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Earth Surface Dynamics An interactive open-access journal of the European Geosciences Union

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© Author(s) 2018. This work is distributed under
the Creative Commons Attribution 4.0 License.
Research article
16 Apr 2018
Review status
This discussion paper is a preprint. It is a manuscript under review for the journal Earth Surface Dynamics (ESurf).
Scaling and similarity of a stream-power incision and linear diffusion landscape evolution model
Nikos Theodoratos1, Hansjörg Seybold1, and James W. Kirchner1,2 1Dept. of Environmental Systems Science, ETH Zurich, Zurich, 8092, Switzerland
2Swiss Federal Research Institute WSL, Birmensdorf, 8903, Switzerland
Abstract. Scaling and similarity of fluvial landscapes can reveal fundamental aspects of the physics driving their evolution. Here we perform dimensional analysis on a widely used landscape evolution model (LEM) that combines stream-power incision and linear diffusion laws. Our analysis assumes that length and height are conceptually distinct dimensions, and uses characteristic scales that depend only on the model parameters (incision coefficient, diffusion coefficient, and uplift rate) rather than on the size of the domain or of landscape features. We use a previously defined characteristic length scale, but introduce new characteristic height and time scales. We use these characteristic scales to non-dimensionalize the LEM, such that it includes only dimensionless variables and no parameters. This significantly simplifies the LEM by removing all parameter-related degrees of freedom. The only remaining degrees of freedom are in the boundary and initial conditions. Thus, for any given set of dimensionless boundary and initial conditions, all simulations, regardless of parameters, are just re-scaled copies of each other, both in steady state and throughout their evolution. Therefore, the entire model parameter space can be explored by temporally and spatially re-scaling a single simulation. This is orders of magnitude faster than performing multiple simulations to span multi-dimensional parameter spaces. The characteristic length, height, and time scales are geomorphologically interpretable; they define relationships between topography and the relative strengths of landscape-forming processes. The characteristic height scale specifies how drainage areas and slopes must be related to curvatures for a landscape to be in steady state, and leads to methods for defining valleys, estimating model parameters, and testing whether real topography follows the LEM. The characteristic length scale is roughly equal to the scale of the transition from diffusion-dominated to advection-dominated propagation of topographic perturbations (e.g., knickpoints). We introduce a modified definition of the landscape Péclet number, which quantifies the relative influence of advective versus diffusive propagation of perturbations. Our Péclet number definition can account for the scaling of basin length with basin area, which depends on topographic convergence versus divergence.
Citation: Theodoratos, N., Seybold, H., and Kirchner, J. W.: Scaling and similarity of a stream-power incision and linear diffusion landscape evolution model, Earth Surf. Dynam. Discuss.,, in review, 2018.
Nikos Theodoratos et al.
Nikos Theodoratos et al.
Nikos Theodoratos et al.


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Publications Copernicus
Short summary
We perform dimensional analysis on a frequently used landscape evolution model (LEM). Defining characteristic scales in a novel way, we significantly simplify the LEM and develop an efficient numerical modeling approach. Our characteristic scales are physically meaningful; they quantify competitions between landscape-forming processes and are related to salient properties of landscape topography. Dimensional analyses of other LEMs may benefit from our approach in defining characteristic scales.
We perform dimensional analysis on a frequently used landscape evolution model (LEM). Defining...