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[1] This paper deals with the long-term statistics for extreme nonlinear crest heights. First, a new analytical solution for the return period R(h), of a sea storm in which the maximum nonlinear crest height exceeds a fixed threshold h, is obtained by applying the 'Equivalent Triangular Storm' model and a second-order crest height distribution. The probability P(h c max > hj[0, L]) that maximum nonlinear crest height in the time span L exceeds a fixed threshold is then derived from R(h) solution, assuming that the occurrence of storms with highest crest larger than h is given by a Poisson process. In the applications, both R(h) and P(h c max > hj[0, L]) are calculated for some locations. It is shown that narrowband second-order approach is slightly conservative, with respect to the more general condition of crest distribution for second-order three-dimensional waves. Finally, a comparison with Boccotti, Jasper and Krogstad models is presented.

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In this paper some statistical properties of random waves in a sea storm are investigated. The classical Borgman’s approach is applied to obtain the analytical expressions of both the probability PK(H) that in a sea storm only K waves higher than a fixed threshold H occur, and the probability P≥K(H) that in a sea storm at least K waves higher than a fixed threshold H occur, with K = 1, 2, 3,… Moreover, it is shown that, if the number K is negligible in comparison with the number of waves occurring in the storm, the results may be expressed in an integral form. This integral form is very useful to particularize both PK(H) and P≥K(H) for a storm with a triangular time history. Finally, the results are validated with Montecarlo simulations of random waves in a sea storm of given time history.