Analysis and Interpretation of Space-Time Extreme Waves

An observational space–time ensemble of sea surface elevations was analyzed in search of high waves. Data were gathered by means of a stereo-camera system mounted on top of a fixed oceanographic platform located in the northern Adriatic Sea (Italy). Waves were measured during a mature sea state with average wind speed of 11 m/s.

3D wave groups have been isolated while evolving in the 2D space and grabbed ‘when and where’ they were close to the apex of their development. In these conditions the waves exhibited large surface displacements. We have selected the wave groups displaying maximal crest height exceeding 1.25 Hs, that is the threshold adopted to define rogue waves in a time record.

Time series at the spatial positions where such large crests occurred have been analyzed to derive the empirical distributions of crest and wave heights. The distributions were compared against standard statistical linear and nonlinear models. Maximal observed wave crests resulted outliers of the standard statistics, behaving as isolated members of the sample, apparently uncorrelated with other waves of the record.

The study has found that these unexpectedly large wave crests are better approximated by a space–time model for extreme crest heights. The space–time model performance has been improved, deriving a second-order approximation of the linear model. The nonlinear model provided a fair agreement with the empirical maxima.

The present investigation suggests that very large waves may be more numerous than generally expected.