Articles | Volume 27, issue 3
https://doi.org/10.5194/npg-27-429-2020
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the Creative Commons Attribution 4.0 License.
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https://doi.org/10.5194/npg-27-429-2020
© Author(s) 2020. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Review article
| Highlight paper
| 
17 Sep 2020
Review article | Highlight paper |
| 17 Sep 2020
| 17 Sep 2020
Review article: Hilbert problems for the climate sciences in the 21st century – 20 years later
Geosciences Department and Laboratoire de Météorologie Dynamique (CNRS and IPSL), Ecole normale supérieure, Paris Sciences et Lettres (PSL) University, Paris, France
Atmospheric and Oceanic Sciences Department, University of California at Los Angeles, Los Angeles, California, USA
Invited contribution by Michael Ghil, recipient of the EGU 2004 Lewis Fry Richardson Medal.
Related authors
Michael Ghil and Denisse Sciamarella
Nonlin. Processes Geophys., 30, 399–434, https://doi.org/10.5194/npg-30-399-2023, https://doi.org/10.5194/npg-30-399-2023, 2023
Short summary
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.
This article is included in the Encyclopedia of Geosciences
Keno Riechers, Takahito Mitsui, Niklas Boers, and Michael Ghil
Clim. Past, 18, 863–893, https://doi.org/10.5194/cp-18-863-2022, https://doi.org/10.5194/cp-18-863-2022, 2022
Short summary
Short summary
Building upon Milancovic's theory of orbital forcing, this paper reviews the interplay between intrinsic variability and external forcing in the emergence of glacial interglacial cycles. It provides the reader with historical background information and with basic theoretical concepts used in recent paleoclimate research. Moreover, it presents new results which confirm the reduced stability of glacial-cycle dynamics after the mid-Pleistocene transition.
This article is included in the Encyclopedia of Geosciences
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
Short summary
Short summary
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.
This article is included in the Encyclopedia of Geosciences
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
Short summary
Short summary
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.
This article is included in the Encyclopedia of Geosciences
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.
This article is included in the Encyclopedia of Geosciences
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.
This article is included in the Encyclopedia of Geosciences
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.
This article is included in the Encyclopedia of Geosciences
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.
This article is included in the Encyclopedia of Geosciences
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.
This article is included in the Encyclopedia of Geosciences
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.
This article is included in the Encyclopedia of Geosciences
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
Michael Ghil and Denisse Sciamarella
Nonlin. Processes Geophys., 30, 399–434, https://doi.org/10.5194/npg-30-399-2023, https://doi.org/10.5194/npg-30-399-2023, 2023
Short summary
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.
This article is included in the Encyclopedia of Geosciences
Keno Riechers, Takahito Mitsui, Niklas Boers, and Michael Ghil
Clim. Past, 18, 863–893, https://doi.org/10.5194/cp-18-863-2022, https://doi.org/10.5194/cp-18-863-2022, 2022
Short summary
Short summary
Building upon Milancovic's theory of orbital forcing, this paper reviews the interplay between intrinsic variability and external forcing in the emergence of glacial interglacial cycles. It provides the reader with historical background information and with basic theoretical concepts used in recent paleoclimate research. Moreover, it presents new results which confirm the reduced stability of glacial-cycle dynamics after the mid-Pleistocene transition.
This article is included in the Encyclopedia of Geosciences
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
Short summary
Short summary
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.
This article is included in the Encyclopedia of Geosciences
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
Short summary
Short summary
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.
This article is included in the Encyclopedia of Geosciences
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.
This article is included in the Encyclopedia of Geosciences
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.
This article is included in the Encyclopedia of Geosciences
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.
This article is included in the Encyclopedia of Geosciences
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.
This article is included in the Encyclopedia of Geosciences
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.
This article is included in the Encyclopedia of Geosciences
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.
This article is included in the Encyclopedia of Geosciences
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
Related subject area
Subject: Bifurcation, dynamical systems, chaos, phase transition, nonlinear waves, pattern formation | Topic: Climate, atmosphere, ocean, hydrology, cryosphere, biosphere | Techniques: Theory
Existence and influence of mixed states in a model of vegetation patterns
Rate-induced tipping in ecosystems and climate: the role of unstable states, basin boundaries and transient dynamics
Review article: Dynamical systems, algebraic topology and the climate sciences
Sensitivity of the nocturnal and polar boundary layer to transient phenomena
Review article: Large fluctuations in non-equilibrium physics
Climate bifurcations in a Schwarzschild equation model of the Arctic atmosphere
Effects of rotation and topography on internal solitary waves governed by the rotating Gardner equation
Anthropocene climate bifurcation
Baroclinic and barotropic instabilities in planetary atmospheres: energetics, equilibration and adjustment
Lilian Vanderveken, Marina Martínez Montero, and Michel Crucifix
Nonlin. Processes Geophys., 30, 585–599, https://doi.org/10.5194/npg-30-585-2023, https://doi.org/10.5194/npg-30-585-2023, 2023
Short summary
Short summary
In semi-arid regions, hydric stress affects plant growth. In these conditions, vegetation patterns develop and effectively allow for vegetation to persist under low water input. The formation of patterns and the transition between patterns can be studied with small models taking the form of dynamical systems. Our study produces a full map of stable and unstable solutions in a canonical vegetation model and shows how they determine the transitions between different patterns.
This article is included in the Encyclopedia of Geosciences
Ulrike Feudel
Nonlin. Processes Geophys., 30, 481–502, https://doi.org/10.5194/npg-30-481-2023, https://doi.org/10.5194/npg-30-481-2023, 2023
Short summary
Short summary
Many systems in nature are characterized by the coexistence of different stable states for given environmental parameters and external forcing. Examples can be found in different fields of science, ranging from ecosystems to climate dynamics. Perturbations can lead to critical transitions (tipping) from one stable state to another. The study of these transitions requires the development of new methodological approaches that allow for modeling, analyzing and predicting them.
This article is included in the Encyclopedia of Geosciences
Michael Ghil and Denisse Sciamarella
Nonlin. Processes Geophys., 30, 399–434, https://doi.org/10.5194/npg-30-399-2023, https://doi.org/10.5194/npg-30-399-2023, 2023
Short summary
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.
This article is included in the Encyclopedia of Geosciences
Amandine Kaiser, Nikki Vercauteren, and Sebastian Krumscheid
EGUsphere, https://doi.org/10.5194/egusphere-2023-1519, https://doi.org/10.5194/egusphere-2023-1519, 2023
Short summary
Short summary
Current numerical weather prediction models encounter challenges in accurately representing regimes stably stratified atmospheric boundary layer (SBL) and the transitions between them. Stochastic modeling approaches are a promising framework to analyze when transient possible small-scale phenomena can trigger regime transitions. Therefore, we conducted a sensitivity analysis of the SBL to transient phenomena by augmenting a surface energy balance model with meaningful randomizations.
This article is included in the Encyclopedia of Geosciences
Giovanni Jona-Lasinio
Nonlin. Processes Geophys., 30, 253–262, https://doi.org/10.5194/npg-30-253-2023, https://doi.org/10.5194/npg-30-253-2023, 2023
Short summary
Short summary
Non-equilibrium is dominant in geophysical and climate phenomena. Most of the processes that characterize energy flow occur far from equilibrium. These range from very large systems, such as weather patterns or ocean currents that remain far from equilibrium, owing to an influx of energy, to biological structures. In the last decades, progress in non-equilibrium physics has come from the study of very rare fluctuations, and this paper provides an introduction to these theoretical developments.
This article is included in the Encyclopedia of Geosciences
Kolja L. Kypke, William F. Langford, Gregory M. Lewis, and Allan R. Willms
Nonlin. Processes Geophys., 29, 219–239, https://doi.org/10.5194/npg-29-219-2022, https://doi.org/10.5194/npg-29-219-2022, 2022
Short summary
Short summary
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.
This article is included in the Encyclopedia of Geosciences
Karl R. Helfrich and Lev Ostrovsky
Nonlin. Processes Geophys., 29, 207–218, https://doi.org/10.5194/npg-29-207-2022, https://doi.org/10.5194/npg-29-207-2022, 2022
Short summary
Short summary
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.
This article is included in the Encyclopedia of Geosciences
Kolja Leon Kypke, William Finlay Langford, and Allan Richard Willms
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
Short summary
Short summary
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.
This article is included in the Encyclopedia of Geosciences
Peter Read, Daniel Kennedy, Neil Lewis, Hélène Scolan, Fachreddin Tabataba-Vakili, Yixiong Wang, Susie Wright, and Roland Young
Nonlin. Processes Geophys., 27, 147–173, https://doi.org/10.5194/npg-27-147-2020, https://doi.org/10.5194/npg-27-147-2020, 2020
Short summary
Short summary
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.
This article is included in the Encyclopedia of Geosciences
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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.
The scientific questions posed by the climate sciences are central to socioeconomic concerns...
