The long-term mean value of runoff is the basic descriptor of available water resources. This paper focuses on the accuracy that can be achieved when mapping this variable across space and along main rivers for a given stream gauging network. Three stochastic interpolation schemes for estimating average annual runoff across space are evaluated and compared. Two of the schemes firstly interpolate runoff to a regular grid net and then integrate the grid values along rivers. One of these schemes includes a constraint to account for the lateral water balance along the rivers. The third scheme interpolates runoff directly to points along rivers. A drainage basin in China with 20 gauging sites is used as a test area. In general, all three approaches reproduce the sample discharges along rivers with postdiction errors along main river branches around 10%. Using more objective cross-validation results, it was found that the two schemes based on basin integration, and especially the one with a constraint, performed significantly better than the one with direct interpolation to points along rivers. The analysis did not allow identification of possible influence of surface water use.