A chaotically driven model climate: extreme events and snapshot attractors

Bódai, Tamás; Károlyi, György; Tél, Tamás

doi:10.5194/npg-18-573-2011

Cited by 35 publications

(40 citation statements)

References 29 publications

(30 reference statements)

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“…We would like to point out some recent results [92,93,59,94] which seem to suggest that a mathematically sound treatment of time-dependent extremes in numerical models is within reach. The authors studied a time dependent modification of the socalled Lorenz '84 [341] minimal model of the mid-latitude atmospheric circulation: x = −y 2 − z 2 − ax − aF (t) (11.3.8) y = xy − bxz − y + 1 (11.3.9) z = xz + bxy − z (11.3.10) where one unit of time corresponds to 5 d = 1/73 y, and we use the classical values for the parameters a = 1/4 and b = 4.…”

Section: Extremes Coarse Graining and Parametrizationsmentioning

confidence: 99%

“…Both in the case of deterministically and random driven system, the challenge is to extend the encouraging results discussed in [92,93,59,94] to high dimensional chaotic systems, e.g. when studying climate models data, and find effective ways to beat the curse of dimensionality, while keeping a sound mathematical approach and physical significance in the analysis of the results.…”

Section: A Note On Randomly Perturbed Dynamical Systemsmentioning

confidence: 99%

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Extremes and Recurrence in Dynamical Systems

Lucarini¹,

Faranda²,

Freitas³

et al. 2016

178

253

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ii 4.1.2 The New Conditions 44 4.1.3 The Existence of EVL for General Stationary Stochastic Processes under Weaker Hypotheses 46 4.1.4 Proofs of Theorem 4.1.4 and Corollary 4.1.5 48 4.2 Extreme Values for Dynamically Defined Stochastic Processes 53 4.2.1 Observables and Corresponding Extreme Value Laws 55 4.2.2 Extreme Value Laws for Uniformly Expanding Systems 59 4.2.3 Example 4.2.1 revisited 61 4.2.4 Proof of the Dichotomy for Uniformly Expanding Maps 63 4.3 Point Processes of Rare Events 64 4.3.1 Absence of Clustering 64 4.3.2 Presence of Clustering 65 4.3.3 Dichotomy for Uniformly Expanding Systems for Point Processes 67 4.4 Conditions Д q (u n ), D 3 (u n ), D p (u n ) * and Decay of Correlations 68 4.5 Specific Dynamical Systems where the Dichotomy Applies 71 4.5.1 Rychlik Systems 72 4.5.2 Piecewise Expanding Maps in Higher Dimensions 73 4.6 Extreme Value Laws for Physical Observables 74

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Section: Extremes Coarse Graining and Parametrizationsmentioning

confidence: 99%

Section: A Note On Randomly Perturbed Dynamical Systemsmentioning

confidence: 99%

Extremes and Recurrence in Dynamical Systems

Lucarini¹,

Faranda²,

Freitas³

et al. 2016

178

253

View full text Add to dashboard Cite

show abstract

“…In this paper, we wish to apply the WL parametrization to a simple dynamical system introduced by Bódai et al (2011) and constructed by coupling the Lorenz 84 (Lorenz, 1984) model with the Lorenz 63 (Lorenz, 1963) model. In what follows, we want to parametrize the dynamical effect of the variables corresponding to the Lorenz 63 system on the variables corresponding to the Lorenz 84 system.…”

Section: Introductionmentioning

confidence: 99%

Evaluating a stochastic parametrization for a fast–slow system using the Wasserstein distance

Vissio

Lucarini

2018

Nonlin. Processes Geophys.

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Abstract. Constructing accurate, flexible, and efficient parametrizations is one of the great challenges in the numerical modeling of geophysical fluids. We consider here the simple yet paradigmatic case of a Lorenz 84 model forced by a Lorenz 63 model and derive a parametrization using a recently developed statistical mechanical methodology based on the Ruelle response theory. We derive an expression for the deterministic and the stochastic component of the parametrization and we show that the approach allows for dealing seamlessly with the case of the Lorenz 63 being a fast as well as a slow forcing compared to the characteristic timescales of the Lorenz 84 model. We test our results using both standard metrics based on the moments of the variables of interest as well as Wasserstein distance between the projected measure of the original system on the Lorenz 84 model variables and the measure of the parametrized one. By testing our methods on reduced-phase spaces obtained by projection, we find support for the idea that comparisons based on the Wasserstein distance might be of relevance in many applications despite the curse of dimensionality.

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“…Note that a substantially similar construction, the snapshot attractor, has been proposed and fruitfully used to address a variety of time-dependent problems, including some of climatic relevance [31][32][33][34].…”

Section: Pullback Attractor and Climate Responsementioning

confidence: 99%

“…We will frame the problem of studying the statistical properties of a non-autonomous, forced and dissipative complex system using the mathematical construction of the pullback attractor [28][29][30]-see also the closely related concept of snapshot attractor [31][32][33][34]-and will use as theoretical framework the Ruelle response theory [22,35] to compute the effect of small time-dependent perturbations on the background state. We will stick to the linear approximation, which has proved its effectiveness in various examples of geophysical interest [23,36].…”

Section: Introductionmentioning

confidence: 99%

Predicting Climate Change Using Response Theory: Global Averages and Spatial Patterns

Lucarini

Ragone

Lunkeit³

2016

J Stat Phys

132

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The provision of accurate methods for predicting the climate response to anthropogenic and natural forcings is a key contemporary scientific challenge. Using a simplified and efficient open-source general circulation model of the atmosphere featuring O(10 5 ) degrees of freedom, we show how it is possible to approach such a problem using nonequilibrium statistical mechanics. Response theory allows one to practically compute the time-dependent measure supported on the pullback attractor of the climate system, whose dynamics is nonautonomous as a result of time-dependent forcings. We propose a simple yet efficient method for predicting-at any lead time and in an ensemble sense-the change in climate properties resulting from increase in the concentration of CO 2 using test perturbation model runs. We assess strengths and limitations of the response theory in predicting the changes in the globally averaged values of surface temperature and of the yearly total precipitation, as well as in their spatial patterns. The quality of the predictions obtained for the surface temperature fields is rather good, while in the case of precipitation a good skill is observed only for the global average. We also show how it is possible to define accurately concepts like the inertia of the climate system or to predict when climate change is detectable given a scenario of forcing. Our analysis can be extended for dealing with more complex portfolios of forcings and can be adapted to treat, in principle, any climate observable. Our conclusion is that climate change is indeed a problem that can be effectively seen through a statistical mechanical lens, and that there is great potential for optimizing the current coordinated modelling exercises run for the preparation of the subsequent reports of the Intergovernmental Panel for Climate Change.Paper prepared for the special issue of the Journal of Statistical Physics dedicated to the 80th birthday of Y.

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A chaotically driven model climate: extreme events and snapshot attractors

Cited by 35 publications

References 29 publications

Extremes and Recurrence in Dynamical Systems

Extremes and Recurrence in Dynamical Systems

Evaluating a stochastic parametrization for a fast–slow system using the Wasserstein distance

Predicting Climate Change Using Response Theory: Global Averages and Spatial Patterns

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