This paper deals with the analysis of extreme wave heights and their uncertainties. The main purpose is to assess confidence intervals using a conventional extreme value, and a Bayesian approach. It is shown how the introduction of an a priori information helps to bound the upper confidence limit. The analysis is performed with wave-height data recorded off the Spanish Catalan coast (NW Mediterranean) and wave-height data from the Dutch coast (North Sea). An analysis with natural-scale and log-transformed wave-height time series has been performed. This scale selection is proven to be advantageous for naturally bounded variables and also better captures some distribution features. The paper ends with a discussion on how the different techniques can be used to select a statistically robust threshold for an extreme event definition. This affects the evaluation of risk in low-lying coastal areas, associated to variables controlling flooding and erosion risks.

Extreme events, such as wave-storms, need to be characterized for coastal infrastructure design purposes. Such description should contain information on both the univariate behaviour and the joint-dependence of storm-variables. These two aspects have been here addressed through generalized Pareto distributions and hierarchical Archimedean copulas. A non-stationary model has been used to highlight the relationship between these extreme events and non-stationary climate. It has been applied to a Representative Concentration Pathway 8.5 Climate-Change scenario, for a fetch-limited environment (Catalan Coast). In the non-stationary model, all considered variables decrease in time, except for storm-duration at the northern part of the Catalan Coast. The joint distribution of storm variables presents cyclical fluctuations, with a stronger influence of climate dynamics than of climate itself.Peer ReviewedPostprint (author's final draft

The characterization of future wave-storms and their relationship to large-scale climate can provide useful information for environmental or urban planning at coastal areas. A hybrid methodology (process-based and statistical) was used to characterize the extreme wave-climate at the northwestern Black Sea. The Simulating WAve Nearshore spectral wave-model was employed to produce wave-climate projections, forced with wind-fields projections for two climate change scenarios: Representative Concentration Pathways (RCPs) 4.5 and 8.5. A non-stationary multivariate statistical model was built, considering significant wave-height and peak-wave-period at the peak of the wave-storm, as well as storm total energy and storm-duration. The climate indices of the North Atlantic Oscillation, East Atlantic Pattern, and Scandinavian Pattern have been used as covariates to link to storminess, wave-storm threshold, and wave-storm components in the statistical model. The results show that, first, under both RCP scenarios, the mean values of significant wave-height and peak-wave-period at the peak of the wave-storm remain fairly constant over the 21st century. Second, the mean value of storm total energy is more markedly increasing in the RCP4.5 scenario than in the RCP8.5 scenario. Third, the mean value of storm-duration is increasing in the RCP4.5 scenario, as opposed to the constant trend in the RCP8.5 scenario. The variance of each wave-storm component increases when the corresponding mean value increases under both RCP scenarios. During the 21st century, the East Atlantic Pattern and changes in its pattern have a special influence on wave-storm conditions. Apart from the individual characteristics of each wave-storm component, wave-storms with both extreme energy and duration can be expected in the 21st century. The dependence between all the wave-storm components is moderate, but grows with time and, in general, the severe emission scenario of RCP8.5 presents less dependence between storm total energy and storm-duration and among wave-storm components.

Standard practice of wave-height hazard analysis often pays little attention to the uncertainty of assessed return periods and occurrence probabilities. This fact favors the opinion that, when large events happen, the hazard assessment should change accordingly. However, uncertainty of the hazard estimates is normally able to hide the effect of those large events. This is illustrated using data from the Mediterranean coast of Spain, where the last years have been extremely disastrous. Thus, it is possible to compare the hazard assessment based on data previous to those years with the analysis including them. With our approach, no significant change is detected when the statistical uncertainty is taken into account. The hazard analysis is carried out with a standard model. Time-occurrence of events is assumed Poisson distributed. The wave-height of each event is modelled as a random variable which upper tail follows a Generalized Pareto Distribution (GPD). Moreover, wave-heights are assumed independent from event to event and also independent of their occurrence in time. A threshold for excesses is assessed empirically. The other three parameters (Poisson rate, shape and scale parameters of GPD) are jointly estimated using Bayes' theorem. Prior distribution accounts for physical features of ocean waves in the Mediterranean sea and experience with these phenomena. Posterior distribution of the parameters allows to obtain posterior distributions of other derived parameters like occurrence probabilities and return periods. Predictives are also available. Computations are carried out using the program BGPE v2.0.