Publications

2012
Chekroun, Mickaël D., and Jean Roux. “Homeomorphisms group of normed vector space: Conjugacy problems and the Koopman operator.” Discrete and Continuous Dynamical Systems - Series A 33 (2012): 3957–3980.
Chekroun, Mickaël D., and N. E. Glatt-Holtz. “Invariant measures for dissipative dynamical systems: Abstract results and applications.” Communications in Mathematical Physics 316 (2012): 723–761.
Deremble, B., E. Simonnet, and Michael Ghil. “Multiple equilibria and oscillatory modes in a mid-latitude ocean-forced atmospheric model.” Nonlinear Processes in Geophysics 19, no. 5 (2012): 479–499.
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Alessio, Silvia, Gianna Vivaldo, Carla Taricco, and Michael Ghil. “Natural variability and anthropogenic effects in a Central Mediterranean core.” Climate of the Past 8, no. 2 (2012): 831–839.
Groth, Andreas, Michael Ghil, Stéphane Hallegatte, and Patrice Dumas. “The Role of Oscillatory Modes in U.S. Business Cycles.” Fondazione Eni Enrico Mattei (FEEM) 26 (2012): 1. Publisher's Version Abstract

We apply the advanced time-and-frequency-domain method of singular spectrum analysis to study business cycle dynamics in a set of nine U.S. macroeconomic indicators. This method provides a robust way to identify and reconstruct shared oscillations, whether intermittent or modulated. We address the problem of spurious cycles generated by the use of detrending filters and present a Monte Carlo test to extract significant oscillations. Finally, we demonstrate that the behavior of the U.S. economy changes significantly between episodes of growth and recession; these variations cannot be generated by random shocks alone, in the absence of endogenous variability.

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Hannart, A., Michael Ghil, J. L. Dufresne, and P. Naveau. “The uncertain future of climate uncertainty.” Geophysical Research Letters (2012).
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2011
Daae, M., Y. Y. Shprits, B. Ni, J. Koller, Dmitri Kondrashov, and Y. Chen. “Reanalysis of radiation belt electron phase space density using various boundary conditions and loss models.” Advances in Space Research 48, no. 8 (2011): 1327 - 1334. Publisher's Version
Ghil, Michael. “Toward a Mathematical Theory of Climate Sensitivity.” International Congress on Industrial and Applied Mathematics (ICIAM), Vancouver, 2011. Abstract

Presentation
SIAM News article
Chekroun, Mickaël D., Eric Simonnet, and Michael Ghil. “Stochastic climate dynamics: Random attractors and time-dependent invariant measures.” Physica D 240, no. 21 (2011): 1685-–1700. Abstract
This article attempts a unification of the two approaches that have dominated theoretical climate dynamics since its inception in the 1960s: the nonlinear deterministic and the linear stochastic one. This unification, via the theory of random dynamical systems (RDS), allows one to consider the detailed geometric structure of the random attractors associated with nonlinear, stochastically perturbed systems. We report on high-resolution numerical studies of two idealized models of fundamental interest for climate dynamics. The first of the two is a stochastically forced version of the classical Lorenz model. The second one is a low-dimensional, nonlinear stochastic model of the El Niño-Southern Oscillation (ENSO). These studies provide a good approximation of the two models' global random attractors, as well as of the time-dependent invariant measures supported by these attractors; the latter are shown to have an intuitive physical interpretation as random versions of Sina\"ı-Ruelle-Bowen (SRB) measures.
Chekroun, Mickaël D., F. Di Plinio, N. E. Glatt-Holtz, and V. Pata. “Asymptotics of the Coleman-Gurtin model.” Discrete and Continuous Dynamical Systems - Series S 4, no. 2 (2011): 351–369.
Feliks, Yizhak, Michael Ghil, and Andrew W. Robertson. “The atmospheric circulation over the North Atlantic as induced by the SST field.” Journal of Climate 24 (2011): 522–542. Abstract

Spectral analyses of the sea surface temperature (SST) in the Simple Ocean Data Analysis (SODA) reanalysis for the past half-century identify prominent and statistically significant interannual oscillations in two regions along the Gulf Stream front over the North Atlantic. A model of the atmospheric marine boundary layer coupled to a baroclinic quasi-geostrophic model of the free atmosphere is then forced with the SST history from the SODA reanalysis. Two extreme states are found in the atmospheric simulations: they consist of (1) an eastward extension of the westerly jet associated with the front, which occurs mainly during boreal winter; and (2) a quiescent state of very weak flow found predominantly in the summer. This vacillation of the oceanic-front–induced jet in the model is found to exhibit periodicities similar to those identified in the observed Gulf Stream SST front itself. In addition, a close correspondence is found between interannual spectral peaks in the observed North Atlantic Oscillation (NAO) index, and the SODA-induced oscillations in the atmospheric model. In particular, significant oscillatory modes with periods of 8.5, 4.2 and 2.8 years are found in both the observed and simulated indices, and shown to be highly synchronized and of similar energy in both time series. These oscillatory modes in the simulations are shown to be suppressed when either (a) the Gulf Stream front or (b) its interannual oscillations are omitted from the SST field. Moreover, these modes also disappear when (c) the SST front is spatially smoothed, thus confirming that they are indeed induced by the oceanic front.

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Coluzzi, Barbara, Michael Ghil, Stéphane Hallegatte, and Gérard Weisbuch. “Boolean delay equations on networks in economics and the geosciences.” International Journal of Bifurcation and Chaos 21, no. 12 (2011): 3511–3548.
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Dumas, Patrice, Michael Ghil, Andreas Groth, and Stéphane Hallegatte. “Dynamic coupling of the climate and macroeconomic systems.” Math. & Sci. hum. / Mathematics and Social Sciences (2011). Abstract

This review paper presents a modeling framework for macroeco- nomic growth dynamics that is motivated by recent attempts to formulate and study “integrated models” of the coupling between natural and socio-economic phenomena. The challenge is to describe the interfaces between human acti- vities and the functioning of the earth system. We examine the way that this interface works in the presence of endogenous business cycle dynamics, based on a non-equilibrium dynamic model, and review the macroeconomic response to natural disasters. Our model exhibits a larger response to natural disasters during expansions than during recessions, and we raise questions about the as- sessment of climate change damages or natural disaster losses that are based purely on long-term growth models. In order to compare the theoretical fin- dings with observational data, we present a new method for extracting cyclic behavior from the latter, based on multivariate singular spectral analysis.

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Kravtsov, Sergey, Dmitri Kondrashov, I. Kamenkovich, and Michael Ghil. “An empirical stochastic model of sea-surface temperatures and surface winds over the Southern Ocean.” Ocean Science 7, no. 6 (2011): 755–770. Publisher's Version Abstract

This study employs NASA's recent satellite measurements of sea-surface temperatures (SSTs) and sea-level winds (SLWs) with missing data filled-in by Singular Spectrum Analysis (SSA), to construct empirical models that capture both intrinsic and SST-dependent aspects of SLW variability. The model construction methodology uses a number of algorithmic innovations that are essential in providing stable estimates of the model's propagator. The best model tested herein is able to faithfully represent the time scales and spatial patterns of anomalies associated with a number of distinct processes. These processes range from the daily synoptic variability to interannual signals presumably associated with oceanic or coupled dynamics. Comparing the simulations of an SLW model forced by the observed SST anomalies with the simulations of an SLW-only model provides preliminary evidence for the ocean driving the atmosphere in the Southern Ocean region.

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.

Variability of the Indian summer monsoon is decomposed into an interannually modulated annual cycle (MAC) and a northward-propagating, intraseasonal (30-60-day) oscillation (ISO). To achieve this decomposition, we apply multi-channel singular spectrum analysis (M-SSA) simultaneously to unfiltered daily fields of observed outgoing long-wave radiation (OLR) and to reanalyzed 925-hPa winds over the Indian region, from 1975 to 2008. The MAC is essentially given by the year-to-year changes in the annual and semi-annual components; it displays a slow northward migration of OLR anomalies coupled with an alternation between the northeast winter and southwest summer monsoons. The impact of these oscillatory modes on rainfall is then analyzed using a 1-degree gridded daily data set, focusing on Monsoonal India (north of 17°N and west of 90°E) during the months of June to September. Daily rainfall variability is partitioned into three states using a Hidden Markov Model. Two of these states are shown to agree well with previous classifications of "active" and "break" phases of the monsoon, while the third state exhibits a dipolar east-west pattern with abundant rainfall east of about 77°E and low rainfall to the west. Occurrence of the three rainfall states is found to be an asymmetric function of both the MAC and ISO components. On average, monsoon active phases are favored by large positive anomalies of MAC, and breaks by negative ones. ISO impact is decisive when the MAC is near neutral values during the onset and withdrawal phases of the monsoon. Active monsoon spells are found to require a synergy between the MAC and ISO, while the east-west rainfall dipole is less sensitive to interactions between the two. The driest years, defined from spatially averaged June-September rainfall anomalies, are found to be mostly a result of breaks occurring during the onset and withdrawal stages of the monsoon, e.g., mid-June to mid-July, and during September. These breaks are in turn associated with anomalously late MAC onset or early MAC withdrawal, often together with a large-amplitude, negative ISO event. The occurrence of breaks during the core of the monsoon—from late July to late August—is restricted to a few years when MAC was exceptionally weak, such as 1987 or 2002. Wet years are shown to be mostly associated with more frequent active spells and a stronger MAC than usual, especially at the end of the monsoon season. Taken together, our results suggest that monthly and seasonal precipitation predictability is higher in the early and late stages of the summer monsoon season.

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Kondrashov, Dmitri, Michael Ghil, and Y. Shprits. “Lognormal Kalman filter for assimilating phase space density data in the radiation belts.” Space Weather 9, no. 11 (2011).
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Groth, Andreas, and Michael Ghil. “Multivariate singular spectrum analysis and the road to phase synchronization.” Physical Review E 84 (2011): 036206. Abstract

We show that multivariate singular spectrum analysis (M-SSA) greatly helps study phase synchronization in a large system of coupled oscillators and in the presence of high observational noise levels. With no need for detailed knowledge of individual subsystems nor any a priori phase de?nition for each of them, we demonstrate that M-SSA can automatically identify multiple oscillatory modes and detect whether these modes are shared by clusters of phase- and frequency-locked oscillators. As an essential modi?cation of M-SSA, here we introduce variance-maximization (varimax) rotation of the M-SSA eigenvectors to optimally identify synchronized-oscillator clustering.

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Chekroun, Mickaël D., Dmitri Kondrashov, and Michael Ghil. “Predicting stochastic systems by noise sampling, and application to the El Niño-Southern Oscillation.” Proceedings of the National Academy of Sciences 108, no. 29 (2011): 11766–11771. Abstract

Interannual and interdecadal prediction are major challenges of climate dynamics. In this article we develop a prediction method for climate processes that exhibit low-frequency variability (LFV). The method constructs a nonlinear stochastic model from past observations and estimates a path of the “weather” noise that drives this model over previous finite-time windows. The method has two steps: (i) select noise samples—or “snippets”—from the past noise, which have forced the system during short-time intervals that resemble the LFV phase just preceding the currently observed state; and (ii) use these snippets to drive the system from the current state into the future. The method is placed in the framework of pathwise linear-response theory and is then applied to an El Niño–Southern Oscillation (ENSO) model derived by the empirical model reduction (EMR) methodology; this nonlinear model has 40 coupled, slow, and fast variables. The domain of validity of this forecasting procedure depends on the nature of the system’s pathwise response; it is shown numerically that the ENSO model’s response is linear on interannual time scales. As a result, the method’s skill at a 6- to 16-month lead is highly competitive when compared with currently used dynamic and statistic prediction methods for the Niño-3 index and the global sea surface temperature field.

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