Correlation and covariance of runoff

The application of objective methods for interpolation of stochastic fields is based on the assumption of homogeneity with respect to the correlation function, i.e. only the relative distance between two points is of importance. This is not the case for runoff data which is demonstrated in this paper. Taking into consideration the structure of the river network and the related drainage basin supporting areas theoretical expressions are derived for the correlation function for flow along a river from its outlet and upstream. The results are exact for a rectangular drainage basin. For more complex basin geometry a grid approximation is suggested. The found relations are demonstrated on a real world example with a good agreement between the theoretically calculated correlation functions and empirical data.