Parallel Drainage Patterns and the Origin of Scaling in River Networks

We investigate the formation of parallel drainage patterns in river networks and implications for the origin of network scaling, using simulations of an erosion model. As the slope of initial conditions is increased, drainage patterns transition from dendritic to parallel, consistent with the role of gradient in natural drainage patterns. Several features of natural parallel networks, such as considerable variation in basin shape between nearby basins, form spontaneously in the model. As initial slope is increased and networks become more parallel, the scaling of network properties shows increasing deviation from simple power laws. This results from a scale-dependent effect of initial slope on network structure, reinforced by parallel network topology. Since model dynamics do not guarantee power-law scaling, we suggest that a combination of dynamics, initial conditions, and perturbations over time is necessary to explain Hack's law and other river network scaling relations.