An automated threshold selection method based on the characteristic of extrapolated significant wave heights

Abstract

The reasonable estimation of design wave heights is crucial for coastal and offshore engineering practices. To obtain sufficient data for model estimation, the peak over threshold (POT) method with the generalized Pareto distribution (GPD) model is employed. When using this method (i.e., the POT/GPD method), peak excesses over a sufficiently large value (i.e., threshold) are fitted. The extrapolated significant wave heights are highly dependent on the threshold, which must carefully be determined. In this study, significant wave heights from a 40 year (1975-2014) hindcast of tropical cyclone waves in the South China Sea (SCS) are adopted as the initial dataset to study extreme significant wave heights. Based on this initial dataset, the threshold selection is studied by analysing the influence of the excluded samples on the return significant wave heights when the threshold continuously increases. A stable threshold range corresponding to stable return significant wave heights is found, which exhibits a high probability of containing the suitable threshold. To determine the suitable threshold within the stable threshold range, an automated threshold selection method based on the characteristic of extrapolated significant wave heights (ATSME) is proposed. As shown by the reliability (via asymptotic tail approximation and estimation uncertainty) of the POT/GPD method and comparison with other threshold selection methods (i.e., the GPD parameter plot and automated threshold selection method based on the characteristic of the modified scale parameter (ATSMP)), the thresholds obtained by the ATSME are reasonable. Considering that the proposed method is based on the characteristic of extrapolated significant wave heights, data (such as measured, simulated and calculated data) participating in the extrapolation must carefully be processed, which influence the extrapolated results.