A probabilistic approach for the quantification of prediction error in deterministic phase-resolved wave forecasting

This paper presents a semi-analytical methodology for the determination of prediction error statistics in deterministic sea wave predictions (DSWP), based on linear wave models. The underlying wave elevation is modelled as a Gaussian stochastic process and the coefficients of the wave propagation model are assumed to be determined by linear fitting on available measurements in time and/or space. The possible data contamination due to measurement error is also explicitly considered. The resulting approach eventually provides a Linear Estimator of Prediction Error (LEPrE) in time and space, in terms of prediction error standard deviation, given the fitting procedure and the sea spectrum. The presented approach allows supplementing deterministic predictions based on phase-resolved linear wave models with a sound prediction error measure, and allows defining the concept of "Predictability Region" in a consistent probabilistic framework. Example applications are reported, both for long-crested and short-crested waves, with verification through Monte Carlo simulations. Single point wave gauge/wave buoy measurements as well as wave radar measurements have been considered as simulated examples. The developed methodology is also compared with existing approaches highlighting and discussing both the differences and the interesting qualitative commonalities.