Transport on river networks: A dynamical approach

TL;DR

This paper models environmental transport on river networks using a dynamical approach, revealing self-similar structures and a universal phase transition in transport dynamics across different geographical networks.

Contribution

It introduces a dynamic tree framework for river network transport, demonstrating self-similarity and identifying a universal phase transition in transport behavior.

Findings

Dynamic trees are self-similar, mirroring static network structures.

Identified a universal phase transition in river network transport dynamics.

Observed different phase transition behaviors in networks from California and Italy.

Abstract

This study is motivated by problems related to environmental transport on river networks. We establish statistical properties of a flow along a directed branching network and suggest its compact parameterization. The downstream network transport is treated as a particular case of nearest-neighbor hierarchical aggregation with respect to the metric induced by the branching structure of the river network. We describe the static geometric structure of a drainage network by a tree, referred to as the static tree, and introduce an associated dynamic tree that describes the transport along the static tree. It is well known that the static branching structure of river networks can be described by self-similar trees (SSTs); we demonstrate that the corresponding dynamic trees are also self-similar. We report an unexpected phase transition in the dynamics of three river networks, one from California and two from Italy, demonstrate the universal features of this transition, and seek to interpret it in hydrological terms.