In the United States, estimation of flood frequency quantiles at ungauged locations has been largely based on regional regression techniques that relate measurable catchment descriptors to flood quantiles. More recently, spatial interpolation techniques of point data have been shown to be effective for predicting streamflow statistics (i.e., flood flows and low-flow indices) in ungauged catchments. Literature reports successful applications of two techniques, canonical kriging, CK (or physiographical-space-based interpolation, PSBI), and topological kriging, TK (or top-kriging). CK performs the spatial interpolation of the streamflow statistic of interest in the two-dimensional space of catchment descriptors. TK predicts the streamflow statistic along river networks taking both the catchment area and nested nature of catchments into account. It is of interest to understand how these spatial interpolation methods compare with generalized least squares (GLS) regression, one of the most common approaches to estimate flood quantiles at ungauged locations. By means of a leave-one-out cross-validation procedure, the performance of CK and TK was compared to GLS regression equations developed for the prediction of 10, 50, 100 and 500 yr floods for 61 streamgauges in the southeast United States. TK substantially outperforms GLS and CK for the study area, particularly for large catchments. The performance of TK over GLS highlights an important distinction between the treatments of spatial correlation when using regression-based or spatial interpolation methods to estimate flood quantiles at ungauged locations. The analysis also shows that coupling TK with CK slightly improves the performance of TK; however, the improvement is marginal when compared to the improvement in performance over GLS.

An empirical period-of-record flow–duration curve (FDC) describes the percentage of time (duration) in which a given streamflow was equaled or exceeded over an historical period of time. In many practical applications one has to construct FDCs in basins that are ungauged or where very few observations are available. We present an application strategy of top-kriging, which makes the geostatistical procedure capable of predicting FDCs in ungauged catchments. Previous applications of top-kriging mainly focused on the prediction of point streamflow indices (e.g. flood quantiles, low-flow indices, etc.); here the procedure is used to predict the entire curve in ungauged sites as a weighted average of standardised empirical FDCs through the traditional linear-weighting scheme of kriging methods. In particular, we propose to standardise empirical FDCs by a reference index-flow value (i.e. mean annual flow, or mean annual precipitation × the drainage area) and to compute the overall negative deviation of the curves from this reference value. We then propose to use these values, which we term total negative deviation (TND), for expressing the hydrological similarity between catchments and for deriving the geostatistical weights. We focus on the prediction of FDCs for 18 unregulated catchments located in central Italy, and we quantify the accuracy of the proposed technique under various operational conditions through an extensive cross-validation and sensitivity analysis. The cross-validation points out that top-kriging is a reliable approach for predicting FDCs with Nash–Sutcliffe efficiency measures ranging from 0.85 to 0.96 (depending on the model settings) very low biases over the entire duration range, and an enhanced representation of the low-flow regime relative to other regionalisation models that were recently developed for the same study region.

Our study develops and tests a geostatistical technique for locally enhancing macro-scale rainfall–runoff simulations on the basis of observed streamflow data that were not used in calibration. We consider Tyrol (Austria and Italy) and two different types of daily streamflow data: macro-scale rainfall–runoff simulations at 11 prediction nodes and observations at 46 gauged catchments. The technique consists of three main steps: (1) period-of-record flow–duration curves (FDCs) are geostatistically predicted at target ungauged basins, for which macro-scale model runs are available; (2) residuals between geostatistically predicted FDCs and FDCs constructed from simulated streamflow series are computed; (3) the relationship between duration and residuals is used for enhancing simulated time series at target basins. We apply the technique in cross-validation to 11 gauged catchments, for which simulated and observed streamflow series are available over the period 1980–2010. Our results show that (1) the procedure can significantly enhance macro-scale simulations (regional LNSE increases from nearly zero to ≈0.7) and (2) improvements are significant for low gauging network densities (i.e. 1 gauge per 2000 km ² ).

Flow–duration curves (FDCs) are essential to support decisions on water resources management, and their regionalization is fundamental for the assessment of ungauged basins. In comparison with calibrated rainfall–runoff models, statistical methods provide data-driven estimates representing a useful benchmark. The objective of this work is the interpolation of FDCs from ~500 discharge gauging stations in the Danube. To this aim we use total negative deviation top-kriging (TNDTK), as multi-regression models are shown to be unsuitable for representing FDCs across all durations and sites. TNDTK shows a high accuracy for the entire Danube region, with overall Nash-Sutcliffe efficiency values computed in a leave-p-out cross-validation scheme (p equal to one site, one-third and half of the sites), all above 0.88. A reliability measure based on kriging variance is attached to each interpolated FDC at ~4000 prediction nodes. The GIS layer of regionalized FDCs is made available for broader use in the region.