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

Landscape evolution models often utilize the stream power incision model to simulate river incision: E Combining double low line 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 m0.5. Yet all models have limitations. Here, we show that when hillslope diffusion (which operates only on small scales) is neglected, the choice m/n Combining double low line0.5 yields a curiously unrealistic result: The predicted landscape is invariant to horizontal stretching. That is, the steady-state landscape for a 10km2 horizontal domain can be stretched so that it is identical to the corresponding landscape for a 1000km2 domain.