Sampling Hyperspheres via Extreme Value Theory: Implications for Measuring Attractor Dimensions

Pons, Flavio; Messori, Gabriele; Alvarez-Castro, M. Carmen; Faranda, Davide

doi:10.1007/s10955-020-02573-5

Cited by 19 publications

(18 citation statements)

References 42 publications

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“…The dynamical systems approach has been successfully applied to a variety of climate fields and datasets (Faranda et al 2017a(Faranda et al , b, 2019a(Faranda et al ,2020Messori et al 2017;Buschow and Friedrichs 2018;Rodrigues et al 2018;Brunetti et al 2019;Hochman et al 2019Hochman et al , 2020De Luca et al 2020a, b;Pons et al 2020). Specifically, it has been shown that d and θ −1 can provide an objective dynamical characterization of synoptic systems over both the North Atlantic (Faranda et al 2017a;Messori et al 2017;Rodrigues et al 2018) and the Eastern Mediterranean (Hochman et al 2019(Hochman et al , 2020.…”

Section: Introductionmentioning

confidence: 99%

Dynamics and predictability of cold spells over the Eastern Mediterranean

et al. 2020

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The accurate prediction of extreme weather events is an important and challenging task, and has typically relied on numerical simulations of the atmosphere. Here, we combine insights from numerical forecasts with recent developments in dynamical systems theory, which describe atmospheric states in terms of their persistence (θ−1) and local dimension (d), and inform on how the atmosphere evolves to and from a given state of interest. These metrics are intuitively linked to the intrinsic predictability of the atmosphere: a highly persistent, low-dimensional state will be more predictable than a low-persistence, high-dimensional one. We argue that θ−1 and d, derived from reanalysis sea level pressure (SLP) and geopotential height (Z500) fields, can provide complementary predictive information for mid-latitude extreme weather events. Specifically, signatures of regional extreme weather events might be reflected in the dynamical systems metrics, even when the actual extreme is not well-simulated in numerical forecasting systems. We focus on cold spells in the Eastern Mediterranean, and particularly those associated with snow cover in Jerusalem. These rare events are systematically associated with Cyprus Lows, which are the dominant rain-bearing weather system in the region. In our analysis, we compare the ‘cold spell Cyprus Lows’ to other ‘regular’ Cyprus Low days. Significant differences are found between cold spells and ‘regular’ Cyprus Lows from a dynamical systems perspective. When considering SLP, the intrinsic predictability of cold spells is lowest hours before the onset of snow. We find that the cyclone’s location, depth and magnitude of air-sea fluxes play an important role in determining its intrinsic predictability. The dynamical systems metrics computed on Z500 display a different temporal evolution to their SLP counterparts, highlighting the different characteristics of the atmospheric flow at the different levels. We conclude that the dynamical systems approach, although sometimes challenging to interpret, can complement conventional numerical forecasts and forecast skill measures, such as model spread and absolute error. This methodology outlines an important avenue for future research, which can potentially be fruitfully applied to other regions and other types of weather extremes.

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Section: Introductionmentioning

confidence: 99%

Dynamics and predictability of cold spells over the Eastern Mediterranean

et al. 2020

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“…There, the authors show that finite-time deviations of d and θ from the asymptotic, unknown values contain information about the underlying system, since they are linked to the presence of unstable or periodic points of the dynamics. Similarly, both analytical and empirical evidence from Pons et al (2020) shows that, although affected by the curse of dimensionality, estimates of d from finite time series may be used in a relative sense to characterise the dynamics of a system -i.e. by comparing values of d to one another.…”

Section: Theoretical Underpinnings Of the Dynamical Systems Frameworkmentioning

confidence: 99%

Technical note: Characterising and comparing different palaeoclimates with dynamical systems theory

Messori

Faranda

2021

Clim. Past

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Abstract. Numerical climate simulations produce vast amounts of high-resolution data. This poses new challenges to the palaeoclimate community – and indeed to the broader climate community – in how to efficiently process and interpret model output. The palaeoclimate community also faces the additional challenge of having to characterise and compare a much broader range of climates than encountered in other subfields of climate science. Here we propose an analysis framework, grounded in dynamical systems theory, which may contribute to overcoming these challenges. The framework enables the characterisation of the dynamics of a given climate through a small number of metrics. These may be applied to individual climate variables or to several variables at once, and they can diagnose properties such as persistence, active number of degrees of freedom and coupling. Crucially, the metrics provide information on instantaneous states of the chosen variable(s). To illustrate the framework's applicability, we analyse three numerical simulations of mid-Holocene climates over North Africa under different boundary conditions. We find that the three simulations produce climate systems with different dynamical properties, such as persistence of the spatial precipitation patterns and coupling between precipitation and large-scale sea level pressure patterns, which are reflected in the dynamical systems metrics. We conclude that the dynamical systems framework holds significant potential for analysing palaeoclimate simulations. At the same time, an appraisal of the framework's limitations suggests that it should be viewed as a complement to more conventional analyses, rather than as a wholesale substitute.

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“…Caby et al [14] study both the case of deterministic and of stochastic dynamical systems, and present also an example of analysis of actual atmospheric data. Extreme value theory is used by Pons et al [100] to propose a way to address well-known problem of the curse of dimensionality in estimating the Hausdorff dimension of the attractor from time series. The methodology is applied to study recurrences in synthetically generated as well as real-life financial and climate data and define the degree of non-randomness of the system.…”

Section: This Special Issuementioning

confidence: 99%

Introduction to the Special Issue on the Statistical Mechanics of Climate

Lucarini

2020

J Stat Phys

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We introduce the special issue on the Statistical Mechanics of Climate by presenting an informal discussion of some theoretical aspects of climate dynamics that make it a topic of great interest for mathematicians and theoretical physicists. In particular, we briefly discuss its nonequilibrium and multiscale properties, the relationship between natural climate variability and climate change, the different regimes of climate response to perturbations, and critical transitions.

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Sampling Hyperspheres via Extreme Value Theory: Implications for Measuring Attractor Dimensions

Cited by 19 publications

References 42 publications

Dynamics and predictability of cold spells over the Eastern Mediterranean

Dynamics and predictability of cold spells over the Eastern Mediterranean

Technical note: Characterising and comparing different palaeoclimates with dynamical systems theory

Introduction to the Special Issue on the Statistical Mechanics of Climate

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