This paper was written by Walter B. Langbein and Luna B. Leopold and published in 1962. It was a geological survey paper written for the United States Department of the Interior. H.T. Odum wrote that Leopold and Langbein describe how the steepness and meander of streams develop in ways that help “maximize the power of a region’s total energy flows” (Odum, 1983, p. 118).
The abstract of the paper states: “The concept of entropy is expressed in terms of probability of various states. Entropy treats of the distribution of energy. The principle is introduced that the most probable condition exists when energy in a river system is as uniformly distributed as may be permitted by physical constraints. From these general considerations, equations for the longitudinal profiles of rivers are derived that are mathematically comparable to those observed in the field. The most probable river profiles approach the condition in which the downstream rate of production of entropy per unit mass is constant.
Hydraulic equations are insufficient to determine the velocity, depths, and slopes of rivers that are themselves authors of their own hydraulic geometries. A solution becomes possible by introducing the concept that the distribution of energy tends toward the most probable. This solution leads to a theoretical definition of the hydraulic geometry of river channels that agrees closely with field observations.
The most probable state for certain physical systems can also be illustrated by random-walk models. Average longitudinal profiles and drainage networks were so derived and these have the properties implied by the theory. The drainage networks derived from random walks have some of the principal properties demonstrated by the Horton analysis; specifically, the logarithms of stream length and stream numbers are proportional to stream order.”
Langbein, W.A., B. Leopold. 1962. The concept of entropy in landscape evolution. U. S. Geological Survey Professional Paper 550A.
H. T. Odum. 1983. Systems Ecology: An Introduction. New York: John Wiley & Sons.
Walter B. Langbein and Luna B. Leopold
