Bivariate Statistical Approach to Check Adequacy of Dam Spillway

Michele, Carlo De; Salvadori, Gianfausto; Canossi, M.; Petaccia, A.; Rosso, Renzo

doi:10.1061/(asce)1084-0699(2005)10:1(50)

Cited by 307 publications

(191 citation statements)

References 9 publications

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“…As a matter of principle, other bivariate distributions (i.e., copulas other than the one cited) could provide valuable fits; note that such tests can easily be carried out using empirical copulas [Nelsen, 1999;De Michele and Salvadori, 2003;De Michele et al, 2004;Favre et al, 2004].…”

Section: Case Of Shiau [2003]mentioning

confidence: 99%

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

Salvadori

Michele

2004

Water Resources Research

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539

385

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[1] In this paper we provide a general theoretical framework exploiting copulas for studying the return periods of hydrological events; in particular, we consider events depending upon the joint behavior of two nonindependent random variables, an approach which can easily be generalized to the multivariate case. We show that using copulas may greatly simplify the calculations and may even yield analytical expressions for the isolines of the return periods, both in the unconditional and in the conditional case. In addition, we show how a new probability distribution may be associated with the return period of specific events and introduce the definitions of sub-, super-, and critical events as well as those of primary and secondary return periods. An illustration of the techniques proposed is provided by analyzing some case studies already examined in literature.

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Section: Case Of Shiau [2003]mentioning

confidence: 99%

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

Salvadori

Michele

2004

Water Resources Research

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539

385

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“…The use of bivariate copulas offers one possibility to do this (e.g. Favre et al, 2004;De Michele et al, 2005). However, the design of technical flood detention is getting more complex with increasing area of the watershed and the related branching of the river network.…”

Section: Introductionmentioning

confidence: 99%

Extensive spatio-temporal assessment of flood events by application of pair-copulas

Schulte

Schumann

2015

Proc. IAHS

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Abstract. Although the consequences of floods are strongly related to their peak discharges, a statistical classification of flood events that only depends on these peaks may not be sufficient for flood risk assessments. In many cases, the flood risk depends on a number of event characteristics. In case of an extreme flood, the whole river basin may be affected instead of a single watershed, and there will be superposition of peak discharges from adjoining catchments. These peaks differ in size and timing according to the spatial distribution of precipitation and watershed-specific processes of flood formation. Thus, the spatial characteristics of flood events should be considered as stochastic processes. Hence, there is a need for a multivariate statistical approach that represents the spatial interdependencies between floods from different watersheds and their coincidences. This paper addresses the question how these spatial interdependencies can be quantified. Each flood event is not only assessed with regard to its local conditions but also according to its spatio-temporal pattern within the river basin. In this paper we characterise the coincidence of floods by trivariate Joe-copula and pair-copulas. Their ability to link the marginal distributions of the variates while maintaining their dependence structure characterizes them as an adequate method. The results indicate that the trivariate copula model is able to represent the multivariate probabilities of the occurrence of simultaneous flood peaks well. It is suggested that the approach of this paper is very useful for the risk-based design of retention basins as it accounts for the complex spatio-temporal interactions of floods.

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“…Copulas are widely used to investigate multivariate distribution in hydrology. However, most research focuses on rainfall and floods (De Michele and Salvadori, 2003;Favre et al, 2004;de Michele, 2004a, 2004b;De Michele et al, 2005;Shiau et al, 2006;Grimaldi and Serinaldi, 2006;Salvadori and de Michele, 2006;Zhang and Singh, 2006;Kao and Govindaraju, 2007;Renard and Lang, 2007;Zhang and Singh, 2007;Evin and Favre, 2008;Kao and Govindaraju, 2008). To our knowledge, Shiau (2006) is the first use the copula method to investigate the drought problem.…”

Section: Introductionmentioning

confidence: 99%

Copula‐based drought severity‐duration‐frequency analysis in Iran

Shiau

Modarres

2009

Meteorological Applications

235

130

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Drought is a complex and multi-attribute natural hazard that has worldwide effects. Defined by a commonly used standardized precipitation index (SPI), each drought event is characterized by three correlated attributes: severity, duration and frequency. A probabilistic approach is developed to establish a drought severity-duration-frequency (SDF) relationship. Copulas are employed to construct the joint distribution function of drought severity and duration. Drought frequency, in terms of recurrence interval of drought events, is then related to the copula-based distribution function via a conditional distribution function. The derived analytic drought SDF thus becomes a function of univariate distribution functions of drought severity and duration, a copula function which links the fitted univariate models, and the arrival rate of drought events. In this study, rainfall data for the period of 1954-2003 from two gauge stations in Iran, Abadan in the southwestern semi-arid region and Anzali in the north humid region, are employed as an example to illustrate the proposed approach. From the derived drought SDF, drought severity in Anzali station is greater than those in Abadan station for given drought duration and recurrence interval. The results imply that the drought severity in humid region might be more severe if high rainfall fluctuations exist in that region.

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Bivariate Statistical Approach to Check Adequacy of Dam Spillway

Cited by 307 publications

References 9 publications

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

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

Extensive spatio-temporal assessment of flood events by application of pair-copulas

Copula‐based drought severity‐duration‐frequency analysis in Iran

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