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.

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Fig. 1: 10Be-measured erosion rates and channel steepness from tropical granitic landscapes.
Fig. 2: Global occurrence of 10Be erosion rates and channel steepness.
Fig. 3: Global distribution of channel steepness.
Fig. 4: Channel relief and steepness predicted by the power-law incision model.

Data availability

The authors declare that all data supporting the findings of this study are available within the article, its Supplementary Information and at

Code availability

The code to reproduce the results of this work can be accessed at and


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G.E.H. acknowledges support from the NSF Career Grant EAR-TECT-105581. G.E.H. and S.P. acknowledge support from the NSF Grant DEB-BIO-0918234. S.P. acknowledges support from the Andrew Mellon Foundation. F.A. acknowledges support from Fondo Nacional de Desarrollo Científico y Tecnológico (FONDECYT-Chile) grant 3150116 and Fondo de Financiamiento de Centros de Investigación en Áreas Prioritarias (FONDAP-Chile), Research Center 15110017.

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G.E.H. and S.P. designed the experiment, collected and analysed the samples and wrote the manuscript; G.E.H., F.A., C.W.B., S.A.J., F.L., R.S., A.S. and H.H.Y. participated in the topographic analysis and exploration, contributed to the Supplementary Information and provided feedback on the manuscript text.

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Correspondence to George E. Hilley.

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Hilley, G.E., Porder, S., Aron, F. et al. Earth’s topographic relief potentially limited by an upper bound on channel steepness. Nat. Geosci. 12, 828–832 (2019).

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