Goodness-Of-Fit of Crest Height Distributions in Varying Sea States

Abstract This paper addresses the statistical distribution of wave crests in ocean environments. This is required in many ocean engineering applications and is an important input for design of marine structures. However, state-of-the art models do not necessarily describe the crest height distributions well in every sea state; commonly used models do not accurately describe the upper tail in certain unstable wave conditions. This paper exploits a comprehensive dataset of crest heights measured in different sea states to investigate this and tests the goodness-of-fit of several candidate crest height distributions. The relationship between the rejection rates of the various statistical models and selected sea state parameters is analyzed to identify wave conditions where alternative statistical models are needed. Results indicate that the well-known Forristall distribution fails to perform well in some sea states, but that different variants of the Tayfun-Fedele distribution represent a slight improvement. Sea state parameters such as significant wave height (HS), significant wave steepness (S1) and the Benjamin-Feir index (BFI) do not seem to influence the probability of rejecting these distributions notably, but empirical skewness and kurtosis are found to be important. The implications of this for describing the distribution of crest heights in certain sea state conditions are discussed.