Non-asymptotic distributions of water extremes: much ado about what?

Abstract. Non-asymptotic (𝒩𝒜) probability distributions of block maxima (BM) have been proposed as an alternative to asymptotic distributions of BM derived by means of classic extreme-value theory (EVT). Their advantage should be the inclusion of moderate quantiles, as well as of extremes, in the inference procedures. This would increase the amount of information used and reduce the uncertainty characterizing the inference based on short samples of BM or peaks over high thresholds. In this study, we show that the 𝒩𝒜 distributions of BM suffer from two main drawbacks that make them of little usefulness for practical applications. Firstly, unlike classic EVT distributions, 𝒩𝒜 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, the unconditional parent distribution is readily available, and the corresponding 𝒩𝒜 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 hydroclimatic records, 𝒩𝒜 distributions of BM devised for independent data are strongly biased even if the original process exhibits low or moderate autocorrelation. On the other hand, 𝒩𝒜 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.