The study presents an approach to depict the two first order moments of runoff as a function of area (and thus on a map). The focal point is the mapping of the statistical properties of runoff q=q(A,D) in space (area A) and time (time interval D). The problem is divided into two steps. Firstly the first order moment (the long term mean value) is analysed and mapped applying an interpolation procedure for river runoff. In a second step a simple random model for the river runoff process is proposed for the instantaneous point runoff normalised with respect to the long term mean. From this model theoretical expressions for the time-space variance-covariance of the inflow to the river network are developed, which then is used to predict how the second order moment vary along rivers from headwaters to the mouth. The observation data are handled in the frame of a hydrological information system HydroDem, which allows displaying the results either in the form of area dependence of moments along the river branches to the basin outlet or as a map of the variation of the moments across the basin space. The findings are demonstrated on the example of the Moselle drainage basin (French part).