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

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doi:10.5194/esurf-2017-15
© Author(s) 2017. This work is distributed
under the Creative Commons Attribution 3.0 License.
Research article
20 Mar 2017
Review status
This discussion paper is under review for the journal Earth Surface Dynamics (ESurf).
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 1Department of Civil and Environmental Engineering, University of Illinois at Urbana - Champaign, Urbana, IL, USA
2Departmnet 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 = vertical incision rate, K = erodibility constant, A =  upstream drainage area, S = 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; indeed, this ratio has been deemed to yield the “optimal channel network.” Yet all models have limitations. Here, we show that when hillslope diffusion (which operates only at 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 1 m2 horizontal domain can be stretched so that it is identical to the corresponding landscape for a 100 km2 domain.

Citation: Kwang, J. S. and Parker, G.: Landscape evolution models using the stream power incision model show unrealistic behavior when m/n equals 0.5, Earth Surf. Dynam. Discuss., doi:10.5194/esurf-2017-15, in review, 2017.
Jeffrey S. Kwang and Gary Parker
Jeffrey S. Kwang and Gary Parker
Jeffrey S. Kwang and Gary Parker

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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 m × 1 m 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 condition.
A prevalent bedrock incision relation used in landscape evolution is the stream power incision...
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