The Gumbel mixed model for flood frequency analysis
ABSTRACT Many hydrological engineering planning, design, and management problems require a detailed knowledge of flood event characteristics, such as flood peak, volume and duration. Flood frequency analysis often focuses on flood peak values, and hence, provides a limited assessment of flood events. This paper proposes the use of the Gumbel mixed model, the bivariate extreme value distribution model with Gumbel marginals, to analyze the joint probability distribution of correlated flood peaks and volumes, and the joint probability distribution of correlated flood volumes and durations. Based on the marginal distributions of these random variables, the joint distributions, the conditional probability functions, and the associated return periods are derived. The model is tested and validated using observed flood data from the Ashuapmushuan river basin in the province of Quebec, Canada. Results indicate that the model is suitable for representing the joint distributions of flood peaks and volumes, as well as flood volumes and durations.
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ABSTRACT: The paper focuses on the extension of the average conditional exceedance rate (ACER) method for estimation of extreme wind speed statistics to the case of bivariate wind speed time series. Using the ACER method, it is often possible to provide an estimate of the exact extreme value distribution of a univariate time series. This is obtained by introducing a cascade of conditioning approximations to the exact extreme value distribution. The cascade is expressed in terms of the ACER functions, which can be estimated from the given data time series. When the cascade has converged, an empirical estimate of the extreme value distribution has been obtained. In the paper it is shown how the univariate ACER method can be extended in a natural way to also cover the case of bivariate data. Application of the bivariate ACER method will be demonstrated for simultaneous wind speed measurements from two separate locations.Journal of Wind Engineering and Industrial Aerodynamics 04/2015; 139. DOI:10.1016/j.jweia.2015.01.011 · 1.70 Impact Factor
Hydrology Research 02/2011; 42(2–3):193. DOI:10.2166/nh.2011.065 · 1.16 Impact Factor
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ABSTRACT: In watershed management, flood frequency analysis (FFA) is performed to quantify the risk of flooding at different spatial locations and also to provide guidelines for determining the design periods of flood control structures. The traditional FFA was extensively performed by considering univariate scenario for both at-site and regional estimation of return periods. However, due to inherent mutual dependence of the flood variables or characteristics [i.e., peak flow (P), flood volume (V) and flood duration (D), which are random in nature], analysis has been further extended to multivariate scenario, with some restrictive assumptions. To overcome the assumption of same family of marginal density function for all flood variables, the concept of copula has been introduced. Although, the advancement from univariate to multivariate analyses drew formidable attention to the FFA research community, the basic limitation was that the analyses were performed with the implementation of only parametric family of distributions. The aim of the current study is to emphasize the importance of nonparametric approaches in the field of multivariate FFA; however, the nonparametric distribution may not always be a good-fit and capable of replacing well-implemented multivariate parametric and multivariate copula-based applications. Nevertheless, the potential of obtaining best-fit using nonparametric distributions might be improved because such distributions reproduce the sample’s characteristics, resulting in more accurate estimations of the multivariate return period. Hence, the current study shows the importance of conjugating multivariate nonparametric approach with multivariate parametric and copula-based approaches, thereby results in a comprehensive framework for complete at-site FFA. Although the proposed framework is designed for at-site FFA, this approach can also be applied to regional FFA because regional estimations ideally include at-site estimations. The framework is based on the following steps: (i) comprehensive trend analysis to assess nonstationarity in the observed data; (ii) selection of the best-fit univariate marginal distribution with a comprehensive set of parametric and nonparametric distributions for the flood variables; (iii) multivariate frequency analyses with parametric, copula-based and nonparametric approaches; and (iv) estimation of joint and various conditional return periods. The proposed framework for frequency analysis is demonstrated using 110 years of observed data from Allegheny River at Salamanca, New York, USA. The results show that for both univariate and multivariate cases, the nonparametric Gaussian kernel provides the best estimate. Further, we perform FFA for twenty major rivers over continental USA, which shows for seven rivers, all the flood variables followed nonparametric Gaussian kernel; whereas for other rivers, parametric distributions provide the best-fit either for one or two flood variables. Thus the summary of results shows that the nonparametric method cannot substitute the parametric and copula-based approaches, but should be considered during any at-site FFA to provide the broadest choices for best estimation of the flood return periods.Journal of Hydrology 04/2015; 525:658-675. DOI:10.1016/j.jhydrol.2015.04.024 · 2.69 Impact Factor