Threshold modeling of extreme spatial rainfall

Thibaud, Emeric; Mutzner, Raphaël; Davison, A. C.

doi:10.1002/wrcr.20329

Cited by 78 publications

(82 citation statements)

References 76 publications

(83 reference statements)

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“…Wadsworth and Tawn (2012) show that max-stable processes are not well adapted for modeling wave height data in North Sea and that inverted models are preferred. Thibaud et al (2013) compare the fits of Gaussian, max-stable, and inverted max-stable models for extreme spatial rainfall in a small mountain catchment, and conclude that the last fits their data best.…”

Section: Applicationsmentioning

confidence: 99%

“…When individual events are recorded, more efficient inference is feasible. Since the max-stable models are suitable only above some predetermined high threshold, inference is usually made using a censored approach (Huser andJeon and Smith 2012;Thibaud et al 2013). Furthermore, following Stephenson and Tawn (2005), Davison and Gholamrezaee (2012) and Wadsworth and Tawn (2013) show how to incorporate the occurrence times of extreme events, use of which both simplifies the likelihood and allows much more efficient inference in cases of moderate to low spatial dependence.…”

Section: Inferencementioning

confidence: 99%

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Geostatistics of Dependent and Asymptotically Independent Extremes

2013

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Spatial modeling of rare events has obvious applications in the environmental sciences and is crucial when assessing the effects of catastrophic events (such as heatwaves or widespread flooding) on food security and on the sustainability of societal infrastructure. Although classical geostatistics is largely based on Gaussian processes and distributions, these are not appropriate for extremes, for which maxstable and related processes provide more suitable models. This paper provides a brief overview of current work on the statistics of spatial extremes, with an emphasis on the consequences of the assumption of max-stability. Applications to winter minimum temperatures and daily rainfall are described.

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Section: Applicationsmentioning

confidence: 99%

Section: Inferencementioning

confidence: 99%

Geostatistics of Dependent and Asymptotically Independent Extremes

2013

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“…The probabilities Pr(W D = 0 | R > r) and Pr(W D > 0 | R > r) can be calculated similarly. Substituting into expression (18) we obtain the results in Theorem 4.…”

Section: Proof Of Theoremmentioning

confidence: 93%

“…In the analysis of multivariate data, it is often difficult to make a choice between AD and AI; see, e.g., [3], [11] and [18]. By having a model that has both AD and AI components, we can avoid having to make this key decision.…”

Section: Introductionmentioning

confidence: 99%

Properties of extremal dependence models built on bivariate max-linearity

Kereszturi

Tawn

2017

Journal of Multivariate Analysis

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Please cite this article as: M. Kereszturi, J. Tawn, Properties of extremal dependence models built on bivariate max-linearity, Journal of Multivariate Analysis (2016), http://dx.doi.org/10. 1016/j.jmva.2016.12.001 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. Properties of extremal dependence models built on bivariate max-linearityMónika Kereszturi * and Jonathan Tawn STOR-i Centre for Doctoral Training, Lancaster University, UK AbstractBivariate max-linear models provide a core building block for characterizing bivariate max-stable distributions. The limiting distribution of marginally normalized component-wise maxima of bivariate max-linear models can be dependent (asymptotically dependent) or independent (asymptotically independent). However, for modeling bivariate extremes they have weaknesses in that they are exactly max-stable with no penultimate form of convergence to asymptotic dependence, and asymptotic independence arises if and only if the bivariate max-linear model is independent. In this work we present more realistic structures for describing bivariate extremes. We show that these models are built on bivariate max-linearity but are much more general. In particular, we present models that are dependent but asymptotically independent and others that are asymptotically dependent but have penultimate forms. We characterize the limiting behavior of these models using two new different angular measures in a radial-angular representation that reveal more structure than existing measures.

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“…In Dupuis and Tawn (2001), the effects of mis-specification of the dependence structure on bivariate extreme-value problems were studied on synthetic data while Dupuis (2007) showed the effect of model mis-specification on bivariate hydrometric data sets. More recently, Blanchet and Davison (2011) and Thibaud et al (2013) (see also references therein) performed model selection of spatial processes for extremes of snow and rainfall, respectively, in Switzerland. These studies show that the choice of the spatial dependence structure for extremes must be made with great care and that the metaGaussian distribution can fit very poorly.…”

Section: Introductionmentioning

confidence: 99%

Multivariate density model comparison for multi-site flood-risk rainfall in the French Mediterranean area

Carreau

Bouvier

2015

Stoch Environ Res Risk Assess

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The French Mediterranean area is subject to intense rainfall events which might cause flash floods, the main natural hazard in the area. Flood-risk rainfall is defined as rainfall with a high spatial average and encompasses rainfall which might lead to flash floods. We aim to compare eight multivariate density models for multi-site flood-risk rainfall. In particular, an accurate characterization of the spatial variability of flood-risk rainfall is crucial to help understand flash flood processes. Daily data from eight rain gauge stations at the Gardon at Anduze, a small Mediterranean catchment, are used in this work. Each multivariate density model is made of a combination of a marginal model and a dependence structure. Two marginal models are considered: the Gamma distribution (parametric) and the Log-Normal mixture (nonparametric). Four dependence structures are included in the comparison: Gaussian, Student t, Skew Normal and Skew t in increasing order of complexity. They possess a representative set of theoretical properties (symmetry/asymmetry and asymptotic dependence/independence). The multivariate models are compared in terms of three types of criteria: (1) separate evaluation of the goodness-of-fit of the margins and of the dependence structures, (2) model selection with a leave-one-out evaluation of the AndersonDarling and Cramer-Von Mises statistics and (3) comparison in terms of two hydrologically interpretable quantities (return periods of the spatial average and conditional probabilities of exceedances). The key outcome of the comparison is that the Skew Normal with the Log-Normal mixture margins outperform significantly the other models. The asymmetry introduced by the Skew Normal is an added-value with respect to the Gaussian. Therefore, the Gaussian dependence structure, although widely used in the literature, is not recommended for the data in this study. In contrast, the asymptotically dependent models did not provide a significant improvement over the asymptotically independent ones.

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Threshold modeling of extreme spatial rainfall

Cited by 78 publications

References 76 publications

Geostatistics of Dependent and Asymptotically Independent Extremes

Geostatistics of Dependent and Asymptotically Independent Extremes

Properties of extremal dependence models built on bivariate max-linearity

Multivariate density model comparison for multi-site flood-risk rainfall in the French Mediterranean area

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