Characterizing the Responses of Channel Networks to Constraints using Deviations from Planform Self-Similarity

A substantial body of literature has demonstrated that the planform features of channel networks are approximately self-similar when the networks developed without strong topographic or geologic constraints. It has also been shown that this self-similarity can be reproduced by a broad class of river basin evolution models including models based on stream power. In this research, attention is turned toward the morphology of channel networks that have developed under significant constraints. Such networks are often qualitatively described as parallel, pinnate, rectangular, or trellis, depending on their appearance and underlying constraints, but little quantitative understanding is available to distinguish these networks from unconstrained dendritic networks. We hypothesize that such network types represent distinct deviations from the planform self-similarity of dendritic networks that can be quantified with relatively few measures. Three measures are evaluated: drainage area increments along channels (which is a measure of basin shape), the irregularity of channel paths, and the angles formed by merging channels. These measures are normalized so that they are constant across scales if self-similarity occurs. Both parallel and pinnate networks are found to exhibit anisotropic scaling, which appears to be consistent with self-affinity. Junction angles increase with scale for parallel networks, while they decrease for pinnate networks. Rectangular and trellis networks are both roughly self-similar like dendritic networks, but rectangular networks have more irregular stream courses across all scales, and trellis networks have distinctively low rates of area accumulation across all scales. Together these results allow for an objective classification of drainage networks that is successful in 44 of the 50 networks tested. They also describe the quantitative responses of natural channel networks to topographic and geologic constraints and represent a series of possible tests to evaluate and potentially improve existing river basin evolution models.