Quantifying error in deterministic predictions based on phase-resolved linear wave models

Ship operational safety is most frequently addressed from a statistical point of view, making reference to probabilistic measures of ship motions and/or wave characteristics. However, in the recent years, thanks to the technological advances in wave sensing, complementary approaches, based on the deterministic forecasting of wave elevation and ship motions, have been developed. Nevertheless, deterministic wave forecasting approaches are still lacking an associated sound measure of the prediction uncertainty. In trying to contribute filling this identified gap, a theoretically consistent measure of prediction error is developed in this work, starting only from fundamental assumptions about the water wave elevation field and the employed phase-resolved wave prediction model. Specifically, assuming linear wave theory and gaussianity of the wave elevation field, a Linear Estimator of Prediction Error (LEPrE) is derived. Some example applications are re-ported where the developed approach is applied and verified.