Channel concavity controls plan-form complexity of branching drainage networks

Abstract. The plan-form geometry of branching drainage networks controls the topography of landscapes as well as 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 plan-form complexity of natural drainage networks. An analytic model based on geomorphic scaling relations and optimal channel network simulations employing an energy minimization principle reveal that landscapes with low concavity channels attain stable plan-form configuration only through simple geometry. In contrast, landscapes with high-concavity channels achieve plan-form stability with various degrees of network complexity, including extremely complex geometries. Landscape evolution simulations demonstrate that the concavity index and its effect on the multiplicity of available geometries control the tendency of networks to preserve the legacy of former environmental 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 plan-form geometry of landscapes.