On the suitability of the Generalised Pareto to model extreme waves

Abstract

Dealing with extreme events implies working with events that have low probability of occurrence. To characterize these, the peak-over-threshold method alongside the generalized Pareto distribution is commonly applied. However, when it comes to significant wave heights, this approach is not recommended. Here, the generalized Pareto distribution is discussed based on data collected around the coast of Ireland. A careful choice of threshold takes place, and a new methodology to establish the threshold level is introduced. Five indicators to evaluate the fitting are considered to compare the different statistical models. No evidence was identified to justify the rejection of the generalized Pareto distribution to model exceedances. Results show that it may be statistically less, equally or more adequate, depending on the peak-over-threshold implementation. Nevertheless, the generalized Pareto bounded character is of elementary interest for wave statistics. In some circumstances not considering it might lead to unrealistic significant wave return levels.