Evolutionary Changes in Link Lengths: Further Evidence for Stream Abstraction

Abstract

Two simple deductive models are developed which indicate that abstraction of streams (exterior links) from a natural drainage network as relief declines tends to increase the mean lengths of both interior and exterior links remaining in the network. The exterior link length model, however, is complicated by the fact that exterior links necessarily become shorter before being abstracted. Unfortunately, it is not possible to deduce which of the opposing processes of stream shortening or stream abstraction will have the greater effect on the lengths of such links; but the dominant process can be identified by hindsight after the relationship between the mean exterior link length and relief has been determined empirically. Rank correlation analyses for a sample of drainage basins from the Bobadah area in eastern Australia, where it has been previously established that bifurcation ratios decline with relief, reveal that the mean lengths of both interior and exterior links increase, while link frequency and drainage density decrease, as relief is erosionally reduced. These results, together with those obtained previously for bifurcation ratios, constitute persuasive evidence that stream abstraction has occurred in the Bobadah landscape, and by implication, in other landscapes of declining relief. IN a previous study of five mature fluvially eroded landscapes in eastern Australia (Abrahams, 1972), factor analyses of a number of morphometric properties of third-order drainage basins suggested that, in the two landscapes of lowest relief, the number of Strahler streams in each basin was related to basin relief. Subsequent regression analyses revealed that in these two landscapes, named Bobadah and Goulds Country, the geometric mean bifurcation ratio tended to decline with basin relief. This tendency was attributed to stream (exterior link) abstraction accompanying the erosional degradation of relief. Stream abstraction might reasonably be expected to affect not only the topological charac- teristics of natural drainage networks, but the link-length properties as well. In order to be able to determine from these properties whether or not stream abstraction has occurred in a particular network, two simple deductive models are developed which indicate, with varying degrees of success, the direction of change in the mean lengths of interior and exterior links as streams are progressively abstracted from a drainage network. Since such changes in mean link lengths are likely to be quite small, they will be most readily detected in networks where systematic variations in link lengths arising from inhomogeneities in the environment are at a minimum. The Bobadah drainage network was therefore selected for the present study, because it experiences a sensibly uniform climate and, unlike the Goulds Country network, appears to be relatively free of geological controls. The object of this study is to ascertain whether link lengths in the Bobadah network exhibit evidence of stream abstraction consistent with that gained previously from the analysis of bifurcation ratios. DESCRIPTION OF DRAINAGE NETWORK