Comparison of Fractal Dimension Calculation Methods for Channel Bed Profiles

Abstract

Research on channel bed profiles is one of the basic topics of river dynamics and fluvial process studies, since it was closely associated with the problems such as turbulent structure, flow resistance and sediment transportation in alluvial rivers. As a result of motion water flow interacting with sediment, channel bed profiles have irregular plane structures and self-similar microstructures, which were better analyzed by fractal method to reflect the intrinsic rough characteristics. In this study, several existing fractal dimension calculation methods were compared quantitatively, along with the discussion of their non-scale zones, correlation coefficients and computational accuracies. The following methods are included in this paper: Yard Stick Method, Box Counting Method, Variation Method, Structure Function Method, Root Mean Square Method and R/S Analysis Method. Finally, it is suggested that the Structure Function Method is suitable for calculating fractal dimension of rough channel bed profiles, which can provide references for future micro-fractal studies on fluvial process, flow resistance and waterway regulations.