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https://doi.org/10.5194/hess-2023-234
https://doi.org/10.5194/hess-2023-234
18 Oct 2023
 | 18 Oct 2023
Status: this preprint is currently under review for the journal HESS.

Non-asymptotic distributions of water extremes: Superlative or superfluous?

Francesco Serinaldi, Federico Lombardo, and Chris G. Kilsby

Abstract. Non-asymptotic (๐’ฉ๐’œ) probability distributions of block maxima (BM) have been proposed as an alternative to asymptotic distributions of BM derived by classic extreme value theory (EVT). Their advantage should be the inclusion of moderate quantiles as well as extremes in the inference procedures. This would increase the amount of used information and reduce the uncertainty characterizing the inference based on short samples of BM or peaks over high threshold.  In this study, we show that ๐’ฉ๐’œ distributions of BM suffer from two main drawbacks that make them of little usefulness for practical applications. Firstly, unlike classic EVT distributions, ๐’ฉ๐’œ models of BM imply the preliminary definition of their conditional parent distributions, which explicitly appears in their expression. However, when such conditional parent distributions are known or estimated also the unconditional parent distribution is readily available, and the corresponding ๐’ฉ๐’œ distribution of BM is no longer needed, as it is just an approximation of the upper tail of the parent. Secondly, when declustering procedures are used to remove autocorrelation characterizing hydro-climatic records, ๐’ฉ๐’œ distributions of BM devised for independent data are strongly biased even if the original process exhibits low/moderate autocorrelation. On the other hand, ๐’ฉ๐’œ distributions of BM accounting for autocorrelation are less biased but still of little practical usefulness. Such conclusions are supported by theoretical arguments, Monte Carlo simulations, and re-analysis of sea level data.

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Francesco Serinaldi, Federico Lombardo, and Chris G. Kilsby

Status: final response (author comments only)

Comment types: AC โ€“ author | RC โ€“ referee | CC โ€“ community | EC โ€“ editor | CEC โ€“ chief editor | : Report abuse
  • CC1: 'Comment on hess-2023-234', Sarah Han, 27 Oct 2023
  • RC1: 'Comment on hess-2023-234', Anonymous Referee #1, 18 Mar 2024
  • RC2: 'Comment on hess-2023-234', Francesco Marra, 20 May 2024
Francesco Serinaldi, Federico Lombardo, and Chris G. Kilsby
Francesco Serinaldi, Federico Lombardo, and Chris G. Kilsby

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Short summary
Non-asymptotic probability distributions of block maxima (BM) have been proposed as an alternative to asymptotic distributions from classic extreme value theory. We show that the non-asymptotic models are unnecessary and redundant approximations of the corresponding parent distributions, which are readily available, are not affected by serial dependence, have simpler expression, and describe the probability of all quantiles of the process of interest, not only the probability of BM.