The paper treats the problem of interpolating annual runoff from regul
ar streamflow measurements in a regional scale applying objective meth
ods. These methods are adapted to point processes like temperature and
precipitation. Modifications are needed to account for the fact that
streamflow is an integrated process following the hierarchical structu
re of river systems. The most straightforward method is therefore to r
elate the interpolation to the existing river network. For theoretical
reasons it is preferable to interpolate the lateral inflow rather tha
n the flow in the river itself. Procedures for the interpolation with
the different approaches are developed and discussed. Special attentio
n is put on the question how the equation of continuity can be satisfi
ed. The Laagen drainage basin in southern Norway is used as a test are
a. The data consist of annual observations of streamflow and digital m
ap information on river networks and drainage basin boundaries.