Scale-Specific Landforms and Aspects of the Land Surface

The land surfaces of Earth, of other planets and of moons show both scalespecific and scaling behaviour. Size and spacing of landforms often show clustering around characteristic scales or between limits related to process thresholds or to the space available. This is clearest for various bedforms, in dynamic equilibrium with the last dominant flow or several flows. It is also clear for glacial cirques and for some types of landslides, sinkholes, abyssal hills and volcanoes. Strong scale-specificity as in cirques may be global. Weaker forms of scale specificity are also recognised, limited by either material or process variations to regions or to locales. The implications of global, regional and local scale-specificity are explored. Even the weaker forms of scale-specificity are not expected on surfaces generated by fractal models. The contrast between efficiency of surface flow and of consistently channelled flow imposes a lower characteristic scale (length of slope, drainage density) on fluvial erosional topography. The most common horizontal scales observed in the Earth’s topography are (1) tens or hundreds of m for slopes to (minor) streams; (2) km for major slopes, relevant to deep bedrock landsliding; and (3) tens to hundreds of km for broader tectonic and volcanic relief features. The internal properties of the Earth’s lithosphere and mantle impose limits to relief. Scaling may involve statistical self-similarity or self-affinity (fractal behaviour) over a few orders of magnitude, but is bounded by both upper and lower limits. Scaling is also found, over more limited ranges, for the characteristics of scale-specific features such as cirques and dunes. Scaling may be isometric (constant shape) or allometric (shape changes with size). Clear thresholds in the impact cratering process give changes in morphology and breaks of slope in depth: diameter scaling plots; these vary in orderly fashion between different planets and moons. Given the number of scale thresholds evident in geomorphology, it is dangerous to use scaling relationships for extrapolation beyond the data on which they are based.