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Mathematical Problems in Engineering
Volume 2013 (2013), Article ID 416212, 6 pages
Research Article

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

Natural Ocean Engineering Laboratory, Department DICEAM, “Mediterranea” University, 89122 Reggio Calabria, Italy

Received 12 August 2012; Revised 8 January 2013; Accepted 28 January 2013

Academic Editor: P. Liatsis

Copyright © 2013 Felice Arena et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.