Fractal structures of river plan forms

Abstract

The basis of existing methods for the quantitative description of the plan geometry of rivers is determination of the characteristics of individual meander bends (macroforms). This approach is effective when one is working with a few well‐defined macroforms. However, the plan pattern of many rivers is really determined at the next higher geometric level, the morphologically homogeneous river section, which may comprise many tens of macroforms, often with several superimposed scales. At this level, macroform parameters alone do not seem adequate to describe the geometry of the section. New indices are required. The concept of fractals affords a natural way of defining such indices. The presence of hierarchical features (superimposed sinuosity on various scales, braiding with superimposed bars of a range of sizes, etc.) suggests fractal behavior, at least over certain ranges of spatial scale. In this paper we demonstrate fractal behavior for 46 river sections in Moldavia from measurements made from existing topographic maps. We also introduce the notion of internal and external fractal scales that limit the range of fractal behavior; here the internal and external scales are the width of the river channel B and of its valley floor B0, respectively. Using this idea together with elements of fractal geometry, we obtain a relation among the sinuosity, B, B0, and the fractal dimension D of the river bed pattern. We propose the use of D as a new and informative parameter for describing the internal structure of the plan pattern of both single‐thread and multithread rivers.