Controls of the Topological Connectivity on the Structural and Functional Complexity of River Networks.

Catchments are complex systems containing channel networks and hillslopes. Channel networks interact with hillslopes and are pathways for transporting water, sediment, and nutrients. Understanding the branching and flux transport patterns of channel networks is critical for predicting the response of catchments to external forcing such as climate and tectonics. However, factors creating complexities in catchments are not fully understood. Here, we propose a new framework based on multiscale entropy approach to evaluate complexity of catchments using two different representations of channel networks. First, we investigate the structural complexity using the width‐function, which characterizes the spatial arrangement of channels. Second, we utilize the incremental area‐function along the main channel to study the functional complexity that captures the patterns of transport of fluxes. Our analysis reveals stronger controls of topological connectivity on the functional complexity than on structural complexity, indicating unchannelized surface (hillslope) contribution to the increase of heterogeneity in transport processes. Plain Language Summary: Catchments are complex natural landscape systems that contain hillslopes and channel networks. Understanding and quantifying features and processes that result in catchment complexity is important for predicting their response to changing human and climatic conditions. In this paper, we use an entropy‐based approach to explore the role of channel network and hillslope toward the contribution to catchment's complexity. Based on 40 natural catchments with minimum human impact across the United States in different climatic and geologic conditions, our results show that hillslopes add significant complexity to the catchments and suggest the amount of hillslope information one needs to account for in accurate predictive modeling of hydrologic processes at the catchment scale. Key Points: Topology controls structural and functional complexityFunctional complexity is higher than structural complexity due to contribution from hillslope processesScale of peak difference between the impact of topology on functional and structural complexity indicates the average hillslope length scale [ABSTRACT FROM AUTHOR]