Drainage networks

In the previous chapters we concluded that landscapes generally obey fractal statistics. Analyses of shore lines and topographic contours using ruler or box-counting methods provide statistical correlations with the self-similar fractal relation (2.1). Spectral studies of topography and bathymetry correlate well with the self-affine fractal relation (7.41). We will show in this chapter that drainage networks are fractal trees. Landforms evolve as a result of the tectonic processes that produce them and the erosional processes that destroy them. Landforms are a classic example of a complex phenomenon that can be quantified using fractal concepts (Turcotte 1993, 1994b, 1995).

We will begin our study of geomorphic processes by considering drainage networks. Drainage networks are a universal feature of landscapes on the earth. Over a large fraction of land areas, water eventually flows into an ocean. The surface area that drains into an ocean through a river defines the drainage basin of that river. The streams and rivers that drain into the Mississippi River and eventually drain into the Gulf of Mexico define the Mississippi River basin. Small streams merge to form larger streams, large streams merge to form rivers, and so forth. A typical example of a drainage network is given in Figure 8.1, from the Volfe and Bell Canyons in the San Gabriel Mountains near Glendora, California. We will show that drainage networks are classic examples of fractal trees (Tarboton et al., 1988; Beer and Borgas, 1993; Garcia-Ruiz and Otalora, 1992).