A Generalized Width Function of Fractal River Network for the Calculation of Hydrologic Responses

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.

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“…Some others are one‐dimensional, e.g. the width function (Wang and Wang, ), or more local, e.g. stream length.…”

Section: Methodsmentioning

confidence: 99%

Regional watershed characterization and classification with river network analyses

Gaucherel

Frelat

Salomon

et al. 2017

Earth Surf Processes Landf

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“…Different generators were chosen by researchers for tackling SSN [4][5][6][7] . However, most of selected generators were chosen unreasonably.…”

Section: Basic Generator Sequencementioning

confidence: 99%

“…Claps et al [6] generated SSN by the method of recursive and iterative calculation. Wang and Wang [7] proposed the method to obtain SSN by using the interior and exterior generators. Veitzer et al [8,9] conceptualized the random SSN to describe the traditional Horton parameters in the form of probability dis-tribution and applied it to the hydrological simulation in river basins.…”

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confidence: 99%

The quantization of river network morphology based on the Tokunaga network

Zhang

Dai

Wang

et al. 2009

Sci. China Ser. D-Earth Sci.

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River network morphology not only reflects the structure of river stream but also has great effects on hydrological process, soil erosion, river evolution, and watershed topography. Here we propose and define a new sequence of self-similar networks and corresponding parameters for the generated Tokunaga network. We also discuss the topological and numerical characteristics of self-similar networks with different iteration rules by utilizing links and fractal dimension. Application results indicate that the proposed method could be used to generate river network, which is much consistent with natural river network. The proposed parameter λ could well reflect the river network morphology.fractal dimension, river network morphology, Tokunaga networkIn a distributed hydrological model, the river basin under study is usually divided into several sub-basins or even very small basic units. The rainfall-runoff process of each basic unit is simulated by the way of modeling hydrological process of both the slop and channel. Therefore, relevant parameters of those hydrological units directly affect simulation results of the runoff process in the whole river basin. However, those hydrological units would have different spatial resolutions because of limited topographic data. Therefore, it inevitably results in parameter variation and scale transformation issues when using river networks for hydrological simulation. Thus, a rough river network would be downscaled to be a finer one based on its self-similarity. Because river network morphology has significant effects on hydrological process, soil erosion, river evolution, and watershed topography, simple and efficient parameters are desired to describe and distinguish river network morphology. The relation between these parameters and hydrological process could then be established.Currently, there are mainly three methods to describe river network morphology. One is the Horton-Strahler classification method [1][2][3] in which geometric laws are given. In this method, channels with different scale and order are considered as basic units. The other is random river network method, which contains the random walk model and Shreve-Smart random topological model [1][2][3] . The basic unit of a river network in the latter method is a link connected by any two adjacent nodes. The third one is the Self-Similar Network (SSN) method, which is proposed based on the river network self-similarity and fractal theory. The SSN method is more consistent with the geometric features of river streams. Furthermore, it creates a new research field on the erosion topography evolution and river stream development. Tokunaga proposed the Tokunaga SSN with statistic meaning based on the Horton-Strahler classification method [4,5] . Claps et al. [6] generated SSN by the method of recursive and iterative calculation. Wang and Wang [7] proposed the method to obtain SSN by using the interior and exterior generators. Veitzer et al. [8,9] conceptualized the random

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“…Hung & Wang (2005a,b) do not explain whether, and if so which, such characteristics are used in the proposed generating process, either as generating constraints or as likelihood tests and indicators. Instead of this: -The generator pattern seems to be very artificially shaped, particularly as regards systematic right angles and inference of sub-patterns from the middle of links (Wang & Wang, 2002 address this issue precisely). -The process seems to be highly dependent on both the initialization through the basic pattern and the number of iterations.…”

Section: Modelling Geomorphometric Variables and Functionsmentioning

confidence: 99%

On width function-based unit hydrographs deduced from separately random self-similar river networks and rainfall variability: Discussion of “Coding random self-similar river networks and calculating geometric distances: 1. General methodology” and “2. Application to runoff simulations”

Cudennec¹

2007

Hydrological Sciences Journal

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A Generalized Width Function of Fractal River Network for the Calculation of Hydrologic Responses

Cited by 10 publications

References 9 publications

Regional watershed characterization and classification with river network analyses

Regional watershed characterization and classification with river network analyses

The quantization of river network morphology based on the Tokunaga network

On width function-based unit hydrographs deduced from separately random self-similar river networks and rainfall variability: Discussion of “Coding random self-similar river networks and calculating geometric distances: 1. General methodology” and “2. Application to runoff simulations”

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