Delta channel networks: 2. Metrics of topologic and dynamic complexity for delta comparison, physical inference, and vulnerability assessment

Abstract

Deltas are landforms that deliver water, sediment and nutrient fluxes from upstream rivers to the deltaic surface and eventually to oceans or inland water bodies via multiple pathways. Despite their importance, quantitative frameworks for their analysis lack behind those available for tributary networks. In a companion paper, delta channel networks were conceptualized as directed graphs and spectral graph theory was used to design a quantitative framework for exploring delta connectivity and flux dynamics. Here we use this framework to introduce a suite of graph-theoretic and entropy-based metrics, to quantify two components of a delta's complexity: (1) Topologic, imposed by the network connectivity and (2) Dynamic, dictated by the flux partitioning and distribution. The metrics are aimed to facilitate comparing, contrasting, and establishing connections between deltaic structure, process, and form. We illustrate the proposed analysis using seven deltas in diverse morphodynamic environments and of various degrees of channel complexity. By projecting deltas into a topo-dynamic space whose coordinates are given by topologic and dynamic delta complexity metrics, we show that this space provides a basis for delta comparison and physical insight into their dynamic behavior. The examined metrics are demonstrated to relate to the intuitive notion of vulnerability, measured by the impact of upstream flux changes to the shoreline flux, and reveal that complexity and vulnerability are inversely related. Finally, a spatially explicit metric, akin to a delta width function, is introduced to classify shapes of different delta types.

Delta channel networks: 1. A graph‐theoretic approach for studying connectivity and steady state transport on deltaic surfaces

“…The companion paper [Tejedor et al, 2015] discusses several definitions of the ''complexity'' of each subnetwork in terms of the number of paths joining the apex to the outlet, number of shared paths with other subnetworks, and number of paths that ''leak'' fluxes to other subnetworks; this complexity can be used to compare and contrast deltas as well as provide insight into their vulnerability to perturbations.…”

Controllability of Surface Water Networks

“…These networks include Colville, Irrawaddy, Mossy, Niger, Parana, Wax Lake and Yukon deltas. For more information regarding their location and geographical properties, the readers are referred to Tejedor et al (2015b). Note that the number of nodes and links presented in Table 1 (Smart & Moruzzi, 1971).…”

“…Typically, a network is represented as a collection of nodes symbolizing junctions, inlets and outlets, and links symbolizing stream paths. Topology-based metrics have been developed to quantitatively analyze and compare surface water networks in three structurally distinct categories: (i) tributary rivers, where the flux converges from several upstream inlets to a single downstream outlet (Bertuzzo et al, 2007;Rodriguez-Iturbe & Rinaldo, 1997), (ii) braided rivers, where a single stream undergoes multiple branching/merging and eventually joins into a single stream (Foufoula-Georgiou & Sapozhnikov, 2001;Howard et al, 1970;Marra et al, 2014;Sapozhnikov & Foufoula-Georgiou, 1996, 1999, and (iii) deltas, where the flux is distributed from a single upstream inlet to several downstream outlets (Edmonds et al, 2011;Passalacqua, 2017;Smart & Moruzzi, 1971;Tejedor et al, 2015aTejedor et al, , 2015b. These studies have significantly advanced our understanding of rivers and streams as networks.…”

Catalyzing action towards the sustainability of deltas

“…This framework allowed the research team to develop a suite of metrics that capture the topologic (connectivity structure of channel pathways) and dynamic (exchange of fluxes among delta apex-to-outlet sub-networks) complexity of deltas [26]. This Topo-Dynamic perspective of delta networks sets the foundation for quantitative and comparative classifications of deltas.…”

“…The same group [5] used empirically defined indicators to locate 48 global deltas within the risk space defined by these three components, supporting a comparative assessment of relative levels of risk. The indicator-based risk framework can be used effectively in large-scale inter-delta comparative studies, especially as a complement to higher-resolution studies at the local scale [45,26]. Deriving indicators from cross-disciplinary data can be a major challenge, though GIS tools have helped to provide common frameworks for geographical data.…”