Probabilistic characterization of drought properties through copulas

Serinaldi, Francesco; Bonaccorso, Brunella; Cancelliere, Antonino; Grimaldi, Salvatore

doi:10.1016/j.pce.2008.09.004

Cited by 199 publications

(96 citation statements)

References 25 publications

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“…In hydrological studies, four different estimators have been commonly considered (Poulin et al 2007;Villarini et al 2008;Serinaldi et al 2009;AghaKouchak et al 2010AghaKouchak et al , 2013; Janga Reddy and Singh 2014, among others): k SS U (Schmidt and Stadtmüller 2006), the ''secant-based'' estimator k SEC U (Joe et al 1992), k CFG U (Capéraà et al 1997;Frahm et al 2005), and k CHT U (Coles et al 1999;Frahm et al 2005). As was summarized by Villarini et al (2008), the first method is unbiased but can show high variance; the second estimator can be interpreted as the slope of the secant along the copula diagonal [close to the point (1, 1)], and therefore it can misspecify the value of k U when data are not accumulated along the diagonal; the third one assumes that the empirical copula function approximates an extreme value (EV) copula but the estimator could be biased and show very low variance; while the fourth one is the nonparametric counterpart of the v estimator proposed by Coles et al (1999).…”

Section: K U Estimatorsmentioning

confidence: 99%

“…1. Therefore, trying to use such tools on small samples such as less than 100 annual maxima without additional information (e.g., Serinaldi et al 2009; Janga Reddy and Singh 2014) is essentially a speculation exercise such as inferring the EV nature of the underlying dependence structure. …”

Section: Formal Statistical Tests For Upper Tail Independencementioning

confidence: 99%

“…The fast growth of multivariate frequency analysis (thanks partly to the introduction of apparently more manageable statistical tools such as copulas) has led to an extensive application of multivariate models to a variety of hydrological analyses going from the the study of the relationships between the characteristics of objects such as drought events and hydrographs (e.g., Serinaldi et al 2009;Volpi and Fiori 2012) to the study of the occurrence of extreme events at multiple sites (e.g., Ghizzoni et al 2010) to spatial interpolation and simulation problems (e.g., Bárdossy 2006;Bárdossy and Li 2008;Bárdossy and Pegram 2013). This intense activity resulted in a large body of literature that was almost unavoidably focused on showing the potential application rather than on the actual nature of the variables at hand, the possible shortcomings of the methods used, and the reliability of multivariate methods applied to the usually very short hydrological time series.…”

Section: Introductionmentioning

confidence: 99%

“…This habit led to a rather blind use of the k CFG U and other k U estimators whose application is justified by sentences such as ''The [k CFG U ] estimator is based on the assumption that the empirical copula can be approximated by an extreme value copula. It also works well when this hypothesis is not fulfilled, except in the case that the real UTD is null'' (Requena et al 2013) or ''Though the estimator assumes that the underlying copula can be approximated by an extreme-value copula, studies have shown that the estimator performs well even if the copula does not belong to extreme value classes (Frahm et al 2005)'' (Villarini et al 2008;Serinaldi et al 2009;Janga Reddy and Singh 2014). Serinaldi and Kilsby (2014a) showed how rainfall fields simulated by meta-Gaussian spatial dependence structure exhibit k U estimates comparable with those of the observed rainfall fields, thus suggesting caution about the recommendation of AghaKouchak et al (2013) of using k U estimates to assist in planning and policy making as well as validating numerical models.…”

Section: Introductionmentioning

confidence: 99%

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Upper tail dependence in rainfall extremes: would we know it if we saw it?

Serinaldi

Bàrdossy

Kilsby

2014

Stoch Environ Res Risk Assess

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The simultaneous occurrence of extreme events, such as simultaneous storms and floods at different locations, has a serious impact on risk assessment and mitigation strategies. The joint occurrence of extreme events can be measured by the so-called upper tail dependence (UTD) coefficient k U . In this study, we reconsider the properties of the most popular k U estimators and show that their strong bias and uncertainty make most of the empirical results reported in the hydrological literature questionable. In order to overcome the limits of k U analysis, we test several alternative tools such as a pool of formal statistical tests devised for recognizing upper tail independence and graphical diagnostics based on binary correlation and binary entropy. The reliability of all the methods is preliminarily checked by Monte Carlo experiments. Statistical tests and graphical diagnostics are therefore applied to three different rainfall data sets that allow us to explore the properties of the spatial dependence structure of rainfall extremes over a wide range of spatio-temporal scales ranging from 30 min and 1 km to 30 days and %3000 km. Results highlight that (1) classical estimators provide non zero tail dependence even for cases where it should be zero; (2) formal tests and binary correlation highlight that the pairwise spatial dependence structure can be weaker than Gaussian, thus excluding UTD calculated in a pairwise manner; (3) the binary entropy computed on triples of locations shows that the pairwise UTD is not enough to explain the spatial dependence structure of extreme rainfall, whose complexity becomes evident only after resorting to higher order correlation measures. The results concerning the bias and uncertainty of k U estimators are fully general and suggest avoiding their use especially for the short time series usually available in hydrology.

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Section: K U Estimatorsmentioning

confidence: 99%

Section: Formal Statistical Tests For Upper Tail Independencementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Upper tail dependence in rainfall extremes: would we know it if we saw it?

Serinaldi

Bàrdossy

Kilsby

2014

Stoch Environ Res Risk Assess

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show abstract

“…Yue et al 1999, Yue 2000a, Yue and Rasmussen 2002, Shiau 2003, De Michele et al 2005, Grimaldi and Serinaldi 2006b, Zhang and Singh 2006, Klein et al 2010, drought events (e.g. Serinaldi et al 2009, Wong et al 2010, and Mishra and Singh 2011 for a review on the probabilistic characterization of droughts), sea storms (e.g. De Michele et al 2007) and regional frequency analysis (e.g.…”

Section: Introductionmentioning

confidence: 99%

Design event selection in bivariate hydrological frequency analysis

Volpi

Fiori

2012

Hydrological Sciences Journal

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In the bivariate analysis of hydrological events, such as rainfall storms or flood hydrographs, the choice of an appropriate return period for structure design leads to infinite combinations of values of the related random variables (e.g. peak and volume in the analysis of floods). These combinations are generally not equivalent, from a practical point of view. In this paper, a methodology is proposed to identify a subset of the critical combinations set that includes a fixed and arbitrarily chosen percentage in probability of the events, on the basis of their probability of occurrence. Therefore, several combinations can be selected within the subset, taking into account the specific characteristic of the design problem, in order to evaluate the effects of different hydrological loads on a structure. The proposed method is applicable to any type of bivariate distribution, thus providing a simple but effective rule to narrow down the infinite possible choices for the hydrological design variables. In order to illustrate how the proposed methodology can be easily used in practice, it is applied to a study case in the context of bivariate flood frequency analysis.Key words bivariate frequency analysis; design events; return period; hydrology; floods Sélection d'événements de projet en analyse de fréquence hydrologique bivariée Résumé Dans l'analyse bivariée des événements hydrologiques, comme les averses ou les crues, le choix d'une période de retour appropriée pour la conception des ouvrages conduit à des combinaisons infinies de valeurs de variables aléatoires liées (par exemple pointe et volume dans l'analyse des crues). En général, ces combinaisons ne sont pas équivalentes du point de vue pratique. Dans cet article, une méthodologie est proposée afin d'identifier dans l'ensemble critique des combinaisons un sous-ensemble qui comprend un pourcentage fixe et arbitrairement choisi en probabilité des événements, sur la base de leur probabilité d'occurrence. Plusieurs combinaisons peuvent alors être choisies dans le sous-ensemble, en tenant compte de la spécificité du problème de conception afin d'évaluer les effets des différentes sollicitations hydrologiques sur un ouvrage. La méthodologie proposée est applicable à tous les types de distributions bivariées, fournissant ainsi une règle simple mais efficace pour affiner l'infinité de choix possibles pour les variables hydrologiques de conception. Afin d'illustrer comment la méthodologie proposée peut être facilement utilisé en pratique, elle a été appliquée à une étude dans le contexte d'une analyse de fréquence de crue bivariée.

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Hydraulic structures subject to bivariate hydrological loads: Return period, design, and risk assessment

Volpi

Fiori

2014

Water Resour. Res.

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During the recent years, there has been an increasing interest in multivariate frequency analysis of hydrological variables, e.g., those describing extreme events like rainfall, floods, or droughts. The multivariate analysis provides a better understanding of the phenomena under investigation and an additional insight about the interrelationships between the different variables (e.g., peak, volume, and duration of the flood), exploiting the complete structure of the problem and making a full use of the available data. However, while the developments on multivariate analysis of hydrological data have produced a large body of literature, a clear assessment of the use of these methods in the design and risk assessment of hydraulic structures is still a matter of debate. In the present work, we illustrate a general, structure-based framework for the design and/or risk assessment of hydraulic structures in a bivariate environment; we also compare it to recently proposed methods which are based on the assumption of hydrological design events (as is customary in the univariate context). For illustration purposes, both the structure-based and the design event-based approaches are applied to the design of an idealized structure, thus exploring the differences among the methods as function of the parameters involved. Our work highlights that the return period of structure failure in a multivariate environment strictly depends on the particular structure under design, and in most cases, the design of a hydraulic structure cannot be based on a single, hydrological multivariate design event. This acts as a warning for practitioners against the use of design methods based on single hydrological events, as usually done in the context of univariate hydrology, thus neglecting the interplay between the structure and the hydrological loads acting on it.

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Probabilistic characterization of drought properties through copulas

Cited by 199 publications

References 25 publications

Upper tail dependence in rainfall extremes: would we know it if we saw it?

Upper tail dependence in rainfall extremes: would we know it if we saw it?

Design event selection in bivariate hydrological frequency analysis

Hydraulic structures subject to bivariate hydrological loads: Return period, design, and risk assessment

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