A TEST OF THE TOPOLOGICAL STRUCTURE OF RIVER NETS

Abstract

Two basically different models have been proposed in order to give a rational explanation of Horton's law of stream numbers: the “cyclic” model and the “random graph” model. In the cyclic model, a “Horton net” must be Hortonian in all its parts, and therefore channels of different (Strahler) order must be hierarchically arranged to form successive “generations” of rivers; in the random graph model, channels join in a completely random fashion, and a “Horton net” is simply a net in which Horton's law of stream numbers is numerically satisfied. In the present paper, these two models have been tested on a large stream population: the Wabash river system, in the continental U.S.A. This network is Hortonian, since the law of stream numbers is numerically satisfied with little scatter; but it shows no structural regularity at all. This seems to be a fairly general case. Therefore, the concept of structural regularity does not have its counterpart in nature; accordingly, the cyclic model does not correspond to reality. The random graph model, on the contrary, explains very well the observed facts: its basic statistical assumption, moreover, is found to be in agreement with observation.