Channel concavity controls planform complexity of branching drainage networks

Abstract

The planform geometry of branching drainage networks controls the topography of landscapes and their geomorphic, hydrologic, and ecologic functionality. The complexity of networks' geometry shows significant variability, from simple, straight channels that flow along the regional topographic gradient to intricate, tortuous flow patterns. This variability in complexity presents an enigma, as models show that it emerges independently of any heterogeneity in the environmental conditions. We propose to quantify networks' complexity based on the distribution of lengthwise asymmetry between paired flow pathways that diverge from a divide and rejoin at a junction. Using the lengthwise asymmetry definition, we show that the channel concavity index, describing downstream changes in channel slope, has a primary control on the planform complexity of natural drainage networks. An analytic model and optimal channel network simulations employing an energy minimization principle reveal that landscapes with low concavity channels attain planform stability only with simple network geometry. In contrast, landscapes with high concavity channels can achieve planform stability with various configurations, displaying different degrees of network complexity, including extremely complex geometries. Consequently, landscapes with high concavity index channels can preserve the legacy of former environmental conditions, whereas landscapes with low concavity index channels reorganize in response to environmental changes, erasing the former conditions. Consistent with previous findings showing that channel concavity correlates with climate aridity, we find a significant empirical correlation between aridity and network complexity, suggesting a climatic signature embedded in the large-scale planform geometry of landscapes.