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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The scientific questions posed by the climate sciences are central to socioeconomic concerns today. This paper revisits several crucial questions, starting with
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The CoCEB model is used to evaluate hypotheses on the long-term effect of investment in emission abatement, and on the comparative efficacy of different approaches to abatement. While many studies in the literature treat abatement costs as an unproductive loss of income, we show that mitigation costs do slow down economic growth over the next few decades, but only up to the mid-21st century or even earlier; growth reduction is compensated later on by having avoided climate negative impacts.
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Our conceptual model describes global temperature and vegetation extent. We use elements from Daisyworld and classical energy balance models and add an ocean with sea ice. The model exhibits oscillatory behavior within a plausible range of parameter values.
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Keno Riechers, Takahito Mitsui, Niklas Boers, and Michael Ghil
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Denis-Didier Rousseau, Witold Bagniewski, and Michael Ghil
Clim. Past, 18, 249–271, https://doi.org/10.5194/cp-18-249-2022, https://doi.org/10.5194/cp-18-249-2022, 2022
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The study of abrupt climate changes is a relatively new field of research that addresses paleoclimate variations that occur in intervals of tens to hundreds of years. Such timescales are much shorter than the tens to hundreds of thousands of years that the astronomical theory of climate addresses. We revisit several high-resolution proxy records of the past 3.2 Myr and show that the abrupt climate changes are nevertheless affected by the orbitally induced insolation changes.
Eviatar Bach and Michael Ghil
Nonlin. Processes Geophys. Discuss., https://doi.org/10.5194/npg-2021-35, https://doi.org/10.5194/npg-2021-35, 2021
Preprint withdrawn
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Data assimilation (DA) is the process of combining model forecasts with observations in order to provide an optimal estimate of the system state. When models are imperfect, the uncertainty in the forecasts may be underestimated, requiring inflation of the corresponding error covariance. Here, we present a simple method for estimating the magnitude and structure of the model error covariance matrix. We demonstrate the efficacy of this method with idealized experiments.
Michael Ghil
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Short summary
The scientific questions posed by the climate sciences are central to socioeconomic concerns today. This paper revisits several crucial questions, starting with
What can we predict beyond 1 week, for how long, and by what methods?, and ending with
Can we achieve enlightened climate control of our planet by the end of the century?We review the progress in dealing with the nonlinearity and stochasticity of the Earth system and emphasize major strides in coupled climate–economy modeling.
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, https://doi.org/10.5194/cp-16-713-2020, https://doi.org/10.5194/cp-16-713-2020, 2020
Short summary
Short summary
New investigations of European loess records from MIS 6 reveal the occurrence of paleosols and horizon showing slight pedogenesis similar to those from the last climatic cycle. These units are correlated with interstadials described in various marine, continental, and ice Northern Hemisphere records. Therefore, these MIS 6 interstadials can confidently be interpreted as DO-like events of the penultimate climate cycle.
Stefano Pierini, Mickaël D. Chekroun, and Michael Ghil
Nonlin. Processes Geophys., 25, 671–692, https://doi.org/10.5194/npg-25-671-2018, https://doi.org/10.5194/npg-25-671-2018, 2018
Short summary
Short summary
A four-dimensional nonlinear spectral ocean model is used to study the transition to chaos induced by periodic forcing in systems that are nonchaotic in the autonomous limit. The analysis makes use of ensemble simulations and of the system's pullback attractors. A new diagnostic method characterizes the transition to chaos: this is found to occur abruptly at a critical value and begins with the intermittent emergence of periodic oscillations with distinct phases.
Niklas Boers, Mickael D. Chekroun, Honghu Liu, Dmitri Kondrashov, Denis-Didier Rousseau, Anders Svensson, Matthias Bigler, and Michael Ghil
Earth Syst. Dynam., 8, 1171–1190, https://doi.org/10.5194/esd-8-1171-2017, https://doi.org/10.5194/esd-8-1171-2017, 2017
Short summary
Short summary
We use a Bayesian approach for inferring inverse, stochastic–dynamic models from northern Greenland (NGRIP) oxygen and dust records of subdecadal resolution for the interval 59 to 22 ka b2k. Our model reproduces the statistical and dynamical characteristics of the records, including the Dansgaard–Oeschger variability, with no need for external forcing. The crucial ingredients are cubic drift terms, nonlinear coupling terms between the oxygen and dust time series, and non-Markovian contributions.
Niklas Boers, Bedartha Goswami, and Michael Ghil
Clim. Past, 13, 1169–1180, https://doi.org/10.5194/cp-13-1169-2017, https://doi.org/10.5194/cp-13-1169-2017, 2017
Short summary
Short summary
We introduce a Bayesian framework to represent layer-counted proxy records as probability distributions on error-free time axes, accounting for both proxy and dating errors. Our method is applied to NGRIP δ18O data, revealing that the cumulative dating errors lead to substantial uncertainties for the older parts of the record. Applying our method to the widely used radiocarbon comparison curve derived from varved sediments of Lake Suigetsu provides the complete uncertainties of this curve.
Keroboto B. Z. Ogutu, Fabio D'Andrea, Michael Ghil, and Charles Nyandwi
Earth Syst. Dynam. Discuss., https://doi.org/10.5194/esd-2016-64, https://doi.org/10.5194/esd-2016-64, 2017
Preprint retracted
Short summary
Short summary
The CoCEB model is used to evaluate hypotheses on the long-term effect of investment in emission abatement, and on the comparative efficacy of different approaches to abatement. While many studies in the literature treat abatement costs as an unproductive loss of income, we show that mitigation costs do slow down economic growth over the next few decades, but only up to the mid-21st century or even earlier; growth reduction is compensated later on by having avoided climate negative impacts.
J. Rombouts and M. Ghil
Nonlin. Processes Geophys., 22, 275–288, https://doi.org/10.5194/npg-22-275-2015, https://doi.org/10.5194/npg-22-275-2015, 2015
Short summary
Short summary
Our conceptual model describes global temperature and vegetation extent. We use elements from Daisyworld and classical energy balance models and add an ocean with sea ice. The model exhibits oscillatory behavior within a plausible range of parameter values.
Its periodic solutions have sawtooth behavior that is characteristic of relaxation oscillations, as well as suggestive of Quaternary glaciation cycles. The model is one of the simplest of its kind to produce such oscillatory behavior.
D.-D. Rousseau, M. Ghil, G. Kukla, A. Sima, P. Antoine, M. Fuchs, C. Hatté, F. Lagroix, M. Debret, and O. Moine
Clim. Past, 9, 2213–2230, https://doi.org/10.5194/cp-9-2213-2013, https://doi.org/10.5194/cp-9-2213-2013, 2013
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Subject: Bifurcation, dynamical systems, chaos, phase transition, nonlinear waves, pattern formation | Topic: Climate, atmosphere, ocean, hydrology, cryosphere, biosphere | Techniques: Theory
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Climate change is causing rapid temperature increases in the polar regions. A fundamental question is whether these temperature increases are reversible. If we control carbon dioxide emissions, will the temperatures revert or will we have passed a tipping point beyond which return to the present state is impossible? Our mathematical model of the Arctic climate indicates that under present emissions the Arctic climate will change irreversibly to a warm climate before the end of the century.
Karl R. Helfrich and Lev Ostrovsky
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Internal solitons are an important class of nonlinear waves commonly observed in coastal oceans. Their propagation is affected by the Earth's rotation and the variation in the water depth. We consider an interplay of these factors using the corresponding extension of the Gardner equation. This model allows a limiting soliton amplitude and the corresponding increase in wavelength, making the effects of rotation and topography on a shoaling wave especially significant.
Michael Ghil
Nonlin. Processes Geophys., 27, 429–451, https://doi.org/10.5194/npg-27-429-2020, https://doi.org/10.5194/npg-27-429-2020, 2020
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What can we predict beyond 1 week, for how long, and by what methods?, and ending with
Can we achieve enlightened climate control of our planet by the end of the century?We review the progress in dealing with the nonlinearity and stochasticity of the Earth system and emphasize major strides in coupled climate–economy modeling.
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Nonlin. Processes Geophys., 27, 391–409, https://doi.org/10.5194/npg-27-391-2020, https://doi.org/10.5194/npg-27-391-2020, 2020
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The climate of Earth is governed by nonlinear processes of geophysics. This paper presents energy balance models (EBMs) embracing these nonlinear processes which lead to positive feedback, amplifying the effects of anthropogenic forcing and leading to bifurcations. We define bifurcation as a change in the topological equivalence class of the system. We initiate a bifurcation analysis of EBMs of Anthropocene climate, which shows that a catastrophic climate change may occur in the next century.
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Baroclinic and barotropic instabilities are well known as the processes responsible for the production of the most important energy-containing eddies in the atmospheres and oceans of Earth and other planets. Linear and nonlinear instability theories provide insights into when such instabilities may occur, grow to a large amplitude and saturate, with examples from the laboratory, simplified numerical models and planetary atmospheres. We conclude with a number of open issues for future research.
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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,...
