Space-time extreme wind waves: Analysis and prediction of shape and height

In this study, we present the analysis of the temporal profile and height of space-time (ST) extreme wind waves. Wave data were gathered from an observational ST sample of sea surface elevations collected during an active sea state, and they were examined to detect the highest waves (exceeding the rogue wave threshold) of specific 3D wave groups close to the apex of their development. Two different investigations are conducted. Firstly, local maximum elevations of the groups are examined within the framework of statistical models for ST extreme waves, and compared with observations and predictions of maxima derived by one-point time series of sea surface elevations. Secondly, the temporal profile near the maximum wave crests is analyzed and compared with the expectations of the linear and second-order nonlinear extension of the Quasi-Determinism (QD) theory. Our goal is to verify, with real sea data, to what extent, one can estimate the shape and the crest-to-trough height of near-focusing large 3D wave groups using the QD and ST extreme model results. From this study, it emerges that the elevations close to the crest apex are narrowly distributed around a mean profile, whilst a larger dispersion is observed away from the maximum elevation. Yet the QD model furnishes, on average, a fair prediction of the maximum wave heights, especially when nonlinearities are taken into account. Moreover, we discuss how the combination of ST extreme and QD model predictions allows establishing, for a given sea condition, the portrait of waves with very large crest height. Our results show that these theories have the potential to be implemented in a numerical spectral model for wave extreme prediction.