Extreme-coastal-water-level estimation and projection: a comparison of statistical methods

Accurate estimates of the probability of extreme sea levels are pivotal for assessing risk and for designing coastal defense structures. This probability is typically estimated by modeling observed sea-level records using one of a few statistical approaches. In this study we comparatively apply the generalized-extreme-value (GEV) distribution, based on block maxima (BM) and peaks-over-threshold (POT) formulations, and the recent metastatistical extreme-value distribution (MEVD) to four long time series of sea-level observations distributed along European coastlines. A cross-validation approach, dividing available data into separate calibration and test sub-samples, is used to compare their performances in high-quantile estimation. To address the limitations posed by the length of the observational time series, we quantify the estimation uncertainty associated with different calibration sample sizes from 5 to 30 years. We study extreme values of the coastal water level - the sum of the water level setup induced by meteorological forcing and of the astronomical tide - and we find that the MEVD framework provides robust quantile estimates, especially when longer sample sizes of 10-30 years are considered. However, differences in performance among the approaches explored are subtle, and a definitive conclusion on an optimal solution independent of the return period of interest remains elusive. Finally, we investigate the influence of end-of-century projected mean sea levels on the probability of occurrence of extreme-total-water-level (the sum of the instantaneous water level and the increasing mean sea level) frequencies. The analyses show that increases in the value of total water levels corresponding to a fixed return period are highly heterogeneous across the locations explored.