25.
River networks have been shown to obey power scaling laws and to follow self‐organization principles. Their self‐similar (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
Dl 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
Dl 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. Copyright © 2011 John Wiley & Sons, Ltd.
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