Patterns of Drainage Areas with Random Topology *

Christian Werner Patterns of Drainage Areas with Random Topology* After several years of rather successful investigation of the geometry and topology of channel networks by theoretical analysis and simulation models, one is tempted to pose the question of whether other morphological patterns of the physical landscape can be approached with a similar meth- odology. The problem with which this paper is concerned is a direct trans- fer of Shreve’s investigation of channel networks 171 to the subject of drainage divide patterns. Thus, the problem can be formulated as follows: Assume that, in the absence of environmental control, all topologically different patterns formed by the drainage areas (drainage polygons) of the links of a channel network of given magnitude n are equally likely to occur. What will be the expected distribution of drainage polygons when grouped according to the number of their sides? Do empirical d a b support the hypothetical assumption above through close correspondence to the the- oretical distribution deduced from this assumption? *The support of the National Science Foundation, Grant GS-2989, is gratefully acknowledged. Christian Werner is associate professor of geography, University of Cali- fornia, Irvine.