Articles | Volume 30, issue 4
Review article
05 Oct 2023
Review article |  | 05 Oct 2023

Review article: Dynamical systems, algebraic topology and the climate sciences

Michael Ghil and Denisse Sciamarella

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Orbital insolation variations, intrinsic climate variability, and Quaternary glaciations
Keno Riechers, Takahito Mitsui, Niklas Boers, and Michael Ghil
Clim. Past, 18, 863–893,,, 2022
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Abrupt climate changes and the astronomical theory: are they related?
Denis-Didier Rousseau, Witold Bagniewski, and Michael Ghil
Clim. Past, 18, 249–271,,, 2022
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Brief communication: An innovation-based estimation method for model error covariance in Kalman filters
Eviatar Bach and Michael Ghil
Nonlin. Processes Geophys. Discuss.,,, 2021
Preprint withdrawn
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Review article: Hilbert problems for the climate sciences in the 21st century – 20 years later
Michael Ghil
Nonlin. Processes Geophys., 27, 429–451,,, 2020
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Dansgaard–Oeschger-like events of the penultimate climate cycle: the loess point of view
Denis-Didier Rousseau, Pierre Antoine, Niklas Boers, France Lagroix, Michael Ghil, Johanna Lomax, Markus Fuchs, Maxime Debret, Christine Hatté, Olivier Moine, Caroline Gauthier, Diana Jordanova, and Neli Jordanova
Clim. Past, 16, 713–727,,, 2020
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Related subject area

Subject: Bifurcation, dynamical systems, chaos, phase transition, nonlinear waves, pattern formation | Topic: Climate, atmosphere, ocean, hydrology, cryosphere, biosphere | Techniques: Theory
Review article: Large fluctuations in non-equilibrium physics
Giovanni Jona-Lasinio
Nonlin. Processes Geophys., 30, 253–262,,, 2023
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Rate-induced tipping in ecosystems and climate: the role of unstable states, basin boundaries and transient dynamics
Ulrike Feudel
Nonlin. Processes Geophys. Discuss.,,, 2023
Revised manuscript accepted for NPG
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Climate bifurcations in a Schwarzschild equation model of the Arctic atmosphere
Kolja L. Kypke, William F. Langford, Gregory M. Lewis, and Allan R. Willms
Nonlin. Processes Geophys., 29, 219–239,,, 2022
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Effects of rotation and topography on internal solitary waves governed by the rotating Gardner equation
Karl R. Helfrich and Lev Ostrovsky
Nonlin. Processes Geophys., 29, 207–218,,, 2022
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Review article: Hilbert problems for the climate sciences in the 21st century – 20 years later
Michael Ghil
Nonlin. Processes Geophys., 27, 429–451,,, 2020
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Cited articles

Abarbanel, H. D. I. and Kennel, M. B.: Local false nearest neighbors and dynamical dimensions from observed chaotic data, Phys. Rev. E, 47, 3057–3068,, 1993. a
Aguirre, L. A., Letellier, C., and Maquet, J.: Forecasting the time series of sunspot numbers, Solar Phys., 249, 103–120, 2008. a
Amon, A. and Lefranc, M.: Topological signature of deterministic chaos in short nonstationary signals from an optical parametric oscillator, Phys. Rev. Lett., 92, 094101,, 2004. a
Arnold, L.: Random Dynamical Systems, Springer-Verlag, New York/Berlin, 1998. a
Arnol'd, V. I.: Geometrical Methods in the Theory of Ordinary Differential Equations, Springer Science & Business Media; first Russian edition 1978, 2012. a, b, c
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.