Predictable zone for phase-resolved reconstruction and forecast of irregular waves

Our interest is the phase-resolved reconstruction and forecast of multidirectional irregular gravity wave fields based on specific wave measurements. We consider the theoretical predictable zone P in space-time within which the phase-resolved wave field can be fully reconstructed/forecasted based on the given measurements. Using linearized wave theory and reasonable assumptions of the frequency and directional extent of the wave field, we obtain closed-form expressions for P in terms of set theory expressions involving the individual measurement. We derive and illustrate P obtained for measurements at one or more fixed locations over time, for moving probes, for whole-area wave measurements, and combinations of these. We also consider the problem of optimal deployment of these measurements to maximize the volume of P in space-time. For J probes under optimal deployment, we show that the volume of P relative to that of a single probe scales as J3 for large J.