Design event selection in bivariate hydrological frequency analysis

Abstract

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.

Maximum Entropy-Copula Method for Hydrological Risk Analysis under Uncertainty: A Case Study on the Loess Plateau, China

“…Therefore, appropriate methods for identifying the unique design realization from the return level curve is of great necessity. In the present study, the most-likely design event method is utilized, as described previously in the literature [23,60,62]. The constructed MEP-copula is applied to estimate the most-likely design event.…”

Probabilistic flood hazard mapping: effects of uncertain boundary conditions

“…5a indicate the (q, v) pairs used to discretise the Tr200 contour line in our study, by means of which we took into account the natural variability of flood hydrographs. These events are not equivalent in terms of flood volume and peak discharges and they also differ in terms of their probability of occurrence (Volpi and Fiori, 2012). We assigned to each one of the five selected (q, v) pairs (or scenarios) a probability of occurrence estimated as follows: we computed the joint probability density function (joint pdf) along the contour line based on marginal probabilities (see e.g.…”

“…We assigned to each one of the five selected (q, v) pairs (or scenarios) a probability of occurrence estimated as follows: we computed the joint probability density function (joint pdf) along the contour line based on marginal probabilities (see e.g. Volpi and Fiori, 2012); the contour line has been discretised into five stretches, which were identified by halving the curvilinear distance between two scenarios; finally, the relative frequency of occurrence of each scenario was estimated as the integral of the joint pdf over each stretch and standardised by the integral of the joint pdf over the entire level curve (see legend of Fig. 5b).…”

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

“…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.…”