Bayesian MCMC approach to regional flood frequency analyses involving extraordinary flood events at ungauged sites

Gaumé, Éric; Gaál, Ladislav; Viglione, Alberto; Szolgay, Ján; Kohnová, Silvia; Blöschl, Günter

doi:10.1016/j.jhydrol.2010.01.008

Cited by 139 publications

(95 citation statements)

References 45 publications

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“…This assumption is systematically made in the hydrology field (Gaume et al, 2010). However, extreme WL exhibit long-term trends that cannot be ignored.…”

Section: Likelihood Formulationmentioning

confidence: 99%

How historical information can improve estimation and prediction of extreme coastal water levels: application to the Xynthia event at La Rochelle (France)

Bulteau

Idier

Lambert

et al. 2015

Nat. Hazards Earth Syst. Sci.

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Abstract. The knowledge of extreme coastal water levels is useful for coastal flooding studies or the design of coastal defences. While deriving such extremes with standard analyses using tide-gauge measurements, one often needs to deal with limited effective duration of observation which can result in large statistical uncertainties. This is even truer when one faces the issue of outliers, those particularly extreme values distant from the others which increase the uncertainty on the results. In this study, we investigate how historical information, even partial, of past events reported in archives can reduce statistical uncertainties and relativise such outlying observations. A Bayesian Markov chain Monte Carlo method is developed to tackle this issue. We apply this method to the site of La Rochelle (France), where the storm Xynthia in 2010 generated a water level considered so far as an outlier. Based on 30 years of tide-gauge measurements and 8 historical events, the analysis shows that (1) integrating historical information in the analysis greatly reduces statistical uncertainties on return levels (2) Xynthia's water level no longer appears as an outlier, (3) we could have reasonably predicted the annual exceedance probability of that level beforehand (predictive probability for 2010 based on data until the end of 2009 of the same order of magnitude as the standard estimative probability using data until the end of 2010). Such results illustrate the usefulness of historical information in extreme value analyses of coastal water levels, as well as the relevance of the proposed method to integrate heterogeneous data in such analyses.

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“…This assumption is systematically made in the hydrology field (Gaume et al, 2010). However, extreme WL exhibit long-term trends that cannot be ignored.…”

Section: Likelihood Formulationmentioning

confidence: 99%

How historical information can improve estimation and prediction of extreme coastal water levels: application to the Xynthia event at La Rochelle (France)

Bulteau

Idier

Lambert

et al. 2015

Nat. Hazards Earth Syst. Sci.

View full text Add to dashboard Cite

show abstract

“…Unsurprisingly, extreme flood events are seldom observed locally, and hydrologists have little or no chance of gathering data from an adequate sample of catastrophes for analysis, especially for prediction at ungauged sites, with the exception of post-event surveys (see e.g. Marchi et al, 2010;Gaume et al, 2010). It is therefore important that effective and practical procedures are available, to assist hydrologists in making inferences about flood risk, both at gauged and at ungauged sites Salinas et al, 2013).…”

Section: Introductionmentioning

confidence: 99%

Regional parent flood frequency distributions in Europe – Part 1: Is the GEV model suitable as a pan-European parent?

Salinas

Castellarin

Viglione

et al. 2014

Hydrol. Earth Syst. Sci.

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Abstract. This study addresses the question of the existence of a parent flood frequency distribution on a European scale. A new database of L-moment ratios of flood annual maximum series (AMS) from 4105 catchments was compiled by joining 13 national data sets. Simple exploration of the database presents the generalized extreme value (GEV) distribution as a potential pan-European flood frequency distribution, being the three-parameter statistical model that with the closest resemblance to the estimated average of the sample L-moment ratios. Additional Monte Carlo simulations show that the variability in terms of sample skewness and kurtosis present in the data is larger than in a hypothetical scenario where all the samples were drawn from a GEV model. Overall, the generalized extreme value distribution fails to represent the kurtosis dispersion, especially for the longer sample lengths and medium to high skewness values, and therefore may be rejected in a statistical hypothesis testing framework as a single pan-European parent distribution for annual flood maxima. The results presented in this paper suggest that one single statistical model may not be able to fit the entire variety of flood processes present at a European scale, and presents an opportunity to further investigate the catchment and climatic factors controlling European flood regimes and their effects on the underlying flood frequency distributions.

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“…In fact, novel approaches are continuously being introduced, adapting the standard statistical methods to the actual properties found in the observed data series, which are in most cases relatively short and therefore only provide a limited view of a very complex, variable and potentially slow-changing processes. Examples of studies attempting to address issues of incomplete information on long-term change and variability in the flood series include Salas and Obeysekera (2014), who revise the methods for return period estimation using a geometric distribution and introduce changing probabilities over time; in order to reduce the variability of return period estimates obtained by the short recorded annual maxima series, Macdonald et al (2013) and Gaume et al (2010) propose to include historical evidence of large floods; Cohn and Lins (2005) discuss the importance of accounting for long-term persistence in the data series and how this would affect tests for non-stationarity; Renard et al (2008) discuss methods to simultaneously analyse data from homogeneous regions to assess regional consistency and field significance; Merz et al (2012) point out that a more rigorous approach is needed when reporting cause-effect claims and stress the need for sound hypothesis-testing frameworks. The methods presented in this work deal with the analysis of annual and seasonal maxima, although peaks over the threshold (POT) methods are also widely used in flood frequency analysis: rather than using the maximum recorded in each year these models are used to model series of exceedances of a high threshold (e.g.…”

Section: Prosdocimi Et Al: Non-stationarity In the Ukmentioning

confidence: 99%

Non-stationarity in annual and seasonal series of peak flow and precipitation in the UK

Prosdocimi

Kjeldsen

Svensson

2014

Nat. Hazards Earth Syst. Sci.

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Abstract. When designing or maintaining an hydraulic structure, an estimate of the frequency and magnitude of extreme events is required. The most common methods to obtain such estimates rely on the assumption of stationarity, i.e. the assumption that the stochastic process under study is not changing. The public perception and worry of a changing climate have led to a wide debate on the validity of this assumption. In this work trends for annual and seasonal maxima in peak river flow and catchment-average daily rainfall are explored. Assuming a two-parameter log-normal distribution, a linear regression model is applied, allowing the mean of the distribution to vary with time. For the river flow data, the linear model is extended to include an additional variable, the 99th percentile of the daily rainfall for a year. From the fitted models, dimensionless magnification factors are estimated and plotted on a map, shedding light on whether or not geographical coherence can be found in the significant changes. The implications of the identified trends from a decisionmaking perspective are then discussed, in particular with regard to the Type I and Type II error probabilities. One striking feature of the estimated trends is that the high variability found in the data leads to very inconclusive test results. Indeed, for most stations it is impossible to make a statement regarding whether or not the current design standards for the 2085 horizon can be considered precautionary. The power of tests on trends is further discussed in the light of statistical power analysis and sample size calculations. Given the observed variability in the data, sample sizes of some hundreds of years would be needed to confirm or negate the current safety margins when using at-site analysis.

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Bayesian MCMC approach to regional flood frequency analyses involving extraordinary flood events at ungauged sites

Cited by 139 publications

References 45 publications

How historical information can improve estimation and prediction of extreme coastal water levels: application to the Xynthia event at La Rochelle (France)

How historical information can improve estimation and prediction of extreme coastal water levels: application to the Xynthia event at La Rochelle (France)

Regional parent flood frequency distributions in Europe – Part 1: Is the GEV model suitable as a pan-European parent?

Non-stationarity in annual and seasonal series of peak flow and precipitation in the UK

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