Regional prediction of flow-duration curves using a three-dimensional kriging

The relationship between magnitude and frequency of daily streamflows over a number of years for a given basin is often termed long-term Flow-Duration Curve (FDC). This analysis addresses the problem of predicting FDCs in ungauged basins by means of a three-dimensional (3D) kriging interpolation of empirical FDCs. A three-dimensional $xyz$ space is defined to perform the interpolation, where $x$ and $y$ are functions of physiographic and climatic catchment descriptors, while $z$ represents the streamflow duration in terms of standard-normal variate. The 3D interpolation technique is applied to several catchments located in two broad geographical regions of Northern (Alpine catchments) and Central (Apenninic catchments) Italy, for which several geomorphological and climatic descriptors are available. An extensive cross-validation procedure is used to quantify the accuracy of the proposed technique in both case studies, and to compare it to traditional regionalization procedures. The cross-validation points out that 3D kriging is a reliable and robust approach, which performs as well as or better than traditional regional models. In particular the approach significantly outperforms conventional approaches for the prediction of low-flows (i.e. streamflows associated with high durations) in ungauged basins.