Frequency analysis via copulas: Theoretical aspects and applications to hydrological events

Salvadori, Gianfausto; Michele, Carlo De

doi:10.1029/2004wr003133

Cited by 561 publications

(409 citation statements)

References 24 publications

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“…[29] As a difference with the modeling proposed in Kao and Govindaraju [2010], which exploits the approach outlined in Salvadori and De Michele [2004], here we use the one recently sketched in (to which we make reference for all the details), which uses the joint sur-…”

Section: Multivariate Frequency Analysismentioning

confidence: 99%

Multivariate assessment of droughts: Frequency analysis and dynamic return period

et al. 2013

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[1] Droughts, like floods, are extreme expressions of the river flow dynamics. Here, droughts are intended as episodes during which the streamflow is below a given threshold, and are described as multivariate events characterized by two variables: average intensity and duration. In this work, we introduce the new concept of Dynamic Return Period, formulated using the theory of Copulas, and calculated via a Survival Kendall's approach. We show how it can be used (i) to monitor the temporal evolution of a drought event, and (ii) to perform real time assessment. In addition, a randomization strategy is introduced, in order to get rid of repeated measurements, which may adversely affect the statistical analysis of the available data, as well as the calculation of the return periods of interest: a practical example is shown, involving the fit of the drought duration distribution. The case study of the Po river basin (Northern Italy) is used as an illustration.

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Section: Multivariate Frequency Analysismentioning

confidence: 99%

Multivariate assessment of droughts: Frequency analysis and dynamic return period

et al. 2013

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“…[7] Most importantly, the proposed approach yields a bounded safe region (a natural request in applications), thus avoiding the possible nuisance of safe events characterized by diverging values of one (or more) variables-in particular, this latter inconvenient is present in some approaches available in literature [see e.g., Salvadori and De Michele, 2004;Salvadori et al [2011], and references therein) and has motivated the present study.…”

Section: Introductionmentioning

confidence: 99%

Multivariate return period calculation via survival functions

Salvadori

Durante

Michele

2013

Water Resources Research

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112

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[1] The concept of return period is fundamental for the design and the assessment of many engineering works. In a multivariate framework, several approaches are available to its definition, each one yielding different solutions. In this paper, we outline a theoretical framework for the calculation of return periods in a multidimensional environment, based on survival copulas and the corresponding survival Kendall's measures. The present approach solves the problems raised in previous publications concerning the coherent foundation of the notion of return period in a multivariate setting. As an illustration, a practical hydrological application is presented.

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“…When the correlated random variables describing the event are all relevant to risk analyses or design purposes, the joint study of their probabilistic characteristics leads to a better understanding of the phenomena under investigation and avoids the over-or under-estimation of the risk that would be produced by univariate analyses (see e.g. Salvadori and De Michele 2004).…”

Section: Introductionmentioning

confidence: 99%

“…This definition, together with the one involving the simultaneous exceedence of critical thresholds, is of greatest interest in hydrological applications (Salvadori and De Michele 2004). An alternative formulation is given by Salvadori and De Michele (2010).…”

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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Frequency analysis via copulas: Theoretical aspects and applications to hydrological events

Cited by 561 publications

References 24 publications

Multivariate assessment of droughts: Frequency analysis and dynamic return period

Multivariate assessment of droughts: Frequency analysis and dynamic return period

Multivariate return period calculation via survival functions

Design event selection in bivariate hydrological frequency analysis

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