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Discussion papers | Copyright
© Author(s) 2018. This work is distributed under
the Creative Commons Attribution 4.0 License.

Research article 10 Apr 2018

Research article | 10 Apr 2018

Review status
This discussion paper is a preprint. It is a manuscript under review for the journal Hydrology and Earth System Sciences (HESS).

Modeling the spatial dependence of floods using the Fisher copula

Manuela I. Brunner1,2,3, Reinhard Furrer4, and Anne-Catherine Favre2 Manuela I. Brunner et al.
  • 1Department of Geography, University of Zurich, Zurich, Switzerland
  • 2Univ. Grenoble Alpes, CNRS, IRD, Grenoble INP, IGE, Grenoble, France
  • 3Swiss Federal Institute for Forest, Snow and Landscape Research WSL, Birmensdorf ZH, Switzerland
  • 4Department of Mathematics and Department of Computational Science, University of Zurich, Zurich, Switzerland

Abstract. Floods do often not only affect a single location but a whole region. Flood frequency analysis should therefore be undertaken at a regional scale which requires the considerations of the dependence of events at different locations. This dependence is often neglected even though its consideration is essential to derive reliable flood estimates. A model used in regional multivariate frequency analysis should ideally consider the dependence of events at multiple sites which might show dependence in the lower and/or upper tail of the distribution. We here seek at proposing a simple model that on the one hand considers this dependence with respect to the network structure of the region and on the other hand, allows for the simulation of stochastic event sets at both gauged and ungauged locations. The new Fisher copula model is used for representing the spatial dependence of flood events in the nested Thur catchment in Switzerland. Flood event samples generated for the gauged stations using the Fisher copula are compared to samples generated by other dependence models allowing for modeling multivariate data including elliptical copulas, R-vine copulas, and max-stable models. The comparison of the dependence structures of the generated samples shows that the Fisher copula is a suitable model for capturing the spatial dependence in the data. We therefore use the copula in a way such that it can be used in an interpolation context to simulate event sets comprising gauged and ungauged locations. The spatial event sets generated using the Fisher copula well capture the general dependence structure in the data and the upper tail dependence, which is of particular interest when looking at extreme flood events and when extrapolating to higher return periods. The Fisher copula is therefore a suitable model for the stochastic simulation of flood event sets at multiple gauged and ungauged locations.

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