Long-term distributions of individual wave and crest heights

Abstract

This paper considers three types of method for calculating return periods of individual wave and crest heights. The methods considered differ in the assumptions made about serial correlation in wave conditions. The long-term distribution of individual waves is formed under the assumption that either (1) individual waves, (2) the maximum wave height in each sea state or (3) the maximum wave height in each storm are independent events. The three types of method are compared using long time series of synthesised storms, where the return periods of individual wave heights are known. The methods which neglect serial correlation in sea states are shown to produce a positive bias in predicted return values of wave heights. The size of the bias is dependent on the shape of the tail of the distribution of storm peak significant wave height, with longer-tailed distributions resulting in larger biases. It is shown that storm-based methods give accurate predictions of return periods of individual wave heights. In particular, a Monte Carlo storm-based method is recommend for calculating return periods of individual wave and crest heights. Of all the models considered, the Monte Carlo method requires the fewest assumptions about the data, the fewest subjective judgements from the user and is simplest to implement.