No 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.

In order to understand and manage a hydrological region, one usually needs to comprehensively characterize the watersheds (basins) and their river networks. This usually and primarily involves analysis of hydrological and geomorphological properties of the watershed derived from the digital terrain model (DTM), but this approach neglects the information content of the associated river networks. In this study, we used a combination of traditional DTM and original river network-related indices to the watersheds of an understudied region, Haiti. We also used Monte Carlo simulations to estimate index confidence levels of these indices. Compared to commonly used indices, the network indices provided valuable information that could then be used in statistical analyses as a way to identify the dominant features of the country's watershed morphology.On this basis, we identified four watershed groups in Haiti: (i) high, elongated watersheds, (ii) lowlands, with sinuous networks and relatively slow runoff, (iii) high watersheds with dendritic networks, and (iv) lowlands with high downstream-upstream contrast in properties and rapid runoffs. We argue that river network features provide complementary information in terms of flow topology, highly relevant to characterize contrasting relief countries, such as Haiti. Hence, more exhaustive characterization of watersheds would predictably benefit from the approach outlined in this paper.