Abstract
Flood frequency analysis is usually based on the fitting of an extreme value distribution to the local streamflow series. However, when the local data series is short, frequency analysis results become unreliable. Regional frequency analysis is a convenient way to reduce the estimation uncertainty. In this work, we propose a regional Bayesian model for short record length sites. This model is less restrictive than the index flood model while preserving the formalism of “homogeneous regions”. The performance of the proposed model is assessed on a set of gauging stations in France. The accuracy of quantile estimates as a function of the degree of homogeneity of the pooling group is also analysed. The results indicate that the regional Bayesian model outperforms the index flood model and local estimators. Furthermore, it seems that working with relatively large and homogeneous regions may lead to more accurate results than working with smaller and highly homogeneous regions.
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Acknowledgements
The authors wish to thank the DIREN Rhône-Alpes for providing data. The authors are also very grateful to the two referees for their constructive remarks which improved the document.
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Appendix: Properties of the index flood on GP parameters
Appendix: Properties of the index flood on GP parameters
We provide in this appendix the proof for the following theorem:
Theorem 1Let X be a random variable GP distributed. So X has the cumulative distribution function defined by:
LetY = CXwhere\(C \in \mathbb{R}_{*}^{+}.\)Then, Y is also GP distributed with parameters (μ C,σ C,ξ).
Proof Let X be a r.v. GP distributed with parameters (μ, σ, ξ) and Y = CX where \(C \in \mathbb{R}_{*}^{+}.\) Then:
So, Y is also GP distributed with parameters (μ C,σ C,ξ). The proof for the GEV case can be established in the same way.
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Ribatet, M., Sauquet, E., Grésillon, JM. et al. A regional Bayesian POT model for flood frequency analysis. Stoch Environ Res Risk Assess 21, 327–339 (2007). https://doi.org/10.1007/s00477-006-0068-z
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DOI: https://doi.org/10.1007/s00477-006-0068-z