Many offshore platforms have suffered from significant wave loading on their lower deck (BeaXuStearRamos1999), and floating production storage and offloading (FPSOs) systems have also suffered topside damage from ``green water'' on their decks during storms (e.g. Leonhardsen2001). However, our understanding of the wave kinematics such as crest velocities, accelerations, and overtopping rates for extreme events remains rudimentary.
Many recent advances have been made in predicting the extreme wave and crest height distributions in relation to the deck clearance or air gap problem. Determining the deck elevation above the calm water level is one of the most important aspects in the design of an offshore platform. For example, Haring shows that large wave heights observed in storms are on the order of 10 percent less than those predicted by the Rayleigh distribution. Forristall84, and Myrhaug87 reported that occurrence probabilities of large wave heights in the field are smaller than the values predicted by the Rayleigh distribution. Recently, Forristall2000 investigated the influence of sensor type in field measurements of total wave height and crest elevation. He indicated that a surface buoy cannot accurately measure the distribution of wave crests, and he reported that occurrence probabilities of large wave crest heights measured in the field by laser are larger than the Rayleigh distribution. On the other hand, numerical investigations by Yasuda et al. (Yasuda94a; Mori2001d) found that the third order nonlinear interactions enhance occurrence probabilities of extreme wave heights compared to the Rayleigh distribution. Stans93 found the same results in his experimental work. There are also several empirical or semi-empirical formulations for the distribution of wave crest/trough amplitudes for weakly nonlinear deep-water waves (e.g. Mori2001e). The occurrence probabilities of extreme wave heights is still an active area of research.
Although the overtopping of shallow water coastal structures has been well studied, there have been very few studies on overtopping of a fixed deck in deep water with high wave steepness (i.e. storm conditions). For the case of extreme waves on fixed and floating structures, particularly for wave loading on lower decks (e.g. BeaXuStearRamos1999; HellanISOPE2001) as well as for vane breakwaters to deflect the water on the deck (e.g. BuchnerOTC1995), it is important to be able to estimate overtopping volume, overtopping rate and velocity distribution. Although one of these parameters may be more important than another for a particular design problem, these events are linked together.
This paper presents the formulations for a statistical model developed to predict wave overtopping of extreme waves on a fixed deck. The objective of this work are (1) to extend existing theories developed for extreme crest statistics to the problem of wave overtopping and (2) to compare the theoretical model to experimentally determined overtopping probability distributions. Second section of this paper presents the statistical formulation of the problem and shows the sensitivity of the derived probability functions to nonlinearity and deck clearance. `Physical Model Study' section presents the experimental setup and procedures of the small-scale hydraulic model test. `Model/Data Comparisons' section presents a detailed discussion of the model-data comparisons, and the last section summarizes and concludes this paper.