Predicting annual and long-term flow-duration curves in ungauged basins

The construction of flow-duration curves is a fundamental task for several activities related to water resources management. The scarcity of observed streamflow data is a diffuse problem in the real world, and flow-duration curves often need to be constructed for ungauged basins. We address this problem by regionalising the stochastic index-flow model of flow-duration curves proposed by Castellarin et al. [Castellarin A, Vogel RM, Brath A. A stochastic index flow model of flow-duration curves. Water Resour Res 2004;40:W03104. doi:10.1029/2003WR002524]. The index-flow model differs from any other stochastic model of flow-duration curves proposed in the literature because it can be used for deriving long-term as well as annual flow-duration curves. The former are constructed on the basis of several years of streamflow data, whereas the latter refer to a given water or calendar year (a typical hydrologic year or a particularly wet or dry year). We apply an extensive cross-validation procedure to quantify the uncertainty of the proposed regional model and to compare it with the uncertainty of traditional regional models of flow-duration curves proposed in the literature. The results of the study indicate that the regional index-flow model is as reliable as or more reliable than traditional regional models for estimating long-term flow-duration curves. Also, the proposed model is more versatile than previous regional models as it can be used for estimating long-term and annual flow-duration curves and for reproducing the variance of annual flow-duration curves.