The relationship between the number of links and the number of segments of natural drainage networks is restricted to a narrow envelope. Theoretically, within this envelope a family of curves with the general form y = 2x ‐ (2n ‐ 1) is defined, where y is the number of links, x is the number of segments, and n is the Strahler stream order defined for n = 2, 3, 4, or 5. A comparison of these curves with >100 natural drainage networks indicates that these curves delineate threshold and hypothetical boundary conditions that can be used to predict stream order. Although a number of Strahler orders are possible for a network composed of a fixed set of links and segments, the data suggest that only one most probable order appears in nature. As drainage networks develop from simple to complex, the range of bifurcation ratios fluctuates until a nearly constant value is reached. For any network of given order, the bifurcation ratio increases to an improbable value. When this value is reached, branching increases the order of the network, and thus the bifurcation ratio is decreased.
Water Resources Research – Wiley
Published: Dec 1, 1972
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