On the return period and design in a multivariate framework

Salvadori, Gianfausto; Michele, Carlo De; Durante, Fabrizio

doi:10.5194/hess-15-3293-2011

Cited by 292 publications

(323 citation statements)

References 45 publications

(38 reference statements)

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“…Following the above example, once the survival Kendall's quantile q is identified, the corresponding survival critical layer L F q provides the set of realizations sharing the same desired SKRP T. Equivalently, according to equation (3), it suffices to spot the isohypersurface of level q of the survival copulaĈ. In turn, it is then possible to use suitable strategies for multivariate design [see e.g., Salvadori et al, 2011;Corbella and Stretch, 2012] and provide (bounded) target values of the variables X 1 ; . .…”

Section: Multivariate Rpmentioning

confidence: 99%

“…[22] For the numerical inversion of K, the simulation algorithm presented in Salvadori et al [2011] can be used. Following the above example, once the survival Kendall's quantile q is identified, the corresponding survival critical layer L F q provides the set of realizations sharing the same desired SKRP T. Equivalently, according to equation (3), it suffices to spot the isohypersurface of level q of the survival copulaĈ.…”

Section: Multivariate Rpmentioning

confidence: 99%

“…[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%

“…As a consequence, the sole concept of RP may not be sufficient in order to provide meaningful and consistent design values for multivariate phenomena. In the streamline of Salvadori et al [2011], we outline in this work a probabilistically well-founded framework for the calculation of RPs in a multidimensional environment: as we shall see, this approach is of immediate application and shares many of the features (and facilities) of the univariate one. In addition, it provides a significant support for multivariate designing, thus offering new possibilities of performing risk analysis and assessment in a multidimensional context.…”

Section: Introductionmentioning

confidence: 99%

“…As stated earlier, the partition depends on the chosen RP, which provides the criterion to discriminate between safe and dangerous realizations. Then, the search for a design realization with a given multivariate RP is restricted to the choice of a suitable alert occurrence (see Salvadori et al [2011] and Corbella and Stretch [2012] for possible strategies).…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Multivariate return period calculation via survival functions

Salvadori

Durante

Michele

2013

Water Resources Research

Self Cite

109

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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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Section: Multivariate Rpmentioning

confidence: 99%

Section: Multivariate Rpmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Multivariate return period calculation via survival functions

Salvadori

Durante

Michele

2013

Water Resources Research

Self Cite

109

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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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Global warming and changes in risk of concurrent climate extremes: Insights from the 2014 California drought

AghaKouchak

Cheng

Mazdiyasni

et al. 2014

Geophysical Research Letters

541

348

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Global warming and the associated rise in extreme temperatures substantially increase the chance of concurrent droughts and heat waves. The 2014 California drought is an archetype of an event characterized by not only low precipitation but also extreme high temperatures. From the raging wildfires, to record low storage levels and snowpack conditions, the impacts of this event can be felt throughout California. Wintertime water shortages worry decision-makers the most because it is the season to build up water supplies for the rest of the year. Here we show that the traditional univariate risk assessment methods based on precipitation condition may substantially underestimate the risk of extreme events such as the 2014 California drought because of ignoring the effects of temperature. We argue that a multivariate viewpoint is necessary for assessing risk of extreme events, especially in a warming climate. This study discusses a methodology for assessing the risk of concurrent extremes such as droughts and extreme temperatures.

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On the return period and design in a multivariate framework

Cited by 292 publications

References 45 publications

Multivariate return period calculation via survival functions

Multivariate return period calculation via survival functions

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

Global warming and changes in risk of concurrent climate extremes: Insights from the 2014 California drought

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