Theoretical model of optimal drainage networks

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Abstract
A simulation model of drainage network optimization is presented in which channels shift to minimize total stream power pgQS within the network. The simulation model starts from an arbitrary initial stream network developed on a square matrix, such as produced by random headward growth. Discrete stream capture then is simulated within the network, occurring wherever a new stream linkage would produce a steeper course than the original. Such capture produces a network with minimum power optimization but flow directions constrained to eight directions. Individual segment end points are then allowed to migrate by iterative relaxation with a direction and rapidity of motion governed by the gradient of stream power at the node. This valley migration is subject to the constraint that the sources and outlet remain fixed. The resulting networks are visually and morphometrically more similar to natural stream networks than the original networks produced by the random headward growth model.