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Unsurprising surprises: The frequency of record‐breaking and over‐threshold hydrological extremes under spatial and temporal dependence

Lookup NU author(s): Dr Francesco Serinaldi, Professor Chris Kilsby



This is the final published version of an article that has been published in its final definitive form by Wiley-Blackwell Publishing, Inc., 2018.

For re-use rights please refer to the publisher's terms and conditions.


Record-breaking (RB) events are the highest or lowest values assumed by a given variable, such as temperature and precipitation, since the beginning of the observation period. Research in hydro-climatic fluctuations and their link with this kind of extreme events recently renewed the interest in RB events. However, empirical analyses of RB events usually rely on statistical analyses based on too restrictive hypotheses such as independent and identically distributed (i/id) random variables, or non-general numerical methods. In this study, we propose some exact distributions along with accurate approximations describing the occurrence probability of RB and peak over threshold (POT) events under general spatio-temporal dependence, which enable analyses based on more appropriate assumptions. We show that (i) the Poisson binomial distribution is the exact distribution of the number of RB events under i/id, (ii) equivalent binomial distributions are accurate approximations under i/id, (iii) beta-binomial distributions provide the exact distribution of POT occurrences under spatio-temporal dependence, and (iv) equivalent beta-binomial distributions provide accurate approximations for the distribution of RB occurrences under spatio-temporal dependence. To perform numerical validations, we also introduce a generator of spatially and temporally correlated binary processes, called BetaBitST. As examples of application, we study RB occurrences for monthly precipitation and temperature over the conterminous United States, and reanalyze Mauna Loa daily temperature data. Results show that accounting for spatio-temporal dependence yields strikingly different conclusions, making the observed RB events much less surprising than expected, and calling into question previous results reported in the literature.

Publication metadata

Author(s): Serinaldi F, Kilsby CG

Publication type: Article

Publication status: Published

Journal: Water Resources Research

Year: 2018

Volume: 54

Issue: 9

Pages: 6460-6487

Print publication date: 01/09/2018

Online publication date: 29/06/2018

Acceptance date: 22/06/2018

Date deposited: 26/06/2018

ISSN (print): 0043-1397

ISSN (electronic): 1944-7973

Publisher: Wiley-Blackwell Publishing, Inc.


DOI: 10.1029/2018WR023055


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