Size relationships of water discharge in rivers: scaling of discharge with catchment area, main‐stem length and precipitation

AbstractScaling relationships between water turnover or discharge and water system size may help to reveal and understand general patterns and processes in regional and global hydrological systems. In the present study, we derived global as well as climate‐specific scaling relationships between average or maximum river discharge and catchment area, main‐stem length and precipitation, based on data from 663 monitoring stations worldwide. Data were retrieved from a Global Runoff Data Centre (GRDC) database. The scaling relationships were established with ordinary least square (OLS) and standard major axis (SMA) regressions. The focus was on the SMA regressions because this method provides better estimates of the slope.The overall empirical regressions derived were highly significant (p < 0.01). Average discharge (Q) and maximum discharge (Qmax) scaled to catchment area (A) with SMA slopes of 1.23 (r2 = 0.40) and 0.99 (r2 = 0.41), respectively. Average discharge (Q) scaled to length (L) with a slope of 2.16 (r2 = 0.40), while catchment area (A) scaled to main‐stem length (L) with a slope of 1.76 (r2 = 0.91). The addition of precipitation (P), yielding a multiple regression of discharge versus catchment area and precipitation, improved the explained variability to r2 = 0.56 and r2 = 0.52 for average and maximum discharge, respectively. Slopes of climate zone‐specific regressions tended to be similar to the slopes of the overall relationships. The uncertainties of the regressions were discussed and, where possible, compared to regressions derived in other studies. Copyright © 2013 John Wiley & Sons, Ltd.