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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.

The objective of this paper is to compare two methodologies adopted in the context of long-terms statistics: Equivalent Triangular Storm (ETS) and Peak Over Threshold (POT), applied both with the Goda model and with the Generalized Pareto Distribution. Both methodologies are currently used for conducting long-term statistics oriented to the determination of relevant input parameters adopted in the design of coastal structures. The paper proposes a dissemination of the key characteristics of the methods and elucidates the fundamental steps necessary for mechanizing the methods starting from available wave data. Then, it discusses numerical results pertaining to both Mediterranean and Ocean data. In this context, the paper focuses on the stability of the methods with respect to the (subjectively) selected storm thresholds. It shows that the ETS method is more stable than the POT. Results pertain to both omnidirectional and directional return values.

The paper concerns the statistical properties of extreme ocean waves in the space-time domain. In this regard, a solution for the exceedance probability of the maximum crest height during a sea state over a certain area is obtained. The approach is based on the Adler's solution for the extremal probability for Gaussian random processes in a multidimensional domain. The method is able to include the effects of spatial variability of three-dimensional sea waves on short-term prediction, both over an assigned area XY and in a given direction. Next, the storm-term predictions in the space-time are investigated. For this purpose, the exceedance probability of ηmax⁡ during an ocean storm over an assigned area A is derived. This solution gives a generalization to the space-time of the Borgman's time-based model for nonstationary processes. The validity of the model is assessed from wave data of two buoys of the NOOA-NDBC network located along the Pacific and the Atlantic U.S. coasts. The results show that the size of the spatial domain A remarkably influences the expected maximum crest height during a sea storm. Indeed, the exceedance probabilities of the maximum crest height during an ocean storm over a certain area significantly deviate from the classical Borgman's model in time for increasing area. Then, to account for the nonlinear contributions on crest height, the proposed model is exploited jointly with the Forristall's distribution for nonlinear crest amplitudes in a given sea state. Finally, Monte Carlo simulations of a sea storm are performed showing a very good agreement with theoretical results.

The objective of this paper is to investigate the long-term statistics associated with extreme nonlinear sea wave crests. For this purpose, an equivalent power storm methodology is exploited for modeling the non-stationary time variability of the significant wave height. The method involves the identification of the real storm time histories and a subsequent replacement of each real storm by a fictitious storm that is equivalent to the real one in a statistical sense. Such an approach allows deriving the closed form expression of the return period of a nonlinear wave crest. Numerical results pertain to the calculation of this quantity starting from wave data recorded at the Gulf of Mexico and comparison with alternative methodology recommended in the practice. Next, the paper investigates effects relevant to the design of marine structures in the proximity of a coast. Specifically, the paper considers the effect of the water depth on the return values of the significant wave height and of the maximum expected crest height. The water depth influence relates to a magnification of the return values of wave crest despite the fact that the offshore significant wave height is larger than the near-shore one for a certain value of the return period, due to shoaling-refraction effects.

An analytical non-linear theory is presented for the interaction between three-dimensional sea wave groups and a seawall during an exceptionally high crest or deep trough in the water elevation. The solution to the second-order of the free-surface displacement and the velocity potential is derived by considering an irrotational, inviscid, incompressible flow bounded by a horizontal seabed and a vertical impermeable seawall. From this, an analytical expression for the non-linear wave pressure is obtained. The resulting theory can fully describe the mechanics at the seawall and in front of it, which are represented by a strongly inhomogeneous wave field, and demonstrate that it is influenced by characteristic parameters and wave conditions. The theoretical results are in good agreement with measurements conducted during a small-scale field experiment at the Natural Ocean Engineering Laboratory in Reggio Calabria (Italy). Comparisons of the theoretical and experimental results show that some distinctive phenomena involving the wave pressures of very high standing wave groups at a seawall, in the absence of either overturning or breaking waves, may be associated with non-linear effects.

A method for obtaining the directional spectrum, on assuming that the frequencies of the elementary waves are all different from one another, is re-proposed in a form suitable for applications to sea states near a coast. The method is applied to an interval of 10 h during which the sea state remained basically steady state off the beach at Reggio Calabria (east coast of the Straits of Messina). It is shown that the directional spectrum converges as the length of the time series data grows. A numerical simulation of a 10 h sea state confirms that the directional spectrum converges as the length of the time series grows, and the convergence is onto the known directional spectrum used to make the numerical simulation. Through the numerical simulation, it is proved that the method, generally, is suitable for applications even with short time series of wind waves (duration of about 100Tp). Finally, it is shown that the method is not necessarily inadequate even with short records of multimodal sea states with different modal directions, modal amplitude ratios and intermodal distances.

The objective of this paper is to provide a synthetic tool for determining expeditiously the wave climate conditions in several areas of the Mediterranean Sea. In the open literature, several authors have already conducted this specific analysis also for the area under examination in this paper. However, the need of discussing aspects strictly related to the design of wave energy harvesters is still relevant. Therefore, considering the variety of devices and the amount of information needed for conducting both an energy-wise optimization and a structural reliability assessment, a holistic view on the topic is provided. Specifically, the paper elucidates the theoretical aspects involved in the estimation of wave energy statistics and in the calculation of relevant return values. Next, it provides synthetic data representing the mean wave power and the return value of extreme events in several coastal areas of the Mediterranean Sea. In this regard, the paper complements information available in the open literature by discussing the influence of the directional pattern of the sea states in the determination of sea state statistics as well as in the design of a wave energy harvester. © 2014 Elsevier Ltd.

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.

The paper proposes the directional analysis of the severest storms recorded by the Italian Wave Measurement Network (RON). For this purpose the buoy data have been processed and all the storms have been selected; for the strongest storms, the direction of the sea states, which form them, has been analyzed. The directional return period of sea storms in which the maximum significant wave height exceeds a threshold is then obtained, by applying the ETS model. It is found that, for the prediction of extreme storms off Italy, it is possible to assume the duration of storms constant, with an error smaller than 4%.Copyright © 2006 by ASME

Arena, F.; Malara, G.; Barbaro, G.; Romolo, A., and Ghiretti, S., 2013. Long-term modelling of wave run-up and overtopping during sea storms. This paper is concerned with the determination of the return period of a sea storm in which response (run-up or overtopping) of a coastal structure exceeds a fixed threshold. The method is based on long-term statistical analysis of the sea states interacting with the structure and on practical formulas proposed in the past decades for determining response of coastal structures. The proposed methodology accounts for nonstationarity of sea states in time domain by the equivalent triangular storm model, which allows us to determine closed-form solutions of the return period of a storm where maximum significant wave height is larger than a fixed threshold. In this paper the analytical solution is supplemented by a practical application pertaining calculation of the response of a coastal structure. A rubble-mound breakwater is supposed to be placed at a known wa...

The paper proposes an analysis of ocean storms carried out starting from significant wave height time series of HOMERE sea-states hindcast database based on WAVEWATCH III model. Considering that wave spectra often exhibit multiple peaks due to the coexistence of wind waves and swells, here sea states are described by partitioned sea states that can be interpreted physically as representing independent wave systems. The analysis presented here in the paper deals with the contribution of swells to the storm peaks and on how they influence the long term statistics. The sensitivity of return values of significant wave height to swell contribution is investigated via an application of the Equivalent Triangular Storm Model (ETS). The ETS model provides analytical solution for the calculation of the return period R(Hs>h) of a sea storm whose maximum significant wave height exceeds a given threshold h. The approach of ETS consists in substituting each actual storm with an ETS described by two parameters: the storm intensity, that is the triangle height and it is equal to the maximum significant wave height during the actual storm; the storm duration, that is achieved imposing the equality between the maximum expected wave height of actual and equivalent storms. It has been experimentally proved that the actual storm and associated ETS are statistically equivalent because they have the same maximum significant wave height and the same probability P(Hmax>H) that the maximum wave height exceeds a given threshold H. The sequence of ETSs obtained in this way represents the equivalent sea, while the sequence of actual storms is the actual sea. The equivalent and actual seas present the same wave risk because they are characterized by the same number of storm events, each of them with the same intensity and the same P(Hmax>H). For the proposed analysis a set of four points from open sea to the coast is considered in area of the Gulf of Biscay (France). The results show that the contribution of swells is more significant for the storms of small and medium intensity and decreases for increasing storm intensities. Further return values variability neglecting swell is less than 7% at any point for return periods up to 100 years.