Convergence of Extreme Value Statistics in a Two-Layer Quasi-Geostrophic Atmospheric Model

Gálfi, Vera Melinda; Bódai, Tamás; Lucarini, Valerio

doi:10.1155/2017/5340858

Cited by 19 publications

(22 citation statements)

References 55 publications

(133 reference statements)

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“…The approximation of the estimates to the theoretical value takes place very slowly, and they have different rates for different observables. Different rates of convergence of the estimates of the shape parameter for different observables had also been reported in Gálfi, Bódai, and Lucarini (2017).…”

Section: Discussionmentioning

confidence: 59%

“…A comprehensive summary of the main results of extreme events of observables of deterministic systems with examples and applications can be found in . This link has been reexamined by Gálfi, Bódai, and Lucarini (2017), in which the authors presented the convergence of shape parameter estimates to the theoretical value in a two-level quasi-geostrophic atmospheric model, or the lack of it, as this convergence could be observed only in the model with a strong forcing. Furthermore, Bódai (2017) argued that the convergence of the shape parameter can be observed typically for high-dimensional systems, and in low-dimensional systems, such as the Lorenz'84 and one-level Lorenz'96 models that he studied, the shape parameter estimates can increase nonmonotonically with the block size, or fluctuate owing to the fractality of the natural measure, in which latter case no extreme value law exists in a strict sense.…”

Section: Introductionmentioning

confidence: 97%

“…In an earlier study, Franzke (2012) showed that a reduced order model constructed by systematic stochastic mode reduction strategy has similar extreme value statistics as the full dynamical model for a wide range of time-scale separations. As a contribution to the main goal of this paper, like Franzke (2012); Gálfi et al (2017); Bódai (2017), we also examine the convergence/approximation of the shape parameter estimates of the said different models to the theoretical value of the two-level L96. Note that the shape parameter of a stochastic model is most probably not the same as that of a deterministic model.…”

Section: Introductionmentioning

confidence: 99%

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Effects of stochastic parametrization on extreme value statistics

Bódai

Lucarini

2019

Chaos: An Interdisciplinary Journal of Nonlinear Science

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Extreme geophysical events are of crucial relevance to our daily life: they threaten human lives and cause property damage. To assess the risk and reduce losses, we need to model and probabilistically predict these events. Parametrizations are computational tools used in Earth system models, which are aimed at reproducing the impact of unresolved scales on resolved scales. The performance of parametrizations has usually been examined on typical events rather than on extreme events. In this paper we consider a modified version of the two-level Lorenz'96 model and investigate how two parametrizations of the fast degrees of freedom perform in terms of the representation of extreme events. One parametrization is constructed following Wilks (2005) and is constructed through an empirical fitting procedure; the other parametrization is constructed through the statistical mechanical approach proposed by Lucarini (2012, 2013). The two strategies show different advantages and disadvantages. We discover that the agreement between parametrized models and true model is in general worse when looking at extremes rather than at the bulk of the statistics. The results suggest that stochastic parametrizations should be accurately and specifically tested against their performance on extreme events, as usual optimization procedures might neglect them.arXiv:1903.05514v2 [nlin.CD] 17 Jul 2019 the polynomial coefficients by regressing P k (X k (t i )) againstThe estimated coefficients are a 0 = −1.81, a 1 = −0.1467, a 2 = 0.001357, a 3 = −0.001446, and a 4 = 0.0001313. Next we fit the residual of the polynomial fitting a 1 , a 2 , a 3 , a 4 ) with the first-order autoregressive model (Eq. 6). In our computation, we get φ = 0.9997 and σ e = 0.8965; we refer to Neumaier and Schneider (2001) for the estimation of parameters of autoregressive models. The Wilks parametrization is an empirical parametrization which is constructed based on the fact that in the two-level L96 the unresolved tendency is strongly and nonlinearly dependent on the value of the resolved variable (Wilks, 2005). The implementation of the two modifications to the original model do not change this characteristic, therefore, the Wilks parametrization is still valid. A weakness of the empirical parametrizations is that their parameters need to be recalculated if the configuration of the full model is changed.

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Section: Discussionmentioning

confidence: 59%

Section: Introductionmentioning

confidence: 97%

Section: Introductionmentioning

confidence: 99%

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Effects of stochastic parametrization on extreme value statistics

Bódai

Lucarini

2019

Chaos: An Interdisciplinary Journal of Nonlinear Science

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“…In another example studied by Gálfi (2015), a quasi-geosthropic two-layer model of midlatitude atmospheric dynamics, estimates of the shape parameter seem to converge from below to the true value (say, ξ ≈ −0.002), but very slowly. This is believed to be because the system is very highdimensional (D KY ≈ 600), and so its observables are approximately normally distributed, entailing an (approximately) Gumbel EVD (ξ ≈ 0).…”

Section: Discussionmentioning

confidence: 99%

“…Here we go beyond this and consider higher dimensional systems. Given preliminary indication that higher-dimensional systems produce -perhaps typically -fairly regular EVS (Vannitsem, 2007;Gálfi, 2015), it is an interesting question how high does the dimension need to be for regularity; what is the transition like from low to high dimensions? We will also investigate if integer-dimensional systems produce regular EVS.…”

Section: Physical Observables Of the Lorenz 96 Modelmentioning

confidence: 99%

Extreme Value Analysis in Dynamical Systems: Two Case Studies

Bódai¹

2016

Nonlinear and Stochastic Climate Dynamics

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We give here a brief summary of classical Extreme Value Theory for random variables, followed by that for deterministic dynamical systems, which is a rapidly developing area of research. Here we would like to contribute to that by conducting a numerical analysis designed to show particular features of extreme value statistics in dynamical systems, and also to explore the validity of the theory. We find that formulae that link the extreme value statistics with geometrical properties of the attractor hold typically for high-dimensional systems-whether a so-called geometric distance observable or a physical observable is concerned. In very low-dimensional settings, however, the fractality of the attractor prevents the system from having an extreme value law, which might well render the evaluation of extreme value statistics meaningless and so ill-suited for application.

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Extreme Value Statistics

Jacob

Neves

Greetham

2019

Forecasting and Assessing Risk of Individual Electricity Peaks

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When studying peaks in electricity demand, we may be interested in understanding the risk of a certain large level for demand being exceeded. For example, there is potential interest in finding the probability that the electricity demand of a business or household exceeds the contractual limit. An alternative, yet in principle equivalent way, involves assessment of maximal needs for electricity over a certain period of time, like a day, a week or a season within a year. This would stem from the potential interested in quantifying the largest electricity consumption for a substation, household or business. In either case, we are trying to infer about extreme traits in electricity loads for a certain region assumed fairly homogeneous with the ultimate aim of predicting the likelihood of an extreme event which might have never been observed before. While the exact truth may be not be possible to determine, it may be possible come up with an educated guess (an estimate) and ascertain confidence margins around it. In this chapter, not only we will list and describe mainstream statistical methodology for drawing inference on extreme and rare events, but we will also endeavour to elucidate what sets the semiparametric approach apart from the classical parametric approach and how these two eventually align with one another. For details on possible approaches and related statistical methodologies we refer to [1, 2]. We hope that, through this chapter, practitioners and users of extreme value theory will be able to see how the theoretical results in Chap. 3 translate in practice and how conditions can be checked. We will be mainly concerned with semi-parametric inference for univariate extremes. This statistical methodology builds strongly on the fundamental results expounded in the previous section, most notably the theory of extended regular variation (see e.g. [3], Appendix B). Despite the numerous approaches whereby extreme values can be statistically analysed, these are generally classed into two main frameworks: methods for maxima over fixed intervals (blocks) and methods for exceedances (peaks) over high

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Convergence of Extreme Value Statistics in a Two-Layer Quasi-Geostrophic Atmospheric Model

Cited by 19 publications

References 55 publications

Effects of stochastic parametrization on extreme value statistics

Effects of stochastic parametrization on extreme value statistics

Extreme Value Analysis in Dynamical Systems: Two Case Studies

Extreme Value Statistics

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