Assessment of structural sediment connectivity within catchments: insights from graph theory

To describe the sedimentary signal delivered at catchment outlets, many authors now refer to the concept of connectivity. In this framework, the sedimentary signal is seen as an emergent organization of local links and interactions. The challenge is thus to open the black boxes that remain within a sediment cascade, which requires both accurate geomorphic investigations in the field (reconstruction of sequences of geomorphic evolution, description of sediment pathways) and the development of tools dedicated to sediment cascade modeling. More precisely, the development of tools devoted to the study of connectivity in geomorphology is still in progress, although graph theory offers promising perspectives (Heckmann and Schwanghart, 2013). In this paper, graph theory is applied to abstract the network structure of sediment cascades, keeping only the nodes (sediment sources, sediment stores, outlet) and links (linkage by a transportation agent), represented as vertices and edges. From the description of the assemblages of sedimentary flows, we provide three main indices to explore how small-scale processes may result in significant broad-scale geomorphic patterns. The main hypothesis guiding this work is that the network structure dictates how sediment inputs from various sources interact at tributary junctions and finally at the outlet of a cascading system. First, we use the flow index to assess the potential contribution of each node to the sediment delivery at the outlet. Second, we measure the influence of each node regarding how it is accessible from both sediment sources and the outlet (using the Shimbel index). Third, we propose a new connectivity index named Network Structural Connectivity index (NSC) revealing whether the potential contribution of a node is lower or higher than expected from its location within the network. These indices are first computed for a conceptual sediment cascade network and then applied to a catchment located in the southern French Alps. We demonstrate that this index may be used to simulate sediment transfer and help in identifying the hotspots of geomorphic change. In the present case, we try to predict how a sediment cascade may be impacted by an edge disruption or a reconnection.