# Uni- and bivariate statistical analysis of long-term wave climates

Uni- and bivariate statistical analysis of long-term wave climates

Author ContributorGelder, P.H.A.J.M. (mentor)

Voortman, H.G. (mentor)

Holthuijsen, L.H. (mentor)

Vrijling, J.K. (mentor)

1998-08-01

AbstractFor the probability-based design and assesment of marine structures interacting with sea waves, a reliable knowledge of the long-term wave climate is required. Wave climate data are commonly presented in the form of histograms of spectral wave parameters. The severity of a sea state is usually expressed in terms of significant wave height H, and corresponding wave period T. From the earlier stages of the development of a statistical approach to wave climate, the advantage of an analytical representation of empirical distributions of data through parametric models was recognized. The compactness of analytical description, the standardization of the representation, and the filling of information gaps, led researchers to use specific marginal and bivariate parameter models, suitable for the description of wave height and wave period statistics. A large amount of case studies is present in the literature with regard to the marginal distribution functions of H, and T and with regard to the bivariate distribution functions of Hs and T.Besides the above bivariate models that are based on the marginal distribution functions also exist. The aim of the present study is to find a particular bivariate distribution function for Hs and T, which provides a close fit to long-term (extreme) wave data presenting a deep water wave field. Several types of joint distribution function for H, and T are compared with reference to measured data. The comparison is based on the utility of the distribution functions for predictions of extreme sea states. The report is thus concerned with the estimation of extreme significant wave heights and wave periods (zero-up-crossing periods or spectral peak periods). The present study of bivariate functions is similar to the above mentioned case studies of marginal distributions. It provides a detailed analysis of the influence of the data selection procedure, the parameter estimation method and the chosen distribution function on the estimation of bivariate return values. In total flve bivariate probability models are tested for the joint statistics of Hs and T. These are: 1. the bivariate Log-normal distribution 2. the bivariate Log-normal distribution with correction for skewness (the Fang and Hogben distribution) 3. the bivariate distribution constructed from a marginal distribution for Hs and a conditional distribution for T 4. the bivariate distribution based on a marginal distribution for Hs and a marginal distribution for the (deepwater) wave steepness 5. the bivariate distribution with given marginals developed by Morton and Bowers (1997) The fourth model is proposed by Vrijling (1996). It is based on the assumption that the significant wave height (Hs) and the wave steepness (s) are independent. With in the calculations, first the bivariate distribution of Hs and s is computed by simply taking the product of the marginals of Hs and s. Then the bivariate distribution of Hs and T is determined by transforming the joint model of H, and s. The fifth model is a distribution of the Frechet class. Morton and Bowers (1997) have published an article in which a detailed description is given about the application of the model to extreme wave height and windspeed observations. They obtained good results. No further tests of the model are known to the author. Therefore, the model is included in the present study.

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