Mathematical characterization of fractal river networks

Abstract

Carraro and Altermatt1 performed an extensive analysis to study scaling properties of river networks. They concluded that: (1) branching "probability" is better termed as branching "ratio" for real river networks because it is not a probability; (2) branching ratio is a scale-dependent quantity as the value changes across spatial resolutions at which river networks are extracted (expressed as the threshold catchment area AT that initiates channels or pixel size l); (3) Optimal Channel Networks most accurately predicted the metapopulation stability and capacity. However, the supporting ground for these conclusions is either seriously flawed or inconclusive due to the improper use of branching probability, scale invariance, dimensions, and units.