Review & Encyclopedia

Ghil, Michael, and Eric Simonnet. “Geophysical Fluid Dynamics, Nonautonomous Dynamical Systems, and the Climate Sciences.” In Mathematical Approach to Climate Change and its Impacts: MAC2I, edited by Piermarco Cannarsa, Daniela Mansutti, and Antonello Provenzale, 3–81. Springer International Publishing, 2020. Abstract
This contribution introduces the dynamics of shallow and rotating flows that characterizes large-scale motions of the atmosphere and oceans. It then focuses on an important aspect of climate dynamics on interannual and interdecadal scales, namely the wind-driven ocean circulation. Studying the variability of this circulation and slow changes therein is treated as an application of the theory of nonautonomous dynamical systems. The contribution concludes by discussing the relevance of these mathematical concepts and methods for the highly topical issues of climate change and climate sensitivity.
Ghil, Michael. “A Century of Nonlinearity in the Geosciences.” Earth and Space Science 6, no. 7 (2019): 1007–1042. Publisher's Version
Chavez, M., Michael Ghil, and J. Urrutia-Fucugauchi, ed. Extreme Events: Observations, Modeling and Economics. Geophysical Monographs. Vol. 214. Washington, DC: American Geophysical Union & Wiley, 2015. Publisher's Version Abstract

The monograph covers the fundamentals and the consequences of extreme geophysical phenomena like asteroid impacts, climatic change, earthquakes, tsunamis, hurricanes, landslides, volcanic eruptions, flooding, and space weather. This monograph also addresses their associated, local and worldwide socio-economic impacts. The understanding and modeling of these phenomena is critical to the development of timely worldwide strategies for the prediction of natural and anthropogenic extreme events, in order to mitigate their adverse consequences. This monograph is unique in as much as it is dedicated to recent theoretical, numerical and empirical developments that aim to improve: (i) the understanding, modeling and prediction of extreme events in the geosciences, and, (ii) the quantitative evaluation of their economic consequences. The emphasis is on coupled, integrative assessment of the physical phenomena and their socio-economic impacts. With its overarching theme, Extreme Events: Observations, Modeling and Economics will be relevant to and become an important tool for researchers and practitioners in the fields of hazard and risk analysis in general, as well as to those with a special interest in climate change, atmospheric and oceanic sciences, seismo-tectonics, hydrology, and space weather.

Ghil, Michael. “A mathematical theory of climate sensitivity or, How to deal with both anthropogenic forcing and natural variability?” In Climate Change: Multidecadal and Beyond, edited by C. P. Chang, Michael Ghil, Mojib Latif, and J. M. Wallace, 31–51. World Scientific Publ. Co./Imperial College Press, 2015. Abstract

Recent estimates of climate evolution over the coming century still differ by several degrees. This uncertainty motivates the work presented here. There are two basic approaches to apprehend the complexity of climate change: deterministically nonlinear and stochastically linear, i.e., the Lorenz and the Hasselmann approach. The grand unification of these two approaches relies on the theory of random dynamical systems. We apply this theory to study the random attractors of nonlinear, stochastically perturbed climate models. Doing so allows one to examine the interaction of internal climate variability with the forcing, whether natural or anthropogenic, and to take into account the climate system's non-equilibrium behavior in determining climate sensitivity. This non-equilibrium behavior is due to a combination of nonlinear and random effects. We give here a unified treatment of such effects from the point of view of the theory of dynamical systems and of their bifurcations. Energy balance models are used to illustrate multiple equilibria, while multi-decadal oscillations in the thermohaline circulation illustrate the transition from steady states to periodic behavior. Random effects are introduced in the setting of random dynamical systems, which permit a unified treatment of both nonlinearity and stochasticity. The combined treatment of nonlinear and random effects is applied to a stochastically perturbed version of the classical Lorenz convection model. Climate sensitivity is then defined mathematically as the derivative of an appropriate functional or other function of the system’s state with respect to the bifurcation parameter. This definition is illustrated by using numerical results for a model of the El Niño–Southern Oscillation. The concept of a hierarchy of models is the thread that runs across this chapter, and the robustness of elementary bifurcations across such a hierarchy is emphasized.

Ghil, Michael. “Climate variability: nonlinear and random effects.” Encyclopedia of Atmospheric Sciences. Elsevier (2012): 1–6.
Ghil, Michael, P. Yiou, S. Hallegatte, B. D. Malamud, P. Naveau, A. Soloviev, P. Friederichs, et al.Extreme events: dynamics, statistics and prediction.” Nonlinear Processes in Geophysics 18, no. 3 (2011): 295–350. Abstract

We review work on extreme events, their causes and consequences, by a group of Euro- pean and American researchers involved in a three-year project on these topics. The review covers theoretical aspects of time series analysis and of extreme value theory, as well as of the deteministic modeling of extreme events, via continuous and discrete dynamic models. The applications include climatic, seismic and socio-economic events, along with their prediction.

Ghil, Michael, Peter Read, and Leonard Smith. “Geophysical flows as dynamical systems: the influence of Hide's experiments.” Astronomy & Geophysics 51, no. 4 (2010): 4–28.
Simonnet, Eric, Henk A. Dijkstra, and Michael Ghil. “Bifurcation analysis of ocean, atmosphere, and climate models.” In Handbook of numerical analysis, edited by R. Temam and J. Tribbia, 14:187–229. Elsevier, 2009.
Hillerbrand, Rafaela, and Michael Ghil. “Anthropogenic climate change: Scientific uncertainties and moral dilemmas.” Physica D 237, no. 14-17 (2008): 2132–2138. Abstract

This paper considers the role of scientific expertise and moral reasoning in the decision making process involved in climate-change issues. It points to an unresolved moral dilemma that lies at the heart of this decision making, namely how to balance duties towards future generations against duties towards our contemporaries. At present, the prevailing moral and political discourses shy away from addressing this dilemma and evade responsibility by falsely drawing normative conclusions from the predictions of climate models alone. We argue that such moral dilemmas are best addressed in the framework of Expected Utility Theory. A crucial issue is to adequately incorporate into this framework the uncertainties associated with the predicted consequences of climate change on the well-being of future generations. The uncertainties that need to be considered include those usually associated with climate modeling and prediction, but also moral and general epistemic ones. This paper suggests a way to correctly incorporate all the relevant uncertainties into the decision making process.

Ghil, Michael, Ilya Zaliapin, and Barbara Coluzzi. “Boolean delay equations: A simple way of looking at complex systems.” Physica D: Nonlinear Phenomena 237, no. 23 (2008): 2967–2986.
Ghil, Michael, Mickaël D. Chekroun, and Eric Simonnet. “Climate dynamics and fluid mechanics: Natural variability and related uncertainties.” Physica D 237 (2008): 2111–2126.
Dijkstra, Henk A., and Michael Ghil. “Low-frequency variability of the large-scale ocean circulation: a dynamical systems approach.” Reviews of Geophysics 43 (2005). Abstract

Oceanic variability on interannual, interdecadal, and longer timescales plays a key role in climate variability and climate change. Paleoclimatic records suggest major changes in the location and rate of deepwater formation in the Atlantic and Southern oceans on timescales from millennia to millions of years. Instrumental records of increasing duration and spatial coverage document substantial variability in the path and intensity of ocean surface currents on timescales of months to decades. We review recent theoretical and numerical results that help explain the physical processes governing the large-scale ocean circulation and its intrinsic variability. To do so, we apply systematically the methods of dynamical systems theory. The dynamical systems approach is proving successful for more and more detailed and realistic models, up to and including oceanic and coupled ocean-atmosphere general circulation models. In this approach one follows the road from simple, highly symmetric model solutions, through a “bifurcation tree,” toward the observed, complex behavior of the system under investigation. The observed variability can be shown to have its roots in simple transitions from a circulation with high symmetry in space and regularity in time to circulations with successively lower symmetry in space and less regularity in time. This road of successive bifurcations leads through multiple equilibria to oscillatory and eventually chaotic solutions. Key features of this approach are illustrated in detail for simplified models of two basic problems of the ocean circulation. First, a barotropic model is used to capture major features of the wind-driven ocean circulation and of the changes in its behavior as wind stress increases. Second, a zonally averaged model is used to show how the thermohaline ocean circulation changes as buoyancy fluxes at the surface increase. For the wind-driven circulation, multiple separation patterns of a “Gulf-Stream like” eastward jet are obtained. These multiple equilibria are followed by subannual and interannual oscillations of the jet and of the entire basin's circulation. The multiple equilibria of the thermohaline circulation include deepwater formation near the equator, near either pole or both, as well as intermediate possibilities that bear some degree of resemblance to the currently observed Atlantic overturning pattern. Some of these multiple equilibria are subject, in turn, to oscillatory instabilities with timescales of decades, centuries, and millennia. Interdecadal and centennial oscillations are the ones of greatest interest in the current debate on global warming and on the relative roles of natural and anthropogenic variability in it. They involve the physics of the truly three-dimensional coupling between the wind-driven and thermohaline circulation. To arrive at this three-dimensional picture, the bifurcation tree is sketched out for increasingly complex models for both the wind-driven and the thermohaline circulation.

Ghil, Michael. “Did celestial chaos kill the dinosaurs?The Observatory 123, no. 1177 (2003): 328–333.
Ghil, Michael, Dmitri Kondrashov, F. Lott, and Andrew W. Robertson. “Intraseasonal oscillations in the mid-latitudes: observations, theory, and GCM results.” In Proceedings ECMWF/CLIVAR Workshop on Simulation and Prediction of Intra-Seasonal Variability with Emphasis on the MJO, 3–6, 2003, 3–6.
Ghil, Michael, M. R. Allen, M. D. Dettinger, Kayo Ide, Dmitri Kondrashov, M. E. Mann, Andrew W. Robertson, et al.Advanced spectral methods for climatic time series.” Reviews of Geophysics 40, no. 1 (2002): 1–41.
Ghil, Michael. “Climate variability: Nonlinear aspects.” In Encyclopedia of Atmospheric Sciences, edited by J. R. Holton, J. Pyle, and J. A. Curry, 432–438. Academic Press, 2002.
Ghil, Michael. “Natural climate variability.” In Encyclopedia of Global Environmental Change, edited by M. MacCracken and J. Perry, 1:544–549. Wiley & Sons, Chichester/New York, 2002.
Ghil, Michael, and Andrew W. Robertson. “``Waves'' vs. ``particles'' in the atmosphere's phase space: A pathway to long-range forecasting?Proceedings of the National Academy of Sciences 99 (2002): 2493–2500. Abstract

Thirty years ago, E. N. Lorenz provided some approximate limits to atmospheric predictability. The details—in space and time—of atmospheric flow fields are lost after about 10 days. Certain gross flow features recur, however, after times of the order of 10–50 days, giving hope for their prediction. Over the last two decades, numerous attempts have been made to predict these recurrent features. The attempts have involved, on the one hand, systematic improvements in numerical weather prediction by increasing the spatial resolution and physical faithfulness in the detailed models used for this prediction. On the other hand, theoretical attempts motivated by the same goal have involved the study of the large-scale atmospheric motions’ phase space and the inhomoge- neities therein. These ‘‘coarse-graining’’ studies have addressed observed as well as simulated atmospheric data sets. Two distinct approaches have been used in these studies: the episodic or intermittent and the oscillatory or periodic. The intermittency approach describes multiple-flow (or weather) regimes, their per- sistence and recurrence, and the Markov chain of transitions among them. The periodicity approach studies intraseasonal oscil- lations, with periods of 15–70 days, and their predictability. We review these two approaches, ‘‘particles’’ vs. ‘‘waves,’’ in the quantum physics analogy alluded to in the title of this article, discuss their complementarity, and outline unsolved problems.

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Ghil, Michael. “Hilbert problems for the geosciences in the 21st century.” Nonlinear Processes in Geophysics 8, no. 4/5 (2001): 211–211.
Ghil, Michael. “The essence of data assimilation or why combine data with models.” In Proc. 3rd WMO Intl Symp. Assimilation of Observations in Meteorology & Oceanography, 1–4, 2000, 1–4.