Bayesian MCMC flood frequency analysis with historical information

Reis, Dirceu S.; Stedinger, Jery R.

doi:10.1016/j.jhydrol.2005.02.028

Cited by 267 publications

(228 citation statements)

References 47 publications

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“…Such return periods appear consistent with the observed probability of flooding events (8 in 94.4 years) and as a first approximation, our choice seems reasonable. For other applications, where DZ and X 0 could be more difficult to estimate, the Bayesian framework should make the integration of DZ and X 0 uncertainties within the HIBEVA method possible (Reis and Stedinger, 2005).…”

Section: Discussionmentioning

confidence: 99%

“…Benito et al (2004) for a review). Among the statistical techniques developed to combine both sources of data (recent observations and historical information), Bayesian methods provide the most flexible and adequate framework because of their natural ability for handling uncertainties in extreme value models (Reis and Stedinger, 2005;Coles and Tawn, 2005). Surprisingly, we found only one reference (Van Gelder, 1996) developing such a method for sea water levels.…”

Section: Introductionmentioning

confidence: 99%

“…In the hydrology field, Reis and Stedinger (2005) developed a Bayesian Markov chain Monte Carlo (MCMC) approach to tackle the issue of integrating partial historical information within EVA. The essence of the approach is to incorporate partial historical data into the model likelihood as censored observations.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

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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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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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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“…Parent and Bernier 2003;Reis and Stedinger 2005;Neppel et al 2010). As discussed in Stedinger and Cohn (1986) the likelihood in Eq.…”

Section: The Inclusion Of Historical Data For Frequency Estimationmentioning

confidence: 99%

German tanks and historical records: the estimation of the time coverage of ungauged extreme events

Prosdocimi

2017

Stoch Environ Res Risk Assess

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The use of historical data can significantly reduce the uncertainty around estimates of the magnitude of rare events obtained with extreme value statistical models. For historical data to be included in the statistical analysis a number of their properties, e.g. their number and magnitude, need to be known with a reasonable level of confidence. Another key aspect of the historical data which needs to be known is the coverage period of the historical information, i.e. the period of time over which it is assumed that all large events above a certain threshold are known. It might be the case though, that it is not possible to easily retrieve with sufficient confidence information on the coverage period, which therefore needs to be estimated. In this paper methods to perform such estimation are introduced and evaluated. The statistical definition of the problem corresponds to estimating the size of a population for which only few data points are available. This problem is generally refereed to as the German tanks problem, which arose during the second world war, when statistical estimates of the number of tanks available to the German army were obtained. Different estimators can be derived using different statistical estimation approaches, with the maximum spacing estimator being the minimum-variance unbiased estimator. The properties of three estimators are investigated by means of a simulation study, both for the simple estimation of the historical coverage and for the estimation of the extreme value statistical model. The maximum spacing estimator is confirmed to be a good approach to the estimation of the historical period coverage for practical use and its application for a case study in Britain is presented.

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“…Several methods have been used in the estimation of the statistical parameters for the selected distribution functions . The most efficient methods to incorporate imprecise and categorical data are (1) maximum likelihood estimators (Leese, 1973;Stedinger and Cohn, 1986;Francés, 2001); (2) the method of expected moments (Cohn et al, 1997;England et al, 2003); and (3) Bayesian methods (Kuczera, 1999;O'Connell et al, 2002;O'Connell, 2005;Reis and Stedinger, 2005). Several reviews of these methods have been published by Stedinger et al (1993) and , and case study applications in Europe can be found, among others in Calenda et al (2009) and Botero and Francés (2010).…”

Section: Flood Frequency Analysismentioning

confidence: 99%

Quantitative historical hydrology in Europe

Benito

Brázdil

Herget

et al. 2015

Hydrol. Earth Syst. Sci.

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Abstract. In recent decades, the quantification of flood hydrological characteristics (peak discharge, hydrograph shape, and runoff volume) from documentary evidence has gained scientific recognition as a method to lengthen flood records of rare and extreme events. This paper describes the methodological evolution of quantitative historical hydrology under the influence of developments in hydraulics and statistics. In the 19th century, discharge calculations based on flood marks were the only source of hydrological data for engineering design, but were later left aside in favour of systematic gauge records and conventional hydrological procedures. In the last two decades, there has been growing scientific and public interest in understanding long-term patterns of rare floods, in maintaining the flood heritage and memory of extremes, and developing methods for deterministic and statistical application to different scientific and engineering problems. A compilation of 46 case studies across Europe with reconstructed discharges demonstrates that (1) in most cases present flood magnitudes are not unusual within the context of the last millennium, although recent floods may exceed past floods in some temperate European rivers (e.g. the Vltava and Po rivers); (2) the frequency of extreme floods has decreased since the 1950s, although some rivers (e.g. the Gardon and Ouse rivers) show a reactivation of rare events over the last two decades. There is a great potential for gaining understanding of individual extreme events based on a combined multiproxy approach (palaeoflood and documentary records) providing high-resolution time flood series and their environmental and climatic changes; and for developing non-systematic and non-stationary statistical models based on relations of past floods with external and internal covariates under natural low-frequency climate variability.

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Bayesian MCMC flood frequency analysis with historical information

Cited by 267 publications

References 47 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)

German tanks and historical records: the estimation of the time coverage of ungauged extreme events

Quantitative historical hydrology in Europe

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