Formal Analysis of Ridge and Channel Patterns in Maturely Eroded Terrain

Abstract

Abstract The ridges delineating the drainage basins of a channel network and its sub-networks from themselves a network. This network spatially penetrates, or interlocks with, the channel network. Under fairly weak axiomatic assumptions, interlocking ridge and channel networks are of equal magnitude, and there exists a one-to-one relationship between their respective paths such that each pair of corresponding ridge and channel paths delineates a contiguous area called a drainage complex. In the limiting case that the link number of the channel path is zero, the complex coincides with the familiar concept of a drainage basin. Data sampled from natural ridge and channel networks indicate that, for a given complex magnitude, the link numbers of the two paths follow an essentially random distribution; in contrast, the sum of the link numbers is closely dependent on the complex magnitude. Thus, while the internal connectivity of any ridge or channel network in the study area seems to be largely a matter of chance, the respective connectivities of interlocking networks exercise tight control over each other. The observed dependency is interpreted as the result of both geometric and geomorphic constraints limiting the minimum and maximum length of drainage area boundaries. Key Words: channel networksridge networksmaturely eroded terrainnetwork axiomatizationnetwork interdependency