An approach for estimating mean monthly runoff at ungauged sites is presented. Special attention is paid to include effects of local features such as karst and river regulation by reservoirs. The developments introduced conform with hydrostochastic concepts in that simple physical and statistical laws are inherent in the methods used for mapping. Hence, the approach developed here is consistent with the water balance along the river network. The suggested method combines an application of empirical orthogonal functions and an adapted stochastic interpolation scheme to match the runoff data. The observation data are handled in the frame of a hydrological information system. This allows the display of results either in the form of the change in a statistical parameter along the river branches towards the basin outlet or as a map of the variation of the parameters across the basin or region space. The approach is demonstrated for France.