On the return period and design in a multivariate framework

By G. Salvadori, Carlo De Michele, Fabrizio Durante. 2011

336 citations recorded by the source corpus.

Abstract. Calculating return periods and design quantiles in a multivariate environment is a difficult problem: this paper tries to make the issue clear. First, we outline a possible way to introduce a consistent theoretical framework for the calculation of the return period in a multi-dimensional environment, based on Copulas and the Kendall's measure. Secondly, we introduce several approaches for the identification of suitable design events: these latter quantities are of utmost importance in practical applications, but their calculation is yet limited, due to the lack of an adequate theoretical environment where to embed the problem. Throughout the paper, a case study involving the behavior of a dam is used to illustrate the new concepts outlined in this work.

Subfields: Global and Planetary Change, Ocean Engineering, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/4d0ed22e30050bb92ceab5004e6f6193ae560342

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In Global and Planetary Change

In Ocean Engineering

In Statistics and Probability

Citations in the corpus

Uncertainty Analysis of Bivariate Design Flood Estimation and its Impacts on Reservoir Routing (2018, methodology): “As a consequence, the bivariate phenomenon of flood peak and volume for this particular situation is defined base on OR JRP, and it can be defined by copulas accordingly (Salvadori et al. 2011; Zhang et al. 2015b):”
A multivariate copula‐based framework for dealing with hazard scenarios and failure probabilities (2016, background): “A d-dimensional Kendall HS is given by the region SKt 5fy 2 Rd : FðyÞ > tg5fy 2 Rd : CðF1ðy1Þ; . . . ; FdðydÞÞ > tg; (11) and the associated level a is [Salvadori et al., 2011] SALVADORI ET AL.”
Multivariate statistical modelling of compound events via pair-copula constructions: analysis of floods in Ravenna (Italy) (2017, neutral): “…useful when assessing the risk of CEs through, e.g., multivariate return periods of the contributing variables Y (e.g. Graeler et al., 2016, 2013; Salvadori et al., 2016, 2011; Wahl et al., 2015; Aghakouchak et al., 2014; Saghaﬁan and Mehdikhani, 2013; Shiau et al., 2007; Shiau, 2003) Moreover,…”
Copula based analysis of rainfall severity and duration: a case study (2013, methodology): “Recently Salvadori et al. (2011) and Vandenberghe et al. (2012) have provided an approach based on recurrent events.”
Bivariate flood frequency analysis using the copula function: a case study of the Litija station on the Sava River (2015, methodology): “…2011): TU>ujV≤v ¼ μ 1 Cu;v u; vð Þ u ; TU>ujV>v ¼ μ1 u 1 1 u vþ Cu;v u; vð Þ (9) The secondary return period, called Kendall’s return period, is defined as follows (Salvadori et al., 2011): T>x ¼ μ 1 Kc tð Þ (10) where KC is Kendall’s distribution, associated with theoretical copula function Cθ…”
Dependence of drivers affects risks associated with compound events (2017, methodology): “Model fitting To obtain uniform distributions in the marginals, we transformed marginal distributions into normalized ranks, which is a common procedure when working with copulas (52, 53) and is the only reasonable choice if goodness of fit is to be tested appropriately (54).”
Multivariate hydrologic design methods under nonstationary conditions and application to engineering practice (2018, methodology): “For the general multivariate case, the Kendall’s distribution function cannot be analytically formulated as a specific expression, but can be numerically estimated through the Monte Carlo method (Niederreiter, 1978; Salvadori et al., 2011).”
An uncertain journey around the tails of multivariate hydrological distributions (2013, methodology): “…XY x; yð Þ; ð5bÞ p< ¼ P X xjY y½ ¼ F<XY x; yð Þ; ð5cÞ pK ¼ P FXY x; yð Þ w½ ¼ KC : ð5dÞ [18] These probabilities are just a few examples and are related to different definitions of joint return periods through the general transformation T ¼ = 1 pð Þ [Salvadori, 2004; Salvadori et al., 2007, 2011].”
Copula-based risk assessment of drought in Yunnan province, China (2015, background): “…critical threshold t 2 I is given by t ¼ inffs 2 I : KcðsÞ ¼ pg ¼ Kc½ 1 ðpÞ ð19Þ Kc is a distribution function, and t represents the corresponding proper quantile of the order p. Salvadori et al. (2011) introduced coherent notions of multivariate threshold (critical layer) and total order in…”
Bivariate frequency analysis of nonstationary low‐flow series based on the time‐varying copula (2015, background): “applied in hydrological frequency analysis (Salvadori and De Michele, 2010; Salvadori et al., 2011; De Michele et al., 2013; Salvadori et al., 2013).”
Use of a nonstationary copula to predict future bivariate low flow frequency in the Connecticut river basin (2016, background): “A return period is defined as ‘the average time elapsing between two successive occurrences of a prescribed event’ (Salvadori et al., 2011).”