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The knowledge of extreme events of environmental variables is an issue of increasing concern to the scientific community. Within the branch of coastal and ocean engineering there are many fields of application where an accurate estimation of long term return period events is needed, i.e. coastal defenses design, coastal flooding management, estimation of changes of the littoral morphology, offshore and onshore renewable energy devices design, etc. But not only the engineers are concerned by extreme events; biological communities in the open sea and estuarine systems are also exposed to extreme events that may affect its natural development (i.e. extreme sea levels in estuarine environments could raze fields of plants not able to deal with salt in just a few hours). But the analysis of environmental variables and their extreme behaviors is not an easy task. In most cases the problem to be solved presents a multivariate nature, which makes it of a special complexity. For instance, in the case of flooding analysis, an estimation of joint probability density of astronomical tide, storm surge and waves is needed; or in the case of floating offshore devices the parameters of interest would be waves, winds and currents. Complex mathematical methods and techniques are needed to be able to estimate the joint probability of occurrence of more than one variable at the same time. In addition, some considerations must be taken regarding the quality of the data in order to be able to guarantee the achievement of reliable estimations. In this document, an analysis of the problem of extreme value analyses, the existing methods, their limitations, and some hints to proceed are exposed. The document is divided as follows: a first part will introduce the main problems or aspects that need to be considered concerning data and exposes the main methods to solve univariate problems and the way to estimate statistical parameters; a second part is focused on the main multivariate methods; then, a fourth part will focus on the principal techniques to estimate the uncertainties; finally in the last part the available softwares useful for EV analysis are exposed. In the appendices is presented the application of these methods in two different case studies, one proposed by IFREMER and based on the design of an offshore structure mooring and the second one proposed by BRGM with a focus on a practical application to flood risk in coastal areas.

Many records in environmental sciences exhibit asymmetric trajectories and there is a need for simple and tractable models which can reproduce such features. In this paper we explore an approach based on applying both a time change and a marginal transformation on Gaussian processes. The main originality of the proposed model is that the time change depends on the observed trajectory. We first show that the proposed model is stationary and ergodic and provide an explicit characterization of the stationary distribution. This result is then used to build both parametric and non-parametric estimates of the time change function whereas the estimation of the marginal transformation is based on up-crossings. Simulation results are provided to assess the quality of the estimates. The model is applied to shallow water wave data and it is shown that the fitted model is able to reproduce important statistics of the data such as its spectrum and marginal distribution which are important quantities for practical applications. An important benefit of the proposed model is its ability to reproduce the observed asymmetries between the crest and the troughs and between the front and the back of the waves by accelerating the chronometer in the crests and in the front of the waves.

The design of catenary risers, riser towers, and export lines is key to oil and gas production in the deep ocean. Winds, waves, surface currents and current profiles are essential inputs to the design of these riser systems. With regards to current loading, the variety and abundance of current profiles can make it difficult to determine which profiles are most appropriate for determining extreme and fatigue loading on risers. The choices become increasingly difficult on the frontier of deepwater oil and gas developments as risers are increasingly being required to successfully operate in harsher environments and deeper water. However, longer and more detailed current measurements from in-situ deployments continue to become available. Two or three year current profile records are now common. In order to progress in the specification of current profiles and in the methodologies of using these profiles in the riser design, four oil & gas companies, BP Exploration Operating Company Limited, PETRÓLEO BRASILEIRO S.A. - PETROBRAS, Statoil ASA and TOTAL E&P Recherche Développement SAS, have funded the WACUP project (Worldwide Approximations of Current Profiles). The first objective of the WACUP project is to establish best practices for reducing large current profile databases into a smaller, representative set of profiles that can be used for designing risers. Three techniques have been compared in their ability in reducing measured in-situ databases: Empirical Orthogonal Function (EOF), Self Organizing Maps (SOM) and classical Current Profile Characterisation (CPC). For Vortex Induced Vibration (VIV) fatigue analysis we evaluate the skill of these three techniques in estimating VIV damage to a Steel Catenary Riser (SCR). Our measure of skill is the comparison of the results from the reduced data sets with results from the complete database. The standard techniques are modified, improving the accuracy of the database reduction. We recommend that any of these techniques can be made suitable for concept selection or preliminary engineering, but it may be desirable to run the full set of Gold Standard profiles for full detailed structural design. The second objective is to better understand the means to deal with extreme current profiles, in one part for fatigue damage and in another part for static loads analyses, to compare to traditional methods and to propose, if necessary, better practices. For fatigue, due to the complexity of the relation between current profile shape and damage, extrapolation on Gold Standard damage is the only way to produce quality n-year damage return values. Concerning extreme static response, the first analyses show that CCA profiles, used in exhaustive directions, produce realistic n-year return values. The ability of the available numerical current models to complement the in-situ measurements is also assessed. Models are superior to measurements for providing a large scale regional interpretation of key oceanographic processes. They can also be used to cost-effectively quantify spatial variability in the current regime. However they must be properly validated and calibrated before use in any engineering application. The primary source of data for characterisation of current profiles in riser design remains full water column, site specific, in-situ measurement.

Since the Rogue Waves 2000 and 2004 workshops, researchers have pursued activity in the proposition of models and descriptions that can improve our understanding of rogue waves. The Brest Rogue Waves 2008 workshop gathered again many scientists and engineers to an opportunity to confront and discuss their views on the subject. It provided an assessment of the State of the Art of research on those matters, and was one more step forward towards efficient mitigation measures., Depuis les colloques Rogue Waves 2000 et 2004, la recherche s'est poursuivie pour la proposition de modèles susceptibles d'améliorer notre compréhension des vagues scélérates. Le colloque Rogue Waves 2008 a de nouveau rassemblé à Brest de nombreux scientifiques et ingénieurs qui ont pu y confronter et discuter leurs positions sur le sujet. Les dernières avancées dans le domaine ont pu y être évaluées, et un nouveau pas a été ainsi fait vers des mesures appropriées face au risque de ces événements.

When Newman's approximation is used to calculate the low frequency part of the nonlinear transfer between the waves and the forces on an LNG carrier, the CPU time to make the time series reconstruction of wave loads is a small part of the total. However, using full QTF-matrices increases the required work by a factor equal to the number of wave components in the sea states and the total simulation time can be increased by 5 or 10. Moreover, if we consider the multi-directional sea, the double summation becomes a quadruple summation at second order which is extremely time-consuming. There is a way to accelerate this computation by making an algebraic or system approximation of the QTF. The aim of this report is to present the solutions, the problems and the performances of such system approximation. A particular case of approximation consists of factorising the full matrix of QTF, considering only the main (highest modulus) eigenvalues and corresponding eigenvectors. This study will compare the different approaches of this method on a case study furnished by Bureau Veritas. Extensive results are given for QTF uni-directional and some first results are commented for QTF multi-directional.

In this study we discuss various methods to assess the statistics of extreme response of a floating structure subjected to random waves. This issue is of great importance in the case of low frequency motion of floating bodies in shallow water. Those methods are based on the evaluation of the level crossing rate, which is easily related to the extreme value statistics for stationary random processes and large levels. Four main methods are considered, namely the Rice formula with either a Gaussian assumption or an approximation of the joint distribution of the response and its first derivative by a projection method; the Breitung's formula; the Hagberg's approaches using either an asymptotic expansion or a Monte-Carlo integration and finally the time domain simulation which serves as the reference solution. All these methods are applied to the surge motion of a floating body subjected to unidirectional waves. In that case, the Rice formula under the Gaussian assumption strongly underestimates the level crossing rate. The other methods are more or less accurate compared to the time domain simulation, but Hagberg's Monte-Carlo integration is shown to give the best approximation.

Since the Rogue Waves 2000 workshop, significant advances have been made in the proposition of models and descriptions that may improve our understanding of rogue waves. Questions arise now on how those results should influence standard practices in the shipbuilding and offshore industries, and whether they allow to improve forecast and warning systems. The Brest Rogue Waves 2004 workshop gathered again many scientists and engineers to an opportunity to confront and discuss their views on the subject., Depuis le colloque Rogue Waves 2000, des avancées significatives ont été réalisées dans la description et la proposition de modèles susceptibles d’améliorer notre compréhension des vagues scélérates. Les questions qui se posent maintenant concernent l’influence que ces résultats doivent avoir sur les normes et pratiques de la construction navale et offshore, et s'ils apportent des possibilités d'amélioration pour les systèmes de prévision et d’alerte. Le colloque Rogue Waves 2004 de Brest a de nouveau rassemblé de nombreux scientifiques et ingénieurs qui ont pu y confronter et discuter leurs positions sur le sujet.

The OGP Workshop on the Metocean and Engineering Aspects of Floating Systems which was held at St. Albans in April 2001 identified better discrimination of the low frequency end of the wave spectrum as one of the most pressing problems for the design and analysis of floating systems. The responses of many floating systems have proven to be very sensitive not only to the amplitude and frequency of the swell, but also to the details of the shape of the swell peak in the spectrum. There has been relatively little serious study of the low frequency end of the wave spectrum compared to the effort that has gone into the study of the high frequency tail of the spectrum. Much of the present interest in swell comes from the active deep water developments taking place off West Africa. The West African environment is generally mild, but swell from storms in the Southern Ocean is persistent and can reach fairly high amplitudes with very low periods. Enough data is now available so that a serious study of the characteristics of swell off West Africa can be made. In response to this need and opportunity, Shell Global Solutions, in association with Ifremer and Oceanweather, formed a Joint Industry Project to analyze and compare the available data on swell off West Africa. This report describes the results of that West Africa Swell Project (WASP).

Physical events, such as swell or internal waves, have a strong signature on ocean SAR (synthetic aperture radar) images. The spatial periodicity of these phenomena justifies the use of spectral analysis tools for their detection, localization and pertinent parameter estimation (wavelength, direction of propagation, energy, ...). However, these spectral phenomena are highly non-stationary, especially near the coast where the bathymetric conditions greatly influences the propagation. As the study of these variations are important near the coast, because of human activity, spectral analysis tools robust in non-stationary situations have to be considered. For that purpose, investigations were carried out to evaluate the efficiency of the Wigner-Ville distribution. This representation exhibits very good properties and has been quite extensively studied, even if the numerical implementation still presents some difficulties.

A method for artificially generating operational sea state histories has been developed. This is a distribution free method to simulate bivariate non stationary and non Gaussian random processes. This method is applied to the simulation of the bivariate process (H-s, T-p) of sea state parameters. The time series respects the physical constraints existing between the significant wave height and the peak period. Furthermore, we show that the persistence properties of the simulations match to those of the observations.

Despite its great theoretical and practical importance, the statistical distribution of crest heights has remained poorly known. The uncertainties are due to difficulties both with the theory, where nonlinear effects must be accurately modeled, and with measurements, where different sensors appear to give different results. In response to this uncertainty, the Wave Crest Sensor Intercomparison Study (WACSIS) was formed as a Joint Industry Project in order to provide data for comparing the response of wave sensors and for comparing theories of crest height distributions with the measurements. The key to the WACSIS experiment was to place all of the popular sensors on the same platform located where they were likely to experience large waves in one season. The location of the measurements was in shallow water because the nonlinearities that produce extreme wave crests are stronger in shallow water. Measurements in shallow water thus give better tests of both instruments and theories. The project was set up on the Meetpost Noordwijk (MPN) measurement platform. The platform is a piled steel jacket structure in 18 meters deep water, located 9 kilometers off the Dutch coast near the coastal resort of Noordwijk, whence it got its name. The platform is one of the stations of the North Sea Monitoring Network ('Meetnet Noordzee', MNZ), that gathers on-line hydrological and meteorological information from the North Sea. A complete description of the project is given by van Unen et al. (1998). WACSIS was very successful in collecting a nearly complete data set from all of the instruments during the winter of 1997-98. The second phase of the WACSIS project focused on the interpretation of the wave data. Many aspects of wave statistics have been studied, but the main emphasis has been on crest height distributions, and recommendations for crest heights to be used in air gap calculations. This report will describe, first the different steps which have been followed to construct a common data base from the raw data collected at the Meetpost Noordwijk measurement platform, secondly various analyses of the data base in term of crest height-period joint distributions, intercomparison of the crest measurements by the sensors and comparisons with numerical second order irregular wave models. Finally, new models of crest distribution will be proposed and compared with other state of the art models. Ref. van Unen, R.F., van Beuzekom, A.A., Forristall, G.Z., Mathisen, J.-P., Starke, J., 1998, "Wacsis - wave crest sensor intercomparison study at the Meetpost Noordwijk measurement platform", Proc. Oceans Conf.