Spatial self-organization in geomorphology: from periodic bedforms and patterned ground to scale-invariant topography

Abstract

A rich diversity of spatial order can be discerned in landforms and small-scale features of landscapes, with spatial order ranging in scale from 10 7 m to 10 −2 m, and in geometry from pronounced two-dimensional periodicity to three-dimensional scale-invariance. Ripples of wind-blown sand with their strikingly uniform spacing, and mountainous topography with its fractal characteristics illustrate the range of geomorphic self-organization. Patterns on the land surface are often very distinct, easily observed and readily studied because of their accessibility, and yet the systematic quantitative study of geomorphic self-organization is only in its infancy. It offers difficult challenges but also exceptional opportunities particularly for those versed in modern techniques used in studies of self-organization. In this overview, diverse examples of spontaneous organization in geomorphic systems and recent pertinent studies are described, starting with spatial structures that are generally most distinct and best understood. They include: (1) periodic structures that form on various substrates as water or air transports, erodes and deposits sediments-ripples and dunes, meanders and bar/pool topography of rivers, and rhythmic shoreline features; (2) polygonal patterns that result either from the growth cracks in such contrasting media as freezing lava and frozen ground, or from freeze/thaw alternations in soils; (3) large-scale periodic structures dictated by the deformation of magma or of the Earth's crust-linear arrays of evenly spaced volcanoes and sequences of alternating valleys and mountain ranges; and (4) scale-invariant structures revealed in drainage networks and topography.