Statistical properties of successive wave heights and successive wave periods

Hanne T. Wist*, Dag Myrhaug, Haavard Rue

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

44 Scopus citations

Abstract

Two successive wave heights are modeled by a Gaussian copula, which is referred to as the Nataf model. Results with two initial distributions for the transformation are presented, the Næss model [Næss A. On the distribution of crest to trough wave heights. Ocean Engineering (1985);12(3):221-34] and a two-parameter Weibull distribution, where the latter is in best agreement with data. The results are compared with existing models. The Nataf model has also been used for modeling three successive wave heights. Results show that the Nataf transformation of three successive wave heights can be approximated by a first order autoregressive model. This means that the distribution of the wave height given the previous wave height is independent of the wave heights prior to the previous wave height. Thus, the joint distribution of three successive wave heights can be obtained by combining conditional bivariate distributions. The simulation of successive wave heights can be done directly without simulating the time series of the complete surface elevation. Successive wave periods with corresponding wave heights exceeding a certain threshold have also been studied. Results show that the distribution for successive wave periods when the corresponding wave heights exceed the root-mean-square value of the wave heights, can be approximated by a multivariate Gaussian distribution. The theoretical distributions are compared with observed wave data obtained from field measurements in the central North Sea and in the Japan Sea, with laboratory data and numerical simulations.

Original languageEnglish (US)
Pages (from-to)114-136
Number of pages23
JournalApplied Ocean Research
Volume26
Issue number3-4
DOIs
StatePublished - May 1 2004

Keywords

  • Copulas
  • Field data
  • First order autoregressive model
  • Laboratory data
  • Nataf transformation
  • Simulations
  • Successive wave heights
  • Successive wave periods

ASJC Scopus subject areas

  • Ocean Engineering

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