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

Abstract

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.

Dismissing return periods!

“…In this context, the structure-based return period introduced by Volpi and Fiori (2014) allows us to further expand the above discussion. The authors highlighted that ''being strictly dependent on the particular structure under examination, the return period of structure failure usually does not match that of the hydrological loads.…”

“…Finally, Eq. 16 refers to the so-called ''structure-based'' return period introduced by Volpi and Fiori (2014), where g is a functional relationship linking the forcing (environmental) variables with the design (structural) variable Z ¼ gðU; VÞ.…”

“…This entails that the multivariate approach may not fully rely on the assumption of hydrological design events, i.e., a multivariate event or an ensemble of events which all share the same (multivariate) return period''. These remarks led Volpi and Fiori (2014) to introduce a so-called structurebased return period T S . Also in this case, reasoning in terms of probabilities provides a clearer picture than working with return periods.…”

Multivariate statistical modelling of compound events via pair-copula constructions: analysis of floods in Ravenna (Italy)

“…This unconditional model does not allow for changes in the contributing variables Y and in the impact due to variations of the predictors X. In general, formalizing the impact h of a CE as in step 1 -to then assess the risk of CE based on values of h -corresponds to the structural approach (Salvadori et al, 2015;Serinaldi, 2015;Volpi and Fiori, 2014), which has recently been formalized in Salvadori et al (2016). Here, the advantage of the general model we propose is that it allows for taking into account variations of the impact h driven by temporal changes in the predictors X.…”

Dealing with uncertainty in the probability of overtopping of a flood mitigation dam

“…De Michele et al (2005) were the first to check the adequacy of a dam's spillway under a bivariate hydrological load, followed by Requena et al (2013), while Volpi and Fiori (2014) formalised the idea that the return period of a failure of a structure depends on the structure of interest, and therefore the interaction between the hydrological loads and the structure should be taken into consideration by fixing a "structure-based" return period.…”