Extreme Value Statistics of the Total Energy in an Intermediate-Complexity Model of the Midlatitude Atmospheric Jet. Part I: Stationary Case

Felici, Mara; Lucarini, Valerio; Speranza, Antonio; Vitolo, Renato

doi:10.1175/jas3895.1

Cited by 33 publications

(56 citation statements)

References 44 publications

(87 reference statements)

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“…Here, a sample size of 82 events, for example, yields a change of -0.1 m s −1 , whereas it is -1.1 m s −1 when 137 events are considered. This confirms that the GPD is also sensitive to lower wind speed data and not only to the most extreme values (e.g., Felici et al, 2007). The high variability in V , however, is within the confidence intervals for the whole range displayed.…”

Section: Parameter Sensitivity To a Variable Sample Sizesupporting

confidence: 76%

Assessment of extreme wind speeds from Regional Climate Models – Part 1: Estimation of return values and their evaluation

Kunz

Mohr

Rauthe

et al. 2010

Nat. Hazards Earth Syst. Sci.

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Abstract. Frequency and intensity of gust wind speeds associated with severe mid-latitude winter storms are estimated by applying extreme value statistics to data sets from regional climate models (RCM). Maximum wind speeds related to probability are calculated with the classical peaks over threshold method, where a statistical distribution function is fitted to the reduced sample describing the tail of the distribution function. From different sensitivity studies it is found that the Generalized Pareto Distribution in combination with a Maximum-Likelihood estimator provide the most reliable and robust results.For a reference period from 1971 to 2000, the ability of the RCMs to realistically simulate extreme wind speeds is investigated. For this purpose, data from three RCM scenarios, including the REMO-UBA simulations at 10 km resolution and the so-called consortial runs performed with the CCLM at 18 km resolution (two runs), are evaluated with observations and a pre-existing storm hazard map for Germany. It is found that all RCMs tend to underestimate the magnitude of the gusts in a range between 10 and 30% for a 10-year return period. Averaged over the investigation area, the underestimation is higher for CCLM compared to REMO. The spatial distribution of the gusts, on the other hand, is well reproduced, in particular by REMO.

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Section: Parameter Sensitivity To a Variable Sample Sizesupporting

confidence: 76%

Assessment of extreme wind speeds from Regional Climate Models – Part 1: Estimation of return values and their evaluation

Kunz

Mohr

Rauthe

et al. 2010

Nat. Hazards Earth Syst. Sci.

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show abstract

“…Nonetheless, in many practical applications, one is interested in studying a different sort of observables, the so-called physical observables [81,44], which a priori have nothing to do with the recurrence of an orbit near a given reference point, but rather describe macroscopic or anyway physically relevant properties of the system. As a simple example, one may consider the extremes of the energy [82] or of temperature [48] in a model of geophysical fluid . The extremes of physical observables permits the study of rather sophisticated aspects of the geometry of the attractor of the underlying system, providing a formidable tool for analyzing at the properties of the unstable and stable components of the tangent space.…”

Section: Extremes Observables and Dynamicsmentioning

confidence: 99%

Extremes and Recurrence in Dynamical Systems

Lucarini¹,

Faranda²,

Freitas³

et al. 2016

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190

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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“…See [4] for a detailed account of this methodology. The selection of just one maximum in a fixed period may lead to the loss of relevant information on the large fluctuations of the system, especially when there are many large values in a given period [5].…”

Section: Introductionmentioning

confidence: 99%

Universal Behaviour of Extreme Value Statistics for Selected Observables of Dynamical Systems

2012

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The main results of the extreme value theory developed for the investigation of the observables of dynamical systems rely, up to now, on the Gnedenko approach. In this framework, extremes are basically identified with the block maxima of the time series of the chosen observable, in the limit of infinitely long blocks. It has been proved that, assuming suitable mixing conditions for the underlying dynamical systems, the extremes of a specific class of observables are distributed according to the so called Generalized Extreme Value (GEV) distribution. Direct calculations show that in the case of quasi-periodic dynamics the block maxima are not distributed according to the GEV distribution. In this paper we show that, in order to obtain a universal behaviour of the extremes, the requirement of a mixing dynamics can be relaxed if the Pareto approach is used, based upon considering the exceedances over a given threshold. Requiring that the invariant measure locally scales with a well defined exponent -the local dimension -, we show that the limiting distribution for the exceedances of the observables previously studied with the Gnedenko approach is a Generalized Pareto distribution where the parameters depends only on the local dimensions and the value of the threshold. This result allows to extend the extreme value theory for dynamical systems to the case of regular motions. We also provide connections with the results obtained with the Gnedenko approach. In order to provide further support to our findings, we present the results of numerical experiments carried out considering the well-known Chirikov standard map.

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Extreme Value Statistics of the Total Energy in an Intermediate-Complexity Model of the Midlatitude Atmospheric Jet. Part I: Stationary Case

Cited by 33 publications

References 44 publications

Assessment of extreme wind speeds from Regional Climate Models – Part 1: Estimation of return values and their evaluation

Assessment of extreme wind speeds from Regional Climate Models – Part 1: Estimation of return values and their evaluation

Extremes and Recurrence in Dynamical Systems

Universal Behaviour of Extreme Value Statistics for Selected Observables of Dynamical Systems

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