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

Abstract

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.

Access options

Rent or Buy article

Get time limited or full article access on ReadCube.

from$8.99

All prices are NET prices.

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 https://doi.org/10.25740/vp967gh7489.

Code availability

The code to reproduce the results of this work can be accessed at https://github.com/stgl/GlobalSteepness and https://github.com/stgl/TopoAnalysis.

References

  1. 1.

    Whipple, K. X., Kirby, E. & Brocklehurst, S. H. Geomorphic limits to climate-induced increases in topographic relief. Nature 401, 39–43 (1999).

    Article  Google Scholar 

  2. 2.

    Willett, S. D. Orogeny and orography: the effects of erosion on the structure of mountain belts. J. Geophys. Res. 104, 28957–28981 (1999).

    Article  Google Scholar 

  3. 3.

    Hilley, G. E., Strecker, M. R. & Ramos, V. A. Growth and erosion of fold-and-thrust belts with an application to the Aconcagua fold-and-thrust belt, Argentina. J. Geophys. Res. 109, B01410 (2004).

    Google Scholar 

  4. 4.

    Whipple, K. X. & Meade, B. J. Controls on the strength of coupling among climate, erosion, and deformation in two-sided, frictional orogenic wedges at steady state. J. Geophys. Res. 109, F01011 (2004).

    Article  Google Scholar 

  5. 5.

    Wobus, C. et al. Tectonics from topography: procedures, promise, and pitfalls. Geol. Soc. Am. Spec. Pap. 398, 55–74 (2006).

    Google Scholar 

  6. 6.

    Seidl, M. A. & Dietrich, W. E. The problem of channel erosion into bedrock. Funct. Geomorphol. 23, 101–124 (1992).

    Google Scholar 

  7. 7.

    Howard, A. D. & Kerby, G. Channel changes in badlands. Geol. Soc. Am. Bull. 94, 739–752 (1983).

    Article  Google Scholar 

  8. 8.

    Howard, A. D. A detachment-limited model of drainage basin evolution. Water Resour. Res. 30, 2261–2285 (1994).

    Article  Google Scholar 

  9. 9.

    Flint, J. J. Stream gradient as a function of order, magnitude, and discharge. Water Resour. Res. 10, 969–973 (1974).

    Article  Google Scholar 

  10. 10.

    Whipple, K. X. & Tucker, G. E. Dynamics of the stream-power river incision model: implications for height limits of mountain ranges, landscape response timescales, and research needs. J. Geophys. Res. 104, 17661–17674 (1999).

    Article  Google Scholar 

  11. 11.

    Stock, J. D. & Montgomery, D. R. Geologic constraints on bedrock river incision using the stream power law. J. Geophys. Res. B 104, 4983–4993 (1999).

    Article  Google Scholar 

  12. 12.

    Hack, J. T. Studies of Longitudinal Stream Profiles in Virginia and Maryland (US Government Printing Office, 1957).

  13. 13.

    Perron, J. T. & Royden, L. An integral approach to bedrock river profile analysis. Earth Surf. Process. Landf. 38, 570–576 (2013).

    Article  Google Scholar 

  14. 14.

    Whipple, K. X., Hancock, G. S. & Anderson, R. S. River incision into bedrock: mechanics and relative efficacy of plucking, abrasion, and cavitation. Geol. Soc. Am. Bull. 112, 490–503 (2000).

    Article  Google Scholar 

  15. 15.

    Granger, D. E., Kirchner, J. W. & Finkel, R. Spatially averaged long-term erosion rates measured from in situ-produced cosmogenic nuclides in alluvial sediment. J. Geol. 104, 249–257 (1996).

    Article  Google Scholar 

  16. 16.

    Harel, M.-A., Mudd, S. M. & Attal, M. Global analysis of the stream power law parameters based on worldwide 10Be denudation rates. Geomorphology 268, 184–196 (2016).

    Article  Google Scholar 

  17. 17.

    Gudmundsdottir, M. H. et al. Restraining bend tectonics in the Santa Cruz mountains, California, imaged using 10Be concentrations in river sands. Geology 41, 843–846 (2013).

    Article  Google Scholar 

  18. 18.

    DiBiase, R. A., Whipple, K. X., Heimsath, A. M. & Ouimet, W. B. Landscape form and millennial erosion rates in the San Gabriel Mountains, CA. Earth Planet. Sci. Lett. 289, 134–144 (2010).

    Article  Google Scholar 

  19. 19.

    Kirby, E. & Ouimet, W. Tectonic geomorphology along the eastern margin of Tibet: insights into the pattern and processes of active deformation adjacent to the Sichuan Basin. Geol. Soc. Lond. Spec. Publ. 353, 165–188 (2011).

    Article  Google Scholar 

  20. 20.

    Harkins, N., Kirby, E., Heimsath, A., Robinson, R. & Reiser, U. Transient fluvial incision in the headwaters of the yellow river, northeastern Tibet, China. J. Geophys. Res. 112, F03S04 (2007).

    Article  Google Scholar 

  21. 21.

    Ouimet, W. et al. Regional incision of the eastern margin of the Tibetan Plateau. Lithosphere 2, 50–63 (2010).

    Article  Google Scholar 

  22. 22.

    Vance, D., Bickle, M., Ivy-Ochs, S. & Kubik, P. W. Erosion and exhumation in the Himalaya from cosmogenic isotope inventories of river sediments. Earth Planet. Sci. Lett. 206, 273–288 (2003).

    Article  Google Scholar 

  23. 23.

    Portenga, E. W. & Bierman, P. R. Understanding Earth’s eroding surface with 10Be. GSA Today 21, 4–10 (2011).

    Article  Google Scholar 

  24. 24.

    Lehner, B., Verdin, K. & Jarvis, A. New global hydrography derived from spaceborne elevation data. Eos 89, 93–94 (2008).

    Article  Google Scholar 

  25. 25.

    Stock, J. & Dietrich, W. E. Valley incision by debris flows: evidence of a topographic signature. Water Resour. Res. 39, 1089 (2003).

    Article  Google Scholar 

  26. 26.

    Sklar, L. S. & Dietrich, W. E. A mechanistic model for river incision into bedrock by saltating bed load. Water Resour. Res. 40, W06301 (2004).

    Article  Google Scholar 

  27. 27.

    Duvall, A., Kirby, E. & Burbank, D. Tectonic and lithologic controls on bedrock channel profiles and processes in coastal california. J. Geophys. Res. 109, F03002 (2004).

    Article  Google Scholar 

  28. 28.

    Shobe, C. M., Tucker, G. E. & Rossi, M. W. Variable‐threshold behavior in rivers arising from hillslope‐derived blocks. J. Geophys. Res. Earth Surf. 123, 1931–1957 (2018).

    Article  Google Scholar 

  29. 29.

    Rosenbloom, N. A. & Anderson, R. S. Hillslope and channel evolution in a marine terraced landscape, Santa Cruz, California. J. Geophys. Res. 99, 14013–14029 (1994).

    Article  Google Scholar 

  30. 30.

    Wobus, C. W., Hodges, K. V. & Whipple, K. X. Has focused denudation sustained active thrusting at the Himalayan topographic front? Geology 31, 861–864 (2003).

    Article  Google Scholar 

  31. 31.

    Moon, S. et al. Climatic control of denudation in the deglaciated landscape of the Washington Cascades. Nat. Geosci. 4, 469–473 (2011).

    Article  Google Scholar 

  32. 32.

    Barnes, R., Lehman, C. & Mulla, D. Priority-flood: an optimal depression-filling and watershed-labeling algorithm for digital elevation models. Comput. Geosci. 62, 117–127 (2014).

    Article  Google Scholar 

  33. 33.

    O’Callaghan, J. F. & Mark, D. M. The extraction of drainage networks from digital elevation data. Comput. Vis. Graph. Image Process. 28, 323–344 (1984).

    Article  Google Scholar 

  34. 34.

    Farr, T. G. et al. The shuttle radar topography mission. Rev. Geophys. 45, RG2004 (2007).

    Article  Google Scholar 

Download references

Acknowledgements

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.

Author information

Affiliations

Authors

Contributions

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.

Corresponding author

Correspondence to George E. Hilley.

Ethics declarations

Competing interests

The authors declare no competing interests.

Additional information

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Supplementary information

Supplementary Information

Supplementary methods, figs and tables.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

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). https://doi.org/10.1038/s41561-019-0442-3

Download citation

Further reading

Search

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing