On the distribution of ocean wave crest heights in varying wave conditions

Abstract This paper addresses the statistical distribution of wave crest heights in ocean environments. This is much needed in several engineering applications including risk and reliability assessment of marine and coastal structures and is an important input for design of ocean structures. However, even though crest height distributions have received a lot of attention within both academia and the industry, current state-of-the-art models have notable shortcomings and do not describe the distribution of crest heights well in all sea states. In particular, commonly used models do not accurately describe the upper tail in certain unstable wave conditions. This will be addressed in this paper, which investigates in what sea-state conditions, established crest height distributions describe the data well and under what conditions, these models fail to fit well to the data. A large dataset of crest heights observed in different sea states is analyzed, and various goodness-of-fit tests are applied to determine when the different statistical models are appropriate. Then rejection rates of the various statistical models will be linked to selected sea-state parameters to identify wave conditions where alternative statistical models are needed. Results from this study indicate that the well-known Forristall distribution, which is known to capture second-order effects well, fails to perform well in some sea states. Different variants of the Tayfun–Fedele distribution are also analyzed, and results suggest that this represent a slight improvement. Somewhat surprisingly, sea-state parameters such as significant wave height ( $$H_S$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>H</mml:mi> <mml:mi>S</mml:mi> </mml:msub> </mml:math> ), significant wave steepness ( $$S_1$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>S</mml:mi> <mml:mn>1</mml:mn> </mml:msub> </mml:math> ), and the Benjamin–Feir index ( BFI ) do not seem to be very influential on the probability of rejecting these distributions, even though empirical skewness and kurtosis play a significant role. The implications of this for describing the distribution of crest heights well in certain sea-state conditions are discussed.