Statistical Tests of Random Self-similar Networks Using Digital Elevation Models

Abstract

Recently, a new class of construction network models, called the random self-similar network model, has been developed to provide a better approximation of the self-similar structure of real river networks. Random self-similar networks are generated by two-type Galton–Watson branching processes. The model has been employed to study the scaling behavior of river networks and to develop a geophysical scaling theory of floods. In this manuscript, the ability of the random self-similar network model to approximate real river networks was statistically tested. The random self-similar networks were parameterized with river networks extracted from digital elevation model data. Firstly, statistical tests were performed to test the invariance of generator distributions. Secondly, values of scaling ratios of extracted river networks were also compared with those that were predicted by the random self-similar model. Finally, whether the appearances of generators follow a geometric distribution was tested using goodness-of-fit test. The results show that not all of the tested basins have invariant generator distributions. The random self-similar network model estimated values of Horton ratios are consistently greater than those obtained by the linear regression method, while the model estimated values of the Hack ratio fall in the reasonable range which was reported by previous researchers. The hypothesis that generator distributions are geometric is rejected for all basins. More empirical research is needed on the comparison between the random self-similar network model and real river networks.