Return Period of a Sea Storm with at Least Two Waves Higher than a Fixed Threshold

Practical applications in ocean engineering require the long-term analysis for prediction of extreme waves, that identify design conditions. If extreme individual waves are investigated, we need to combine long-term statistical analysis of ocean waves with short-term statistics. The former considers the distribution of standard deviation of free surface displacement in the considered location in a long-time span, of order of 10 years or more. The latter analyzes the distribution of individual wave heights in a sea state, which is a Gaussian process in time domain. Recent advanced approaches enable the combination of the two analyses. In the paper the analytical solution is obtained for the return period of a sea storm with at least two individual waves higher than a fixed level. This solution is based on the application of the Equivalent Triangular Storm model for the representation of actual storms. One of the corollaries of the solution gives the exact expression for the probability that at least two waves higher than fixed level are produced during the lifetime of a structure. The previous solution of return period and the relative probability of exceedance may be effectively applied for the risk analysis of ocean structures.