Probability of Occurrence of a “Giant” Wave Crest

On January the 1st 1995, a “giant” wave is observed and measured at the Draupner platform in the North Sea. During a sea state with a significant wave height close to 12 meters, the crest of this isolated wave reached 18.5 meters. The question has been often asked if the physics governing such a wave differ from the physics governing the population of typical waves. Before responding more precisely to this question a first step is to use as accurately as possible, in such extreme situations, the physics governing the typical waves. One of the methodologies to furnish statistics of crest height for individual sea states starting from spectral information is based on Monte Carlo techniques. These techniques ask for the simulation of a very large population to estimate accurately the probability of occurrence of extreme events. As an example, in the sea state conditions of the “Draupner wave”, and using a linear irregular wave model, 40,000,000 simulated waves are necessary to calculate accurately the sea state conditional probability of occurrence of crests higher than 14.6 meters. In this context the more complex reasonably usable model is the irregular second order 3D wave model. In this paper we show how more complicated models (and so more time consuming simulators) can be used without loss in the accuracy of the estimation of the probability of occurrence. In that way, Creamer transform is used which gives the Draupner “giant” crest, 10 times more probable than given by second order models.