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Abstract. While there are numerical landscape evolution modelsthat simulate how steady-state flows of water and sedimentreshape topography over long periods of time,r.sim.terrain is the first tosimulate short-term topographic changefor both steady-state and dynamic flow regimesacross a range of spatial scales.This free and open-sourceGeographic Information Systems (GIS)-based topographic evolution modeluses empirical models for soil erosionand a physics-based modelfor shallow overland water flow and soil erosionto compute short-term topographic change.This model uses either a steady-stateor unsteady representation of overland flowto simulate how overland sediment mass flows reshape topographyfor a range of hydrologic soil erosion regimesbased on topographic, land cover, soil, and rainfall parameters.As demonstrated by a case studyfor the Patterson Branch subwatershedon the Fort Bragg military installation in North Carolina,r.sim.terrain simulates the development offine-scale morphological features includingephemeral gullies, rills, and hillslopes.Applications include land management, erosion control,landscape planning, and landscape restoration.
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Self-similarity and vanishing diffusion in fluvial landscapes
Complex topographies exhibit universal properties when fluvial erosion dominates landscape evolution over other geomorphological processes. Similarly, we show that the solutions of a minimalist landscape evolution model display invariant behavior as the impact of soil diffusion diminishes compared to fluvial erosion at the landscape scale, yielding complete self-similarity with respect to a dimensionless channelization index. Approaching its zero limit, soil diffusion becomes confined to a region of vanishing area and large concavity or convexity, corresponding to the locus of the ridge and valley network. We demonstrate these results using one dimensional analytical solutions and two dimensional numerical simulations, supported by real-world topographic observations. Our findings on the landscape self-similarity and the localized diffusion resemble the self-similarity of turbulent flows and the role of viscous dissipation. Topographic singularities in the vanishing diffusion limit are suggestive of shock waves and singularities observed in nonlinear complex systems.
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- Award ID(s):
- 2235395
- PAR ID:
- 10494722
- Publisher / Repository:
- PNAS
- Date Published:
- Journal Name:
- Proceedings of the National Academy of Sciences
- Volume:
- 120
- Issue:
- 51
- ISSN:
- 0027-8424
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1073/pnas.2302401120
