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Earth Surface Dynamics An interactive open-access journal of the European Geosciences Union
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Volume 6, issue 3
Earth Surf. Dynam., 6, 563-582, 2018
https://doi.org/10.5194/esurf-6-563-2018
© Author(s) 2018. This work is distributed under
the Creative Commons Attribution 4.0 License.
Earth Surf. Dynam., 6, 563-582, 2018
https://doi.org/10.5194/esurf-6-563-2018
© Author(s) 2018. This work is distributed under
the Creative Commons Attribution 4.0 License.

Research article 17 Jul 2018

Research article | 17 Jul 2018

A lattice grain model of hillslope evolution

Gregory E. Tucker1, Scott W. McCoy2, and Daniel E. J. Hobley3 Gregory E. Tucker et al.
  • 1Cooperative Institute for Research in Environmental Science (CIRES) and Department of Geological Sciences, University of Colorado, Boulder, CO 80305, USA
  • 2Department of Geological Sciences and Engineering, University of Nevada, Reno, NV 89557, USA
  • 3School of Earth and Ocean Sciences, Cardiff University, Cardiff, CF10 3AT, Wales

Abstract. This paper describes and explores a new continuous-time stochastic cellular automaton model of hillslope evolution. The Grain Hill model provides a computational framework with which to study slope forms that arise from stochastic disturbance and rock weathering events. The model operates on a hexagonal lattice, with cell states representing fluid, rock, and grain aggregates that are either stationary or in a state of motion in one of the six cardinal lattice directions. Cells representing near-surface soil material undergo stochastic disturbance events, in which initially stationary material is put into motion. Net downslope transport emerges from the greater likelihood for disturbed material to move downhill than to move uphill. Cells representing rock undergo stochastic weathering events in which the rock is converted into regolith. The model can reproduce a range of common slope forms, from fully soil mantled to rocky or partially mantled, and from convex-upward to planar shapes. An optional additional state represents large blocks that cannot be displaced upward by disturbance events. With the addition of this state, the model captures the morphology of hogbacks, scarps, and similar features. In its simplest form, the model has only three process parameters, which represent disturbance frequency, characteristic disturbance depth, and base-level lowering rate, respectively. Incorporating physical weathering of rock adds one additional parameter, representing the characteristic rock weathering rate. These parameters are not arbitrary but rather have a direct link with corresponding parameters in continuum theory. Comparison between observed and modeled slope forms demonstrates that the model can reproduce both the shape and scale of real hillslope profiles. Model experiments highlight the importance of regolith cover fraction in governing both the downslope mass transport rate and the rate of physical weathering. Equilibrium rocky hillslope profiles are possible even when the rate of base-level lowering exceeds the nominal bare-rock weathering rate, because increases in both slope gradient and roughness can allow for rock weathering rates that are greater than the flat-surface maximum. Examples of transient relaxation of steep, rocky slopes predict the formation of a regolith-mantled pediment that migrates headward through time while maintaining a sharp slope break.

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This article presents a new technique for computer simulation of slope forms. The method provides a way to study how events that disturb soil or turn rock into soil add up over time to produce landforms. The model represents a cross section of a hypothetical landform as a lattice of cells, each of which may represent air, soil, or rock. Despite its simplicity, the model does a good job of simulating a range of common of natural slope forms.
This article presents a new technique for computer simulation of slope forms. The method...
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