Several Duality Theorems for Interlocking Ridge and Channel Networks
Published Web Locationhttps://doi.org/10.1029/91WR02322
Many fluvially eroded terrains display an intimate interaction of their patterns of channel and ridge lines. Under the assumption that there is exactly one outer ridge link positioned between any two neighboring outer channel links, the paper analyzes such interlocking networks by investigating their dual graphs. Several formal relationships are established which translate into a set of both existing and new theorems describing the close interdependency of channel and ridge parameters: Interlocking networks are of equal magnitude, the link numbers of the ridge and channel paths enclosing channel and ridge subnetworks have the same mean value, the link number of the boundary path enclosing a subnetwork is equal to the number of boundary paths passing through the root of the subnetwork, there exists a one‐to‐one correspondence between the inner nodes of the two networks as well as between their paths, and every such pair of corresponding ridge and channel paths delineates an area that is closed with regard to slope runoff. Copyright 1991 by the American Geophysical Union.