Evidence of Dispersion Relations for the Nonlinear Response of the Lorenz 63 System

Lucarini, Valerio

doi:10.1007/s10955-008-9675-z

Cited by 66 publications

(103 citation statements)

References 32 publications

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“…Another important property of Axiom A systems is that it is possible to develop a response theory for computing the change in the statistical properties of any observable due to small perturbations to the flow [83,84]. Such a response theory has recently been the subject of intense theoretical [255,256], algorithmic [257,258,259], and numerical investigations [260,261,262,263] and is gaining prominence especially for geophysical fluid dynamical applications. Moreover, the response theory seems to provide powerful tools for studying multiscale systems and deriving parametrizations of the impact of the fast variables on dynamics of the slow variables [264,265].…”

Section: Choosing a Mathematical Frameworkmentioning

confidence: 99%

Extremes and Recurrence in Dynamical Systems

Lucarini¹,

Faranda²,

Freitas³

et al. 2016

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193

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: Choosing a Mathematical Frameworkmentioning

confidence: 99%

Extremes and Recurrence in Dynamical Systems

Lucarini¹,

Faranda²,

Freitas³

et al. 2016

Self Cite

193

253

View full text Add to dashboard Cite

show abstract

“…In this section, for the benefit of the reader, we briefly recapitulate some of the main results recently obtained regarding the description of the non-equilibrium thermodynamical properties of the climate system (Lucarini, 2009a;.…”

Section: Efficiency and Entropy Production In The Climate Systemmentioning

confidence: 99%

“…Rigorous mathematical foundations to this problem can be traced to the Ruelle response theory for non equilibrium steady state systems (Ruelle, 1998(Ruelle, , 2009. Such an approach has been recently proved to have formal analogies with the usual Kubo response theory for quasi-equilibrium systems (Lucarini, 2008a) and to be amenable to numerical investigation (Lucarini, 2009a).…”

Section: Introductionmentioning

confidence: 99%

Thermodynamics of climate change: generalized sensitivities

Lucarini

Fraedrich²,

Lunkeit³

2010

Atmos. Chem. Phys.

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Abstract. Using a recent theoretical approach, we study how global warming impacts the thermodynamics of the climate system by performing experiments with a simplified yet Earth-like climate model. The intensity of the Lorenz energy cycle, the Carnot efficiency, the material entropy production, and the degree of irreversibility of the system change monotonically with the CO 2 concentration. Moreover, these quantities feature an approximately linear behaviour with respect to the logarithm of the CO 2 concentration in a relatively wide range. These generalized sensitivities suggest that the climate becomes less efficient, more irreversible, and features higher entropy production as it becomes warmer, with changes in the latent heat fluxes playing a predominant role. These results may be of help for explaining recent findings obtained with state of the art climate models regarding how increases in CO 2 concentration impact the vertical stratification of the tropical and extratropical atmosphere and the position of the storm tracks.

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“…We will follow this approach in the analysis detailed below. While the methodology is almost trivial in the linear case, it is in principle feasible also when higher order corrections are considered, as long as the response theory is applicable [37,48,49].…”

Section: Pullback Attractor and Climate Responsementioning

confidence: 99%

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

Lucarini

Ragone

Lunkeit³

2016

J Stat Phys

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102

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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Evidence of Dispersion Relations for the Nonlinear Response of the Lorenz 63 System

Cited by 66 publications

References 32 publications

Extremes and Recurrence in Dynamical Systems

Extremes and Recurrence in Dynamical Systems

Thermodynamics of climate change: generalized sensitivities

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

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