Assessing the predictability of random ocean waves

Real-time wave forecasting (RTWF) consists in predicting ocean wave motion or forces, from seconds to minutes in advance, using real-time measurements. For the successful development of RTWF, understanding wave predictability is essential. Usually, a deterministic ‘predictable zone’ (DPZ) is geometrically constructed from the wave group velocities and directions present in the spectrum. DPZs have little experimental evidence, and suffer ambiguities regarding the choice of cutoff frequencies and directions – since actual ocean waves are not band-limited. The present study addresses those shortcomings, by defining probabilistic predictable zones (PPZs) with respect to chosen uncertainty thresholds, using a rigorous statistical framework restricted to near-Gaussian sea states (precisely those where RTWF would be employed). PPZs are examined in idealised spectra and in a stereo dataset of a real wave field. It is shown that the PPZ geometry is quantitatively related to the sea state characteristics, through three physical parameters: two limiting group velocities (similar to the deterministic theory), and a directional spreading effect, which also limits the PPZ extent. While the lower group velocity depends on the chosen uncertainty threshold, the upper group velocity is better approximated by that of the spectrum peak frequency, which is a novel finding. The empirical data support the validity of the present PPZ theory. In contrast, both theoretical and empirical results contradict the fan-shaped predictable zones, constructed in the three-dimensional deterministic theory, thus highlighting the importance of considering stochasticity to understand the predictability of actual ocean waves.