The paper proposes an approach for estimating the long-term statistics of random wave crests occurring over a certain space–time domain. Such a problem is relevant for a number of marine engineering applications, as classical analyses based, exclusively, on time domain approaches underestimates wave crest amplitudes associated with a given return period. The return period of a certain wave crest is derived by combining the Trapezoidal Storm (TS) Model, based on DNV GL storm profile, with the Euleric Characteristic (EC) of an excursion set concept, recently applied to the study of sea wave statistics. By computing the average EC, an explicit solution for the probability distribution of the wave crests during a sea storm can be derived by an approximation of the EC. Return period of linear wave crests is derived in the paper. The proposed solution is applied for the calculation of extreme waves during an ocean storm over a certain area. The results presented can be used as good approximation in design work of offshore installations. An extension of the proposed approach to account for nonlinearities of sea surface will be a subject of future research.

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