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

earth surface dynamics

Landscape evolution models using the stream power incision model show unrealistic behavior when &amp;lt;i&amp;gt;m&amp;lt;/i&amp;gt; ∕ &amp;lt;i&amp;gt;n&amp;lt;/i&amp;gt; equals 0.5