Multifractal Analysis of River Networks in an Urban Catchment on the Taihu Plain, China

Abstract

Multifractal analysis was successfully used to investigate the structure of river networks. In this paper, we performed a multifractal analysis of river networks in an urban catchment that is located on the Taihu Plain in the lower part of the Yangtze River Delta, China. Spatial and temporal variations in the river networks during the period 1960–2010 were investigated. The generalized multifractal dimensions (Dq) and the multifractal spectrum (f(α)) were calculated using a box-counting method. The results indicate that: (i) the river networks in Wuchengxiyu (WXCY), Yangchengdianmao (YCDM), and Hangjiahu (HJH) had obvious multifractal features with capacity dimensions between 1.90 and 1.91 during the period 1960–2010. The multifractal spectrums are asymmetrical inverted-hook-shaped curves with a dominant left arm. The variation in the singularity component (∆α) changed the most in WCXY (an increase of ~ 7.9%), and the height variation in the multifractal spectrum (∆f) increased by ~ 17.5% in HJH; (ii) the changes in ∆α and ∆f of the tributaries in the three areas during the period 1960–2010 were consistent with those of the overall river network, demonstrating the decisive role that the tributaries play in the complexity of the river networks; (iii) compared to the natural factors, the influences of urbanization on the river networks significantly changed with a higher urbanization level; and (iv) there were no border effects. Further applications of multifractal theory in analyses of the relationship between a flood-forming regime and the multifractal structures of river networks will attract more attention. Generally, this approach, when successfully applied to studies of changes in river networks, is of theoretical significance for better describing and quantifying the evolution of river networks’ structures.