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Register a new userModelling non-stationary extremes of storm severity: a tale of two approaches
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Added by
Claudia Neves
Publication date
2020
fields
Mathematical Statistics
and research's language is
English
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Models for extreme values accommodating non-stationarity have been amply studied and evaluated from a parametric perspective. Whilst these models are flexible, in the sense that many parametrizations can be explored, they assume an asymptotic distribution as the proper fit to observations from the tail. This paper provides a holistic approach to the modelling of non-stationary extreme events by iterating between parametric and semi-parametric approaches, thus providing an automatic procedure to estimate a moving threshold with respect to a periodic covariate in circular data. By exploiting advantages and mitigating pitfalls of each approach, a unified framework is provided as the backbone for estimating extreme quantiles, including that of the $T$-year level and finite right endpoint, which seeks to optimize bias-variance trade-off. To this end, two tuning parameters related to the spread of peaks over threshold are introduced. We provide guidance for applying the methodology to the directional modelling of hindcast storm peak significant wave heights recorded in the North Sea. Although the theoretical underpinning for adaptation of well-known estimators in statistics of extremes to circular data is given in some detail, the derivation of their asymptotic properties lays beyond the scope of this paper. A bootstrap technique is implemented for obtaining direction-driven confidence bounds in such a way as to account for the relevant boundary restrictions with minimal sensitivity to initial point. This provides a template for other applications where the analysis of directional extremes is of importance.
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Observed accidents have been the main resource for road safety analysis over the past decades. Although such reliance seems quite straightforward, the rare nature of these events has made safety difficult to assess, especially for new and innovative traffic treatments. Surrogate measures of safety have allowed to step away from traditional safety performance functions and analyze safety performance without relying on accident records. In recent years, the use of extreme value theory (EV) models in combination with surrogate safety measures to estimate accident probabilities has gained popularity within the safety community. In this paper we extend existing efforts on EV for accident probability estimation for two dependent surrogate measures. Using detailed trajectory data from a driving simulator, we model the joint probability of head-on and rear-end collisions in passing maneuvers. In our estimation we account for driver specific characteristics and road infrastructure variables. We show that accounting for these factors improve the head-on collision probability estimation. This work highlights the importance of considering driver and road heterogeneity in evaluating related safety events, of relevance to interventions both for in-vehicle and infrastructure-based solutions. Such features are essential to keep up with the expectations from surrogate safety measures for the integrated analysis of accident phenomena.
Aiming to generate realistic synthetic times series of the bivariate process of daily mean temperature and precipitations, we introduce a non-homogeneous hidden Markov model. The non-homogeneity lies in periodic transition probabilities between the hidden states, and time-dependent emission distributions. This enables the model to account for the non-stationary behaviour of weather variables. By carefully choosing the emission distributions, it is also possible to model the dependance structure between the two variables. The model is applied to several weather stations in Europe with various climates, and we show that it is able to simulate realistic bivariate time series.
Several environmental phenomena can be described by different correlated variables that must be considered jointly in order to be more representative of the nature of these phenomena. For such events, identification of extremes is inappropriate if it is based on marginal analysis. Extremes have usually been linked to the notion of quantile, which is an important tool to analyze risk in the univariate setting. We propose to identify multivariate extremes and analyze environmental phenomena in terms of the directional multivariate quantile, which allows us to analyze the data considering all the variables implied in the phenomena, as well as look at the data in interesting directions that can better describe an environmental catastrophe. Since there are many references in the literature that propose extremes detection based on copula models, we also generalize the copula method by introducing the directional approach. Advantages and disadvantages of the non-parametric proposal that we introduce and the copula methods are provided in the paper. We show with simulated and real data sets how by considering the first principal component direction we can improve the visualization of extremes. Finally, two cases of study are analyzed: a synthetic case of flood risk at a dam (a 3-variable case), and a real case study of sea storms (a 5-variable case).
In light of the strong advances in understanding the mathematical structure of scattering amplitudes, we discuss the Regge limit of QCD and of the ${cal N}=4$ Super Yang-Mills theory.
Severe thunderstorms can have devastating impacts. Concurrently high values of convective available potential energy (CAPE) and storm relative helicity (SRH) are known to be conducive to severe weather, so high values of PROD=$sqrt{mathrm{CAPE}} times$SRH have been used to indicate high risk of severe thunderstorms. We consider the extreme values of these three variables for a large area of the contiguous US over the period 1979-2015, and use extreme-value theory and a multiple testing procedure to show that there is a significant time trend in the extremes for PROD maxima in April, May and August, for CAPE maxima in April, May and June, and for maxima of SRH in April and May. These observed increases in CAPE are also relevant for rainfall extremes and are expected in a warmer climate, but have not previously been reported. Moreover, we show that the El Ni~no-Southern Oscillation explains variation in the extremes of PROD and SRH in February. Our results suggest that the risk from severe thunderstorms in April and May is increasing in parts of the US where it was already high, and that the risk from storms in February tends to be higher over the main part of the region during La Ni~na years. Our results differ from those obtained in earlier studies using extreme-value techniques to analyze a quantity similar to PROD.
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