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An uncertain journey around the tails of multivariate hydrological distributions

Lookup NU author(s): Dr Francesco Serinaldi



This work is licensed under a Creative Commons Attribution 4.0 International License (CC BY 4.0).


Moving from univariate to multivariate frequency analysis, this study extends the KlemeŇ°' 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.

Publication metadata

Author(s): Serinaldi F

Publication type: Article

Publication status: Published

Journal: Water Resources Research

Year: 2013

Volume: 49

Issue: 10

Pages: 6527-6547

Print publication date: 09/10/2013

Online publication date: 09/10/2013

Acceptance date: 12/09/2013

Date deposited: 16/01/2014

ISSN (print): 0043-1397

ISSN (electronic): 1944-7973

Publisher: Wiley-Blackwell Publishing, Inc.


DOI: 10.1002/wrcr.20531


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Funder referenceFunder name
Willis Research Network
EP/I01344X/1Engineering and Physical Sciences Research Council (EPSRC) "UK Infrastructure Transitions Research Consortium"