Space–time long-term statistics of ocean storms

This paper presents an approach for estimating the long-term statistics of random wave crests occurring over a certain space–time domain. Such a problem is relevant in a number of marine engineering applications, as classical analyses based, exclusively, on time domain approaches underestimate wave crest amplitudes associated with a given return period.The return period of a certain wave crest is derived by combining the Equivalent Power Storm model, used in long-term statistical analyses, with the Euler Characteristic (EC) of an excursion set concept, recently applied to the study of sea wave statistics. In this regard, the paper shows that by computing the average EC, the probability distribution of the wave crests can be derived. Specifically, an explicit solution valid for finite crest thresholds can be derived by an approximation of the EC. Thus, removing the limitation of actual solutions, which are valid only for extremely large wave crests. In addition, return period of nonlinear wave crests are derived. In this context, Forristall distribution is adopted and introduced on a heuristic basis in the EC framework.The EC approximation and the reliability of the nonlinear crest distribution is assessed against Monte Carlo data by comparing distributions of maximum wave crests both in a sea state and in a sea storm. Then, return value estimations are discussed for a number of cases.