Abstract

Although the probabilistic-topologic approach to drainage-basin geomorphology that I initiated unifies a wide variety of quantitative empirical geomorphic relationships, some geomorphologists have objected variously that it abandons the scientific method, that its emphasis on topologic properties causes it to miss the geomorphic components of drainage basins, that it lacks physical content, and that it is too complicated to be of practical value. In fact, however, it gives results that are generally simpler, better, and more practical than those given by other methods. It has physical content because it is founded on postulates that are observational statements about actual drainage basins. It emphasizes topologic properties because they dominate the orientation-free planimetric aspects of drainage basins. Finally, it is necessarily probabilistic because of the prominent random element in natural landscapes, which may result from instabilities that amplify small perturbations into large ones.

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