Articles | Volume 30, issue 4
https://doi.org/10.5194/npg-30-399-2023
© 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/npg-30-399-2023
© Author(s) 2023. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Review article
| 
05 Oct 2023
Review article |
| 05 Oct 2023
| 05 Oct 2023
Review article: Dynamical systems, algebraic topology and the climate sciences
Geosciences Department and Laboratoire de Météorologie Dynamique (CNRS and IPSL), École Normale Supérieure and PSL University, 75231 Paris CEDEX 05, France
Department of Atmospheric & Oceanic Sciences, University of California at Los Angeles, Los Angeles, CA 90095-1567, USA
Departments of Mathematics and of Finance, Imperial College London, London, SW7 2BX, UK
Denisse Sciamarella
CORRESPONDING AUTHOR
Institut Franco-Argentin d'Études sur le Climat et ses Impacts (IFAECI) International Reseach Laboratory 3351 (CNRS – IRD – CONICET – UBA) C1428EGA, Buenos Aires, Argentina
Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Buenos Aires, Argentina
Centre National de la Recherche Scientifique, 75794 Paris CEDEX 16, France
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19 citations as recorded by crossref.
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- A four‐dimensional nonlinear dynamical model for an integrated early warning system of rapid‐onset meteorological hazards H. Tatli https://doi.org/10.1002/qj.70136
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- Introduction to Double Focus Issue: Nonautonomous dynamical systems in the sciences P. Ashwin et al. https://doi.org/10.1063/5.0333561
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- To be an extreme event or not: That is the question C. Letellier et al. https://doi.org/10.1063/5.0273928
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- Sandy beaches' chaos: shoreline-sandbar coupling inferred from observational time series M. Aparicio et al. https://doi.org/10.5194/npg-33-197-2026
- Analysis of Correlation Bounds for Uniformly Expanding Maps on [0, 1] M. Abdelkader https://doi.org/10.3390/axioms12121072
- Introduction to the Focus Issue: Nonautonomous dynamics in the climate sciences D. Crisan et al. https://doi.org/10.1063/5.0324361
- Time-series-analysis-based detection of critical transitions in real-world non-autonomous systems K. Lehnertz https://doi.org/10.1063/5.0214733
- Parameter-drift models for plasma physics G. Grime et al. https://doi.org/10.1063/5.0307494
- A templex-based study of the Atlantic Meridional Overturning Circulation dynamics in idealized chaotic models C. Mosto et al. https://doi.org/10.1063/5.0231713
- Pace in concert with phase: rate-induced phase-tipping in birhythmic oscillators R. Kumar K et al. https://doi.org/10.1098/rspa.2024.0629
- Non-linear dynamical approaches for characterizing multi-sector climate impacts under irreducible uncertainty R. Mawalagedara et al. https://doi.org/10.1038/s41612-025-01208-4
- Functorial invariants for chaos topology from data D. Sciamarella https://doi.org/10.1103/zx76-5115
- Elucidating the performance of data assimilation neural networks for chaotic dynamics M. Bocquet et al. https://doi.org/10.5194/npg-33-401-2026
19 citations as recorded by crossref.
- A Minimal Endogenous Business Cycle Model with Memory Effects D. Ohara & M. Ghil https://doi.org/10.2139/ssrn.3959179
- Do rapidly and non-rapidly intensifying tropical cyclones represent two different dynamical regimes J. McBride et al. https://doi.org/10.1038/s41612-026-01329-4
- A four‐dimensional nonlinear dynamical model for an integrated early warning system of rapid‐onset meteorological hazards H. Tatli https://doi.org/10.1002/qj.70136
- Review article: Interdisciplinary perspectives on climate sciences – highlighting past and current scientific achievements V. Galfi et al. https://doi.org/10.5194/npg-31-185-2024
- Accurate deep learning-based filtering for chaotic dynamics by identifying instabilities without an ensemble M. Bocquet et al. https://doi.org/10.1063/5.0230837
- Introduction to Double Focus Issue: Nonautonomous dynamical systems in the sciences P. Ashwin et al. https://doi.org/10.1063/5.0333561
- Fundamentals of Symmetry and Topology: Applications to Materials Science and Condensed Matter Physics M. Yin et al. https://doi.org/10.3390/sym17060807
- To be an extreme event or not: That is the question C. Letellier et al. https://doi.org/10.1063/5.0273928
- Topological modes of variability of the wind-driven ocean circulation G. Charó et al. https://doi.org/10.1063/5.0261968
- Sandy beaches' chaos: shoreline-sandbar coupling inferred from observational time series M. Aparicio et al. https://doi.org/10.5194/npg-33-197-2026
- Analysis of Correlation Bounds for Uniformly Expanding Maps on [0, 1] M. Abdelkader https://doi.org/10.3390/axioms12121072
- Introduction to the Focus Issue: Nonautonomous dynamics in the climate sciences D. Crisan et al. https://doi.org/10.1063/5.0324361
- Time-series-analysis-based detection of critical transitions in real-world non-autonomous systems K. Lehnertz https://doi.org/10.1063/5.0214733
- Parameter-drift models for plasma physics G. Grime et al. https://doi.org/10.1063/5.0307494
- A templex-based study of the Atlantic Meridional Overturning Circulation dynamics in idealized chaotic models C. Mosto et al. https://doi.org/10.1063/5.0231713
- Pace in concert with phase: rate-induced phase-tipping in birhythmic oscillators R. Kumar K et al. https://doi.org/10.1098/rspa.2024.0629
- Non-linear dynamical approaches for characterizing multi-sector climate impacts under irreducible uncertainty R. Mawalagedara et al. https://doi.org/10.1038/s41612-025-01208-4
- Functorial invariants for chaos topology from data D. Sciamarella https://doi.org/10.1103/zx76-5115
- Elucidating the performance of data assimilation neural networks for chaotic dynamics M. Bocquet et al. https://doi.org/10.5194/npg-33-401-2026
Saved (final revised paper)
Latest update: 24 Aug 2026
Short summary
The problem of climate change is that of a chaotic system subject to time-dependent forcing, such as anthropogenic greenhouse gases and natural volcanism. To solve this problem, we describe the mathematics of dynamical systems with explicit time dependence and those of studying their behavior through topological methods. Here, we show how they are being applied to climate change and its predictability.
The problem of climate change is that of a chaotic system subject to time-dependent forcing,...
