An overview of the extremal index

Moloney, Nicholas R.; Faranda, Davide; Sato, Yuzuru

doi:10.1063/1.5079656

Cited by 54 publications

(64 citation statements)

References 56 publications

(53 reference statements)

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“…where ϑ is the extremal index (Moloney et al, 2019), and we estimate it here following Süveges (2007). The dynamical systems persistence is computed as θ −1 (ζ x ) = t/ϑ(ζ x ).…”

Section: Dynamical Systems Metricsmentioning

confidence: 99%

“…The Mediterranean (MED) Basin is considered a climate change hotspot (Giorgi, 2006) and has seen winter drying as well as a pronounced increase in summer heatwaves over recent decades (e.g. Mariotti, 2010;Hoerling et al, 2012;Shohami et al, 2011;Nykjaer, 2009). Summer heatwave trends observed over the historical period are mainly driven by thermodynamic changes, such as increasing temperatures, that exacerbate soil drying and daily maximum temperatures.…”

Section: Introductionmentioning

confidence: 99%

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Compound warm–dry and cold–wet events over the Mediterranean

et al. 2020

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Abstract. The Mediterranean (MED) Basin is a climate change hotspot that has seen drying and a pronounced increase in heatwaves over the last century. At the same time, it is experiencing increased heavy precipitation during wintertime cold spells. Understanding and quantifying the risks from compound events over the MED is paramount for present and future disaster risk reduction measures. Here, we apply a novel method to study compound events based on dynamical systems theory and analyse compound temperature and precipitation events over the MED from 1979 to 2018. The dynamical systems analysis quantifies the strength of the coupling between different atmospheric variables over the MED. Further, we consider compound warm–dry anomalies in summer and cold–wet anomalies in winter. Our results show that these warm–dry and cold–wet compound days are associated with large values of the temperature–precipitation coupling parameter of the dynamical systems analysis. This indicates that there is a strong interaction between temperature and precipitation during compound events. In winter, we find no significant trend in the coupling between temperature and precipitation. However in summer, we find a significant upward trend which is likely driven by a stronger coupling during warm and dry days. Thermodynamic processes associated with long-term MED warming can best explain the trend, which intensifies compound warm–dry events.

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“…where ϑ is the extremal index (Moloney et al, 2019), and we estimate it here following Süveges (2007). The dynamical systems persistence is computed as θ −1 (ζ x ) = t/ϑ(ζ x ).…”

Section: Dynamical Systems Metricsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Compound warm–dry and cold–wet events over the Mediterranean

et al. 2020

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“…The parameters ϑ and σ depend on the chosen point ζ. ϑ is the so‐called extremal index (Moloney et al ., ), and we estimate it here using the approach of Süveges (). The local dimension d is obtained as d (ζ)=1/σ(ζ), while the local persistence is given by θ −1 =Δ t /ϑ, where Δ t is the timestep of the data used and the local persistence is in the same units as the timestep.…”

Section: Dynamical Systems Metricsmentioning

confidence: 99%

Dynamical systems theory sheds new light on compound climate extremes in Europe and Eastern North America

Luca

Messori

Pons

et al. 2020

Quart J Royal Meteoro Soc

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We propose a novel approach to the study of compound extremes, grounded in dynamical systems theory. Specifically, we present the co‐recurrence ratio (α), which elucidates the dependence structure between variables by quantifying their joint recurrences. This approach is applied to daily climate extremes, derived from the ERA‐Interim reanalysis over the 1979–2018 period. The analysis focuses on concurrent (i.e., same‐day) wet (total precipitation) and windy (10 m wind gusts) extremes in Europe and concurrent cold (2 m temperature) extremes in Eastern North America and wet extremes in Europe. Results for wet and windy extremes in Europe, which we use as a test‐bed for our methodology, show that α peaks during boreal winter. High α values correspond to wet and windy extremes in northwestern Europe, and to large‐scale conditions resembling the positive phase of the North Atlantic Oscillation (NAO). This confirms earlier findings which link the positive NAO to a heightened frequency of extratropical cyclones impacting northwestern Europe. For the Eastern North America–Europe case, α extremes once again reflect concurrent climate extremes – in this case cold extremes over North America and wet extremes over Europe. Our analysis provides detailed spatial information on regional hotspots for these compound extreme occurrences, and encapsulates information on their spatial footprint which is typically not included in a conventional co‐occurrence analysis. We conclude that α successfully characterises compound extremes by reflecting the evolution of the associated meteorological maps. This approach is entirely general, and may be applied to different types of compound extremes and geographical regions.

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“…Illustrations can be found in the book [13] and the articles [16,36,35] for an exhaustive account on the formalism, the methodologies and several applications. In particular the extremal index (EI) -a quantity defined in the unit interval -has been used as a powerful statistical indicator to discriminate among different qualitative types of dynamical behaviors in the phase space of a few climate models and in real situations (an extensive overview can be found in [37]). In a series of papers [17,7,19,37,18], the EI was renamed as local persistence indicator, suitable to estimate the average cluster size of the trajectories within the neighborhood of a given point.…”

Section: Introductionmentioning

confidence: 99%

On the Computation of the Extremal Index for Time Series

et al. 2019

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The extremal index is a quantity introduced in extreme value theory to measure the presence of clusters of exceedances. In the dynamical systems framework, it provides important information about the dynamics of the underlying systems. In this paper we provide a review of the meaning of the extremal index in dynamical systems. Depending on the observables used, this quantity can inform on local properties of attractors such as periodicity, stability and persistence in phase space, or on global properties such as the Lyapunov exponents. We also introduce a new estimator of the extremal index and shows its relation with those previously introduced in the statistical literature. We reserve a particular focus to the systems perturbed with noise as they are a good paradigm of many natural phenomena. Different kind of noises are investigated in the annealed and quenched situations. Applications to climate data are also presented.

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An overview of the extremal index

Cited by 54 publications

References 56 publications

Compound warm–dry and cold–wet events over the Mediterranean

Compound warm–dry and cold–wet events over the Mediterranean

Dynamical systems theory sheds new light on compound climate extremes in Europe and Eastern North America

On the Computation of the Extremal Index for Time Series

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