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Discussion papers
https://doi.org/10.5194/nhess-2020-80
© Author(s) 2020. This work is distributed under
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/nhess-2020-80
© Author(s) 2020. This work is distributed under
the Creative Commons Attribution 4.0 License.

Submitted as: research article 19 Mar 2020

Submitted as: research article | 19 Mar 2020

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This preprint is currently under review for the journal NHESS.

Trivariate copula to design coastal structures

Olivier Orcel, Philippe Sergent, and François Ropert Olivier Orcel et al.
  • Cerema, Margny-Lès-Compiègne, 60280, France

Abstract. Some coastal structures must be redesigned in the future due to rising sea levels caused by global warming. The design of structures subjected to the actions of waves requires an accurate estimate of the long return period of such parameters as wave height, wave period, storm surge and more specifically their joint exceedance probabilities. The Defra method that is currently used makes it possible to directly connect the joint exceedance probabilities to the product of the univariate probabilities by means of a simple factor. These schematic correlations do not, however, represent all the complexity of the reality and may lead to damaging errors in coastal structure design.

The aim of this paper is therefore to remedy the lack of accuracy of these current approaches. To this end, we use copula theory with a copula function that aggregates joint distribution function to its univariate margins. We select a bivariate copula that is adapted to our application by the likelihood method with a copula parameter that is obtained by the error method.

In order to integrate extreme events, we also resort to the notion of tail dependence. We can select the copulas with the same tail dependence as data. In the event of an opposite tail dependence structure, we resort to the survival copula. The tail dependence parameter makes it possible to estimate the optimal copula parameter. The most accurate copulas for our practical case with applications in Saint-Malo and Le Havre (France), are the Clayton normal copula and the Gumbel survival copula.

The originality of this paper is the creation of a new and accurate trivariate copula. Firstly, we select the fittest bivariate copula with its parameter for the two most correlated univariate margins. Secondly, we build a trivariate function. For this purpose, we aggregate the bivariate function with the remaining univariate margin with its parameter. We show that this trivariate function satisfies the mathematical properties of the copula. We can finally represent joint trivariate exceedance probabilities for a return period of 10, 100 and 1000 years.

Olivier Orcel et al.

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Olivier Orcel et al.

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Short summary
Coastal structures subjected to the actions of waves must be redesigned due to rising sea levels. Their design requires an estimate of the long return period of wave height, wave period, storm surge and more specifically their joint exceedance probabilities. We confirm that the best results are obtained by first aggregating the most correlated variables that are wave height and wave period. Nevertheless, the choice of method of aggregation is much less important than the choice of the copula.
Coastal structures subjected to the actions of waves must be redesigned due to rising sea...
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