This paper shows that geostatistical modelling can be extended to spatial supports such as directed trees and applied to variables spatially structured along a river network. Specific assumptions were necessary and main methods were redefined introducing modifications on metrics, proper variogram estimates and ad hoc drift models. We also proposed a model-based simulation procedure to generate random functions on directed trees. A case study on fluvisol delineation for the Hérault river (South of France) was analyzed. Clear spatial structures were observed and modelled using variogram based on upstreamdownstream distance along a hydrographic network. A drift was also modelled as a multiplicative term affecting the fluvisol width versus the cumulated length of the upstream network. The significance of the drift was then assessed conditionally to the former spatial variogram using Monte-Carlo simulations of the spatial observed process on the river network.