Power law distribution of discharge in ideal networks

摘要

Data for several river networks show algebraically decaying distribution functions for the mean annual discharge and the dissipation rate (Rodríguez‐Iturbe et al., 1992). We derive a relation between the exponent a in the integrated mean annual discharge distributionP(Q≥q) ∼q−αand the topological dimensionDtof the network, α = 1 − 1/Dt. Using the experimentally determined valueDt≈ 1.8 (Tarboton et al., 1988) we find α ≈ 0.45, in good agreement with the data of (Rodríguez‐Iturbe et al., 1992). For the random model (Shreve, 1967, 1969; Smart and Werner, 1974) we fin