Variable self‐similar sinuosity properties within simulated river networks

Abstract

River networks have been shown to obey power scaling laws and to follow self-organization principles. Their selfsimilar (fractal) properties open a path to relate small scale and large scale hydrological processes, such as erosion, deposition or geological movements. However, the existence of a self-similar dimension has only been checked using either the whole channel network or, on the contrary, a single channel link. No study has explicitly addressed the possible spatial variation of the self-similar properties between these two extreme geomorphologic objects. Here, a new method based on self-similarity maps (SSM) is proposed to spatially explore the stream length self-similar dimension D l within a river network. The mapping principle consists in computing local self-similar dimensions deduced from a fit of stream length estimations using increasing divider sizes. A local uncertainty related to the fit quality is also computed and localized on every stream. To assess the efficiency of the approach, contrasted river networks are simulated using optimal channel networks (OCN), where each network is characterized by an exponent γ conditioning its overall topology. By building SSM of these networks, it is shown that deviations from uniform self-similarity across space occur. Depending on the type of network (γ parameter), these deviations are or are not related to Strahler's order structure. Finally, it is found numerically that the structural averaged stream length self-similar dimension D l is closely related to the more functional γ parameter. Results form a bridge between the studies on river sinuosity (single channel) and growth of channel networks (watershed). As for every method providing spatial information where they were lacking before, the SSM may soon help to accurately interpret natural networks and help to simulate more realistic channel networks.

Regional watershed characterization and classification with river network analyses

“…The spatially explicit way such metrics have been computed [with SSM software, instead of global approaches (Snelder and Biggs, )] allowed to best capture river network properties. While the topographic and geologic features, as well as the vegetation cover are volumetric and surface components of the watershed, the river network has a fractional spatial dimension, capturing the way the drained water ‘fills’ the available space (Moussa, ; Cudennec and Fouad, ; Gaucherel et al , ). For this reason, the network captures the ‘hydrograph clock’ of the water flow, that is, the arrival time at the outlet, thus complementing the other index estimation.…”

“…We developed an open source software dedicated to this task (SSM, http://amap-collaboratif.cirad.fr/pages_logiciels/index.php?page=ssm), and freely available at our website. This software was previously developed in Matlab® (Gaucherel et al , ), and recently translated into the free and open source Java technology. The SSM software computes the earlier‐mentioned indices quantifying river network analysis with their associated maps, as well as many others.…”

“…It is the objective of this paper to show the relevance and complementarity of river network spatial analyses in characterizing and then classifying the watersheds of a region. For this purpose, we developed a specific open source software (called SSM, for Self‐Similarity Map) dedicated to river network analyses and able to generate new instances of already observed watersheds (Gaucherel et al , ; Gaucherel and Salomon, ). Other available software in the discipline (e.g.…”

Effect of Digital Elevation Model Mesh Size on Geomorphic Indices: A Case Study of the Ivaí River Watershed - State of Paraná, Brazil

“…The latter is dedicated to quantify the geometry and topology of stream networks and, therefore, it enables the quantitative analysis of any channel network (Gaucherel, Salomon and Labonne 2011).…”

Evaluation of Elevation, Slope and Stream Network Quality of Spot Dems

“…Thus, we compare the streams extracted from the DEM with the reference river in terms of shape indicators, namely, fractal dimension and sinuosity, which are adapted to the characterization of hydrographical networks morphology (Gaucherel et al, 2011). We also calculate the percentage of sinks along the river and the RMS of the elevation difference between filled and unfilled DEM.…”