An approach to estimate nonparametric flow duration curves in ungauged basins

Abstract

A distance‐based regionalization model is developed for the estimation of dimensionless flow duration curves (FDC) in sites with no or limited available data. The curves are dimensionless because they are preliminarily normalized by an index value (e.g., the mean annual runoff). The model aims at representing the FDC as a nonparametric object rather than providing a parametric representation and trying to relate the parameter values to basin descriptors. The regional approach considers the (dis)similarity between all possible pairs of curves and uses distance measures that can be related to basin descriptors, taken among geographic, geomorphologic, and climatic parameters. The (dis)similarity between curves is computed using a predefined metric based on a linear norm and produces a distance matrix. This matrix is then related, by means of linear regression models, to analogous matrices composed of the difference between all possible values of each descriptor within the set of basins. After identification of significant descriptors, a cluster analysis is applied so that the basins can be grouped together. Each region is supposed to be characterized by a single dimensionless flow duration curve. The procedure is applied to 95 basins located in northwestern Italy and Switzerland. The performance in the regional estimation is assessed by means of a cross‐validation procedure through comparison with “standard” parametric regional approaches based on two‐ and three‐parameter models. In most of the cases, the distance‐based model produces better estimates of the flow duration curves using only few catchment descriptors.