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

Abstract

Self-similarity and plane-filling are intrinsic structure properties of natural river networks. Statistical data indicates that most natural river networks are Tokunaga trees. Researchers have explored to use iterative binary tree networks (IBTNs) to simulate natural river networks. However, the characteristics of natural rivers such as Tokunaga self-similarity and plane-filling cannot be easily guaranteed by the configuration of the IBTN. In this paper, the generator series and a quasi-uniform iteration rule are specified for the generation of nonstochastic quasi-uniform iterative binary tree networks (QU-IBTNs). First, we demonstrate that QU-IBTNs definitely satisfy self-similarity. Second, we show that the constraint for a QU-IBTN to be a Tokunaga tree is that the exterior links must be replaced in the generator series with a neighboring generator that is larger than the interior links during the iterative process. Moreover, two natural river networks are examined to reveal the inherent consistency with QU-IBTN at low Horton-Strahler orders.