Extreme storm surges: a comparative study of frequency analysis approaches
In France, nuclear facilities were designed around very low probabilities of failure. Nevertheless, some extreme climatic events have given rise to exceptional observed surges (outliers) much larger than other observations, and have clearly illustrated the potential to underestimate the extreme water levels calculated with the current statistical methods. The objective of the present work is to conduct a comparative study of three approaches to extreme value analysis, including the annual maxima (AM), the peaks-over-threshold (POT) and the r-largest order statistics ( r-LOS). These methods are illustrated in a real analysis case study. All data sets were screened for outliers. Non-parametric tests for randomness, homogeneity and stationarity of time series were used. The shape and scale parameter stability plots, the mean excess residual life plot and the stability of the standard errors of return levels were used to select optimal thresholds and r values for the POT and r-LOS method, respectively. The comparison of methods was based on (i) the uncertainty degrees, (ii) the adequacy criteria and tests, and (iii) the visual inspection. It was found that the r-LOS and POT methods have reduced the uncertainty on the distribution parameters and return level estimates and have systematically shown values of the 100 and 500-year return levels smaller than those estimated with the AM method. Results have also shown that none of the compared methods has allowed a good fit at the right tail of the distribution in the presence of outliers. As a perspective, the use of historical information was proposed in order to increase the representativeness of outliers in data sets. Findings are of practical relevance, not only to nuclear energy operators in France, for applications in storm surge hazard analysis and flood management, but also for the optimal planning and design of facilities to withstand extreme environmental conditions, with an appropriate level of risk.