Multivariate extreme value identification using depth functions

Chebana, Fateh; Ouarda, Taha B. M. J.

doi:10.1002/env.1089

Cited by 21 publications

(13 citation statements)

References 38 publications

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“…Recently, several efforts have been spent on the issues of multivariate design and quantiles (see, e.g. Serfling, 2002;Belzunce et al, 2007;Ouarda, 2009, 2011b;Chaouch and Goga, 2010, and references therein; for a methodology to identify multivariate extremes by using depth functions see Chebana and Ouarda, 2011a). Here we address the following crucial question: "How is it possible to calculate the critical design event(s) in the multivariate case?"…”

Section: Introductionmentioning

confidence: 99%

On the return period and design in a multivariate framework

Salvadori

Michele

Durante

2011

Hydrol. Earth Syst. Sci.

301

321

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Abstract. Calculating return periods and design quantiles in a multivariate environment is a difficult problem: this paper tries to make the issue clear. First, we outline a possible way to introduce a consistent theoretical framework for the calculation of the return period in a multi-dimensional environment, based on Copulas and the Kendall's measure. Secondly, we introduce several approaches for the identification of suitable design events: these latter quantities are of utmost importance in practical applications, but their calculation is yet limited, due to the lack of an adequate theoretical environment where to embed the problem. Throughout the paper, a case study involving the behavior of a dam is used to illustrate the new concepts outlined in this work.

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Section: Introductionmentioning

confidence: 99%

On the return period and design in a multivariate framework

Salvadori

Michele

Durante

2011

Hydrol. Earth Syst. Sci.

301

321

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“…It has been used in the field of regional flood frequency analysis (Chebana and Ouarda 2008, Wazneh et al 2013a, Wazneh et al 2013b (Chebana and Ouarda 2011b), regionalization of hydrological model parameters (Bardossy and Singh 2011) and robust estimation of hydrological model parameters (Bárdossy and Singh 2008), defining predictive uncertainty of a model , and in selection of critical events for model calibration (Singh and Bárdossy 2012). For more detailed information about the data depth function and its uses in field of water resources, please refer to Chebana and Ouarda (2011a), Chebana and Ouarda (2011c), Guerrero et al (2013), Krauße and Cullmann (2009) and Singh and Bárdossy (2012).…”

Section: Data Depth Functionmentioning

confidence: 99%

Nonparametric catchment clustering using the data depth function

Singh

McMillan

Bàrdossy

et al. 2016

Hydrological Sciences Journal

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The clustering of catchments has been important for prediction in ungauged basins, model parameterization and watershed development and management. The aim of this study is to explore a new measure of similarity among catchments, using a data depth function and comparing it with catchment clustering indices based on flow and physical characteristics. A cluster analysis was performed for each similarity measure using the affinity propagation clustering algorithm. We evaluated the similarity measure based on depth-depth plots (DDplots) as a basis for transferring parameter sets of a hydrological model between catchments.A case study was developed with 21 catchments in a diverse New Zealand region. Results show that clustering based on the depth-depth measure is dissimilar to clustering on catchment characteristics, flow, or flow indices. A hydrological model was calibrated for 21 catchments and the transferability of model parameters among similar catchments was tested within and between clusters defined by each clustering method. The mean model performance for parameters transferred within group always outperformed those from outside the group. The DD-plot based method was found to produce the best in-group performance and second-highest difference between in-group and out-group performance.

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“…Some studies use copulas since the work by De Michele and Salvadori (), for example Salvadori (), Salvadori et al (, , ), whom also define multivariate versions of the return period , and Grimaldi and Serinaldi (). Another alternative is given by Serfling (); Chebana and Ouarda () through depth functions. However, both alternatives have drawbacks when they have to be implemented in high‐dimensional scenarios.…”

Section: Introductionmentioning

confidence: 99%

Directional multivariate extremes in environmental phenomena

et al. 2017

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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). Keywords Directional Multivariate Extremes in Environmental PhenomenaRaúl Torres (ratorres@est-econ.uc3m.es) Carlo De Michele (carlo.demichele@polimi.it) Henry Laniado (hlaniado@est-econ.uc3m.es) Rosa E. Lillo (lillo@est-econ.uc3m.es) AbstractSeveral 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).

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Multivariate extreme value identification using depth functions

Cited by 21 publications

References 38 publications

On the return period and design in a multivariate framework

On the return period and design in a multivariate framework

Nonparametric catchment clustering using the data depth function

Directional multivariate extremes in environmental phenomena

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