Transport and Vulnerability in River Deltas: A Graph-Theoretic Approach

TL;DR

This paper introduces a graph-theoretic framework to analyze river delta topology and transport, enabling the identification of vulnerable links and management scenarios to sustain sediment and water delivery.

Contribution

It presents a novel spectral graph theory-based method for modeling delta transport networks and assessing their vulnerability to perturbations.

Findings

Identified key upstream links affecting sediment and water delivery.

Developed vulnerability maps highlighting critical delta hotspots.

Provided a systematic approach for delta management interventions.

Abstract

Maintaining a sustainable socio-ecological state of a river delta requires delivery of material and energy fluxes to its body and coastal zone in a way that avoids malnourishment that would compromise system integrity. We present a quantitative framework for studying delta topology and transport based on representation of a deltaic system by a rooted directed acyclic graph. Applying results from spectral graph theory allows systematic identification of the upstream and downstream subnetworks for a given vertex, computing steady flux propagation in the network, and finding partition of the flow at any channel among the downstream channels. 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. The results can be used to examine local or spatially distributed delta interventions and develop a system approach to delta management.