Low‐frequency variability of the large‐scale ocean circulation: A dynamical systems approach

Dijkstra, Henk A.; Ghil, Michael

doi:10.1029/2002rg000122

Cited by 235 publications

(271 citation statements)

References 247 publications

(492 reference statements)

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“…We are then back, in a pullback setting, to the notion of local attractors that compose the global attractor and that can be of topologically very different natures. In the autonomous context, such coexistence of topologically distinct local attractors is well known in the climate sciences (Ghil and Childress 1987;Dijkstra and Ghil 2005;Simonnet et al 2005Simonnet et al , 2009, and references therein), while it is also observed in the numerical results of Figs. 5 and 6 herein for the present ocean model.…”

Section: B Interpretationmentioning

confidence: 55%

“…Again as usual, these questions require one to climb the rungs of a hierarchy of successively more complex and detailed climate models (Ghil 2001;Dijkstra and Ghil 2005;, and references therein). Naturally, introducing noise in the forcing may substantially modify the system's behavior: a random dynamical system extension of the present study is in progress.…”

Section: Discussionmentioning

confidence: 99%

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Exploring the Pullback Attractors of a Low-Order Quasigeostrophic Ocean Model: The Deterministic Case

2016

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A low-order quasigeostrophic double-gyre ocean model is subjected to an aperiodic forcing that mimics time dependence dominated by interdecadal variability. This model is used as a prototype of an unstable and nonlinear dynamical system with time-dependent forcing to explore basic features of climate change in the presence of natural variability. The study relies on the theoretical framework of nonautonomous dynamical systems and of their pullback attractors (PBAs), that is, of the time-dependent invariant sets attracting all trajectories initialized in the remote past. The existence of a global PBA is rigorously demonstrated for this weakly dissipative nonlinear model. Ensemble simulations are carried out and the convergence to PBAs is assessed by computing the probability density function (PDF) of localization of the trajectories. A sensitivity analysis with respect to forcing amplitude shows that the PBAs experience large modifications if the underlying autonomous system is dominated by small-amplitude limit cycles, while less dramatic changes occur in a regime characterized by large-amplitude relaxation oscillations. The dependence of the attracting sets on the choice of the ensemble of initial states is then analyzed. Two types of basins of attraction coexist for certain parameter ranges; they contain chaotic and nonchaotic trajectories, respectively. The statistics of the former does not depend on the initial states whereas the trajectories in the latter converge to small portions of the global PBA. This complex scenario requires separate PDFs for chaotic and nonchaotic trajectories. General implications for climate predictability are finally discussed.

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Section: B Interpretationmentioning

confidence: 55%

Section: Discussionmentioning

confidence: 99%

Exploring the Pullback Attractors of a Low-Order Quasigeostrophic Ocean Model: The Deterministic Case

2016

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“…Alternative explanations identified oceanic nonlinearity as a possible source of the oscillatory behavior (Jiang et al 1995;Cessi 2000;Dewar 2001;Dijkstra and Ghil 2005;Simonnet et al 2006). Dewar (2001), in particular, argued for a key role of intrinsic oceanic, eddy-driven variability in controling the spectral content of the coupled system at decadal and longer time scales.…”

Section: Introductionmentioning

confidence: 99%

A mechanistic model of mid-latitude decadal climate variability

Kravtsov

Dewar

Ghil

et al. 2008

Physica D: Nonlinear Phenomena

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A simple heuristic model of coupled decadal ocean-atmosphere modes in middle latitudes is developed. Previous studies have treated atmospheric intrinsic variability as a linear stochastic process modified by a deterministic coupling to the ocean.The present paper takes an alternative view: based on observational, as well as process modeling results, it represents this variability in terms of irregular transitions between two anomalously persistent, high-latitude and low-latitude jet-stream states. Atmospheric behavior is thus governed by an equation analogous to that describing the trajectory of a particle in a double-well potential, subject to stochastic forcing. Oceanic adjustment to a positional shift in the atmospheric jet involves persistent circulation anomalies maintained by the action of baroclinic eddies; this process is parameterized in the model as a delayed oceanic response. The associated sea-surface temperature anomalies provide heat fluxes that affect atmospheric circulation by modifying the shape of the double-well potential. If the latter coupling is strong enough, the model's spectrum exhibits a peak at a periodicity related to the ocean's eddy-driven adjustment time. A nearly analytical approximation of the coupled model is used to study the sensitivity of this behavior to key model parameters.

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“…The DDS analogs are conservative (e.g., Hamiltonian) dynamical systems [28,29] versus forced-dissipative systems (e.g., the well-known Lorenz system [30]). Typical examples of conservative systems occur in celestial mechanics [31,32], while dissipative systems are often used in modeling geophysical [33,34] and many other natural phenomena.…”

Section: Classification Of Bdesmentioning

confidence: 99%

Boolean delay equations: A simple way of looking at complex systems

Ghil

Zaliapin

Coluzzi

2008

Physica D: Nonlinear Phenomena

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Boolean Delay Equations (BDEs) are semi-discrete dynamical models with Boolean-valued variables that evolve in continuous time. Systems of BDEs can be classified into conservative or dissipative, in a manner that parallels the classification of ordinary or partial differential equations. Solutions to certain conservative BDEs exhibit growth of complexity in time. They represent therewith metaphors for biological evolution or human history. Dissipative BDEs are structurally stable and exhibit multiple equilibria and limit cycles, as well as more complex, fractal solution sets, such as Devil's staircases and "fractal sunbursts." All known solutions of dissipative BDEs have stationary variance. BDE systems of this type, both free and forced, have been used as highly idealized models of climate change on interannual, interdecadal and paleoclimatic time scales. BDEs are also being used as flexible, highly efficient models of colliding cascades of loading and failure in earthquake modeling and prediction, as well as in genetics.1 Corresponding author. Phone: 33-(0)1-4432-2244. Fax: 33-(0)1-4336-8392. E-mail: ghil@lmd.ens.fr 2 E-mail: zal@unr.edu 3 E-mail: coluzzi@lmd.ens.fr 1In this paper we review the theory of systems of BDEs and illustrate their applications to climatic and solid-earth problems. The former have used small systems of BDEs, while the latter have used large hierarchical networks of BDEs. We moreover introduce BDEs with an infinite number of variables distributed in space ("partial BDEs") and discuss connections with other types of discrete dynamical systems, including cellular automata and Boolean networks. This research-andreview paper concludes with a set of open questions.

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Low‐frequency variability of the large‐scale ocean circulation: A dynamical systems approach

Abstract: Citation: Dijkstra, H. A., and M. Ghil (2005), Low-frequency variability of the large-scale ocean circulation: A dynamical systems approach, Rev. Geophys., 43, RG3002,

Cited by 235 publications

References 247 publications

Exploring the Pullback Attractors of a Low-Order Quasigeostrophic Ocean Model: The Deterministic Case

Exploring the Pullback Attractors of a Low-Order Quasigeostrophic Ocean Model: The Deterministic Case

A mechanistic model of mid-latitude decadal climate variability

Boolean delay equations: A simple way of looking at complex systems

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