Articles | Volume 5, issue 4
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. Kwang and Gary Parker

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.

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.