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Modelling landscape evolution on geological time scales: a new method based on irregular spatial discretization
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1997
Year
EngineeringGeomorphologyLandscape EvolutionQuantitative GeomorphologyGeological ModelingEarth ScienceSocial SciencesDeformation ModelingComputational GeometryTheoretical GeomorphologyLandscape ProcessesArbitrary Spatial DiscretizationGeographyLandscape ChangeLandscape Evolution ModelGeological Time ScalesTectonicsComputational GeotechnicsLarge‐scale Landscape EvolutionGeomorphic ProcessCivil EngineeringSpatial DiscretizationIrregular Spatial Discretization
The authors introduce a numerical model that simulates large‑scale landscape evolution on tectonic time scales using arbitrary spatial discretization. The model employs computational‑geometry algorithms to compute natural neighbours for irregular point sets, enabling the solution of geomorphic equations with erosion, deposition, and diffusion while handling complex boundaries, radial uplift, strike‑slip faults, variable discretization, and self‑adaptive meshing, and allowing easy inclusion of orographic precipitation and flexural isostasy. Synthetic river networks and landscapes produced by the model follow network‑composition laws and exhibit scaling properties comparable to natural landscapes.
We present simulations of large‐scale landscape evolution on tectonic time scales obtained from a new numerical model which allows for arbitrary spatial discretization. The new method makes use of efficient algorithms from the field of computational geometry to compute the set of natural neighbours of any irregular distribution of points in a plane. The natural neighbours are used to solve geomorphic equations that include erosion/deposition by channelled flow and diffusion. The algorithm has great geometrical flexibility, which makes it possible to solve problems involving complex boundaries, radially symmetrical uplift functions and horizontal tectonic transport across strike‐slip faults. The algorithm is also ideally suited for problems which require large variations in spatial discretization and/or self‐adaptive meshing. We present a number of examples to illustrate the power of the new approach and its advantages over more ‘classical’ models based on regular (rectangular) discretization. We also demonstrate that the synthetic river networks and landscapes generated by the model obey the laws of network composition and have scaling properties similar to those of natural landscapes. Finally we explain how orographically controlled precipitation and flexural isostasy may be easily incorporated in the model without sacrificing efficiency.