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Flood frequency analysis: The Bayesian choice

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After an introduction to the traditional flood frequency analysis methods, this article discusses their limits and the risks associated with their thoughtless use: overconfidence in the estimated values of flood quantiles or return periods and systematic underestimation of risks. The article then presents and illustrates the added value of modern Bayesian flood frequency inference procedures that are statistically consistent, numerically accurate, and now computationally affordable. The implementation of such methods shows that estimated flood frequencies, based on observed samples of limited size, are generally affected by large uncertainties. This acknowledgement should be an incentive for increasing the size of the analyzed samples through a more systematic use of historic information as well as regional approaches in flood frequency analyses. It also clearly points out that the margin of errors should be considered when using inference results for design or risk assessment purposes. Several pieces of software are now available to conduct Bayesian flood frequency analyses relatively straightforwardly. There is no remaining obstacle to the implementation of these modern approaches in operational hydrological studies. This article is categorized under: Science of Water > Methods Science of Water > Water Extremes
Plot of measured stages versus corresponding estimated discharges at the Montcel gauge on the Morge river (France) according to the available dataset (left panel). View of the Morge river in the vicinity of the gauged cross section (right panel). The stage–discharge relation has obviously been modified in 2003 with few changes in its lower part but tremendous evolutions of its upper, extrapolated part
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(Left) Distribution of exceedance probabilities of the 100‐year estimated quantiles for 2,000 samples of 30 values drawn from a GEV(10, 10, −0.2) distribution: red vertical line (theoretical value: 1%), black vertical line (sample average). (Right) Illustration of the “predictive” distribution in red along with parent distribution (bold line), maximum likelihood distribution (continuous line), 90% confidence interval (dotted lines), sample plotting positions (dots)
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Inference results based on a sample of 30 values (left) and on the same sample complemented with historic information over 100 years (right). The two largest historic peak discharges could be estimated with a large uncertainty range (distance between and ) indicated by the dotted lines; 90% credibility limits (black dotted line), maximum likelihood distribution (continuous line), sample plotting positions (dots), GEV(10, 10, −0.2) parent distribution (bold line), historic records (vertical dotted lines). Note that the plotting positions have been recomputed in the right panel to account for the historic records
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(Left) Comparison between the Bayesian–MCMC 90% credibility limits (black dotted line) and the 90% bootstrap confidence interval (gray dotted line) for a sample of 30 values drawn from a GEV(10, 10, −0.2) distribution. Sample plotting positions (dots), parent distribution (bold line), and maximum likelihood distribution (line). (Right) Uniformity test for the confidence intervals computed with the Bayesian MCMC procedure
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Impact of sampling variability. Inference results based on a sample of 30 values (left): moments (continuous line), L‐moments (dashed line), maximum likelihood (dotted line), sample plotting positions (dots), parent GEV (10, 10, −0.2) distribution (bold line). Scattering of the plotting positions for 100 samples of 30 values drawn from the parent distribution (right)
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Boxplots of the 100‐year quantile estimation relative errors for the three standard inference methods. A total of 1,000 series of N values drawn from a parent GEV (10, 10, −0.2) distribution. N = 30 (left) and N = 100 (right)
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Illustration of the two classic flood peak discharge sampling strategies applied to a 10‐year series of discharges measured in Paris on the Seine river: annual block maxima (left) and peaks over threshold (right). Red dots (sampled values), dotted vertical lines (separation between hydrological years), red horizontal line (selected threshold)
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