This presentation aims to propose a methodology to model spatial variation for variables supported on directed tree as hydrographic networks. The bases of geostatistics were revisited from order 2 stationarity to random field simulation process. We were able to characterize the underlying probabilistic model by introducing specific assumptions and redefining the main methods of geostatistics. We presented modifications on metrics, proper variogram estimates and ad-hoc drift model. We had particulary to define the covariance model on the upstream-downstream relationship and to introduce a conditionnal independence to be sure of the positive-definiteness of covariance matrix. Case study is presenting results for the sampled hydraulic characteristic width along an artificial stream network on small cultivated watershed in the south of France. Monte-carlo test on stationarity were developped, for a part from a specific multi-gaussian field simulation based on sequential conditionnal simulations between parts of the tree (rivers). A drift model was then fitted and empirically tested. These first results allows us to extend the concept of spatial structure analysis to a directed tree structure but it shows that to extend geostatistics to support with different topologies requires to be very carefull on model definitions and assumptions. In case of interpolation, which has not been explored in this study, we have to care on additive difficulty : it would be quite difficult to determine kriging system because some pairs covariance will not come simply from the upstream-downstream relationship.