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The generalised Pareto distribution (GPD) is often used to model the distribution of storm peak wave heights exceeding a high threshold, from which return values can be calculated. There are large differences in the performance of various parameter and quantile estimators for the GPD. Commonly used estimation methods such as maximum likelihood or probability weighted moments are not optimal, especially for smaller sample sizes. The performance of several estimators for the GPD is compared by the Monte Carlo simulation and the implications for estimating return values of significant wave height are discussed. Of the estimators compared, the likelihood-moment (LM) estimator has close to the lowest bias and variance over a wide range of sample sizes and GPD shape parameters. The LM estimator always exists, is simple to compute and has a low sensitivity to choice of threshold. It is recommended that the LM estimator is used for calculating return values of significant wave height when the sample size is less than 500. For sample sizes above 500 the NEW estimator of Zhang and Stephens (2009) can give accurate results for low computational cost.

Extreme value theory is commonly used in offshore engineering to estimate extreme significant wave height. To justify the use of extreme value models it is of critical importance either to verify that the assumptions made by the models are satisfied by the data or to examine the effect violating model assumptions. An important assumption made in the derivation of extreme value models is that the data come from a stationary distribution. The distribution of significant wave height varies with both the direction of origin of a storm and the season it occurs in, violating the assumption of a stationary distribution. Extreme value models can be applied to analyse the data in discrete seasons or directional sectors over which the distribution can be considered approximately stationary. Previous studies have suggested that models which ignore seasonality or directionality are less accurate and will underestimate extremes. This study shows that in fact the opposite is true. Using realistic case studies, it is shown that estimates of extremes from non-seasonal models have a lower bias and variance than estimates from discrete seasonal models and that estimates from discrete seasonal models tend to be biased high. The results are also applicable to discrete directional models.

Three theoretical joint distributions of wave height and period are compared with data. Both crest-to-trough waves and zero-upcrossing waves are considered. The data consist of two long Waverider records (of 12 and 8 hr) and a shorter record taken from a reservoir. It is found that a distribution based on the theory of Gaussian processes fits the crest-to-trough waves well in all cases. In contrast, the two narrow band approximations only fit the data from the reservoir, which is more narrow band. The effect of high frequency cut-off on the distribution of height and period are considered.

Methods are described for estimating the parameters of the Fisher-Tippet Type 1 extreme value distribution and associated return values from measured extremes, such as maximum wave height. A comparison of these methods, with simulated data, shows that those using Gumbel's plotting position are least satifactory. Maximum likelihood methods give the smallest mean square errors, but the very much simpler method of moments is nearly as good.