POWER-LAW DISTRIBUTION OF DISCHARGE IN IDEAL NETWORKS

Data for several river networks show algebraically decaying distribution functions for the mean annual discharge and the dissipation rate (Rodriguez-Iturbe et al., 1992). We derived relation between the exponent alpha in the integrated mean annual discharge distribution P(Q greater than or equal to q) similar to q(-alpha) and the topological dimension D-t of the network, alpha = 1 - 1/D-t. Using the experimentally determined value D-t approximate to 1.8 (Tarboton et al., 1988) we find alpha approximate to 0.45, in good agreement with the data of (Rodriguez-Iturbe et al., 1992). For the random model (Shreve, 1967, 1969; Smart and Werner, 1974) we find an exponent of 1/2.