Earth’s topographic relief potentially limited by an upper bound on channel steepness

Rivers limit the maximum elevation of active mountain belts, control the coupling between climate and tectonic processes, and archive the pace and tempo of fault-related rock uplift rates. Topographic profiles along rivers in steep, non-glaciated landscapes have led many to posit that river incision rates vary as a power function of channel discharge and slope. We used 10Be abundance in river sands and topographic analysis to test this relationship in watersheds varying by four orders of magnitude in erosion rate (4.7 × 10–3–7.1 mm yr−1), and supplemented this with a global analysis of erosion rates and topography. Our data and analyses reveal that in steep, rapidly eroding landscapes, channel morphology does not scale with erosion rate as expected. Instead, river profiles reach a threshold steepness, which may provide a bound on the topographic relief of Earth. In this case, increases in channel length may limit topographic relief, as erosion rate becomes increasingly sensitive to small changes in channel slopes in steep landscapes.