Incorporating Wave Spectrum Information in Real-time Free-surface Elevation Forecasting: Real-sea Experiments

Real-time prediction of free-surface elevation is necessary for a variety of applications. Assuming a Gaussian wave field, the wave spectrum can be used to calculate the statistically optimal predictor, for a given prediction configuration (i.e. for a given combination of measurement instants and spatial locations, relative to the instants and locations where and when the wave is predicted). More specifically, the optimal predictor is linear, and its coefficients need only be updated as the wave condition evolves. This spectrum-based prediction (SBP) approach encompasses, in a unified theoretical framework, both “time-series” and “spatially-distributed” prediction configurations. In this paper, the validity of the SBP theoretical framework is tested against real-sea wave data, which originate from a measurement campaign using an Acoustic Doppler Current Profiler (ADCP), and consist of free-surface elevation time series, at the corners and centre of a 25m-by-25m square. The directional wave spectra, corresponding to the sea states where the time series are provided, have also been calculated. The empirical SBP accuracy, obtained by applying the SBP in the real-sea time series, is assessed in various sea conditions and prediction configurations, and compared with the theoretical SBP accuracy, evaluated based on the wave spectra. Although the ADCP measurement layout is clearly not ideal for the purpose of wave forecasting, empirical results are physically and statistically consistent, and show good agreement with theoretical results, thus supporting the relevance of the SBP framework.