This paper estimates 100-year wave height levels from (1) a model fit to all wave heights observed over 18 years in a Northern North Sea location; and (2) an extreme event model that considers only the 18 annual maxima. The result of method (1) is generally found to exceed that from method (2). We seek here to reconcile this difference, considering the effects of clustering, statistical and model uncertainty. The general conclusion is to favor approaches that directly model the large wave height events of interest; e.g., annual maxima or storms. Beyond its relevant to extreme waves, this study aims to show useful results to quantify statistical uncertainty and clustering effects in estimating extremes.
A basic problem in reliability analysis is to estimate extreme load fractiles from limited data. In general there is a tradeoff between (1) global models based on all data; and (2) extreme event models, based on a subset of the largest loads available (e.g., annual maxima). While the global approach (1) utilizes all available data, it can obscure critical tail behavior and introduce correlation among observations (e.g., clustering). In contrast, extreme events in approach (2) may be more nearly independent, but their scarceness increases statistical uncertainty. This study shows convenient analytical methods to quantify these effects of clustering and statistical uncertainty. They are applied here to a measured North Sea wave data set, in which 100-year wave height estimates from approaches (1) and (2) are found to differ. By reconciling the difference in this case, we seek to supplement various studies of extreme wave heights, and their uncertainties (e.g., Guedes Stares and Moan, 1983; Olufsen and Bea, 1990; Winterstein and Haver, 1991). More broadly, we hope to shed light on the general effects of dependence and uncertainty on extreme value estimation.
