Edges and Blocks Matter on Hillslopes, Rivers, and Glacial Landscapes

Abstract:

Many landforms display sharp corners, or edges, that are maintained as they migrate laterally. Our present landscape models, cast largely in terms of patterns of vertical erosion, fail to capture the essence of these landscapes, including flatirons, hogbacks, cliffs, and lumpy outcropped hillslopes; roche moutonée and glacial steps, and river knickpoints. Yet these are the very landscape signatures of rock type and structure. Block sizes, and the fracture distributions that bound the blocks, vary from one rock type or geological setting to another. Removal and transportation of discrete blocks of rock maintains a sharp edge, and results in their upvalley/upslope migration.

Our challenge in developing numerical landscapes is to capture the essential variation, noisiness, and roughness of natural landscapes and their dependence on rock type and structure. The rate of lowering of the landscape is governed by the product of the spatial density of edges, their step height, and their rate of migration. I present cellular automata-like models in which I explicitly incorporate blocks, and utilize algorithms for the susceptibility of any block to motion, and the forces imposed on the surface by the environment. Susceptibility of a block to release is governed by its size, the geometry of the pocket in which it sits, the frictional properties of the bounding discontinuities, and the cohesion across these discontinuities. This is akin to coordination number and bond strengths of atoms in mineral dissolution studies; their atoms are our blocks. Removal of a block requires an event of sufficient magnitude to overcome its resistance. The relevant events include fluctuations in water pressure at the bed of glaciers, turbulence and sediment impacts in rivers, and root throw or earthquakes in hillslopes.

Preliminary models capture the essence of migrating edges. The systems self-organize to produce suites of steps. In glacial beds, for example, migration of steps produces upvalley and downward migrating rocky edges with an angle of descent analogous to the angle of climb of migrating bedforms; this angle reflects the relative importance of abrasion and quarrying. Steps in glacial beds arise from strong gradients in fracture density because the susceptibility to quarrying is strongly governed by block size.