INVARIANCE AND SCALING PROPERTIES IN THE DISTRIBUTIONS OF CONTRIBUTING AREA AND ENERGY IN DRAINAGE BASINS

The cumulative probability distributions for stream order, stream leng th, contributing area, and energy dissipation per unit length of chann el are derived, for an ordered drainage system, from Horton's laws of network composition. It is shown how these distributions can be relate d to the fractal nature of single rivers and river networks. Finally, it is shown that the structure proposed here for these probability dis tributions is able to fit the observed frequency distributions, and th eir deviations from straight lines in a log-log plot.