The quantization of river network morphology based on the Tokunaga network

Abstract

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

Diversified expressions of architectural forms – Searching the laws of space composition and growth from the river network

“…The same phenomenon exists because of many artificial river networks based on random theory. For example the limited layout random drainage system model of Shreve [8] and the random chain length model proposed by Smart [9]. Since fractal geometry emerged in the 1970's, Horton's law and fractal thought have gradually merged.…”

Side Tributary Distribution of Quasi-Uniform Iterative Binary Tree Networks for River Networks

“…Iterative network models must be based on a series of generators. Each generator should be unique, and the generator series should be complete (Zhang et al, 2009;Mantilla et al, 2010).…”

“…Self-similarity has been considered to be an inherent characteristic of river networks since Mandelbrot first described their fractal nature (Mandelbrot, 1982;Peckham, 1995b). Since then, various methods to create synthetic networks have been proposed based on generator iteration (Veitzer and Gupta, 2000;Wang and Wang, 2002;Hung and Wang, 2005;Zhang et al, 2009;Mantilla et al, 2010). However, generators are not sequential and complete until they are cataloged by their topological structure (Zhang et al, 2009; Mantilla et al, 2010).…”

“…Since then, various methods to create synthetic networks have been proposed based on generator iteration (Veitzer and Gupta, 2000;Wang and Wang, 2002;Hung and Wang, 2005;Zhang et al, 2009;Mantilla et al, 2010). However, generators are not sequential and complete until they are cataloged by their topological structure (Zhang et al, 2009; Mantilla et al, 2010). Figure 3 shows the first four generators in a generator series.…”

“…The lack of a rigorous definition of generators (Wang and Wang, 2002;Troutman, 2005) results in an inability to guarantee the basicness and completeness of the generator population. A basic and complete binary generator series has been specially and explicitly defined and graphed by Zhang et al (2009), and has been proved to be effective and fundamental by means of comparison with data from China and the United States (Zhang et al, 2009). Second, the constraints of Tokunaga trees should be strictly added during the generation of synthetic iterative networks.…”