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

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 assumed to be known at each site. In particular, this paper discusses the impact of different catchment grouping procedures on the estimation of percentiles by regional regression models.

In a first step, five parsimonious FDC parametric models are tested to approximate FDCs at gauged sites. The results show that the model based on the expansion of Empirical Orthogonal Functions (EOF) outperforms the other tested models. In the EOF model, each FDC is interpreted as a linear combination of regional amplitude functions with spatially variable weighting factors corresponding to the parameters of the model. In this approach, only one amplitude function is required to obtain a satisfactory fit with most of the observed curves. Thus, the considered model requires only two parameters to be applicable at ungauged locations.

Secondly, homogeneous regions are derived according to hydrological response, on the one hand, and geological, climatic and topographic characteristics on the other hand. Hydrological similarity is assessed through two simple indicators: the concavity index (IC) representing the shape of the dimensionless FDC and the seasonality ratio (SR), which is the ratio of summer and winter median flows. These variables are used as homogeneity criteria in three different methods for grouping catchments: (i) according to an a priori classification of French Hydro-EcoRegions (HERs), (ii) by applying regression tree clustering and (iii) by using neighbourhoods obtained by canonical correlation analysis.

Finally, considering all the data, and subsequently for each group obtained through the tested grouping techniques, we derive regression models between physiographic and/or climatic variables and the two parameters of the EOF model. Results on percentile estimation in cross validation show that a significant benefit is obtained by defining homogeneous regions before developing regressions, particularly when grouping methods make use of hydrogeological information.