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

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.