Least-squares prediction of runoff over ungauged basins

Abstract

One of the major concerns of hydrology is to quantify the hydrological cycle of basins e.g. by means of modeling the hydrological interactions. However, current hydrological models are far from perfect. The main challenge of modeling is the poor spatio-temporal coverage of in situ databases, which are declining steadily over the past few decades. Among the hydrological interactions, river runoff is of great importance, as it represents a catchment’s behaviour. In order to deal with the growing lack of in situ runoff data, we estimate river runoff of ungauged basins by least-squares prediction. In this method, runoff is predicted by mapping the runoff characteristics of gauged basins into ungauged ones through statistical correlations of past data. We follow two scenarios to form the covariance matrices out of available past in situ river runoff: (1) at the signal level, and (2) at the residual level after subtracting monthly mean values. Our validation shows that both scenarios are able to capture runoff values with relative errors less than 15% for 80% of the 25 catchments under study. We obtain Nash-Sutcliffe coefficients of over 0.4 for about 90% and of over 0.75 for about 50% of the catchments under study.We are thus able to avoid the complexity of hydrological modeling and the challenges (e.g. uncertainty) of spaceborne approaches for runoff estimation over ungauged basins.