Fractal geometry of the river network

Abstract

Fractal dimensions of the more than 200 large river networks of the former USSR were calculated. We use the term «fractal» as «a structure consisted of parts which are in some sense alike to the whole». River networks don’t possess the complete self-likeness – fractal dimension changes with the change of measurer unit and the chosen length of the rivers. Therefore the calculations were fulfilled with the measurer length lying within the limits of 1–10 km. Fractal dimension of the river networks of the former USSR changes from 1.1 to 1.7, which corresponds to the aggregate length of the short rivers (1–10 km) consisting 20–80% of total river network length. Then all studied networks have fractal dimension more than Euclidian dimension of line (1) and less than Euclidian dimension of plane (2) as it should be accordingly to the fractal approach. There is a tendency for fractal dimension to grow with the height of the river basin and humidity of the territory. It is also strongly correlated with the network density. Fractal dimension as an index of the river length distribution has some advantages in comparison with the other morphometric indexes used. It augments significantly the possibility of the quantitative analysis of the drainage networks.