Multifractal analysis of braided channel networks using structure functions and fixed-mass measures

Abstract

This study presents a multifractal analysis of braided channel networks using a coupled approach that integrates structure functions and fixed-mass measures. The investigation focuses on three braided river systems (namely, Allaro River, Brahmaputra River and Rakaia River), examining the behavior of the number of wet channels measured along the longitudinal spatial development of the river reach. The number of wet channels is shown to be an intermittent 1D signal, whose physical scaling is governed by scaling laws that can be naturally described by multifractal measures. By employing this combined approach, we were able to identify the maximum order of the moments of the measures that characterizes the multifractal spectrum and multiscaling properties of braided channel systems. The methodology for estimating the multifractal spectra is based on a modified Legendre transform relation for singularity strengths, allowing for a quantitative comparison between the multifractal spectra derived from structure functions and those obtained using the fixed-mass method.