Quantitative Metrics of Robustness in River Deltas

Abstract:

Deltas are landforms with channels that deliver water, sediment and nutrient fluxes from rivers to oceans or inland water bodies via multiple pathways. We conceptualize a delta channel network as a rooted acyclic directed graph where channels are modeled by edges and junctions by vertices. We use spectral graph theory – mainly the geometry of the null space of the directed weighted graph Laplacian – to establish a quantitative framework for extracting important structural and dynamics-related information from river deltas. Using this information, we introduce refined metrics of system complexity, such as entropy. Entropy has been proven to be an important measure of the amount of uncertainty in stochastic systems, and therefore a surrogate of the capacity of the system to undergo changes. Here we present an entropic approach to evaluate the robustness of deltas, showing how the two components of entropy: mutual information and conditional entropy can be interpreted in this framework. We also present other metrics that include, among others, resistance distance and number of alternative paths, which quantify the structural complexity of the system. We use these metrics to better classify deltaic systems, quantify their resilience and propose possible management scenarios.