Spectral Properties of River Networks
Abstract
River networks are important landscape features that have been studied extensively for many years. Although there are some seminal works on characterizing topologic properties of river networks, quantifying spectral properties received limited attention. In this study, through a graph-theoretic formulation of river network topology, we investigate the eigenvalues spectrum of their connectivity matrix (i.e. adjacency matrix). First, we explain the observed range of zero eigenvalues on the spectrum using the notion of multiplicity (i.e. algebraic and geometric multiplicity) for both undirected and directed river networks. Next, we investigate the physical meaning of the multiplicity of zero eigenvalues on the dynamics of river networks. We show that geometric multiplicity of zero eigenvalues is sufficient to determine the minimum set of driver nodes on a river network. The ratio of the number of driver nodes to the total number of nodes can be viewed as a measure of controllability of the river network, which is essential for comprehensive understanding of the dynamics of a system under external influence. In addition, we show that controllability is independent of the geometric size but dependent on the branching structure of the network. We also investigate the dependence of the controllability on energy exponent γ that dictates the branching pattern of the network and characterizes the mechanism of erosional processes on the landscape. Furthermore, spectral features (multiplicity of zero eigenvalues) exhibit significant correlation to the heterogeneity and complexity of the river network. In addition, we explore eigenvectors corresponding to the eigenvalue spectrum. Our results suggest the potential of the multiplicity of zero eigenvalues to help one understand and quantify the physical properties (controllability, heterogeneity and complexity) of river networks.
- Publication:
-
AGU Fall Meeting Abstracts
- Pub Date:
- December 2019
- Bibcode:
- 2019AGUFMEP51C2107S
- Keywords:
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- 0439 Ecosystems;
- structure and dynamics;
- BIOGEOSCIENCES;
- 1804 Catchment;
- HYDROLOGY;
- 1815 Erosion;
- HYDROLOGY;
- 1824 Geomorphology: general;
- HYDROLOGY