On the distribution of maximum crest and wave height at intermediate water depths

Abstract

We report new descriptions for the (probability) distributions of hourly maximum crest and wave height of water surface gravity waves for intermediate water depths. Estimated distributions are based on analysis of laboratory-scale measurements at the DHI wave basin. For a given sea state, the distribution of both hourly maximum crest and hourly maximum wave height, normalised by sea state significant wave height, is found to follow a generalised extreme value (GEV) distribution. Variation of the three parameters of the GEV distribution across sea states, is expressed in terms of a response surface model as a function of non-dimensional sea state Ursell number and wave steepness, and wave directional spreading angle. For inference, conventional Monte Carlo wave basin measurements are supplemented with measurements selected by means of a novel "pre-selection" sampling scheme using numerical simulations. This scheme effectively guarantees that extreme events from tails of distributions are produced, and reduces uncertainties associated with the estimated distributions. Estimation is performed using Bayesian inference, allowing uncertainties to be quantified, and providing estimates of posterior predictive tail distributions for sea states with arbitrary characteristics within the domain of sea state characteristics covered by the model.

A multivariate pseudo-likelihood approach to estimating directional ocean wave models

“…Direct characterisation of the wavefield would require measurements of surface displacement over space and time. Outside of laboratory wave tanks (Forristall, 2015;Schubert et al, 2020), shallow lakes (Young et al, 1996) or coastal regions (Long and Oltman-Shay, 1991;Eastoe et al, 2013), this is very difficult to achieve with current technology. However it is relatively straightforward to measure some characteristics of the wavefield, and to use these measurements to infer properties of the latent spatiotemporal process.…”

Bayesian probabilistic representation of complex systems: With application to wave load modeling

“…In this regard, a continuousvalued storm event may be defined using the realizations in the database that comply with the discrete storm representation by, for example, choosing a specific realization using the CSMS framework or a bootstrap approach. In either case, given the continuous representation of the storm event, the storm content can be defined in terms of significant wave heights (Equation 22), and for each sea state, the distribution of the hourly maximum crest height can be defined by adopting the model of Schubert et al (2020). This model is based on extensive laboratory-scale experiments performed in the wave basin at the Danish Hydraulic Institute (DHI), see Schubert et al (2020) and Bredmose et al (2016) for further details on the experimental data and its postprocessing.…”

“…In either case, given the continuous representation of the storm event, the storm content can be defined in terms of significant wave heights (Equation 22), and for each sea state, the distribution of the hourly maximum crest height can be defined by adopting the model of Schubert et al (2020). This model is based on extensive laboratory-scale experiments performed in the wave basin at the Danish Hydraulic Institute (DHI), see Schubert et al (2020) and Bredmose et al (2016) for further details on the experimental data and its postprocessing. The model is provided in terms of a response surface in the sea state characteristics: Ursell number, wave steepness and wave directional spreading angle, and the water depth.…”

“…This model is based on extensive laboratory‐scale experiments performed in the wave basin at the Danish Hydraulic Institute (DHI), see Schubert et al. (2020) and Bredmose et al. (2016) for further details on the experimental data and its postprocessing.…”

Πιθανοτικός Σχεδιασμός Παράκτιων Έργων

“…Good estimation of extremes of individual wave height H and of maximum wave height H max on some spatio-temporal domain, are essential for the design and assessment of marine and coastal structures [188]. There is a large literature related to this subject.…”