A regional Bayesian POT model for flood frequency analysis

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.

[1]  J. R. Wallis,et al.  Some statistics useful in regional frequency analysis , 1993 .

[2]  Bernard Bobée,et al.  Towards operational guidelines for over-threshold modeling , 1999 .

[3]  Henrik Madsen,et al.  Generalized least squares and empirical bayes estimation in regional partial duration series index‐flood modeling , 1997 .

[4]  J. Stedinger,et al.  Using regional regression within index flood procedures and an empirical Bayesian estimator , 1998 .

[5]  J. R. Wallis,et al.  Regional Frequency Analysis: An Approach Based on L-Moments , 1997 .

[6]  J. Pickands.  Statistical Inference Using Extreme Order Statistics , 1975 .

[7]  M. Parlange,et al.  Statistics of extremes in hydrology , 2002 .

[8]  Martin Crowder,et al.  Bayesian priors based on a parameter transformation using the distribution function , 1992, Annals of the Institute of Statistical Mathematics.

[9]  Jonathan A. Tawn,et al.  A Bayesian Analysis of Extreme Rainfall Data , 1996 .

[10]  Luis R. Pericchi,et al.  Anticipating catastrophes through extreme value modelling , 2003 .

[11]  J. Corcoran.  Modelling Extremal Events for Insurance and Finance , 2002 .

[12]  C. Klüppelberg,et al.  Modelling Extremal Events , 1997 .

[13]  Paul J. Northrop,et al.  Likelihood-based approaches to flood frequency estimation , 2004 .

[14]  M. Acreman,et al.  The regions are dead. Long live the regions. Methods of identifying and dispensing with regions for flood frequency analysis , 1989 .

[15]  Katherine Campbell,et al.  Flood Frequency Analysis , 2001, Technometrics.

[16]  Eric Parent,et al.  Encoding prior experts judgments to improve risk analysis of extreme hydrological events via POT modeling , 2003 .

[17]  Groupe de recherche en hydrologie statistique.  Inter-comparison of regional flood frequency procedures for Canadian rivers , 1996 .

[18]  Oscar J. Mesa,et al.  Multiscaling theory of flood peaks: Regional quantile analysis , 1994 .

[19]  D. Burn.  Evaluation of regional flood frequency analysis with a region of influence approach , 1990 .

[20]  Khaled H. Hamed,et al.  Flood Frequency Analysis , 1999 .

[21]  Chang Shu,et al.  Artificial neural network ensembles and their application in pooled flood frequency analysis , 2004 .

[22]  Murugesu Sivapalan,et al.  An investigation into the physical causes of scaling and heterogeneity of regional flood frequency , 1997 .

[23]  Groupederechercheenhydrologie.  Inter-comparison of regional flood frequency procedures for Canadian rivers , 1996 .

[24]  A. W. Minns,et al.  The application of data mining techniques for the regionalisation of hydrological variables , 2002 .

[25]  R. Fisher,et al.  Limiting forms of the frequency distribution of the largest or smallest member of a sample , 1928, Mathematical Proceedings of the Cambridge Philosophical Society.

[26]  L. Haan,et al.  Residual Life Time at Great Age , 1974 .

[27]  Salvatore Gabriele,et al.  A hierarchical approach to regional flood frequency analysis , 1991 .