Extreme value analysis of complex wave systems

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The design of offshore and coastal hydraulic structures is very much dependent on the hydraulic boundary conditions, such as significant wave height, mean wave period and wave direction, among other parameters. A proper design value of these parameters is required during the design process, based on the corresponding safety philosophy and the lifetime of the structure. In this context, an extreme event is characterised by a combination of unfavourable parameters. However, the interdependencies between the parameters are not always accounted for in the design process, despite the fact that some parameters are clearly related. This potentially leads to an overly conservative or optimistic design.

To complicate matters further, a given sea state might consist of a combination of wind wave and swell systems, sometimes coming from different directions and with different spectral shapes. Different combinations of crossing wave systems might lead to the same total significant wave height, mean wave period and mean wave direction. Only analysing the total wave parameters might oversimplify the situation in the presence of combined wave systems. In this thesis a methodology has been developed to establish extreme offshore wave conditions given the presence of these combined wave systems.

A time series that partitions the total wave into a wind wave- and swell component is used as input for the analysis. The location of interest being off the coast of southern Brazil, where combined sea states are observed regularly. The main objective is to compute design values for all wave parameters of interest. With these design values a number of extreme offshore sea states are described in terms of a single total wave system and equivalent combinations of two wave systems. The former resulting in a single-peaked wave spectrum and the latter in an equivalent double-peaked wave spectrum. The extreme offshore sea states are transformed to the nearshore and compared. The single-peaked and equivalent double-peaked wave spectra may result in very similar values for the wave energy nearshore, albeit with different spectral shapes and directions. For the investigated directional combination, this means that the more elaborate approach with two wave systems potentially affects the design of coastal infrastructure if it is sensitive to spectral shape and direction, although the uncertainty of the result is not quantified. Equivalent wave systems could be compared for other directional combinations in future research to investigate if the more elaborate approach results in a more cost-effective design of coastal infrastructure.

The quality of the multivariate vine copula model, used to compute the set of design values for the wave parameters of interest, is assessed in multiple ways. It is recommended not to pick a single set of design values at a point of high joint probability density. Instead it is suggested to use conditionalised samples from the vine copula model to determine the most unfavourable combination of load parameters, which has to be evaluated case-by-case.