Elsevier

Journal of Hydrology

Volume 258, Issues 1–4, 28 February 2002, Pages 249-259
Journal of Hydrology

Development of regional flood-duration–frequency curves based on the index-flood method

https://doi.org/10.1016/S0022-1694(01)00577-7Get rights and content

Abstract

The aim of this research paper is to develop a statistical model that provides a more complete description of a basin's flood regime. The approach adopted in this paper is based on the flood-duration–frequency (QdF) analysis which takes into account the temporal variability of floods. This approach is analogous to the intensity-duration–frequency (IdF) model commonly used for rainfall analysis. The proposed model allows QdF curves for a given basin to be estimated while using a minimum number of parameters. This model is called ‘converging’ model because of the observed convergence of distributions towards small return periods. A local (at-site) model and a regional approach are developed. The regional approach uses classical concepts of regional hydrologic frequency analysis (index-flood (IF) method) and can be used for basins where no streamflow data is available. Results from 158 catchments located in the provinces of Quebec and Ontario (Canada) are used to illustrate the method.

Introduction

An inadequate understanding of the probabilistic behaviour of extreme flows when designing a hydraulic structure may have significant economical impacts on the project. For this reason a large number of studies have focused on the reduction of uncertainties associated with flood quantile estimates.

When streamflow data at a given site are non-existent or insufficient for a reliable estimation of flood quantiles, regional flood frequency analysis (RFFA) can be used. It usually involves two steps: the identification of groups of hydrologically homogeneous basins and the application of a regional estimation method within the identified homogeneous region. Several approaches have been proposed in the literature for the delineation of homogeneous regions (Wiltshire, 1986, Cavadias, 1990, Burn, 1997, Burn, 1990a, Burn, 1990b, Zrinji and Burn, 1994, Ouarda et al., 2001) and for regional estimation (Dalrymple, 1960, Hosking et al., 1985a, Fill and Stedinger, 1998, Pandey and Nguyen, 1999). Cunnane (1988) provided a general review on the topic of flood frequency analysis. More recently a detailed theoretical and numerical comparison of the various regional estimation methodologies was presented by GREHYS, 1996a, GREHYS, 1996b.

The scientific literature abounds with studies on RFFA. However, most of these studies describe a flood event only by its instantaneous peak or its maximum daily flow. When designing a hydraulic structure or mapping a flood plain, information about flood peaks is essential but insufficient. Indeed, flood severity is not only defined by the flood's peak value but also by its volume and duration. Only a limited number of researchers have attempted to address this topic. Two different approaches can be utilised: the peak–volume analysis and the flood-duration–frequency (QdF) analysis.

The peak–volume analysis has been initiated by Ashkar (1980). For each observed flood, a starting and an ending date are defined and the flood peak, volume and duration are determined and analysed as random variables. Ouarda et al. (2000) proposed a regional flood frequency procedure based on canonical correlation analysis which allows the joint estimation of flood peaks and volumes. It is important to mention that in the peak–volume analysis approach the determination of the flood event starting and ending dates contains a part of subjectivity and must be done with extreme care.

The second approach for completely describing a flood event is the QdF analysis. The main difference with the peak–volume approach is that the duration is not considered as a random variable but as a fixed parameter. QdF analysis is similar to the intensity-duration–frequency (IdF) analysis commonly utilised for rainfall: averaged discharges are computed over different fixed durations d. Then for each duration, a frequency distribution of maximum discharges is analysed. Unlike the IdF analysis for rainfall QdF analysis remains under-utilised despite its strong potential. A limited body of literature dealt with this type of analysis (NERC, 1975, Sherwood, 1994, Balocki and Burges, 1994, Galéa and Prudhomme, 1997). Recently Javelle et al. (1999) proposed a ‘converging’ QdF model based on the assumption of a convergence between the different discharge distributions for small return periods. This formulation has been successfully tested for basins located in France (Javelle et al., 2000), Martinique (Meunier, 2001) and Canada (Javelle, 2001).

The main objective of the research reported in this paper is to present a regional QdF approach combining the local QdF formulation presented by Javelle et al. (1999) and the index-flood (IF) method (Dalrymple, 1960) commonly used in RFFA. The paper is organised as follows: Section 2 presents the local QdF curves formulation and the methodology developed for their estimation. Section 3 generalises the IF method to the QdF approach. Section 4 provides a description of the case study and presents the results of the application of the local and regional QdF models. General conclusions are presented in Section 5.

Section snippets

Variable extraction and sampling

An instantaneous streamflow time series can be used to characterise each observed flood by its instantaneous peak flow (Qmax) and by the maximum values of mean streamflows (Qd1, Qd2, …,QdN) for given durations (d1, d2, …,dN).

Sampling the maximum mean streamflow Qd for a given duration d over the whole time series can be carried out using the following approach: a moving average with a window length d is first computed over the whole instantaneous streamflow time series providing a new time

Brief review of the IF method

The IF method proposed by Dalrymple (1960) was one of the first approaches to regional flood estimation. The main assumption is that floods at different sites within a region are identically distributed except for a scale factor which is a function of the physiographical basin characteristics. Usually the catchment area is the most important factor for explaining flood magnitudes. This method consists in identifying geographically homogeneous regions and determining a regional standardised

Case study

The case study basins are those studied by GREHYS, 1996a, GREHYS, 1996b and are located in the provinces of Quebec and Ontario Canada. Data for 189 streamflow gauging stations (75 in Quebec and 114 in Ontario) each with 20 years or more of data were originally considered but 31 stations were later excluded for various reasons (controlled regime, non-homogeneity, trends, jumps, lake effect, etc.). 158 stations fulfilled the final requirements for inclusion in the case study. The available

Conclusions

The research reported in this paper investigates local and regional QdF methodologies. The local formulation of QdF curves has been presented by Javelle et al. (1999) and is based on two simple assumptions: the affinity of the Q(d,T) distributions (as a function of T) and the hyperbolic decay of Q(d,T) (as a function of d). The modelling introduces a new parameter Δ which controls the hyperbolic decay function which is directly related to the basin's flood dynamics. This model has been applied

Acknowledgements

The authors wish to express their appreciation to the reviewers for their useful comments and suggestions. The financial support provided by Cemagref and CNES for the PhD research of P. Javelle is gratefully acknowledged. The authors also thank for its support the Natural Sciences and Engineering Research Council of Canada (NSERC) Hydro-Quebec and Alcan through the Statistical Hydrology Chair. Environment Canada is also acknowledged for providing the data for the case study. The scientific

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