An uncertain journey around the tails of multivariate hydrological distributions

By F. Serinaldi. 2013

81 citations recorded by the source corpus.

Moving from univariate to multivariate frequency analysis, this study extends the Klemeš' critique of the widespread belief that the increasingly refined mathematical structures of probability functions increase the accuracy and credibility of the extrapolated upper tails of the fitted distribution models. In particular, we discuss key aspects of multivariate frequency analysis applied to hydrological data such as the selection of multivariate design events (i.e., appropriate subsets or scenarios of multiplets that exhibit the same joint probability to be used in design applications) and the assessment of the corresponding uncertainty. Since these problems are often overlooked or treated separately, and sometimes confused, we attempt to clarify properties, advantages, shortcomings, and reliability of results of frequency analysis. We suggest a selection method of multivariate design events with prescribed joint probability based on simple Monte Carlo simulations that accounts for the uncertainty affecting the inference results and the multivariate extreme quantiles. It is also shown that the exploration of the p‐level probability regions of a joint distribution returns a set of events that is a subset of the p‐level scenarios resulting from an appropriate assessment of the sampling uncertainty, thus tending to overlook more extreme and potentially dangerous events with the same (uncertain) joint probability. Moreover, a quantitative assessment of the uncertainty of multivariate quantiles is provided by introducing the concept of joint confidence intervals. From an operational point of view, the simulated event sets describing the distribution of the multivariate p‐level quantiles can be used to perform multivariate risk analysis under sampling uncertainty. As an example of the practical implications of this study, we analyze two case studies already presented in the literature.

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

View Paper: https://www.semanticscholar.org/paper/ed6da2b47864f71cd0552cc7af330d04fbe75304

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In Ocean Engineering

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Citations in the corpus

Upper tail dependence in rainfall extremes: would we know it if we saw it? (2015, methodology): “15 of Serinaldi (2008) and confirm the need for a thorough re-assessment of those analyses (which is done in the next sections) as well as all the studies whose conclusions are based on these estimators.”
Dependence of drivers affects risks associated with compound events (2017, result): “In addition, all results were averaged across >80 model runs (table S1), which reduced some of the uncertainty related to the fitting procedure (57).”
A multivariate copula‐based framework for dealing with hazard scenarios and failure probabilities (2016, background): “3.4 and 5.3], frequently considered in applications for dealing with the extreme joint behavior of the variables at play [see e.g., Poulin et al., 2007; AghaKouchak et al., 2013; Serinaldi, 2013, and references therein].”
Probabilistic modeling of flood characterizations with parametric and minimum information pair-copula model (2016, background): “However, Serinaldi (2013) extends this widespread belief that the increasingly refined mathematical structures of probability functions increase the accuracy and credibility of the fitted models (particularly, in extrapolating upper tails of the fitted models), but we have found some mixed…”
Uncertainty Analysis of Bivariate Design Flood Estimation and its Impacts on Reservoir Routing (2018, methodology): “Almost all the pioneering works (Serinaldi 2013; Zhang et al. 2015a; Dung et al. 2015) revealed that the major uncertainty source in bivariate quantile estimation is sampling uncertainty, whereas uncertainty estimation methods selection and parameter estimation methods are of minor importance.”