Extreme wave events and sampling variability

Abstract

Wave field data are affected not only by the accuracy of instruments recording them but also by sampling variability, an uncertainty due to the limited number of observations. For stationary meteorological conditions, due to the randomness of the sea surface elevation, wave parameters derived from a temporal or spatial wave record will depend on which part of a wave record is used in an analysis as well as on the length of a wave record and/or size of the investigated ocean area. This study demonstrates, using numerical simulations, challenges that sampling variability brings in the interpretation of nonlinear wave characteristics of the surface elevation when single 20- or 30-min field wave records are used in an analysis. As examples, we use sea states in which rogue waves were observed in the North Sea and investigate them using linear, second-, and third-order numerical simulations. The third-order wave data are simulated by a numerical solver based on the higher order spectral method (HOSM) which includes the leading order nonlinear dynamical effects, accounting for the effect of modulational instability. Wave steepness, the maximum wave crest, skewness, and kurtosis are investigated in unidirectional and directional wave fields. The study shows that having a single 20- or 30-min wave record may make it difficult to determine on the degree of wave field nonlinearity and the accuracy of derived wave parameters, as well as to evaluate the validity of wave models. Both single-point temporal and stereo-video camera data are discussed. We demonstrate that numerical simulations represent important supporting tools for wave field measurements.