The paper concerns the statistical properties of extreme ocean waves in the space-time domain. Specifically, a closed-form solution for the exceedance probability of the maximum wave elevation during a sea state over a certain area is derived, which is based on the Adler’s theory for the extremal probability for Gaussian random processes in a multidimensional domain. Then, the method is extended to the long-term predictions in the space-time. In this regards, the exceedance probability of the wave elevation during an ocean storm over an assigned area A is derived both for the actual storm and for the theoretical Equivalent Power Storm (EPS). The solution gives a generalization to the space-time of the Borgman’s time-based model for non-stationary processes. The model is finally applied for predicting the occurrences of extreme events in sea storms, giving an analytical solution for the return period of extreme wave events over a given area. The validity of the model is assessed from wave data of buoy 46006 of the NOOA-NDBC network located along the Atlantic US coast. The results show that the size of the spatial domain A remarkably influences the expected maximum wave elevation during a sea storm. Finally, MonteCarlo simulations of the strongest sea storm recorded by buoy 46006 are performed showing a very good agreement with theoretical results.
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