The influence of the modeling order on the predictable area of non-linear unidirectional ocean waves

Abstract

The influence of non-linear modeling of phase-resolved ocean wave fields on the extent of the accessible predictable area is investigated. Assuming that the ocean surface dynamics is known over a limited spatial domain, e.g. via radar backscatter reconstruction, the linear wave theory as well as the high-order spectral method with various orders of non-linearity are used to propagate the surface with different levels of physical fidelity. The prediction accuracy is quantified by comparing the predicted waves to a reference, i.e. a fully known wave field propagated with a high-fidelity wave model. By doing this, it is made possible to track the spatiotemporal evolution of the prediction accuracy and define the predictable area as the region over which the accuracy is higher than a threshold, here defined by a “surface similarity parameter” lower than 0.1. Different unidirectional wave field characteristics are studied, highlighting the effect of the wave steepness, water depth and wave energy spreading around the peak spectral frequency, all impacting significantly the prediction accuracy, thus the predictable area. It is shown that the extent of the predictable area is highly dependent on the order of the considered wave model, and that the third order generally leads to the largest reachable predictable area in all configurations.