Power-Law between the Apparent Drainage Density and the Pruning Area

Abstract. Self-similar structures of river networks have been quantified as diverse scaling laws. Among them we investigated a power functional relationship between the pruning area A_p and the associated apparent drainage density ρ_a with an exponent η. We analytically derived the relationship between η and other scaling exponents known for fractal river networks. The derivation is supported by analysis of four real river networks. The relationship between η and non-integer fractal dimensions found for natural river networks is suggested. Synthesis of our findings through the lens of fractal dimensions provides an insight that the exponent η has fundamental roots in fractal dimension for the whole river network organization.