How historical information can improve estimation and prediction of extreme coastal water levels: application to the Xynthia event at La Rochelle (France)

Abstract. The knowledge of extreme coastal water levels is useful for coastal flooding studies or the design of coastal defences. While deriving such extremes with standard analyses using tide-gauge measurements, one often needs to deal with limited effective duration of observation which can result in large statistical uncertainties. This is even truer when one faces the issue of outliers, those particularly extreme values distant from the others which increase the uncertainty on the results. In this study, we investigate how historical information, even partial, of past events reported in archives can reduce statistical uncertainties and relativise such outlying observations. A Bayesian Markov chain Monte Carlo method is developed to tackle this issue. We apply this method to the site of La Rochelle (France), where the storm Xynthia in 2010 generated a water level considered so far as an outlier. Based on 30 years of tide-gauge measurements and 8 historical events, the analysis shows that (1) integrating historical information in the analysis greatly reduces statistical uncertainties on return levels (2) Xynthia's water level no longer appears as an outlier, (3) we could have reasonably predicted the annual exceedance probability of that level beforehand (predictive probability for 2010 based on data until the end of 2009 of the same order of magnitude as the standard estimative probability using data until the end of 2010). Such results illustrate the usefulness of historical information in extreme value analyses of coastal water levels, as well as the relevance of the proposed method to integrate heterogeneous data in such analyses.