Investigating Topologic and Geometric Properties of Synthetic and Natural River Networks under Changing Climate

River networks are important landscape features that collect and transport water, sediment and nutrients from regions of higher elevation to lower elevations. These networks have been studied for several decades from a range of geomorphological and hydrological perspectives. Investigating the geometric and topological properties of river networks is important for developing predictive models describing the network dynamics under changing climate as well as for quantifying the physical processes operating upon them. Although these networks have been characterized for a wide range of geomorphic properties, topological properties, and in particular, spectral properties of river networks received limited attention. In this dissertation, we propose a framework to identify critical nodes on river networks in the context of vulnerability under external disruptions. In addition, through a graph-theoretic formulation of river network topology, we investigate the observed range of zero eigenvalues on the spectra using the notion of multiplicity, that can be related to controllability of the river network for a comprehensive understanding of the dynamics of a system under external forcing. Furthermore, we use topological and geometrical signatures of the river networks and their organizational complexity to study advection and diffusion of fluxes on the network. The findings of this research reveal great potential to understand external forcing, e.g. climatic, control on river networks\u27 geometric and topological properties