Multivariate Modeling of Flood Flows

Goel, N. K.; Seth, S. M.; Chandra, Satish

doi:10.1061/(asce)0733-9429(1998)124:2(146)

Cited by 122 publications

(60 citation statements)

References 12 publications

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“…Bivariate distributions have been used for many years by hydrologists. The most commonly applied bivariate distributions are the bivariate normal distribution (Bergmann and Sackl 1989, Goel et al 1998, Yue 1999, and many others), the bivariate exponential distribution (Singh and Singh 1991), the bivariate gamma distribution (Yue 2001) and the bivariate extreme value distribution , Shiau 2003, Shiau et al 2006. However, the functionality of these multivariate distributions in the modelling of the dependence between the correlated random variables has some limitations: (1) the same family is needed for each marginal distribution, which means the individual behaviour of the two variables must be characterized by the same parametric family of univariate distributions; (2) extensions to more than the bivariate case cannot be derived easily; and (3) for some cases parameters of the marginal distributions are also used to model the dependence between the random variables.…”

Section: Introductionmentioning

confidence: 99%

The impact of seasonal flood peak dependence on annual maxima design quantiles

Debele

Bogdanowicz

Strupczewski

2017

Hydrological Sciences Journal

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If the maximum annual peak flow series are a mixture of summer and winter flows, a seasonal approach to flood frequency analysis is necessary. While considering seasonal maxima as mutually independent events, the annual maxima distribution is defined as the product of seasonal distributions. However, if the independency assumption does not hold, a bivariate approach with dependent margins should be applied, i.e. the copula approach. The impact of dependency on design quantiles is investigated here in the context of the Fréchet-Hoeffding inequality defining copula bounds and the definition of dependency. The results of the two approaches are compared using six catchments in the San River basin, where in four cases the dependency of seasonal maxima has been identified as positive significant and no strong dominance of any one season is observed. The product model leads to higher estimates of design quantiles than do models where the dependency is taken into account and, therefore, is safe. ARTICLE HISTORY

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Section: Introductionmentioning

confidence: 99%

The impact of seasonal flood peak dependence on annual maxima design quantiles

Debele

Bogdanowicz

Strupczewski

2017

Hydrological Sciences Journal

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“…In engineering hydrology practice, the statistical analysis of flood peaks and volumes are often dealt with in a multivariate frequency framework. In the past, identical marginal distributions for both random variables have been used (e.g., Goel et al, 1998;Yue et al, 2002). Recently the use of copula-based multivariate models have attracted a lot of attention.…”

Section: Introductionmentioning

confidence: 99%

A process-based analysis of the suitability of copula types for peak-volume flood relationships

et al. 2015

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Abstract. The work aims at analyzing the bivariate relationship between flood peaks and flood volumes, with a particular focus on the type and seasonality of flood generation processes. Instead of the usual approach that deals with an analysis of the annual maxima of flood events, the current analysis includes all independent flood events in a catchment. Flood events are considered independent when they originate from distinguishably different synoptic/meteorological situations. The target region is located in the northern part of Austria, and consists of 72 small and mid-sized catchments. On the basis of the discharge measurements with a time resolution of 1 h from the period 1976-2007, independent flood events were identified and were assigned to one of the three following flood generation type categories: synoptic floods, flash floods and snowmelt floods. These were subsequently divided into two seasons, thereby separating predominantly rainfall-fed and snowmelt-fed floods. Nine frequently-used copula types were locally fitted to the samples of the flood type and seasonal data. Their goodness-of-fit was examined locally as well as analyzed in a regional scope. It was concluded that (i) treating flood processes separately is beneficial for the statistical analysis; (ii) suitability patterns of acceptable copula types are distinguishably different for the seasons/flood types considered, (iii) the Clayton and Joe copulas shows an unacceptable performance for all the seasons/flood types in the region; (iv) the rejection rate of the other copula types depends on the season/flood type and also on the sample size; (v) given that usually more than one statistically suitable dependence model exists, an uncertainty analysis of the design values in the engineering studies resulting from the choice of model seems unavoidable; (vi) reducing uncertainty in the choice of model could be attempted by a deeper hydrological analysis of the dependence structure between flood peaks and volumes in order to give hydrological support to the decision on model's suitability in specific regions and for typical flood generation mechanisms.

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“…Consequently, artificial assumptions have often been recommended, the most common of which is the transformation of the marginals to normality, prior to fitting a multivariate normal distribution. This is the strategy suggested by the World Meteorological Organization [1988] and the one that has been adopted in many studies of the joint distribution of flood peak and volume [Correia, 1987;Sackl and Bergmann, 1987;Goel et al, 1998]. A serious drawback of this proposal is that extremes from a multivariate normal distribution behave like extremes from independent normals [Resnick, 1987, chapter 5], and such incorrect modeling can lead to quite misleading results [Coles and Tawn, 1994].…”

Section: Adamson Et Al: Bivariate Extreme Value Distributionsmentioning

confidence: 99%

Bivariate extreme value distributions: an application of the Gibbs Sampler to the analysis of floods

Adamson¹,

Metcalfe²,

Parmentier³

1999

Water Resources Research

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Abstract. The quantitative definition of the magnitude of a flood episode exclusively in terms of its peak rate of discharge is often insufficient. In common with most episodic hydrological phenomena, floods are intrinsically multivariate random events, characterized not only by their peak flow, but also by their volume and the duration of discharge above critical thresholds. A complete definition in terms of these three component random variables has not found its way into standard analytical practice. This may be partly because the theory of multivariate extremes is not straightforward, and partly because no intuitively attractive way of presenting the component variables in a probabilistic framework has been put forward. We propose that the Gibbs sampler, a member of the new generation of computer intensive methods in computational statistics, bypasses the theoretical difficulties. We demonstrate the Gibbs sampler, and provide graphical presentations of the results, for the annual flood hydrograph on the Mekong River at Vientiane, Laos. We extend the results to evaluate the potential distribution of flood damage to the city.

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Multivariate Modeling of Flood Flows

Cited by 122 publications

References 12 publications

The impact of seasonal flood peak dependence on annual maxima design quantiles

The impact of seasonal flood peak dependence on annual maxima design quantiles

A process-based analysis of the suitability of copula types for peak-volume flood relationships

Bivariate extreme value distributions: an application of the Gibbs Sampler to the analysis of floods

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