Prediction diagrams for deterministic sea wave prediction and the introduction of the data extension prediction method

Abstract

Early in the development of the new discipline of short term deterministic sea wave prediction (DSWP) the prediction region diagram was introduced. This was intended to provide information on the region in space and time where a propagating wave system arose from waves that had been previously totally measured. This diagram is compared here with a space time plot that also incorporates the accuracy of the prediction achievable by the prediction algorithms. In this context certain issues raised in the literature about the relative roles of group and phase velocity are examined. It is shown that the stationary phase approximation, which predicts wave packets propagate at the group velocity, does not hold under the conditions applying to practical DSWP. The numerical work presented introduces a new frequency domain prediction technique termed the data extension method. This is derived from the Papoulis–Gerchberg iteration scheme and reduces prediction errors associated with periodicity artefacts. A method is described for deriving analytic guidelines that allow estimates of prediction performance to be made for standard sea types, with illustrative results being presented for the Pierson–Moskowitz power density spectrum.