Abstract
AbstractIn the past, a great deal of research has been conducted to determine the fractal properties of river networks, and there are many kinds of methods calculating their fractal dimensions. In this paper, we compare two most common methods: one is geomorphic fractal dimension obtained from the bifurcation ratio and the stream length ratio, and the other is box-counting method. Firstly, synthetic fractal trees are used to explain the role of the junction angle on the relation between two kinds of fractal dimensions. The obtained relationship curves indicate that box-counting dimension is decreasing with the increase of the junction angle when geomorphic fractal dimension keeps constant. This relationship presents continuous and smooth convex curves with junction angle from 60° to 120° and concave curves from 30° to 45°. Then 70 river networks in China are investigated in terms of their two kinds of fractal dimensions. The results confirm the fractal structure of river networks. Geomorphic fractal dimensions of river networks are larger than box-counting dimensions and there is no obvious relationship between these two kinds of fractal dimensions. Relatively good non-linear relationships between geomorphic fractal dimensions and box-counting dimensions are obtained by considering the role of the junction angle.
Highlights
One of the most important issues in the field of river hydrology is the quantitative description of river networks
The results show that all these average junction angles for 70 river networks are acute ones and nearly distributed uniformly in the range [55–84]
We compare two of the most common methods: one is geomorphic fractal dimension obtained from the bifurcation ratio and the stream length ratio, and the other to calculate the fractal dimension of river networks is box-counting method
Summary
One of the most important issues in the field of river hydrology is the quantitative description of river networks. It is widely accepted for decades that river networks are scaling, possessing self-similar structures over a huge range of scales. Horton ( , ), the forerunner focusing on the underlying laws of the dendritic structures of river networks initially describes river networks in a quantitative way. Meng et al | Junction angle links two fractal dimensions in the structure of river networks
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