| Abstract: | The notion of randomness has been extensively applied to topological (nondimensional) properties of drainage networks. The spatial (dimensional) organization of five fluvial hierarchies is examined herein through the application of quadrat analysis to random and clustered spatial probability models. The Poisson, Polya-Aeppli, and negative binomial models are compared with point-pattern distributions of river junction location for three basins in Indiana and two fossil systems on an erosion surface in semiarid Australia. The negative binomial model best fits all five networks, suggesting that the branching behavior of fluvial systems follows the mathematical precepts leading to clusteredness of junctions. The degree to which the Polya-Aeppli model fits the data suggests the imposition of a temporally limited set of environmental conditions optimally suited for network growth. Only for the two fossil systems does the Poisson model agree. It is speculated that the effect of prolonged subaerial erosion may be to shift a clustered distribution towards the random state as the surface approaches a pediplained state. |
