Quantifying uncertainty in extreme values of design parameters with resampling techniques

In this paper, a methodology for the selection of statistical models for describing the extreme wave heights on the basis of resampling techniques is presented. Two such techniques are evaluated: the jackknife and the bootstrap. The methods are applied to two high-quality datasets of wave measurements in the Mediterranean and one from the East Coast of the USA. The robustness of the estimates of the extreme values of wave heights at return periods important for coastal engineering design is explored further. In particular, we demonstrate how an ensemble error norm can be used to select the most appropriate extreme probability model from a choice of cumulative distribution functions (CDFs). This error norm is based on the mean error norm of the optimised CDF for each resampled (replicate) data series. The resampling approach is also used to present confidence intervals of the CDF parameters. We provide a brief discussion of the sensitivity of these parameters and the suitability of each model in terms of uncertainty with resampling techniques. The advantages of resampling are outlined, and the superiority of the bootstrap over the jackknife in quantifying the uncertainty of extreme quantiles is demonstrated for these records.