Hydraulic Characterization of River Networks Based on Flow Patterns Simulated by 2-D Shallow Water Modeling: Scaling Properties, Multifractal Interpretation, and Perspectives for Channel Heads Detection

This paper is focused on the contribution that the two-dimensional Shallow Water Equations could provide in respect to the fields of research devoted to the river networks analysis. The novelty introduced in this work is represented, in particular, by the hydraulic characterization of the river drainage networks, starting from flow patterns simulated by the two-dimensional Shallow Water Equations on high-resolution digital elevation model (DEM) through the analysis of water depths flowing down the hillslopes, channelized in both the main river and in all the tributaries or stored in small depressions. The first finding of this research is the determination of scaling laws that describe the relations between the water depth threshold, used to identify the network cells, and a dimensionless area, related to the total area of the network cells themselves. The observed bimodal scaling behavior has been considered as representative of the flow patterns belonging to the channel networks (CN) and hillslope plus channel networks (HCN), the physical and geomorphological interpretation of which has been provided from a multifractal point of view. In particular, the analysis of the multifractal spectra highlights significant variations in the multifractal signatures, between the CN and the HCN structures, leading to the proposal of a novel criterion for channels heads detection that has provided encouraging predictions of field observations.