Least-squares prediction of runoff

Abstract

When modelling hydrological cycles, the runoff of a drainage basin is an important variable, being an output from hydrological models and an input to many hydrological interactions as a quantity used for validation and calibration. In this context, the decrease of the availability of in situ runoff measurements that has been observed over the last years poses a challenge which this study aims to tackle with the methods of least-squares prediction. This research uses the spatial correlations between in situ runoff measurements generated in a training period to predict values for a validation period during which one of the catchments is assumed ungauged. Different methods include the usage of covariance matrices, which are formed 1. on the signal level, or 2. separately for each of the 12 months of the year, or 3. after the reduction of the monthly mean, or 4. after the reduction of the long-term mean for prediction purposes. For validation, the Nash-Sutcliffe model efficiency coefficient, correlation, and RMSE are computed. The impacts of variations in the length of the training period and of the choice of catchments whose observed measurements are used in the prediction process are analysed. The errors then undergo a spectral analysis to test, which prediction methods are able to capture cyclostationary behaviour best. Most of the methods provide viable results, although the prediction based on covariance matrices generated out of residuals is slightly better than the other methods in a vast majority of configurations. After a training period of 20 years of simultaneous data and with a selection of three catchments used in each prediction process, this method can reach a Nash-Sutcliffe coefficient of over 0.4 for about 90% and of over 0.75 for about 50% of the 25 analysed catchments, although viable results can already be achieved with much shorter training periods of one to three years, depending on the predicted catchment.