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Let's get connected: A new graph theory‐based approach and toolbox for understanding braided river morphodynamics

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Our understanding of braided river morphodynamics has improved significantly in recent years, however, there are still large knowledge gaps relating to both long‐term and event‐based change in braided river morphologies. Furthermore, we still lack methods that can take full advantage of the increasing availability of remotely sensed datasets that are well suited to braided river research. Network analysis based on graph theory, the mathematics of networks, offers a largely unexplored toolbox that can be applied to remotely sensed data to quantify the structure and function of braided rivers across nearly the full range of spatiotemporal scales relevant to braided river evolution. In this article, important commonalities between braided rivers and other types of complex network are described, providing a compelling argument for the wider uptake of complex network analysis methods in the study of braided rivers. We provide an overview of the extraction of graph representations of braided river networks from remotely sensed data and detail a suite of metrics for quantitative analysis of these networks. Application of these metrics as new tools for multiscale characterization of braided river planforms that improve upon traditional, spatially averaged approaches is discussed and potential approaches to network‐based analysis of braided river dynamics are proposed, drawing on a range of different concepts from braided river research and other network sciences. Finally, the potential for using graph theory metrics to validate numerical models of braided rivers is discussed. This article is categorized under: Science of Water > Methods
Plots of normalized eBC density functions for graphs derived at times of low, medium, and high discharge on a medium sized braided river. Note that the y axes exceed 1 as the total integral of the bars sums to 1, with the plots showing the relative frequency of eBC in each bin
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Maps of unweighted, normalized edge betweenness centrality and bifurcation angle (°) for reach A (see Figure ) on two dates separated by a series of different flood events, including one bankfull event, on the river Tagliamento. Total braiding index (BIT; Egozi & Ashmore, ) values are 3.3 and 2.9 for the May 19, 2011 and October 01, 2011, respectively. Graphs for this analysis were derived from Landsat 5 TM scenes. Both scenes were captured at low stage and flow is from north to south
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Maps of unweighted, normalized edge betweenness centrality and bifurcation angle (°) between the downstream channel centerlines at each node for three reaches, A–C, on the river Tagliamento, Italy. Graphs for this analysis were derived from a Landsat 5 TM scene captured on June 20, 2011, which is shown, clipped to the braidplain extent, in the bottom left panel. The dashed line in the top left panel shows the location of this section of the river. Flow is from north to south
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(a) Overview of the image processing workflow applied to derive a braided river graph from a raw satellite image. The area in the ellipse is expanded in (b). (b) Close‐up of the graph for a small subnetwork (middle), with an extract of the associated adjacency matrix (top). Node numbers reflect their position in the wider network and decrease in a streamwise direction, indicating flow direction. The adjacency matrix could not be included in full and is weighted to reflect an equal division of flow at each node. The close‐up also highlights two types of shortest path, Euclidean and geodesic (see text) and the boxes (bottom) visually describe the graph theory metrics of node degree and cycles (cycle shown as grey channels; see text for descriptions)
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Looking upstream at the complex channel network of the braided Tagliamento River, Italy
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