On Adler space‐time extremes during ocean storms

The paper concerns the statistical properties of extreme ocean waves in the space‐time domain. In this regard, a solution for the exceedance probability of the maximum crest height during a sea state over a certain area is obtained. The approach is based on the Adler's solution for the extremal probability for Gaussian random processes in a multidimensional domain. The method is able to include the effects of spatial variability of three‐dimensional sea waves on short‐term prediction, both over an assigned area XY and in a given direction. Next, the storm‐term predictions in the space‐time are investigated. For this purpose, the exceedance probability ofη max ⁡during an ocean storm over an assigned area A is derived. This solution gives a generalization to the space‐time of the Borgman's time‐based model for nonstationary processes. The validity of the model is assessed from wave data of two buoys of the NOOA‐NDBC network located along the Pacific and the Atlantic U.S. coasts. The results show that the size of the spatial domain A remarkably influences the expected maximum crest height during a sea storm. Indeed, the exceedance probabilities of the maximum crest height during an ocean storm over a certain area significantly deviate from the classical Borgman's model in time for increasing area. Then, to account for the nonlinear contributions on crest height, the proposed model is exploited jointly with the Forristall's distribution for nonlinear crest amplitudes in a given sea state. Finally, Monte Carlo simulations of a sea storm are performed showing a very good agreement with theoretical results.