EXPLORATIONS INTO THE FORMAL-STRUCTURE OF DRAINAGE BASINS

EARTH SURFACE PROCESSES AND LANDFORMS, VOL. 19,747-762 (1994) EXPLORATIONS INTO THE FORMAL STRUCTURE OF DRAINAGE BASINS CHRISTIAN WERNER University of California. Irvine, C A , 92717, U.S.A. Received 20 May 1993 Revised 7 February 1994 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-the- oretic 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 relation- ships 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. KEY WORDS Drainage basin Drainage divide Graph theory Ridge/channel networks INTRODUCTION AND OUTLINE This paper derives its purpose from Shreve’s (1969) principal statement: ‘. . . to comprehend the geometry of drainage basins and channel networks.. . is prerequisitive to explaining their mechanics.. .’. Its aim is to expand the existing language of formal basin description, to deduce several algebraic functions that govern the interrelations between the descriptive concepts of basin structure, and to relate topologic and geometric parameters of drainage basins to those of the channel networks by which they are drained. Both the geometric and the graph-theoretic analyses of channel networks have progressed steadily since the foundations were laid in the early work of Horton (1945), Strahler (1952), Melton (1957) and Shreve (1966); it has sharpened existing concepts and, very importantly, recognized and defined additional channel network features (Gardiner, 1975; Mark, 1975); it has generated theoretical explanations for a variety of observed regularities, such as some of the Horton laws of drainage composition (Shreve, 1969, 1975; Smart, 1972); and it has successfully separated the effects of formal or physical constraints from those of chance (Abrahams, 1980, 1983, 1984; Werner 1982, 1984). At least in theory, through the formulation of explicit functions relating slope development to channel growth and incision, it should be possible to ‘. . . comprehend the geometry of drainage basins. . .’ simply as a derivation from what is known about CCC 0197-93371941080747-16 0 1994 by John Wiley & Sons, Ltd.