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Earth Surface Dynamics An interactive open-access journal of the European Geosciences Union
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Volume 5, issue 4
Earth Surf. Dynam., 5, 807–820, 2017
https://doi.org/10.5194/esurf-5-807-2017
© Author(s) 2017. This work is distributed under
the Creative Commons Attribution 3.0 License.
Earth Surf. Dynam., 5, 807–820, 2017
https://doi.org/10.5194/esurf-5-807-2017
© Author(s) 2017. This work is distributed under
the Creative Commons Attribution 3.0 License.

Research article 06 Dec 2017

Research article | 06 Dec 2017

Landscape evolution models using the stream power incision model show unrealistic behavior when m ∕ n equals 0.5

Jeffrey S. Kwang1 and Gary Parker1,2 Jeffrey S. Kwang and Gary Parker
  • 1Department of Civil and Environmental Engineering, University of Illinois at Urbana-Champaign, Urbana, IL, USA
  • 2Department of Geology, University of Illinois at Urbana-Champaign, Urbana, IL, USA

Abstract. Landscape evolution models often utilize the stream power incision model to simulate river incision: E = KAmSn, where E is the vertical incision rate, K is the erodibility constant, A is the upstream drainage area, S is the channel gradient, and m and n are exponents. This simple but useful law has been employed with an imposed rock uplift rate to gain insight into steady-state landscapes. The most common choice of exponents satisfies m ∕ n = 0.5. Yet all models have limitations. Here, we show that when hillslope diffusion (which operates only on small scales) is neglected, the choice m ∕ n = 0.5 yields a curiously unrealistic result: the predicted landscape is invariant to horizontal stretching. That is, the steady-state landscape for a 10 km2 horizontal domain can be stretched so that it is identical to the corresponding landscape for a 1000 km2 domain.

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Short summary
A prevalent bedrock incision relation used in landscape evolution is the stream power incision model (SPIM), which relates incision rate to drainage area to the m power and slope to the n power. We show the most commonly used ratio, m ∕ n = 0.5, leads to scale invariance: a landscape that has a horizontal domain of 1 km × 1 km has exactly the same relief pattern as one with a 100 km × 100 km domain. This conclusion indicates that SPIM must yield unrealistic results over a wide range of conditions.
A prevalent bedrock incision relation used in landscape evolution is the stream power incision...
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