Square Error Method for threshold estimation in extreme value analysis of wave heights

One of the methods used to model the probability distribution of extreme values is the peaks over threshold method. It requires an appropriate estimation of the threshold above which exceedances are considered to be a sample from a generalized Pareto distribution. Several methods have been proposed to determine the optimal threshold. In this paper, we assess the applicability of four methods developed for hydrological, coastal engineering, financial and stock market purposes, to the case of wave heights from extreme sea conditions due to storms, where significantly less amount of data may be available. Based on the results of this assessment, an improved square error method is formulated, which further allows evaluating the uncertainty in threshold estimation, as well as the uncertainty in the estimation of wave heights for given return periods. The improved method is applied using significant wave height data from hindcast of tropical and extra-tropical storms in the Gulf of Mexico. Results illustrate the capabilities of the proposed method.