Publications by Type: Journal Article

2011
Groth, Andreas, and Michael Ghil. 2011. “Multivariate singular spectrum analysis and the road to phase synchronization.” Physical Review E 84: 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. 2011. “Predicting stochastic systems by noise sampling, and application to the El Niño-Southern Oscillation.” Proceedings of the National Academy of Sciences 108 (29): 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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Zaliapin, Ilya, and Michael Ghil. 2011. “Reply to G.H. Roe's and M.B. Baker's comment on "Another look at climate sensitivity".” Nonlinear Processes in Geophysics 18 (1). Copernicus GmbH: 129–131.
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2010
Zaliapin, Ilya, and Michael Ghil. 2010. “A delay differential model of ENSO variability, Part 2: Phase locking, multiple solutions, and dynamics of extrema.” Nonlinear Processes in Geophysics 17 (2): 123–135.
Zaliapin, Ilya, and Michael Ghil. 2010. “Another look at climate sensitivity.” Nonlinear Processes in Geophysics 17 (2): 113–122. Abstract

We revisit a recent claim that the Earth's climate system is characterized by sensitive dependence to parameters; in particular, that the system exhibits an asymmetric, large-amplitude response to normally distributed feedback forcing. Such a response would imply irreducible uncertainty in climate change predictions and thus have notable implications for climate science and climate-related policy making. We show that equilibrium climate sensitivity in all generality does not support such an intrinsic indeterminacy; the latter appears only in essentially linear systems. The main flaw in the analysis that led to this claim is inappropriate linearization of an intrinsically nonlinear model; there is no room for physical interpretations or policy conclusions based on this mathematical error. Sensitive dependence nonetheless does exist in the climate system, as well as in climate models – albeit in a very different sense from the one claimed in the linear work under scrutiny – and we illustrate it using a classical energy balance model (EBM) with nonlinear feedbacks. EBMs exhibit two saddle-node bifurcations, more recently called "tipping points," which give rise to three distinct steady-state climates, two of which are stable. Such bistable behavior is, furthermore, supported by results from more realistic, nonequilibrium climate models. In a truly nonlinear setting, indeterminacy in the size of the response is observed only in the vicinity of tipping points. We show, in fact, that small disturbances cannot result in a large-amplitude response, unless the system is at or near such a point. We discuss briefly how the distance to the bifurcation may be related to the strength of Earth's ice-albedo feedback.

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Chekroun, Mickaël D., Michael Ghil, Jean Roux, and Ferenc Varadi. 2010. “Averaging of time-periodic systems without a small parameter.” Discrete and Continuous Dynamical Systems 14 (4). American Institute of Mathematical Sciences (AIMS): 753–782.
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Roques, Lionel, and Mickaël D. Chekroun. 2010. “Does reaction-diffusion support the duality of fragmentation effect?” Ecological Complexity 7 (1). Elsevier: 100–106.
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Kondrashov, Dmitri, Yuri Shprits, and Michael Ghil. 2010. “Gap Filling of Solar Wind Data by Singular Spectrum Analysis.” Geophysical Research Letters 37. CiteSeerX - Scientific Literature Digital Library and Search Engine [http://citeseerx.ist.psu.edu/oai2] (United States): L15101. Abstract

Observational data sets in space physics often contain instrumental and sampling errors, as well as large gaps. This is both an obstacle and an incentive for research, since continuous data sets are typically needed for model formulation and validation. For example, the latest global empirical models of Earth's magnetic field are crucial for many space weather applications, and require time continuous solar wind and interplanetary magnetic field (IMF) data; both of these data sets have large gaps before 1994. Singular spectrum analysis (SSA) reconstructs missing data by using an iteratively inferred, smooth “signal” that captures coherent modes, while “noise” is discarded. In this study, we apply SSA to fill in large gaps in solar wind and IMF data, by combining it with geomagnetic indices that are time continuous, and generalizing it to multivariate geophysical data consisting of gappy “driver” and continuous “response” records. The reconstruction error estimates provide information on the physics of co variability between particular solar wind parameters and geomagnetic indices.

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Ghil, Michael, Peter Read, and Leonard Smith. 2010. “Geophysical flows as dynamical systems: the influence of Hide's experiments.” Astronomy & Geophysics 51 (4). Oxford University Press: 4–28.
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Feliks, Yizhak, Michael Ghil, and Andrew W. Robertson. 2010. “Oscillatory Climate Modes in the Eastern Mediterranean and Their Synchronization with the North Atlantic Oscillation.” Journal of Climate 23 (15): 4060–4079. Abstract

Oscillatory climatic modes over the North Atlantic, Ethiopian Plateau, and eastern Mediterranean were examined in instrumental and proxy records from these regions. Aside from the well-known North Atlantic Oscillation (NAO) index and the Nile River water-level records, the authors study for the first time an instrumental rainfall record from Jerusalem and a tree-ring record from the Golan Heights. The teleconnections between the regions were studied in terms of synchronization of chaotic oscillators. Standard methods for studying synchronization among such oscillators are modified by combining them with advanced spectral methods, including singular spectrum analysis. The resulting cross-spectral analysis quantifies the strength of the coupling together with the degree of synchronization. A prominent oscillatory mode with a 7–8-yr period is present in all the climatic indices studied here and is completely synchronized with the North Atlantic Oscillation. An energy analysis of the synchronization raises the possibility that this mode originates in the North Atlantic. Evidence is discussed for this mode being induced by the 7–8-yr oscillation in the position of the Gulf Stream front. A mechanism for the teleconnections between the North Atlantic, Ethiopian Plateau, and eastern Mediterranean is proposed, and implications for interannual-to-decadal climate prediction are discussed.

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Strounine, K., Sergey Kravtsov, Dmitri Kondrashov, and Michael Ghil. 2010. “Reduced models of atmospheric low-frequency variability: Parameter estimation and comparative performance.” Physica D: Nonlinear Phenomena 239 (3). Elsevier: 145–166. Abstract

Low-frequency variability (LFV) of the atmosphere refers to its behavior on time scales of 10–100 days, longer than the life cycle of a mid-latitude cyclone but shorter than a season. This behavior is still poorly understood and hard to predict. The present study compares various model reduction strategies that help in deriving simplified models of LFV. Three distinct strategies are applied here to reduce a fairly realistic, high-dimensional, quasi-geostrophic, 3-level (QG3) atmospheric model to lower dimensions: (i) an empirical–dynamical method, which retains only a few components in the projection of the full QG3 model equations onto a specified basis, and finds the linear deterministic and the stochastic corrections empirically as in Selten (1995) [5]; (ii) a purely dynamics-based technique, employing the stochastic mode reduction strategy of Majda et al. (2001) [62]; and (iii) a purely empirical, multi-level regression procedure, which specifies the functional form of the reduced model and finds the model coefficients by multiple polynomial regression as in Kravtsov et al. (2005) [3]. The empirical–dynamical and dynamical reduced models were further improved by sequential parameter estimation and benchmarked against multi-level regression models; the extended Kalman filter was used for the parameter estimation. Overall, the reduced models perform better when more statistical information is used in the model construction. Thus, the purely empirical stochastic models with quadratic nonlinearity and additive noise reproduce very well the linear properties of the full QG3 model’s LFV, i.e. its autocorrelations and spectra, as well as the nonlinear properties, i.e. the persistent flow regimes that induce non-Gaussian features in the model’s probability density function. The empirical–dynamical models capture the basic statistical properties of the full model’s LFV, such as the variance and integral correlation time scales of the leading LFV modes, as well as some of the regime behavior features, but fail to reproduce the detailed structure of autocorrelations and distort the statistics of the regimes. Dynamical models that use data assimilation corrections do capture the linear statistics to a degree comparable with that of empirical–dynamical models, but do much less well on the full QG3 model’s nonlinear dynamics. These results are discussed in terms of their implications for a better understanding and prediction of LFV.

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Kondrashov, Dmitri, Sergey Kravtsov, and Michael Ghil. 2010. “Signatures of nonlinear dynamics in an idealized atmospheric model.” Journal of the Atmospheric Sciences 68 (1): 3–12.
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Zaliapin, Ilya, Efi Foufoula-Georgiou, and Michael Ghil. 2010. “Transport on river networks: A dynamic tree approach.” Journal of Geophysical Research: Earth Surface 115 (F2). Wiley Online Library.
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2009
Ni, Binbin, Yuri Shprits, Tsugunobu Nagai, Richard Thorne, Yue Chen, Dmitri Kondrashov, and Hee-jeong Kim. 2009. “Reanalyses of the radiation belt electron phase space density using nearly equatorial CRRES and polar-orbiting Akebono satellite observations.” Journal of Geophysical Research: Space Physics 114 (A5): n/a–n/a. Publisher's Version
Kravtsov, Sergey, Dmitri Kondrashov, and Michael Ghil. 2009. “Empirical model reduction and the modelling hierarchy in climate dynamics and the geosciences.” Stochastic physics and climate modelling. Cambridge University Press, Cambridge, 35–72. Abstract
Modern climate dynamics uses a two-fisted approach in attacking and solving the problems of atmospheric and oceanic flows. The two fists are: (i) observational analyses; and (ii) simulations of the geofluids, including the coupled atmosphere–ocean system, using a hierarchy of dynamical models. These models represent interactions between many processes that act on a broad range of spatial and time scales, from a few to tens of thousands of kilometers, and from diurnal to multidecadal, respectively. The evolution of virtual climates simulated by the most detailed and realistic models in the hierarchy is typically as difficult to interpret as that of the actual climate system, based on the available observations thereof. Highly simplified models of weather and climate, though, help gain a deeper understanding of a few isolated processes, as well as giving clues on how the interaction between these processes and the rest of the climate system may participate in shaping climate variability. Finally, models of intermediate complexity, which resolve well a subset of the climate system and parameterise the remainder of the processes or scales of motion, serve as a conduit between the models at the two ends of the hierarchy. We present here a methodology for constructing intermediate mod- els based almost entirely on the observed evolution of selected climate fields, without reference to dynamical equations that may govern this evolution; these models parameterise unresolved processes as multi- variate stochastic forcing. This methodology may be applied with equal success to actual observational data sets, as well as to data sets resulting from a high-end model simulation. We illustrate this methodology by its applications to: (i) observed and simulated low-frequency variability of atmospheric flows in the Northern Hemisphere; (ii) observed evo- lution of tropical sea-surface temperatures; and (iii) observed air–sea interaction in the Southern Ocean. Similar results have been obtained for (iv) radial-diffusion model simulations of Earth’s radiation belts, but are not included here because of space restrictions. In each case, the reduced stochastic model represents surprisingly well a variety of linear and nonlinear statistical properties of the resolved fields. Our methodology thus provides an efficient means of constructing reduced, numerically inexpensive climate models. These models can be thought of as stochastic–dynamic prototypes of more complex deterministic models, as in examples (i) and (iv), but work just as well in the situation when the actual governing equations are poorly known, as in (ii) and (iii). These models can serve as competitive prediction tools, as in (ii), or be included as stochastic parameterisations of certain processes within more complex climate models, as in (iii). Finally, the methodology can be applied, with some modifications, to geophysical problems outside climate dynamics, as illustrated by (iv).
Vivaldo, Gianna, Carla Taricco, Silvia Alessio, and Michael Ghil. 2009. “Accurate dating of the Gallipoli Terrace (Ionian Sea) sediments as a basis for reliable climate proxy series.” PAGES News 17 (1). PAGES International Project Office: 8–9.
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Deremble, Bruno, Fabio D'Andrea, and Michael Ghil. 2009. “Fixed points, stable manifolds, weather regimes, and their predictability.” Chaos: An Interdisciplinary Journal of Nonlinear Science 19 (4). AIP Publishing: 043109. Publisher's Version
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Zhang, Yunyan, Bjorn Stevens, Brian Medeiros, and Michael Ghil. 2009. “Low-cloud fraction, lower-tropospheric stability, and large-scale divergence.” Journal of Climate 22 (18): 4827–4844.
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Taricco, Carla, Michael Ghil, Silvia Alessio, and Gianna Vivaldo. 2009. “Two millennia of climate variability in the Central Mediterranean.” Climate of the Past 5 (5). European Geosciences Union: 171–181. Abstract

This experimental work addresses the need for high-resolution, long and homogeneous climatic time series that facilitate the study of climate variability over time scales of decades to millennia. We present a high-resolution record of foraminiferal d18O from a Central-Mediterranean sediment core that covers the last two millennia. The record was analyzed using advanced spectral methods and shows highly significant oscillatory components with periods of roughly 600, 350, 200, 125 and 11 years. Over the last millennium, our data show several features related to known climatic periods, such as the Medieval Optimum, the Little Ice Age and a recent steep variation since the beginning of the Industrial Era. During the preceding millennium, the d18O series also reveals a surprising maximum at about 0 AD, suggesting low temperatures at that time. This feature contradicts widely held ideas about the Roman Classical Period; it is, therefore, discussed at some length, by reviewing the somewhat contradictory evidence about this period. We compare the d18O record with an alkenone-derived sea surface temperature time series, obtained from cores extracted in the same Central-Mediterranean area (Gallipoli Terrace, Ionian Sea), as well as with Italian and other European temperature reconstructions over the last centuries. Based on this comparison, we show that the long-term trend and the 200-y oscillation in the records are temperature driven and have a dominant role in describing temperature variations over the last two millennia.

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Bordi, Isabella, Klaus Fraedrich, Michael Ghil, and Alfonso Sutera. 2009. “Zonal flow regime changes in a GCM and in a simple quasigeostrophic model: The role of stratospheric dynamics.” Journal of the Atmospheric Sciences 66 (5): 1366–1383.
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