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The shaping of erosional landscapes by internal dynamics

An Author Correction to this article was published on 28 April 2021

This article has been updated


Erosional landscapes transport sediment downstream, host natural hazards and are geologically active. While perturbations in external forcing, particularly climate and tectonics, sculpt erosional landscapes, similar landforms can be created by internal dynamics, that is, feedbacks between topography, erosion and sediment transport that occur independent of external perturbations. Internal system responses, termed autogenic dynamics, can remain active as landscapes adjust to perturbations in forcing, allowing for complex responses to external perturbations that potentially obscure links between external forcing, topographic form and sedimentary archives. Autogenic dynamics are being increasingly recognized in depositional systems, yet understanding of autogenic dynamics in erosional landscapes is nascent. In this Review, we discuss the mechanisms that contribute to internal dynamics in erosional landscapes. We use examples of autogenic terrace formation, knickpoint formation and river-basin reorganization to show how autogenic dynamics that occur over spatial scales of metres and temporal scales of hours can influence the evolution of mountain ranges over Myr periods. Unravelling the mechanics of autogenic processes allows the interplay of internal dynamics and external forcing to be explored and provides a framework to assess the influence of erosional processes in the geologic record.

Key points

  • Erosional landscapes reflect both internal dynamics and external forcing.

  • River terraces can form autogenically by a meandering river undergoing constant, vertical incision.

  • Autogenic knickpoints may form from the generation of bedrock bedforms, bedrock meander cut-offs and long-lived landslide deposits.

  • Imbalances in the rate of surface-elevation change across drainage divides causes divide migration and can produce complete landscape reorganization.

  • Autogenic dynamics in erosional landscapes can occur over spatial scales of metres to hundreds of kilometres and temporal scales of days to millions of years.

  • Increased understanding of autogenic dynamics will benefit from explicitly accounting for feedbacks between autogenic dynamics and external forcing in physical and numerical models.

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Fig. 1: Internal feedbacks in erosional landscapes.
Fig. 2: Formation of river terraces by autogenic dynamics.
Fig. 3: Autogenic knickpoint development.
Fig. 4: Autogenic knickpoint development under steady and uniform forcing.
Fig. 5: The cascading, non-local feedbacks of stream capture.
Fig. 6: Wholesale reorganization of drainage basins.

Change history


  1. 1.

    Albert, J. S., Schoolmaster, D. R. Jr, Tagliacollo, V. A. & Duke-Sylvester, S. M. Barrier displacement on a neutral landscape: toward a theory of continental biogeography. Syst. Biol. 66, 167–182 (2017).

    Google Scholar 

  2. 2.

    Corenblit, D. et al. Feedbacks between geomorphology and biota controlling Earth surface processes and landforms: A review of foundation concepts and current understandings. Earth Sci. Rev. 106, 307–331 (2011).

    Google Scholar 

  3. 3.

    Gilbert, G. K. Report on the Geology of the Henry Mountains (U.S. Government Print Office, 1877).

  4. 4.

    Willett, S. D., McCoy, S. W. & Beeson, H. W. Transience of the North American High Plains landscape and its impact on surface water. Nature 561, 528–532 (2018).

    Google Scholar 

  5. 5.

    Hilton, R. G. & West, A. J. Mountains, erosion and the carbon cycle. Nat. Rev. Earth Environ. 1, 284–299 (2020).

    Google Scholar 

  6. 6.

    Petley, D. Global patterns of loss of life from landslides. Geology 40, 927–930 (2012).

    Google Scholar 

  7. 7.

    Whipple, K. X., DiBiase, R. A. & Crosby, B. T. in Treatise on Geomorphology Vol. 9 (eds Shroder, J. F. & Wohl, E.) 550–573 (Academic, 2013).

  8. 8.

    Whittaker, A. C. How do landscapes record tectonics and climate? Lithosphere 4, 160–164 (2012).

    Google Scholar 

  9. 9.

    Murray, A. B., Coco, G. & Goldstein, E. B. Cause and effect in geomorphic systems: complex systems perspectives. Geomorphology 214, 1–9 (2014). Reviews how internal feedbacks in depositional landscapes create complex systems that cause the breakdown of direct cause-and-effect relationships between forcing and response.

    Google Scholar 

  10. 10.

    Croissant, T., Lague, D. & Davy, P. Channel widening downstream of valley gorges influenced by flood frequency and floodplain roughness. J. Geophys. Res. Earth Surf. 124, 154–174 (2019).

    Google Scholar 

  11. 11.

    Croissant, T., Lague, D., Steer, P. & Davy, P. Rapid post-seismic landslide evacuation boosted by dynamic river width. Nat. Geosci. 10, 680–684 (2017).

    Google Scholar 

  12. 12.

    Huang, M. Y. F. & Montgomery, D. R. Fluvial response to rapid episodic erosion by earthquake and typhoons, Tachia River, central Taiwan. Geomorphology 175, 126–138 (2012).

    Google Scholar 

  13. 13.

    Crosby, B. T. & Whipple, K. X. Knickpoint initiation and distribution within fluvial networks: 236 waterfalls in the Waipaoa River, North Island, New Zealand. Geomorphology 82, 16–38 (2006).

    Google Scholar 

  14. 14.

    Densmore, A. L. & Hovius, N. Topographic fingerprints of bedrock landslides. Geology 28, 371–374 (2000).

    Google Scholar 

  15. 15.

    Kirby, E. & Whipple, K. X. Expression of active tectonics in erosional landscapes. J. Struct. Geol. 44, 54–75 (2012). Reviews the influence of perturbations in tectonics on erosional landscapes.

    Google Scholar 

  16. 16.

    Beeson, H., McCoy, S. W. & Keen-Zebert, A. Geometric disequilibrium of river basins produces long-lived transient landscapes. Earth Planet. Sci. Lett. 475, 34–43 (2017).

    Google Scholar 

  17. 17.

    Hasbargen, L. E. & Paola, C. Landscape instability in an experimental drainage basin. Geology 28, 1067–1070 (2000). Foundational experimental study that shows a wide range of autogenic dynamics in a downscaled landscape.

    Google Scholar 

  18. 18.

    Limaye, A. B. S. & Lamb, M. P. Numerical simulations of bedrock valley evolution by meandering rivers with variable bank material. J. Geophys. Res. Earth Surf. 119, 927–950 (2014). Proposes criteria to identify autogenically generated river terraces using a numerical model and field data.

    Google Scholar 

  19. 19.

    Willett, S. D., McCoy, S. W., Perron, J. T., Goren, L. & Chen, C. Y. Dynamic reorganization of river basins. Science 343, 1248765 (2014). Highlights the ubiquity of river-basin reorganization and proposes a framework to understand primary causes and a means to visualize recent and likely future reorganization.

    Google Scholar 

  20. 20.

    Scheingross, J. S., Lamb, M. P. & Fuller, B. M. Self-formed bedrock waterfalls. Nature 567, 229–233 (2019).

    Google Scholar 

  21. 21.

    Jerolmack, D. J. & Paola, C. Shredding of environmental signals by sediment transport. Geophys. Res. Lett. 37, L19401 (2010). Documents how sediment transport can filter or ‘shred’ signals from perturbations in external forcing during source-to-sink transport.

    Google Scholar 

  22. 22.

    Hajek, E. A. & Straub, K. M. Autogenic sedimentation in clastic stratigraphy. Annu. Rev. Earth Planet. Sci. 45, 681–709 (2017). Reviews autogenic dynamics in depositional landscapes and the sedimentary record.

    Google Scholar 

  23. 23.

    Burbank, D. W. et al. Bedrock incision, rock uplift and threshold hillslopes in the northwestern Himalayas. Nature 379, 505–510 (1996).

    Google Scholar 

  24. 24.

    Larsen, I. J. & Montgomery, D. R. Landslide erosion coupled to tectonics and river incision. Nat. Geosci. 5, 468–473 (2012).

    Google Scholar 

  25. 25.

    Roering, J. J., Kirchner, J. W., Sklar, L. S. & Dietrich, W. E. Hillslope evolution by nonlinear creep and landsliding: an experimental study. Geology 29, 143–146 (2001).

    Google Scholar 

  26. 26.

    Scherler, D., Lamb, M. P., Rhodes, E. J. & Avouac, J. P. Climate-change versus landslide origin of fill terraces in a rapidly eroding bedrock landscape: San Gabriel River, California. Geol. Soc. Am. Bull. 128, 1228–1248 (2016).

    Google Scholar 

  27. 27.

    Mackey, B. H., Roering, J. J. & Lamb, M. P. Landslide-dammed paleolake perturbs marine sedimentation and drives genetic change in anadromous fish. Proc. Natl Acad. Sci. USA 108, 18905–18909 (2011).

    Google Scholar 

  28. 28.

    Ouimet, W. B., Whipple, K. X., Crosby, B. T., Johnson, J. P. & Schildgen, T. F. Epigenetic gorges in fluvial landscapes. Earth Surf. Process. Landf. 33, 1993–2009 (2008).

    Google Scholar 

  29. 29.

    Ouimet, W. B., Whipple, K. X. & Granger, D. E. Beyond threshold hillslopes: Channel adjustment to base-level fall in tectonically active mountain ranges. Geology 37, 579–582 (2009).

    Google Scholar 

  30. 30.

    Beeson, H., Flitcroft, R. L., Fonstad, M. A. & Roering, J. J. Deep-seated landslides drive variability in valley width and increase connectivity of salmon habitat in the Oregon Coast Range. J. Am. Water Resour. Assoc. 54, 1325–1340 (2018).

    Google Scholar 

  31. 31.

    Golly, A., Turowski, J. M., Badoux, A. & Hovius, N. Controls and feedbacks in the coupling of mountain channels and hillslopes. Geology 45, 307–310 (2017).

    Google Scholar 

  32. 32.

    Lang, K. A., Huntington, K. W. & Montgomery, D. R. Erosion of the Tsangpo Gorge by megafloods, eastern Himalaya. Geology 41, 1003–1006 (2013).

    Google Scholar 

  33. 33.

    Cook, K. L., Andermann, C., Gimbert, F., Adhikari, B. R. & Hovius, N. Glacial lake outburst floods as drivers of fluvial erosion in the Himalaya. Science 362, 53–57 (2018).

    Google Scholar 

  34. 34.

    Baynes, E. R. C. et al. River self-organisation inhibits discharge control on waterfall migration. Sci. Rep. 8, 2444 (2018).

    Google Scholar 

  35. 35.

    Baynes, E. R. C., Lague, D. & Kermarrec, J. Supercritical river terraces generated by hydraulic and geomorphic interactions. Geology 46, 499–502 (2018).

    Google Scholar 

  36. 36.

    Finnegan, N. J. & Balco, G. Sediment supply, base level, braiding, and bedrock river terrace formation: Arroyo Seco, California, USA. Geol. Soc. Am. Bull. 125, 1114–1124 (2013).

    Google Scholar 

  37. 37.

    Malatesta, L. C., Prancevic, J. P. & Avouac, J. P. Autogenic entrenchment patterns and terraces due to coupling with lateral erosion in incising alluvial channels. J. Geophys. Res. Earth Surf. 122, 335–355 (2017).

    Google Scholar 

  38. 38.

    Yang, R., Willett, S. D. & Goren, L. In situ low-relief landscape formation as a result of river network disruption. Nature 520, 526–529 (2015).

    Google Scholar 

  39. 39.

    Murray, A. B. Reducing model complexity for explanation and prediction. Geomorphology 90, 178–191 (2007).

    Google Scholar 

  40. 40.

    Schumm, S. A. in Fluvial Geomorphology (ed. Morisawa, M.) 299–310 (State University of New York, 1973).

  41. 41.

    Paola, C. A mind of their own: recent advances in autogenic dynamics in rivers and deltas. SEPM Spec. Publ. 106, 5–17 (2016).

    Google Scholar 

  42. 42.

    Whittaker, A. C. & Boulton, S. J. Tectonic and climatic controls on knickpoint retreat rates and landscape response times. J. Geophys. Res. Earth Surf. 117, F02024 (2012).

    Google Scholar 

  43. 43.

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

    Google Scholar 

  44. 44.

    Straub, K. M., Duller, R. A., Foreman, B. Z. & Hajek, E. A. Buffered, incomplete, and shredded: The challenges of reading an imperfect stratigraphic record. J. Geophys. Res. Earth Surf. 125, e2019JF005079 (2020).

    Google Scholar 

  45. 45.

    Howard, A. D., Dietrich, W. E. & Seidl, M. A. Modeling fluvial erosion on regional to continental scales. J. Geophys. Res. Solid Earth 99, 13971–13986 (1994).

    Google Scholar 

  46. 46.

    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. Solid Earth 104, 17661–17674 (1999).

    Google Scholar 

  47. 47.

    Paola, C., Ganti, V., Mohrig, D., Runkel, A. C. & Straub, K. M. Time not our time: physical controls on the preservation and measurement of geologic time. Annu. Rev. Earth Planet. Sci. 46, 409–438 (2018).

    Google Scholar 

  48. 48.

    Romans, B. W., Castelltort, S., Covault, J. A., Fildani, A. & Walsh, J. P. Environmental signal propagation in sedimentary systems across timescales. Earth Sci. Rev. 153, 7–29 (2016).

    Google Scholar 

  49. 49.

    Davis, W. M. Geographical Essays (Ginn and Co., 1909).

  50. 50.

    Grimaud, J. L., Paola, C. & Voller, V. Experimental migration of knickpoints: influence of style of base-level fall and bed lithology. Earth Surf. Dyn. 4, 11–23 (2016).

    Google Scholar 

  51. 51.

    Yuan, X. P., Braun, J., Guerit, L., Rouby, D. & Cordonnier, G. A new efficient method to solve the stream power law model taking into account sediment deposition. J. Geophys. Res. Earth Surf. 124, 1346–1365 (2019).

    Google Scholar 

  52. 52.

    Merritts, D. J., Vincent, K. R. & Wohl, E. E. Long river profiles, tectonism, and eustasy: A guide to interpreting fluvial terraces. J. Geophys. Res. Solid Earth 99, 14031–14050 (1994). Separates competing mechanisms for terrace formation, including sea-level change, tectonic uplift and autogenic river migration.

    Google Scholar 

  53. 53.

    Korup, O. Rock-slope failure and the river long profile. Geology 34, 45–48 (2006).

    Google Scholar 

  54. 54.

    Finnegan, N. J., Schumer, R. & Finnegan, S. A signature of transience in bedrock river incision rates over timescales of 104–107 years. Nature 505, 391–394 (2014). Documents how intermittency in vertical erosion can obscure the erosion history constructed from strath terrace records.

    Google Scholar 

  55. 55.

    Bridgland, D. & Westaway, R. Climatically controlled river terrace staircases: A worldwide Quaternary phenomenon. Geomorphology 98, 285–315 (2008).

    Google Scholar 

  56. 56.

    Bucher, W. H. “Strath” as a geomorphic term. Science 75, 130–131 (1932).

    Google Scholar 

  57. 57.

    Pazzaglia, F. J. in Treatise on Geomorphology Vol. 9 (eds Shroder, J. F. & Wohl, E.) 379–412 (Academic, 2013).

  58. 58.

    Erkens, G. et al. Fluvial terrace formation in the northern Upper Rhine Graben during the last 20 000 years as a result of allogenic controls and autogenic evolution. Geomorphology 103, 476–495 (2009).

    Google Scholar 

  59. 59.

    Lave, J. & Avouac, J. P. Active folding of fluvial terraces across the Siwaliks Hills, Himalayas of central Nepal. J. Geophys. Res. Solid Earth 105, 5735–5770 (2000).

    Google Scholar 

  60. 60.

    Bull, W. B. Geomorphic Response to Climate Change (Oxford Univ. Press, 1991).

  61. 61.

    Demir, T. et al. Preservation by basalt of a staircase of latest Pliocene terraces of the River Murat in eastern Turkey: evidence for rapid uplift of the eastern Anatolian Plateau. Glob. Planet. Change 68, 254–269 (2009).

    Google Scholar 

  62. 62.

    Van den Berg, M. W. & Van Hoof, T. in River Basin Sediment Systems: Archives of Environmental Change (eds Maddy, D., Macklin, M. G. & Woodward, J. C.) 45-86 (Balkema, 2001).

  63. 63.

    Gran, K. B. et al. Landscape evolution, valley excavation, and terrace development following abrupt postglacial base-level fall. Geol. Soc. Am. Bull. 125, 1851–1864 (2013).

    Google Scholar 

  64. 64.

    Yanites, B. J., Tucker, G. E., Mueller, K. J. & Chen, Y. G. How rivers react to large earthquakes: Evidence from central Taiwan. Geology 38, 639–642 (2010).

    Google Scholar 

  65. 65.

    Fuller, T. K., Perg, L. A., Willenbring, J. K. & Lepper, K. Field evidence for climate-driven changes in sediment supply leading to strath terrace formation. Geology 37, 467–470 (2009).

    Google Scholar 

  66. 66.

    Hancock, G. S. & Anderson, R. S. Numerical modeling of fluvial strath-terrace formation in response to oscillating climate. Geol. Soc. Am. Bull. 114, 1131–1142 (2002).

    Google Scholar 

  67. 67.

    Schanz, S. A., Montgomery, D. R., Collins, B. D. & Duvall, A. R. Multiple paths to straths: A review and reassessment of terrace genesis. Geomorphology 312, 12–23 (2018).

    Google Scholar 

  68. 68.

    Chadwick, O. A., Hall, R. D. & Phillips, F. M. Chronology of Pleistocene glacial advances in the central Rocky Mountains. Geol. Soc. Am. Bull. 109, 1443–1452 (1997).

    Google Scholar 

  69. 69.

    Pan, B. T. et al. A 900 ky record of strath terrace formation during glacial-interglacial transitions in northwest China. Geology 31, 957–960 (2003).

    Google Scholar 

  70. 70.

    Womack, W. R. & Schumm, S. A. Terraces of Douglas Creek, northwestern Colorado: an example of episodic erosion. Geology 5, 72–76 (1977).

    Google Scholar 

  71. 71.

    Ben Moshe, L., Haviv, I., Enzel, Y., Zilberman, E. & Matmon, A. Incision of alluvial channels in response to a continuous base level fall: Field characterization, modeling, and validation along the Dead Sea. Geomorphology 93, 524–536 (2008).

    Google Scholar 

  72. 72.

    Born, S. M. & Ritter, D. F. Modern terrace development near Pyramid Lake, Nevada, and its geologic implications. Geol. Soc. Am. Bull. 81, 1233–1242 (1970).

    Google Scholar 

  73. 73.

    Hack, J. T. Geology of the Brandywine Area and Origin of the Upland of Southern Maryland (United States Geological Survey, 1955).

  74. 74.

    Pazzaglia, F. J., Gardner, T. W. & Merritts, D. J. in Rivers Over Rock: Fluvial Processes in Bedrock Channels (eds Tinkler, K. J. & Wohl, E. E.) 207–235 (American Geophysical Union, 1998).

  75. 75.

    Finnegan, N. J. & Dietrich, W. E. Episodic bedrock strath terrace formation due to meander migration and cutoff. Geology 39, 143–146 (2011).

    Google Scholar 

  76. 76.

    Limaye, A. B. S. & Lamb, M. P. Numerical model predictions of autogenic fluvial terraces and comparison to climate change expectations. J. Geophys. Res. Earth Surf. 121, 512–544 (2016).

    Google Scholar 

  77. 77.

    Bufe, A., Paola, C. & Burbank, D. Fluvial bevelling of topography controlled by lateral channel mobility and uplift rate. Nat. Geosci. 9, 706–710 (2016).

    Google Scholar 

  78. 78.

    Tofelde, S., Savi, S., Wickert, A. D., Bufe, A. & Schildgen, T. F. Alluvial channel response to environmental perturbations: fill-terrace formation and sediment-signal disruption. Earth Surf. Dyn. 7, 609–631 (2019).

    Google Scholar 

  79. 79.

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

    Google Scholar 

  80. 80.

    Whittaker, A. C., Attal, M. & Allenn, P. A. Characterising the origin, nature and fate of sediment exported from catchments perturbed by active tectonics. Basin Res. 22, 809–828 (2010).

    Google Scholar 

  81. 81.

    Molnar, P. Late Cenozoic increase in accumulation rates of terrestrial sediment: How might climate change have affected erosion rates? Annu. Rev. Earth Planet. Sci. 32, 67–89 (2004).

    Google Scholar 

  82. 82.

    Mukul, M. The geometry and kinematics of the Main Boundary Thrust and related neotectonics in the Darjiling Himalayan fold-and-thrust belt, West Bengal, India. J. Struct. Geol. 22, 1261–1283 (2000).

    Google Scholar 

  83. 83.

    Sadler, P. M. Sediment accumulation rates and the completeness of stratigraphic sections. J. Geol. 89, 569–584 (1981).

    Google Scholar 

  84. 84.

    Sadler, P. M. & Jerolmack, D. J. Scaling laws for aggradation, denudation and progradation rates: the case for time-scale invariance at sediment sources and sinks. Geol. Soc. Spec. Publ. 404, 69–88 (2015).

    Google Scholar 

  85. 85.

    DiBiase, R. A., Whipple, K. X., Lamb, M. P. & Heimsath, A. M. The role of waterfalls and knickzones in controlling the style and pace of landscape adjustment in the western San Gabriel Mountains, California. Geol. Soc. Am. Bull. 127, 539–559 (2015).

    Google Scholar 

  86. 86.

    Gardner, T. W. Experimental study of knickpoint and longitudinal profile evolution in cohesive, homogenous material. Geol. Soc. Am. Bull. 94, 664–672 (1983).

    Google Scholar 

  87. 87.

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

    Google Scholar 

  88. 88.

    Whittaker, A. C., Cowie, P. A., Attal, M., Tucker, G. E. & Roberts, G. P. Bedrock channel adjustment to tectonic forcing: Implications for predicting river incision rates. Geology 35, 103–106 (2007).

    Google Scholar 

  89. 89.

    Mackey, B. H., Scheingross, J. S., Lamb, M. P. & Farley, K. A. Knickpoint formation, rapid propagation, and landscape response following coastal cliff retreat at the last interglacial sea-level highstand: Kaua’i, Hawai’i. Geol. Soc. Am. Bull. 126, 925–942 (2014).

    Google Scholar 

  90. 90.

    Seidl, M. A., Dietrich, W. E. & Kirchner, J. W. Longitudinal profile development into bedrock - an analysis of Hawaiian channels. J. Geol. 102, 457–474 (1994).

    Google Scholar 

  91. 91.

    Wobus, C. W., Tucker, G. E. & Anderson, R. S. Does climate change create distinctive patterns of landscape incision? J. Geophys. Res. Earth Surf. 115, F04008 (2010).

    Google Scholar 

  92. 92.

    Roberts, G. G. & White, N. Estimating uplift rate histories from river profiles using African examples. J. Geophys. Res. Solid Earth 115, B02406 (2010).

    Google Scholar 

  93. 93.

    Attal, M., Tucker, G. E., Whittaker, A. C., Cowie, P. A. & Roberts, G. P. Modeling fluvial incision and transient landscape evolution: Influence of dynamic channel adjustment. J. Geophys. Res. Earth Surf. 113, F03013 (2008).

    Google Scholar 

  94. 94.

    Roberts, G. G., White, N. J. & Shaw, B. An uplift history of Crete, Greece, from inverse modeling of longitudinal river profiles. Geomorphology 198, 177–188 (2013).

    Google Scholar 

  95. 95.

    Whittaker, A. C., Attal, M., Cowie, P. A., Tucker, G. E. & Roberts, G. Decoding temporal and spatial patterns of fault uplift using transient river long profiles. Geomorphology 100, 506–526 (2008).

    Google Scholar 

  96. 96.

    Whittaker, A. C. & Walker, A. S. Geomorphic constraints on fault throw rates and linkage times: examples from the Northern Gulf of Evia, Greece. J. Geophys. Res. Earth Surf. 120, 137–158 (2015).

    Google Scholar 

  97. 97.

    Niemann, J. D., Gasparini, N. M., Tucker, G. E. & Bras, R. L. A quantitative evaluation of Playfair’s law and its use in testing long-term stream erosion models. Earth Surf. Process. Landf. 26, 1317–1332 (2001).

    Google Scholar 

  98. 98.

    Royden, L. & Perron, J. T. Solutions of the stream power equation and application to the evolution of river longitudinal profiles. J. Geophys. Res. Earth Surf. 118, 497–518 (2013).

    Google Scholar 

  99. 99.

    Fox, M., Goren, L., May, D. A. & Willett, S. D. Inversion of fluvial channels for paleorock uplift rates in Taiwan. J. Geophys. Res. Earth Surf. 119, 1853–1875 (2014).

    Google Scholar 

  100. 100.

    Goren, L., Fox, M. & Willett, S. D. Tectonics from fluvial topography using formal linear inversion: Theory and applications to the Inyo Mountains, California. J. Geophys. Res. Earth Surf. 119, 1651–1681 (2014).

    Google Scholar 

  101. 101.

    Whipple, K. X., Forte, A. M., DiBiase, R. A., Gasparini, N. M. & Ouimet, W. B. Timescales of landscape response to divide migration and drainage capture: implications for the role of divide mobility in landscape evolution. J. Geophys. Res. Earth Surf. 122, 248–273 (2017). Explores how the ratio of divide-migration rate to river-channel-adjustment rate sets landscape topographic form.

    Google Scholar 

  102. 102.

    Bursztyn, N., Pederson, J. L., Tressler, C., Mackley, R. D. & Mitchell, K. J. Rock strength along a fluvial transect of the Colorado Plateau - quantifying a fundamental control on geomorphology. Earth Planet. Sci. Lett. 429, 90–100 (2015).

    Google Scholar 

  103. 103.

    Forte, A. M., Yanites, B. J. & Whipple, K. X. Complexities of landscape evolution during incision through layered stratigraphy with contrasts in rock strength. Earth Surf. Process. Landf. 41, 1736–1757 (2016).

    Google Scholar 

  104. 104.

    Gallen, S. F. Lithologic controls on landscape dynamics and aquatic species evolution in post-orogenic mountains. Earth Planet. Sci. Lett. 493, 150–160 (2018).

    Google Scholar 

  105. 105.

    Beeson, H. W. & McCoy, S. W. Geomorphic signatures of the transient fluvial response to tilting. Earth Surf. Dyn. 8, 123–159 (2020).

    Google Scholar 

  106. 106.

    DiBiase, R. A. et al. Stratigraphic control of landscape response to base-level fall, Young Womans Creek, Pennsylvania, USA. Earth Planet. Sci. Lett. 504, 163–173 (2018).

    Google Scholar 

  107. 107.

    Yanites, B. J., Becker, J. K., Madritsch, H., Schnellmann, M. & Ehlers, T. A. Lithologic effects on landscape response to base level changes: a modeling study in the context of the Eastern Jura Mountains, Switzerland. J. Geophys. Res. Earth Surf. 122, 2196–2222 (2017).

    Google Scholar 

  108. 108.

    Brooks, P. C. Experimental Study of Erosional Cyclic Steps. Master’s thesis, Univ. Minnesota (2001).

  109. 109.

    Wohl, E. E. & Ikeda, H. Experimental simulation of channel incision into a cohesive substrate at varying gradients. Geology 25, 295–298 (1997).

    Google Scholar 

  110. 110.

    Izumi, N., Yokokawa, M. & Parker, G. Incisional cyclic steps of permanent form in mixed bedrock-alluvial rivers. J. Geophys. Res. Earth Surf. 122, 130–152 (2017).

    Google Scholar 

  111. 111.

    Yokokawa, M., Kotera, A. & Kyogoku, A. in Advances in River Sediment Research (eds Fukuoka, S., Nakagawa, H., Sumi, T. & Zhang, H.) (CRC, 2013).

  112. 112.

    Scheingross, J. S. & Lamb, M. P. Sediment transport through self-adjusting, bedrock-walled waterfall plunge pools. J. Geophys. Res. Earth Surf. 121, 939–963 (2016).

    Google Scholar 

  113. 113.

    Scheingross, J. S. & Lamb, M. P. A mechanistic model of waterfall plunge pool erosion into bedrock. J. Geophys. Res. Earth Surf. 122, 2079–2104 (2017).

    Google Scholar 

  114. 114.

    Sklar, L. S. & Dietrich, W. E. Sediment and rock strength controls on river incision into bedrock. Geology 29, 1087–1090 (2001).

    Google Scholar 

  115. 115.

    Korup, O., Montgomery, D. R. & Hewitt, K. Glacier and landslide feedbacks to topographic relief in the Himalayan syntaxes. Proc. Natl Acad. Sci. USA 107, 5317–5322 (2010).

    Google Scholar 

  116. 116.

    Lamb, M. P. & Fonstad, M. A. Rapid formation of a modern bedrock canyon by a single flood event. Nat. Geosci. 3, 477–481 (2010).

    Google Scholar 

  117. 117.

    Gallen, S. F. et al. Hillslope response to knickpoint migration in the Southern Appalachians: implications for the evolution of post-orogenic landscapes. Earth Surf. Process. Landf. 36, 1254–1267 (2011).

    Google Scholar 

  118. 118.

    Weissel, J. K. & Seidl, M. A. in Rivers Over rock: Fluvial Processes in Bedrock Channels Geophysical Monograph (eds Tinkler, K. J. & Wohl, E. E.) 189-206 (American Geophysical Union, 1998).

  119. 119.

    Mitchell, N. A. & Yanites, B. J. Spatially variable increase in rock uplift in the northern US Cordillera recorded in the distribution of river knickpoints and incision depths. J. Geophys. Res. Earth Surf. 124, 1238–1260 (2019).

    Google Scholar 

  120. 120.

    Crosby, B. T., Whipple, K. X., Gasparini, N. M. & Wobus, C. W. Formation of fluvial hanging valleys: Theory and simulation. J. Geophys. Res. Earth Surf. 112, F03S10 (2007).

    Google Scholar 

  121. 121.

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

    Google Scholar 

  122. 122.

    Hack, J. T. Studies of Longitudinal Stream Profiles in Virginia and Maryland (United States Geological Survey, 1957).

  123. 123.

    Bishop, P. Drainage rearrangement by river capture, beheading and diversion. Prog. Phys. Geog. 19, 449–473 (1995).

    Google Scholar 

  124. 124.

    Davis, W. M. A river-pirate. Science 13, 108–109 (1889).

    Google Scholar 

  125. 125.

    Braun, J. A review of numerical modeling studies of passive margin escarpments leading to a new analytical expression for the rate of escarpment migration velocity. Gondwana Res. 53, 209–224 (2018).

    Google Scholar 

  126. 126.

    Campbell, M. R. Drainage Modifications and Their Interpretation (Univ. Chicago Press, 1896).

  127. 127.

    Marshall, J. S., Idleman, B. D., Gardner, T. W. & Fisher, D. M. Landscape evolution within a retreating volcanic arc, Costa Rica, Central America. Geology 31, 419–422 (2003).

    Google Scholar 

  128. 128.

    Shugar, D. H. et al. River piracy and drainage basin reorganization led by climate-driven glacier retreat. Nat. Geosci. 10, 370–375 (2017).

    Google Scholar 

  129. 129.

    Wickert, A. D., Mitrovica, J. X., Williams, C. & Anderson, R. S. Gradual demise of a thin southern Laurentide ice sheet recorded by Mississippi drainage. Nature 502, 668–671 (2013).

    Google Scholar 

  130. 130.

    Brocard, G. et al. Rate and processes of river network rearrangement during incipient faulting: the case of the Cahabón River, Guatemala. Am. J. Sci. 312, 449–507 (2012).

    Google Scholar 

  131. 131.

    Henry, C. D. et al. Eocene–Early Miocene paleotopography of the Sierra Nevada–Great Basin–Nevadaplano based on widespread ash-flow tuffs and paleovalleys. Geosphere 8, 1–27 (2012).

    Google Scholar 

  132. 132.

    Johnson, K. N. Causes and Consequences of Meandering in Bedrock Rivers: How Interactions Between Rock Properties and Environmental Conditions Shape Landscapes. PhD thesis, Univ. California Santa Cruz (2016).

  133. 133.

    Kwang, J. S. & Parker, G. Extreme memory of initial conditions in numerical landscape evolution models. Geophys. Res. Lett. 46, 6563–6573 (2019).

    Google Scholar 

  134. 134.

    Montgomery, D. R. & Dietrich, W. E. Channel initiation and the problem of landscape scale. Science 255, 826–830 (1992).

    Google Scholar 

  135. 135.

    Horton, R. E. Erosional development of streams and their drainage basins; hydrophyiscal approach to quantitative morphology. Geol. Soc. Am. Bull. 56, 275–370 (1945).

    Google Scholar 

  136. 136.

    Howard, A. D. Simulation model of stream capture. Geol. Soc. Am. Bull. 82, 1355–1376 (1971).

    Google Scholar 

  137. 137.

    Prince, P. S., Spotila, J. A. & Henika, W. S. Stream capture as driver of transient landscape evolution in a tectonically quiescent setting. Geology 39, 823–826 (2011).

    Google Scholar 

  138. 138.

    Goren, L., Willett, S. D., Herman, F. & Braun, J. Coupled numerical-analytical approach to landscape evolution modeling. Earth Surf. Process. Landf. 39, 522–545 (2014).

    Google Scholar 

  139. 139.

    Perron, J. T., Kirchner, J. W. & Dietrich, W. E. Formation of evenly spaced ridges and valleys. Nature 460, 502–505 (2009).

    Google Scholar 

  140. 140.

    Perron, J. T., Richardson, P. W., Ferrier, K. L. & Lapotre, M. The root of branching river networks. Nature 492, 100–103 (2012).

    Google Scholar 

  141. 141.

    Bonnet, S. Shrinking and splitting of drainage basins in orogenic landscapes from the migration of the main drainage divide. Nat. Geosci. 2, 766–771 (2009).

    Google Scholar 

  142. 142.

    Reinhardt, L. & Ellis, M. A. The emergence of topographic steady state in a perpetually dynamic self-organized critical landscape. Water Resour. Res. 51, 4986–5003 (2015).

    Google Scholar 

  143. 143.

    Whipple, K. X. Fluvial landscape response time: how plausible is steady-state denudation? Am. J. Sci. 301, 313–325 (2001).

    Google Scholar 

  144. 144.

    Whipple, K. X., DiBiase, R. A., Ouimet, W. B. & Forte, A. M. Preservation or piracy: Diagnosing low-relief, high-elevation surface formation mechanisms. Geology 45, 91–94 (2017).

    Google Scholar 

  145. 145.

    Whipple, K. X., DiBiase, R. A., Ouimet, W. B. & Forte, A. M. Preservation or piracy: Diagnosing low-relief, high-elevation surface formation mechanisms: reply. Geology 45, e422 (2017).

    Google Scholar 

  146. 146.

    Willett, S. D. Preservation or piracy: diagnosing low-relief, high-elevation surface formation mechanisms: comment. Geology 45, e421 (2017).

    Google Scholar 

  147. 147.

    Chamberlin, E. P., Hajek, E. A. & Trampush, S. M. Measuring scales of autogenic organization in fluvial stratigraphy: an example from the Cretaceous Lower Williams Fork Formation, Colorado. SEPM Spec. Publ. 106, 132–144 (2016).

    Google Scholar 

  148. 148.

    Trampush, S. M. & Hajek, E. A. Preserving proxy records in dynamic landscapes: Modeling and examples from the Paleocene-Eocene Thermal Maximum. Geology 45, 967–970 (2017).

    Google Scholar 

  149. 149.

    Hajek, E. A., Heller, P. L. & Sheets, B. A. Significance of channel-belt clustering in alluvial basins. Geology 38, 535–538 (2010).

    Google Scholar 

  150. 150.

    Tipper, J. C. The importance of doing nothing: stasis in sedimentation systems and its stratigraphic effects. Geol. Soc. Spec. Publ. 404, 105–122 (2015).

    Google Scholar 

  151. 151.

    Straub, K. M. & Esposito, C. R. Influence of water and sediment supply on the stratigraphic record of alluvial fans and deltas: Process controls on stratigraphic completeness. J. Geophys. Res. Earth Surf. 118, 625–637 (2013).

    Google Scholar 

  152. 152.

    Li, Q., Yu, L. Z. & Straub, K. M. Storage thresholds for relative sea-level signals in the stratigraphic record. Geology 44, 179–182 (2016).

    Google Scholar 

  153. 153.

    Straub, K. M. & Wang, Y. A. Influence of water and sediment supply on the long-term evolution of alluvial fans and deltas: Statistical characterization of basin-filling sedimentation patterns. J. Geophys. Res. Earth Surf. 118, 1602–1616 (2013).

    Google Scholar 

  154. 154.

    Trampush, S. M., Hajek, E. A., Straub, K. M. & Chamberlin, E. P. Identifying autogenic sedimentation in fluvial-deltaic stratigraphy: Evaluating the effect of outcrop-quality data on the compensation statistic. J. Geophys. Res. Earth Surf. 122, 91–113 (2017).

    Google Scholar 

  155. 155.

    Foreman, B. Z. & Straub, K. M. Autogenic geomorphic processes determine the resolution and fidelity of terrestrial paleoclimate records. Sci. Adv. 3, e1700683 (2017).

    Google Scholar 

  156. 156.

    D’Arcy, M., Roda-Boluda, D. C. & Whittaker, A. C. Glacial-interglacial climate changes recorded by debris flow fan deposits, Owens Valley, California. Quat. Sci. Rev. 169, 288–311 (2017).

    Google Scholar 

  157. 157.

    Wobus, C. W., Crosby, B. T. & Whipple, K. X. Hanging valleys in fluvial systems: Controls on occurrence and implications for landscape evolution. J. Geophys. Res. Earth Surf. 111, F02017 (2006).

    Google Scholar 

  158. 158.

    Murray, A. B. et al. Geomorphology, complexity, and the emerging science of the Earth’s surface. Geomorphology 103, 496–505 (2009).

    Google Scholar 

  159. 159.

    Paola, C., Straub, K., Mohrig, D. & Reinhardt, L. The “unreasonable effectiveness” of stratigraphic and geomorphic experiments. Earth Sci. Rev. 97, 1–43 (2009).

    Google Scholar 

  160. 160.

    Lancaster, S. T. A Nonlinear River Meandering Model and its Incorporation in a Landscape Evolution Model. PhD thesis, Massachusetts Institute of Technology (1998).

  161. 161.

    Langston, A. L. & Tucker, G. E. Developing and exploring a theory for the lateral erosion of bedrock channels for use in landscape evolution models. Earth Surf. Dyn. 6, 1–27 (2018).

    Google Scholar 

  162. 162.

    Gasparini, N. M., Whipple, K. X. & Bras, R. L. Predictions of steady state and transient landscape morphology using sediment-flux-dependent river incision models. J. Geophys. Res. Earth Surf. 112, F03S09 (2007).

    Google Scholar 

  163. 163.

    Sklar, L. S. & Dietrich, W. E. Implications of the saltation–abrasion bedrock incision model for steady-state river longitudinal profile relief and concavity. Earth Surf. Process. Landf. 33, 1129–1151 (2008).

    Google Scholar 

  164. 164.

    Zhang, L. et al. Bedrock-alluvial streams with knickpoint and plunge pool that migrate upstream with permanent form. Sci. Rep. 9, 6176 (2019).

    Google Scholar 

  165. 165.

    Glade, R. C., Shobe, C. M., Anderson, R. S. & Tucker, G. E. Canyon shape and erosion dynamics governed by channel-hillslope feedbacks. Geology 47, 650–654 (2019).

    Google Scholar 

  166. 166.

    Zhang, L. et al. How canyons evolve by incision into bedrock: Rainbow Canyon, Death Valley National Park, United States. Proc. Natl Acad. Sci. USA 117, 14730–14737 (2020).

    Google Scholar 

  167. 167.

    Smith, T. R. A theory for the emergence of channelized drainage. J. Geophys. Res. Earth Surf. 115, F02023 (2010).

    Google Scholar 

  168. 168.

    Smith, T. R. Analytic theory of equilibrium fluvial landscapes: the integration of hillslopes and channels. J. Geophys. Res. Earth Surf. 123, 557–615 (2018).

    Google Scholar 

  169. 169.

    Smith, T. R. & Bretherton, F. P. Stability and the conservation of mass in drainage basin evolution. Water Resour. Res. 8, 1506–1529 (1972).

    Google Scholar 

  170. 170.

    Lague, D., Crave, A. & Davy, P. Laboratory experiments simulating the geomorphic response to tectonic uplift. J. Geophys. Res. Solid Earth 108, 2008 (2003).

    Google Scholar 

  171. 171.

    Sweeney, K. E., Roering, J. J. & Ellis, C. Experimental evidence for hillslope control of landscape scale. Science 349, 51–53 (2015).

    Google Scholar 

  172. 172.

    Cook, K. L., Turowski, J. M. & Hovius, N. A demonstration of the importance of bedload transport for fluvial bedrock erosion and knickpoint propagation. Earth Surf. Process. Landf. 38, 683–695 (2012).

    Google Scholar 

  173. 173.

    Tejedor, A., Singh, A., Zaliapin, I., Densmore, A. L. & Foufoula-Georgiou, E. Scale-dependent erosional patterns in steady-state and transient-state landscapes. Sci. Adv. 3, e1701683 (2017).

    Google Scholar 

  174. 174.

    Mudd, S. M., Attal, M., Milodowski, D. T., Grieve, S. W. D. & Valters, D. A. A statistical framework to quantify spatial variation in channel gradients using the integral method of channel profile analysis. J. Geophys. Res. Earth Surf. 119, 138–152 (2014).

    Google Scholar 

  175. 175.

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

    Google Scholar 

  176. 176.

    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).

    Google Scholar 

  177. 177.

    Lague, D. The stream power river incision model: evidence, theory and beyond. Earth Surf. Process. Landf. 39, 38–61 (2014).

    Google Scholar 

  178. 178.

    Malatesta L.C. & Lamb M.P. Formation of waterfalls by intermittent burial of active faults. Geol. Soc. Am. Bull. 130, 522–536 (2018).

    Google Scholar 

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The authors thank Helen Beeson and Sophie Rothman for sharing data and discussion and the Earth-surface processes and sedimentology community that has inspired this work and improved our understanding of autogenic dynamics and landscape evolution.

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Correspondence to Joel S. Scheingross.

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Erosional landscapes

Landscapes in which the morphology and rate of evolution are set by bedrock erosion.


Sections of a river channel that are locally steeper than the sections above and below.

Autogenic dynamics

Internal feedbacks between topography, erosion and sediment transport that result in non-steady-state behaviour, even under constant external forcing.

Supercritical flow

Flow in which the downstream water velocity is greater than the wave speed.

Complex, non-linear feedbacks

System responses that are not in direct proportion to external forcing, owing largely to internal system feedbacks.

Dynamic equilibrium

For river profiles, the case when rivers maintain constant profile form averaged over long timescales but can deviate from equilibrium form over short timescales, owing to ongoing geomorphic change.

Drainage divides

Ridges or hillslopes that create a boundary between two separate drainage basins.

River-basin reorganization

Changes in the geometry and topology of a network of drainage basins induced by gradual drainage divide migration or discrete capture of drainage area.

Expanding basin

A river basin that gains area owing to divide migration into an adjacent contracting basin.

Contracting basin

A river basin that loses area owing to divide migration from an adjacent expanding basin.


The natural process of river-channel abandonment as flow is diverted from an existing channel to a new channel.

Surface roughness height

A characteristic scale of topographic variation.

Geometric equilibrium

For drainage divides, a state in which divides are stationary because the topology and distribution of drainage areas have adjusted such that erosion rates in all rivers balance the rate of rock uplift.

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Scheingross, J.S., Limaye, A.B., McCoy, S.W. et al. The shaping of erosional landscapes by internal dynamics. Nat Rev Earth Environ 1, 661–676 (2020).

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