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The study presents an approach to represent the two first order moments of temporal runoff variability as a function of catchment area and aggregation time interval, and to map them in space. The problem is divided into two steps. First, the first order moment (the long term 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 analytical 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 varies along rivers from headwaters to the mouth. The observation data are handled by a hydrological information system, which allows to display 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. The findings are demonstrated by the example of the Moselle drainage basin (French part).