Modeling extreme values of processes observed at irregular time steps: Application to significant wave height

Raillard, Nicolas; Ailliot, Pierre; Yao, Jianfeng

doi:10.1214/13-aoas711

Cited by 12 publications

(16 citation statements)

References 39 publications

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“…In applying pairwise likelihood we must account for the fact that exceedances may occur in both variables, in one variable or in neither, whereas the bivariate density associated to is only valid when both variables exceed the threshold v . To do so, we apply the censoring approach described by Coles (), section 8.3.1, and used in the context of threshold exceedances of spatial extremes in Bacro and Gaetan (), Huser and Davison (), Raillard et al (), and Thibaud et al (), for example. Writing G i j the bivariate distribution, valid only when both variables exceed v , the likelihood contribution of sites i and j in , is

g_{ij} (y_{it}, y_{jt}) = ({, \begin{matrix} \partial_{i} \partial_{j} G_{ij} (y_{it}, y_{jt}), & y_{it} > v, y_{jt} > v; \\ \partial_{i} G_{ij} (y_{it}, v), & y_{it} > v, y_{jt} \leq v; \\ \partial_{j} G_{ij} (v, y_{jt}), & y_{it} \leq v, y_{jt} > v; \\ G_{ij} (v, v), & y_{it} \leq v, y_{jt} \leq v; \end{matrix})

…”

Section: Methodsmentioning

confidence: 99%

Trend in the Co‐Occurrence of Extreme Daily Rainfall in West Africa Since 1950

et al. 2018

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We propose in this paper a statistical framework to study the evolution of the co‐occurrence of extreme daily rainfall in West Africa since 1950. We consider two regions subject to contrasted rainfall regimes: Senegal and the central Sahel. We study the likelihood of the 3% largest daily rainfall (considering all days) in each region to occur simultaneously and, in a 20 year moving window approach, how this likelihood has evolved with time. Our method uses an anisotropic max‐stable process allowing us to properly represent the co‐occurrence of daily extremes and including the possibility of a preferred direction of co‐occurrence. In Senegal, a change is found in the 1980s, with preferred co‐occurrence along the E‐50‐N direction (i.e., along azimuth 50°) before the 1980s and weaker isotropic co‐occurrence afterward. In central Sahel, a change is also found in the 1980s but surprisingly with contrasting results. Anisotropy along the E‐W direction is found over the whole period, with greater extension after the 1980s. The paper discusses how the co‐occurrence of extremes can provide a qualitative indicator on change in size and propagation of the strongest storms. This calls for further research to identify the atmospheric processes responsible for such contrasted changes in storm properties.

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g_{ij} (y_{it}, y_{jt}) = ({, \begin{matrix} \partial_{i} \partial_{j} G_{ij} (y_{it}, y_{jt}), & y_{it} > v, y_{jt} > v; \\ \partial_{i} G_{ij} (y_{it}, v), & y_{it} > v, y_{jt} \leq v; \\ \partial_{j} G_{ij} (v, y_{jt}), & y_{it} \leq v, y_{jt} > v; \\ G_{ij} (v, v), & y_{it} \leq v, y_{jt} \leq v; \end{matrix})

…”

Section: Methodsmentioning

confidence: 99%

Trend in the Co‐Occurrence of Extreme Daily Rainfall in West Africa Since 1950

et al. 2018

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“…Many of the models available in the literature for the series of exceedances are derived from limiting representations of the extremal behaviour of a stochastic process (see, for example, Smith et al, 1997;Reich et al, 2014;Raillard et al, 2014). The use of asymptotic forms typically induces asymptotic dependence and stability of the temporal structure at levels higher than the base threshold u.…”

Section: Latent Process Models For Exceedancesmentioning

confidence: 99%

“…Different solutions have also been developed, enlarging the class of available dependence models. For example, in Reich et al (2014) and Raillard et al (2014) the sequence of the exceedances is assumed to be a realization of a censored max-stable process (de Haan, 1984) (see also Huser and Davison, 2014, for a space-time example). Alternatively, Bortot and Gaetan (2014) propose a hierarchical model, which will be denoted hereafter by M , that combines a latent process controlling serial dependence with distributional assumptions that guarantee GP margins.…”

Section: Introductionmentioning

confidence: 99%

Latent Process Modelling of Threshold Exceedances in Hourly Rainfall Series

Bortot

Gaetan

2016

JABES

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Two features are often observed in analyses of both daily and hourly rainfall series.One is the tendency for the strength of temporal dependence to decrease when looking at the series above increasing thresholds. The other is the empirical evidence for rainfall extremes to approach independence at high enough levels. To account for these features, Bortot and Gaetan (2014) focus on rainfall exceedances above a fixed high threshold and model their dynamics through a hierarchical approach that allows for changes in the temporal dependence properties when moving further into the right tail.It is found that this modelling procedure performs generally well in analyses of daily rainfalls, but has some inherent theoretical limitations that affect its goodness of fit in the context of hourly data. In order to overcome this drawback, we develop here a modification of the Bortot and Gaetan model derived from a copula-type technique.Application of both model versions to rainfall series recorded in Camborne, England, shows that they provide similar results when studying daily data, but, in the analysis of hourly data the modified version is superior.

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“…One can use altimeters data sets as an alternative, but their major drawback is the non-regularity of satellites tracks through time and space around the globe. Raillard et al (2014) deal with such source of data thanks to max-stable processes, but without looking at the spatial dependence structure in the same time. The last way to observe wave data is the use of numerical simulations.…”

Section: A 52-year Wave Hindcastmentioning

confidence: 99%

“…The performance of such modelling has been shown in applications in other environmental contexts, like for instance the study of heavy snow events in Blanchet and Davison (2011) or heatwaves in Davison and Gholamrezaee (2011). Some investigations on significant waves has been produced by Raillard et al (2014). Jonathan et al (2013) present such applications as a promising way to model extreme waves events.…”

Section: Introductionmentioning

confidence: 99%

Spatial Assessment of Extreme Significant Waves Heights in the Gulf of Lions

Chailan

Toulemonde²,

Bouchette

et al. 2014

Int. Conf. Coastal. Eng.

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In the analysis of coastal hazards, the features of extreme waves are determining information to question the impact of storms to the coast. The spatial behaviour of extreme waves is even more valuable especially since it is sparsely provided. Regarding recent applications in other contexts, a kind of statistical models called max-stable processes is relevant for modelling spatial extreme events. Max-stable processes are extensions of the well-known Generalised Extreme Value (GEV) distribution. Unlike univariate approaches, max-stable processes consider spatial dependence of a phenomenon. Such a modelling also overtakes a standard multivariate approach by providing information continuously over the area studied, even where no observation is available. Relying on such a stochastic modelling, the aim of this study is to discuss the extreme waves hazards in the Gulf of Lions, focusing on their spatial behaviour.

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Modeling extreme values of processes observed at irregular time steps: Application to significant wave height

Cited by 12 publications

References 39 publications

Trend in the Co‐Occurrence of Extreme Daily Rainfall in West Africa Since 1950

Trend in the Co‐Occurrence of Extreme Daily Rainfall in West Africa Since 1950

Latent Process Modelling of Threshold Exceedances in Hourly Rainfall Series

Spatial Assessment of Extreme Significant Waves Heights in the Gulf of Lions

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