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

Abstract. Landscape evolution models often utilize the stream power incision model to simulate river incision: E = KA^mSⁿ, 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.