Network topology, Transport dynamics, and Vulnerability Analysis in River Deltas: A Graph-Theoretic Approach

Abstract:

River deltas are intricate landscapes with complex channel networks that self-organize to deliver water, sediment, and nutrients from the apex to the delta top and eventually to the coastal zone. The natural balance of material and energy fluxes which maintains a stable hydrologic, geomorphologic, and ecological state of a river delta, is often disrupted by external factors causing topological and dynamical changes in the delta structure and function. A formal quantitative framework for studying river delta topology and transport dynamics and their response to change is lacking. Here we present such a framework based on spectral graph theory and demonstrate its value in quantifying the complexity of the delta network topology, computing its steady state fluxes, and identifying upstream (contributing) and downstream (nourishment) areas from any point in the network. We use this framework to construct vulnerability maps that quantify the relative change of sediment and water delivery to the shoreline outlets in response to possible perturbations in hundreds of upstream links. This enables us to evaluate which links (hotspots) and what management scenarios would most influence flux delivery to the outlets, paving the way of systematically examining how local or spatially distributed delta interventions can be studied within a systems approach for delta sustainability.