Comparison with other models for regions. We compare our modelled values with available observations for individual rivers (see Supplementary Table 7 and Supplementary Fig. 4 ) and with the models of Lebreton et al. 9 and Jambeck et al. 8 for regions (see Supplementary Tables 8 , 9 ). R P 2 , R NSE 2 and ME are the Pearson’s coefficient of determination (fraction, 0–1), the Nash–Sutcliffe efficiency (fraction, 0–1) and the Model Error (%), respectively. R P 2 indicates the proportion of the variance in observations that can be explained by the model. R NSE 2 shows how well the observed and modelled values fit the line of 1:1. ME indicates the difference between the observed and modelled values. These statistical indicators are calculated according to Moriasi et al. 80 .