How rare is the Draupner wave event?

Cavaleri et al. (2015) have produced a simulation of the famous Draupner wave event (that occurred on the 1st of January 1995 at 15:20 at the Draupner platform) using a new, high-resolution version of the ECMWF forecasting system. According to this simulation, which has a horizontal resolution of about 10 km and 137 layers in the vertical, there are clear signs that around the time of the wave event evidence of the presence of a polar low is found resulting in a sea state consisting of two systems, namely a windsea and a swell. As suggested by a study of M. Onorato such two-component systems might be more prone toModulational Instability giving rise to higher probabilities of extreme events, but the two systems need both to be narrow band.

After providing an overview of the theoretical probablistic approach that will be followed (which includes new results on how to determine skewness and envelope kurtosis for general spectra), the extreme statistics over the first 20 hours of the forecast at the Draupner platform are presented. It is found that there is some evidence to suggest that at the time of the freak wave event the statistics in terms of ’envelope’ skewness and kurtosis are exceptional. In addition, one might ask the question how likely the occurrence of this freak wave event is. Then, for a domain of 10×10 km², which corresponds to the spatial resolution of the wave model used in the simulation, it is found that the probability that maximum wave height is equal or larger than the maximum Draupner wave height is about 13%. This is a fairly large probability, but it should be noted that in order to achieve these large probabilities, one needs to introduce a number of nonlinear effects, related to skewness and kurtosis, in the probability distribution function (pdf) of wave height. Using Gaussian statistics, corresponding to linear waves, the probability drops to only 0.5%, hence, according to linear theory, the Draupner wave event is not very likely.

Finally, by comparing with results from the T_l 799 (about 25 km) version of the ERA-interim software it is clear that for a realistic simulation of this extreme event spatial resolution matters. The new version of the ECMWF model allows the simulation of a small-scale polar low which is absent in the ERA-interim run. As a consequence, the sea state in the high-resolution run is much steeper and contains longer waves so that near the Draupner location with depth of 69 m shallow water effects are much more important, giving an enhancement of probabilities at the time the Draupner event occurred. On the other hand, the ERA-interim simulation, which has shorter, less steep waves, does not suggest that the sea state has extreme statistics.