The Effect of Declustering in the r-Largest Maxima Model for the Estimation of HS-Design Values

Abstract

A major problem often encountered in design sea-state prediction is the limited amount of available extremetype wave data. The Annual Maxima model is consistent with the conditions of the mathematical background of Extreme Value Theory, yet its application raises statistical uncertainties in cases where the initial data population is limited. Due to this, alternative models of similar theoretical background have been developed to describe extreme values, including the "r-largest maxima method". A main problem in applying this model refers to the appropriate selection of a sample comprising the r independent maxima within each year of the available time series: since in nature environmental extremes tend to appear in clusters, the native time series under examination should be appropriately "de-clustered" to satisfy the independency assumption. Some established declustering procedures refer to: a) the selection of a "Standard Storm Length", b) the combination of a run length k and a relatively high threshold value u (Runs declustering), c) the estimation of wave energy reductions between consecutive sea-state systems (DeClustering Algorithm) and d) the selection of the three largest monthly maxima of each year of the initial significant wave height time series (triple annual maximum series). The aim of this paper is to assess the effect of the aforementioned declustering procedures on the numerical results obtained by the r-largest model.

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