Comparison of catchment grouping methods for flow duration curve estimation at ungauged sites in France

Abstract

Abstract. The study aims at estimating flow duration curves (FDC) at ungauged sites in France and quantifying the associated uncertainties using a large dataset of 1080 FDCs. The interpolation procedure focuses here on 15 percentiles standardised by the mean annual flow, which is supposed to be known at each site. In particular, this paper discusses the relevance of different catchments grouping procedures on percentiles estimation by regional regression models. First, five parsimonious FDC parametric models were tested to approximate FDCs at gauged sites. The results show that the model based on Empirical Orthogonal Functions (EOF) expansion outperforms the other ones. In this model each FDC is interpreted as a linear combination of regional amplitude functions with weights – the parameters of the model – varying in space. Here, only one amplitude function was found sufficient to fit well most of the observed curves. Thus the considered model requires only two parameters to be estimated at ungauged locations. Second, homogeneous regions were derived according to hydrological response on one hand, and geological, climatic and topographic characteristics on the other hand. Hydrological similarity was assessed through two simple indicators: the concavity index (IC) that represents the shape of the standardized FDC and the seasonality ratio (SR) which is the ratio of summer and winter median flows. These variables were used as homogeneity criteria in three different methods for grouping catchments: (i) according to their membership in one of an a priori French classification into Hydro-Eco-Regions (HERs), (ii) by applying a regression tree clustering and (iii) by using hydrological neighbourhood obtained by canonical correlation analysis. Finally, regression models between physiographic and/or climatic variables and the two parameters of the EOF model were derived considering all the data and thereafter for each group obtained through the tested grouping techniques. Results on percentiles estimation in cross validation show a significant benefit to form homogeneous regions before developing regressions, particularly when grouping methods use hydrogeological information.