| Abstract: | Every basin of higher than first order is drained by a channel network composed of two subnetworks. Their basins are separated by a drainage divide line, called the basin divider, which is the primary organizing feature of the main basin. Each basin of magnitude n contains n – 1 subnetworks of higher order, and is therefore organized by a set of n – 1 dividers. The dividers and the basin boundary are interconnected in a graph called the divider network of the basin; in graph-theoretic terms this network forms a tree and has the same magnitude and link numbers as the channel network draining the basin. While the subbasins and subnetworks of a drainage basin form a nesting hierarchy, the corresponding dividers do not; indeed, any two dividers share at most one node in common, and whether they do so is independent of whether the corresponding subbasins are nesting or disjoint. However, the dividers of nesting basins are linked by recursive relationships which permit the derivation of a set of algebraic equations; these equations relate the dividers of a basin to other basin components; for example, their combined length is equal to half the length of all first-order basin boundaries minus the length of the main basin boundary. The second part of the paper explores the dependence of the divider length on other basin parameters. The expected length, as predicted by the assumption of topological randomness, is clearly rejected by the data. An alternative approach (regression) is based on the observed magnitudes of the subbasins separated by each divider, and is reasonably successful in estimating divider length. The last section introduces the concept of the standardized basin defined by a boundary length of unity; the estimated lengths of the basin divider and the basin boundary permit an approximate reconstruction of the idealized basin shape and the location of the divider in it. |
