilan Price, Andrew El-Kadi, Dominic Masters, Stratis Markou, Tom R. Ander- sson, Jacklynn Stott, Remi Lam, Matthew Willson, Alvaro Sanchez-Gonzalez, and Peter Battaglia. Skillful joint probabilistic weather forecasting from marginals, June 2025

    work page 2025

  5. [5]

    Seneviratne

    Lea Beusch, Lukas Gudmundsson, and Sonia I. Seneviratne. Emulating Earth system model temperatures with MESMER: From global mean temperature trajectories to grid-point- 30 0 10 20 30 40 50 60 70 80 Years 0.8 1.0 1.2 1.4 1.6Normalized Values 0 10 20 30 40 50 60 70 80 Time Step (Aggregated) 0.02 0.00 0.02 0.04 0.06 0.08 0.10 T emperature (K) T arget 4 8 12 ...

    work page doi:10.5194/esd-11-139-2020 2040

  6. [6]

    Seneviratne

    Lea Beusch, Zebedee Nicholls, Lukas Gudmundsson, Mathias Hauser, Malte Meinshausen, and Sonia I. Seneviratne. From emission scenarios to spatially resolved projections with a chain of computationally efficient emulators: Coupling of MAGICC (v7.5.1) and MESMER (v0.8.3).Geoscientific Model Development, 15(5):2085–2103, March 2022. ISSN 1991-959X. doi: 10.51...

    work page doi:10.5194/gmd-15-2085-2022 2085

  7. [7]

    Pangu- Weather: A 3D High-Resolution Model for Fast and Accurate Global Weather Forecast, November 2022

    Kaifeng Bi, Lingxi Xie, Hengheng Zhang, Xin Chen, Xiaotao Gu, and Qi Tian. Pangu- Weather: A 3D High-Resolution Model for Fast and Accurate Global Weather Forecast, November 2022

    work page 2022

  8. [8]

    Olivier Boucher, Jérôme Servonnat, Anna Lea Albright, Olivier Aumont, Yves Balkanski, Vladislav Bastrikov, Slimane Bekki, Rémy Bonnet, Sandrine Bony, Laurent Bopp, Pascale Braconnot, Patrick Brockmann, Patricia Cadule, Arnaud Caubel, Frederique Cheruy, Fran- cisCodron, AnneCozic, DavidCugnet, FabioD’Andrea, PaoloDavini, CasimirdeLavergne, Sébastien Denvil...

    work page doi:10.1029/2019ms002010 2020

  9. [9]

    Brenowitz, Tao Ge, Akshay Subramaniam, Aayush Gupta, David M

    Noah D. Brenowitz, Tao Ge, Akshay Subramaniam, Aayush Gupta, David M. Hall, Morteza Mardani, Arash Vahdat, Karthik Kashinath, and Michael S. Pritchard. Climate in a Bottle: Towards a Generative Foundation Model for the Kilometer-Scale Global Atmosphere, May 2025

    work page 2025

  10. [10]

    DYffusion: A Dynamics- informed Diffusion Model for Spatiotemporal Forecasting, October 2023

    Salva Rühling Cachay, Bo Zhao, Hailey Joren, and Rose Yu. DYffusion: A Dynamics- informed Diffusion Model for Spatiotemporal Forecasting, October 2023

    work page 2023

  11. [11]

    Climate Change 2021: The Physical Science Basis,

    Josep G Canadell, Pedro MS Monteiro, Marcos H Costa, Stephen Syampungani, Sönke Zaehle, KirstenZickfeldCanada, andGeorgiiAAlexandrov.2021: Global Carbon and Other Biogeochemical Cycles and Feedbacks. In Climate Change 2021: The Physical Science Basis. Contribution of Working Group I to the Sixth Assessment Report of the Intergovernmental Panel on Climate ...

    work page doi:10.1017/9781009157896 2021

  12. [12]

    McInerney, Michael L

    Stefano Castruccio, David J. McInerney, Michael L. Stein, Feifei Liu Crouch, Robert L. Jacob, and Elisabeth J. Moyer. Statistical Emulation of Climate Model Projections Based on Precomputed GCM Runs.Journal of Climate, 27(5):1829–1844, March 2014. ISSN 0894-8755, 1520-0442. doi: 10.1175/JCLI-D-13-00099.1

    work page doi:10.1175/jcli-d-13-00099.1 2014

  13. [13]

    Samset, Kim Cobb, Aïda Diongue-Niang, Paul Ed- wards, Seita Emori, Sergio Henrique Faria, Ed Hawkins, Pandora Hope, Philippe Huy- brechts, Malte Meinshausen, Sawsan K

    Deliang Chen, Maisa Rojas, Bjørn H. Samset, Kim Cobb, Aïda Diongue-Niang, Paul Ed- wards, Seita Emori, Sergio Henrique Faria, Ed Hawkins, Pandora Hope, Philippe Huy- brechts, Malte Meinshausen, Sawsan K. Mustafa, Gian-Kasper Plattner, and Anne Marie 33 Tréguier. Framing, context, and methods. In Valérie Masson-Delmotte, Panmao Zhai, Anna Pirani, Sarah L. ...

    work page doi:10.1017/9781009157896.001 2021

  14. [14]

    AdaSpeech: Adaptive Text to Speech for Custom Voice, March 2021

    Mingjian Chen, Xu Tan, Bohan Li, Yanqing Liu, Tao Qin, Sheng Zhao, and Tie-Yan Liu. AdaSpeech: Adaptive Text to Speech for Custom Voice, March 2021

    work page 2021

  15. [15]

    Clark, Oliver Watt-Meyer, Anna Kwa, Jeremy McGibbon, Brian Henn, W

    Spencer K. Clark, Oliver Watt-Meyer, Anna Kwa, Jeremy McGibbon, Brian Henn, W. An- dre Perkins, Elynn Wu, Lucas M. Harris, and Christopher S. Bretherton. ACE2-SOM: Coupling an ML atmospheric emulator to a slab ocean and learning the sensitivity of cli- mate to changed CO$_2$, December 2024

    work page 2024

  16. [16]

    ArchesClimate: Probabilistic Decadal Ensemble Generation With Flow Matching, September 2025

    Graham Clyne, Guillaume Couairon, Guillaume Gastineau, Claire Monteleoni, and Anas- tase Charantonis. ArchesClimate: Probabilistic Decadal Ensemble Generation With Flow Matching, September 2025

    work page 2025

  17. [17]

    ArchesWeather & ArchesWeatherGen: A deterministic and generative model for efficient ML weather forecasting, December 2024

    Guillaume Couairon, Renu Singh, Anastase Charantonis, Christian Lessig, and Claire Mon- teleoni. ArchesWeather & ArchesWeatherGen: A deterministic and generative model for efficient ML weather forecasting, December 2024

    work page 2024

  18. [18]

    Espinosa, Raul Moreno, and Matthias Karlbauer

    Nathaniel Cresswell-Clay, Bowen Liu, Dale Durran, Zihui Liu, Zachary I. Espinosa, Raul Moreno, and Matthias Karlbauer. A Deep Learning Earth System Model for Efficient Simulation of the Observed Climate, February 2025

    work page 2025

  19. [19]

    Sea ice–air interactions amplify multidecadal variability in the North Atlantic and Arctic region.Nature Communications, 13(1):2100, April 2022

    Jiechun Deng and Aiguo Dai. Sea ice–air interactions amplify multidecadal variability in the North Atlantic and Arctic region.Nature Communications, 13(1):2100, April 2022. ISSN 2041-1723. doi: 10.1038/s41467-022-29810-7

    work page doi:10.1038/s41467-022-29810-7 2022

  20. [20]

    Alexander, Shang-Ping Xie, and Adam S

    Clara Deser, Michael A. Alexander, Shang-Ping Xie, and Adam S. Phillips. Sea Surface Temperature Variability: Patterns and Mechanisms.Annual Review of Ma- rine Science, 2(1):115–143, January 2010. ISSN 1941-1405, 1941-0611. doi: 10.1146/ annurev-marine-120408-151453

    work page 2010

  21. [21]

    Jakob Deutloff, Hermann Held, and Timothy M. Lenton. High probability of triggering climate tipping points under current policies modestly amplified by Amazon dieback and permafrost thaw.Earth System Dynamics, 16(2):565–583, April 2025. ISSN 2190-4979. doi: 10.5194/esd-16-565-2025

    work page doi:10.5194/esd-16-565-2025 2025

  22. [22]

    Samset, Laura J

    Maura Dewey, Hans-Christen Hansson, Duncan Watson-Parris, Bjørn H. Samset, Laura J. Wilcox, Anna Lewinschal, Maria Sand, Øyvind Seland, Srinath Krishnan, and Annica M. L. Ekman. AeroGP: Machine Learning How Aerosols Impact Regional Climate.Journal of Geophysical Research: Machine Learning and Computation, 2(4):e2025JH000741, 2025. ISSN 2993-5210. doi: 10....

    work page doi:10.1029/2025jh000741 2025

  23. [23]

    Samudra: An AI Global Ocean Emulator for Climate, March 2025

    Surya Dheeshjith, Adam Subel, Alistair Adcroft, Julius Busecke, Carlos Fernandez-Granda, Shubham Gupta, and Laure Zanna. Samudra: An AI Global Ocean Emulator for Climate, March 2025

    work page 2025

  24. [24]

    Damon Matthews

    Mitchell Dickau, Kirsten Zickfeld, and H. Damon Matthews. Irreversible climate changes driven by degree-years of temperature overshoot, September 2025. ISSN 2693-5015. 34

    work page 2025

  25. [25]

    F. J. Doblas-Reyes, A. A. Sörensson, M. Almazroui, A. Dosio, W. J. Gutowski, R. Haarsma, R. Hamdi, B. Hewitson, W.-T. Kwon, B. L. Lamptey, D. Maraun, T. S. Stephenson, I. Takayabu, L. Terray, A. Turner, and Z. Zuo. Linking global to regional climate change. In V. Masson-Delmotte, P. Zhai, A. Pirani, S. L. Connors, C. Péan, S. Berger, N. Caud, Y. Chen, L. ...

    work page doi:10.1017/9781009157896.012 2021

  26. [26]

    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, and Christopher Bretherton. SamudrACE: Fast and Ac- curate Coupled Climate Model...

    work page 2025

  27. [27]

    A., Senior, C

    Veronika Eyring, Sandrine Bony, Gerald A. Meehl, Catherine A. Senior, Bjorn Stevens, Ronald J. Stouffer, and Karl E. Taylor. Overview of the Coupled Model Intercompari- son Project Phase 6 (CMIP6) experimental design and organization.Geoscientific Model Development, 9(5):1937–1958, May 2016. ISSN 1991-959X. doi: 10.5194/gmd-9-1937-2016

    work page doi:10.5194/gmd-9-1937-2016 1937

  28. [28]

    A Fourier Space Perspective on Diffusion Models, May 2025

    Fabian Falck, Teodora Pandeva, Kiarash Zahirnia, Rachel Lawrence, Richard Turner, Ed- ward Meeds, Javier Zazo, and Sushrut Karmalkar. A Fourier Space Perspective on Diffusion Models, May 2025

    work page 2025

  29. [29]

    Nonlinear Aspects of the Climate Response to Greenhouse Gas and Aerosol Forcing.Journal of Climate, 17 (12):2384–2398, June 2004

    Johann Feichter, Erich Roeckner, Ulrike Lohmann, and Beate Liepert. Nonlinear Aspects of the Climate Response to Greenhouse Gas and Aerosol Forcing.Journal of Climate, 17 (12):2384–2398, June 2004. ISSN 0894-8755, 1520-0442. doi: 10.1175/1520-0442(2004) 017<2384:NAOTCR>2.0.CO;2

    work page doi:10.1175/1520-0442(2004 2004

  30. [30]

    Forster, T

    P. Forster, T. Storelvmo, K. Armour, W. Collins, J.-L. Dufresne, D. Frame, D. J. Lunt, T. Mauritsen, M. D. Palmer, M. Watanabe, M. Wild, and H. Zhang. The earth’s energy budget, climate feedbacks, and climate sensitivity. In V. Masson-Delmotte, P. Zhai, A. Pi- rani, S. L. Connors, C. Péan, S. Berger, N. Caud, Y. Chen, L. Goldfarb, M. I. Gomis, M. Huang, K...

    work page doi:10.1017/9781009157896.009 2021

  31. [31]

    Differentiable programming for Earth system modeling.Geoscientific Model Development, 16(11):3123– 3135, June 2023

    Maximilian Gelbrecht, Alistair White, Sebastian Bathiany, and Niklas Boers. Differentiable programming for Earth system modeling.Geoscientific Model Development, 16(11):3123– 3135, June 2023. ISSN 1991-959X. doi: 10.5194/gmd-16-3123-2023

    work page doi:10.5194/gmd-16-3123-2023 2023

  32. [32]

    LUCIE: A Lightweight Uncoupled ClImate Emulator with long-term stability and physical consistency for O(1000)-member ensembles, September 2024

    Haiwen Guan, Troy Arcomano, Ashesh Chattopadhyay, and Romit Maulik. LUCIE: A Lightweight Uncoupled ClImate Emulator with long-term stability and physical consistency for O(1000)-member ensembles, September 2024

    work page 2024

  33. [33]

    D. A. Hauglustaine, F. Hourdin, L. Jourdain, M.-A. Filiberti, S. Walters, J.-F. Lamarque, and E. A. Holland. Interactive chemistry in the Laboratoire de Météorologie Dynamique general circulation model: Description and background tropospheric chemistry evaluation. Journal of Geophysical Research: Atmospheres, 109(D4), 2004. ISSN 2156-2202. doi: 10. 1029/2...

    work page 2004

  34. [34]

    Holton and Gregory J

    James R. Holton and Gregory J. Hakim. Basic Conservation Laws. InAn Introduction to Dynamic Meteorology, pages 31–66. Elsevier, 2013. ISBN 978-0-12-384866-6. doi: 10.1016/ B978-0-12-384866-6.00002-7

    work page 2013

  35. [35]

    Bint Diallo, François Lott, Guillaume Gastineau, Arnaud Caubel, Yann Meur- desoif, and Josefine Ghattas

    Frédéric Hourdin, Catherine Rio, Jean-Yves Grandpeix, Jean-Baptiste Madeleine, Frédérique Cheruy, Nicolas Rochetin, Arnaud Jam, Ionela Musat, Abderrahmane Idelkadi, Laurent Fairhead, Marie-Alice Foujols, Lidia Mellul, Abdoul-Khadre Traore, Jean-Louis Dufresne, Olivier Boucher, Marie-Pierre Lefebvre, Ehouarn Millour, Etienne Vignon, Jean Jouhaud, F. Bint D...

    work page doi:10.1029/2019ms001892 2020

  36. [36]

    Technical Report: Towards Unified Diffusion Models for Multi-Model Climate Emulation at Scale, November 2025

    Francesco Immorlano, Elijah Tavares, Felix Draxler, Padhraic Smyth, Pierre Gentine, and Stephan Mandt. Technical Report: Towards Unified Diffusion Models for Multi-Model Climate Emulation at Scale, November 2025

    work page 2025

  37. [37]

    Elucidating the Design Space of Diffusion-Based Generative Models, October 2022

    Tero Karras, Miika Aittala, Timo Aila, and Samuli Laine. Elucidating the Design Space of Diffusion-Based Generative Models, October 2022

    work page 2022

  38. [38]

    Computing the Full Earth System at 1 km Resolution, November 2025

    Daniel Klocke, Claudia Frauen, Jan Frederik Engels, Dmitry Alexeev, René Redler, Reiner Schnur, Helmuth Haak, Luis Kornblueh, Nils Brüggemann, Fatemeh Chegini, Manoel Römmer, Lars Hoffmann, Sabine Griessbach, Mathis Bode, Jonathan Coles, Miguel Gila, William Sawyer, Alexandru Calotoiu, Yakup Budanaz, Pratyai Mazumder, Marcin Copik, Benjamin Weber, Andreas...

    work page 2025

  39. [39]

    P., and Hoyer, S.: Neural general circulation models for weather and climate, Nature, 632, 1060–1066, https://doi.org/10.1038/s41586-024-07744-y,

    DmitriiKochkov, JanniYuval, IanLangmore, PeterNorgaard, JamieSmith, GriffinMooers, Milan Klöwer, James Lottes, Stephan Rasp, Peter Düben, Sam Hatfield, Peter Battaglia, Alvaro Sanchez-Gonzalez, Matthew Willson, Michael P. Brenner, and Stephan Hoyer. Neu- ral general circulation models for weather and climate.Nature, 632(8027):1060–1066, Au- gust 2024. ISS...

    work page doi:10.1038/s41586-024-07744-y 2024

  40. [40]

    Scientific As- sessment of Ozone Depletion 2018: Executive Summary

    NOAA Chemical Sciences Laboratory (CSL). Scientific As- sessment of Ozone Depletion 2018: Executive Summary. https://csl.noaa.gov/assessments/ozone/2018/executivesummary/#

    work page 2018

  41. [41]

    Schulthess, Ulrich Schättler, Victoria Cherkas, and William Sawyer

    Xavier Lapillonne, Daniel Hupp, Fabian Gessler, André Walser, Andreas Pauling, Annika Lauber, BenjaminCumming, CarlosOsuna, ChristophMüller, ClaireMerker, DanielLeuen- berger, David Leutwyler, Dmitry Alexeev, Gabriel Vollenweider, Guillaume Van Parys, Jonas Jucker, Lukas Jansing, Marco Arpagaus, Marco Induni, Marek Jacob, Matthias Kraushaar, Michael Jähn,...

    work page doi:10.5194/gmd-19-755-2026 2024

  42. [42]

    Leach, Stuart Jenkins, Zebedee Nicholls, Christopher J

    Nicholas J. Leach, Stuart Jenkins, Zebedee Nicholls, Christopher J. Smith, John Lynch, MichelleCain, TristramWalsh, BillWu, JunichiTsutsui, andMylesR.Allen. FaIRv2.0.0: A generalized impulse response model for climate uncertainty and future scenario exploration. Geoscientific Model Development, 14(5):3007–3036, May 2021. ISSN 1991-959X. doi: 10. 5194/gmd-...

    work page 2021

  43. [43]

    Fischer, Lukas Brunner, Reto Knutti, and Ed Hawkins

    Flavio Lehner, Clara Deser, Nicola Maher, Jochem Marotzke, Erich M. Fischer, Lukas Brunner, Reto Knutti, and Ed Hawkins. Partitioning climate projection uncertainty with multiple large ensembles and CMIP5/6.Earth System Dynamics, 11(2):491–508, May 2020. ISSN 2190-4979. doi: 10.5194/esd-11-491-2020

    work page doi:10.5194/esd-11-491-2020 2020

  44. [44]

    Swin Transformer: Hierarchical Vision Transformer using Shifted Windows, August 2021

    Ze Liu, Yutong Lin, Yue Cao, Han Hu, Yixuan Wei, Zheng Zhang, Stephen Lin, and Baining Guo. Swin Transformer: Hierarchical Vision Transformer using Shifted Windows, August 2021

    work page 2021

  45. [45]

    Implementation of the CMIP6 Forcing Data in the IPSL-CM6A-LR Model.Journal of Advances in Modeling Earth Systems, 12(4):e2019MS001940, 2020

    Thibaut Lurton, Yves Balkanski, Vladislav Bastrikov, Slimane Bekki, Laurent Bopp, Pas- cale Braconnot, Patrick Brockmann, Patricia Cadule, Camille Contoux, Anne Cozic, David Cugnet, Jean-Louis Dufresne, Christian Éthé, Marie-Alice Foujols, Josefine Ghattas, Didier Hauglustaine, Rong-Ming Hu, Masa Kageyama, Myriam Khodri, Nicolas Lebas, Guillaume Levavasse...

    work page doi:10.1029/2019ms001940 2020

  46. [46]

    Mloz: A Highly Efficient MachineLearning-BasedOzoneParameterizationforClimateSensitivitySimulations.Jour- nal of Advances in Modeling Earth Systems, 18(4):e2025MS005459, 2026

    Yiling Ma, Nathan Luke Abraham, Stefan Versick, Roland Ruhnke, Andrea Schneidereit, Ulrike Niemeier, Felix Back, Peter Braesicke, and Peer Nowack. Mloz: A Highly Efficient MachineLearning-BasedOzoneParameterizationforClimateSensitivitySimulations.Jour- nal of Advances in Modeling Earth Systems, 18(4):e2025MS005459, 2026. ISSN 1942-2466. doi: 10.1029/2025MS005459

    work page doi:10.1029/2025ms005459 2026

  47. [47]

    Power, and Jochem Marotzke

    Nicola Maher, Scott B. Power, and Jochem Marotzke. More accurate quantification of model-to-model agreement in externally forced climatic responses over the coming century.Nature Communications, 12(1):788, February 2021. ISSN 2041-1723. doi: 10.1038/s41467-020-20635-w

    work page doi:10.1038/s41467-020-20635-w 2021

  48. [48]

    Climate Calculations with a Combined Ocean- Atmosphere Model.Journal of the Atmospheric Sciences, 26(4):786–789, July 1969

    Syukuro Manabe and Kirk Bryan. Climate Calculations with a Combined Ocean- Atmosphere Model.Journal of the Atmospheric Sciences, 26(4):786–789, July 1969. ISSN 0022-4928, 1520-0469. doi: 10.1175/1520-0469(1969)026<0786:CCWACO>2.0.CO;2

    work page doi:10.1175/1520-0469(1969)026 1969

  49. [49]

    Wetherald

    Syukuro Manabe and Richard T. Wetherald. Thermal Equilibrium of the Atmosphere with a Given Distribution of Relative Humidity.Journal of the Atmospheric Sciences, 24(3): 241–259, May 1967. ISSN 0022-4928, 1520-0469. doi: 10.1175/1520-0469(1967)024<0241: TEOTAW>2.0.CO;2

    work page doi:10.1175/1520-0469(1967)024 1967

  50. [50]

    L. A. Mansfield, P. J. Nowack, M. Kasoar, R. G. Everitt, W. J. Collins, and A. Voulgarakis. Predicting global patterns of long-term climate change from short-term simulations using machine learning.npj Climate and Atmospheric Science, 3(1):44, November 2020. ISSN 2397-3722. doi: 10.1038/s41612-020-00148-5

    work page doi:10.1038/s41612-020-00148-5 2020

  51. [51]

    Damon Matthews, Nathan P

    H. Damon Matthews, Nathan P. Gillett, Peter A. Stott, and Kirsten Zickfeld. The pro- portionality of global warming to cumulative carbon emissions.Nature, 459(7248):829–832, June 2009. ISSN 1476-4687. doi: 10.1038/nature08047

    work page doi:10.1038/nature08047 2009

  52. [52]

    M.Meinshausen, S.C.B.Raper, andT.M.L.Wigley. Emulatingcoupledatmosphere-ocean and carbon cycle models with a simpler model, MAGICC6 – Part 1: Model description and calibration.Atmospheric Chemistry and Physics, 11(4):1417–1456, February 2011. ISSN 1680-7316. doi: 10.5194/acp-11-1417-2011

    work page doi:10.5194/acp-11-1417-2011 2011

  53. [53]

    Etheridge, Paul J

    Malte Meinshausen, Elisabeth Vogel, Alexander Nauels, Katja Lorbacher, Nicolai Mein- shausen, David M. Etheridge, Paul J. Fraser, Stephen A. Montzka, Peter J. Rayner, Cathy M. Trudinger, Paul B. Krummel, Urs Beyerle, Josep G. Canadell, John S. Daniel, 37 Ian G. Enting, Rachel M. Law, Chris R. Lunder, Simon O’Doherty, Ron G. Prinn, Ste- fan Reimann, Mauro ...

    work page doi:10.5194/gmd-10-2057-2017 2057

  54. [54]

    Malte Meinshausen, Zebedee R. J. Nicholls, Jared Lewis, Matthew J. Gidden, Elisabeth Vo- gel, Mandy Freund, Urs Beyerle, Claudia Gessner, Alexander Nauels, Nico Bauer, Josep G. Canadell, John S. Daniel, Andrew John, Paul B. Krummel, Gunnar Luderer, Nicolai Mein- shausen, Stephen A. Montzka, Peter J. Rayner, Stefan Reimann, Steven J. Smith, Marten van den ...

    work page doi:10.5194/gmd-13-3571-2020 2020

  55. [55]

    Keller, Andrew H

    Nadine Mengis, David P. Keller, Andrew H. MacDougall, Michael Eby, Nesha Wright, Ka- trin J. Meissner, Andreas Oschlies, Andreas Schmittner, Alexander J. MacIsaac, H. Damon Matthews, and Kirsten Zickfeld. Evaluation of the University of Victoria Earth System Climate Model version 2.10 (UVic ESCM 2.10).Geoscientific Model Development, 13(9): 4183–4204, Sep...

    work page doi:10.5194/gmd-13-4183-2020 2020

  56. [56]

    Kinnison, Rolando R

    OlafMorgenstern, KaneA.Stone, RobynSchofield, HideharuAkiyoshi, YousukeYamashita, Douglas E. Kinnison, Rolando R. Garcia, Kengo Sudo, David A. Plummer, John Scinocca, LukeD.Oman, MichaelE.Manyin, GuangZeng, EugeneRozanov, AndreaStenke, LauraE. Revell, Giovanni Pitari, Eva Mancini, Glauco Di Genova, Daniele Visioni, Sandip S. Dhomse, and Martyn P. Chipperf...

    work page doi:10.5194/acp-18-1091-2018 2018

  57. [57]

    Seneviratne, and Carl-Friedrich Schleussner

    Shruti Nath, Quentin Lejeune, Lea Beusch, Sonia I. Seneviratne, and Carl-Friedrich Schleussner. MESMER-M: An Earth system model emulator for spatially resolved monthly temperature.Earth System Dynamics, 13(2):851–877, April 2022. ISSN 2190-4979. doi: 10.5194/esd-13-851-2022

    work page doi:10.5194/esd-13-851-2022 2022

  58. [58]

    Niemeier and C

    U. Niemeier and C. Timmreck. What is the limit of climate engineering by stratospheric injection of SO2?Atmospheric Chemistry and Physics, 15(16):9129–9141, August 2015. ISSN 1680-7316. doi: 10.5194/acp-15-9129-2015

    work page doi:10.5194/acp-15-9129-2015 2015

  59. [59]

    Nowack, N

    Peer J. Nowack, N. Luke Abraham, Peter Braesicke, and John A. Pyle. The Im- pact of Stratospheric Ozone Feedbacks on Climate Sensitivity Estimates.Journal of Geophysical Research: Atmospheres, 123(9):4630–4641, 2018. ISSN 2169-8996. doi: 10.1002/2017JD027943

    work page doi:10.1002/2017jd027943 2018

  60. [60]

    O’Neill, Claudia Tebaldi, Detlef P

    Brian C. O’Neill, Claudia Tebaldi, Detlef P. van Vuuren, Veronika Eyring, Pierre Friedling- stein, George Hurtt, Reto Knutti, Elmar Kriegler, Jean-Francois Lamarque, Jason Lowe, Gerald A. Meehl, Richard Moss, Keywan Riahi, and Benjamin M. Sanderson. The Scenario Model Intercomparison Project (ScenarioMIP) for CMIP6.Geoscientific Model Develop- ment, 9(9):...

    work page doi:10.5194/gmd-9-3461-2016 2016

  61. [61]

    Hans-Otto Pörtner, Debra Cynthia Roberts, Helen Adams, Ibidun Adelekan, Carolina Adler, Rita Adrian, Paulina Aldunce, Elham Ali, Rawshan Ara Begum, Birgit Bednar- Friedl, Rachel Bezner Kerr, Robbert Biesbroek, Joern Birkmann, Kathryn Bowen, Mar- tina Angela Caretta, Jofre Carnicer, Edwin Castellanos, Tae Sung Cheong, Winston Chow, Gueladio Cissé, Susan Cl...

    work page 2022

  62. [62]

    GenCast: Diffusion-based ensemble forecasting for medium-range weather, December 2023

    Ilan Price, Alvaro Sanchez-Gonzalez, Ferran Alet, Timo Ewalds, Andrew El-Kadi, Jacklynn Stott, Shakir Mohamed, Peter Battaglia, Remi Lam, and Matthew Willson. GenCast: Diffusion-based ensemble forecasting for medium-range weather, December 2023

    work page 2023

  63. [63]

    Ozone and Climate: A Review of Interconnections

    John Pyle, Theodore Shepherd, Gregory Bodeker, Aleksandr Gruzdev, Rolf Müller, Nzioka John Muthama, William Randel, Vitali Fioletov, Jens-Uwe Grooß, Stephen Montzka, Paul Newman, Larry Thomason, Guus Velders, and Mack McFarland. Ozone and Climate: A Review of Interconnections

    work page

  64. [64]

    S.-W. Son, E. P. Gerber, J. Perlwitz, L. M. Polvani, N. P. Gillett, K.-H. Seo, V. Eyring, T.G.Shepherd, D.Waugh, H.Akiyoshi, J.Austin, A.Baumgaertner, S.Bekki, P.Braesicke, C. Brühl, N. Butchart, M. P. Chipperfield, D. Cugnet, M. Dameris, S. Dhomse, S. Frith, H. Garny, R. Garcia, S. C. Hardiman, P. Jöckel, J. F. Lamarque, E. Mancini, M. Marchand, M. Micho...

    work page 2010

  65. [65]

    Arblaster

    Claudia Tebaldi and Julie M. Arblaster. Pattern scaling: Its strengths and limitations, and an update on the latest model simulations.Climatic Change, 122(3):459–471, February

    work page

  66. [66]

    doi: 10.1007/s10584-013-1032-9

    ISSN 0165-0009, 1573-1480. doi: 10.1007/s10584-013-1032-9

    work page doi:10.1007/s10584-013-1032-9

  67. [67]

    Affine representations of fractional processes with applica- tions in mathematical finance.Stochastic Process

    Detlef P. van Vuuren, Keywan Riahi, Katherine Calvin, Rob Dellink, Johannes Emmerling, Shinichiro Fujimori, Samir Kc, Elmar Kriegler, and Brian O’Neill. The Shared Socio- economic Pathways: Trajectories for human development and global environmental change. Global Environmental Change, 42:148–152, January 2017. ISSN 0959-3780. doi: 10.1016/j. gloenvcha.20...

    work page doi:10.1016/j 2017

  68. [68]

    Pritchard, Noah Brenowitz, Yair Cohen, Boris Bonev, Thorsten Kurth, Dale Durran, and Jaideep Pathak

    Chenggong Wang, Michael S. Pritchard, Noah Brenowitz, Yair Cohen, Boris Bonev, Thorsten Kurth, Dale Durran, and Jaideep Pathak. Coupled Ocean-Atmosphere Dynamics in a Machine Learning Earth System Model, June 2024. 39

    work page 2024

  69. [69]

    Ball, Mohamadou Diallo, Birgit Hassler, James Keeble, Peer Nowack, Clara Orbe, Sandro Vattioni, and Timofei Sukhodolov

    Jingyu Wang, Gabriel Chiodo, Blanca Ayarzagüena, William T. Ball, Mohamadou Diallo, Birgit Hassler, James Keeble, Peer Nowack, Clara Orbe, Sandro Vattioni, and Timofei Sukhodolov. Exploring ozone–climate interactions in idealized CMIP6 DECK experiments. Atmospheric Chemistry and Physics, 25(23):17819–17844, December 2025. ISSN 1680-7316. doi: 10.5194/acp-...

    work page doi:10.5194/acp-25-17819-2025 2025

  70. [70]

    Developing Climate Scenarios From Equilibrium GCM Results

    Tom Wigley. Developing Climate Scenarios From Equilibrium GCM Results

    work page

  71. [71]

    Field-Space Attention for Structure-Preserving Earth System Transformers, December 2025

    Maximilian Witte, Johannes Meuer, Étienne Plésiat, and Christopher Kadow. Field-Space Attention for Structure-Preserving Earth System Transformers, December 2025

    work page 2025

  72. [72]

    Womack, Paolo Giani, Sebastian D

    Christopher B. Womack, Paolo Giani, Sebastian D. Eastham, and Noelle E. Selin. Rapid Emulation of Spatially Resolved Temperature Response to Effective Radiative Forcing. Journal of Advances in Modeling Earth Systems, 17(1):e2024MS004523, 2025. ISSN 1942-

    work page 2025

  73. [73]

    doi: 10.1029/2024MS004523. 40

    work page doi:10.1029/2024ms004523