Are Landscapes Scale-invariant?

There is no doubt that channel networks display scale invariance in some respects, but this does not mean that landscapes lack distinctive scales, nor does it mean that the processes that evolve landscapes do not have scale dependence and do not impart distinctive scale-dependent morphology. Rodríguez-Iturbe and Rinaldo (1996) have summarized recent papers on channel networks and have argued for the importance of explaining the apparent scale invariance of landscape organization. Although the ubiquitous branching networks of valleys may indeed be scale-invariant or may possess attributes of multiscaling, knowledge of that cannot explain many of the fundamental issues involved in landscape form and evolution. In this chapter we focus on issues of scale and the importance of linking a process to an appropriate scale. We raise here more questions than answers, but in so doing perhaps make a case that as much as scale invariance is an appealing attribute of landscapes, understanding the controls on the actual scales of landscape features in both space and time can provide critical theoretical and practical insights into landscape processes and evolution.

Part of this discussion about scale in geomorphology is driven by the advent of computer-based analysis of digital topographic surfaces. In effect, our view of landscapes over the past 20 years has shifted from one of limited analysis of topographic contours (usually focusing on individual hillslope and river profiles or calculation of drainage density) to fully two-dimensional (or three-dimensional, depending on how one counts) grid-based investigations.