Articles | Volume 13, issue 5
https://doi.org/10.5194/esurf-13-1003-2025
© Author(s) 2025. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/esurf-13-1003-2025
© Author(s) 2025. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Research article
| 
20 Oct 2025
Research article |
| 20 Oct 2025
| 20 Oct 2025
Impact of noise on landscapes and metrics generated with stream power models
Matthew J. Morris
CORRESPONDING AUTHOR
Department of Earth Science and Engineering, Imperial College London, Royal School of Mines, South Kensington, London, SW7 2AZ, UK
Gareth G. Roberts
Department of Earth Science and Engineering, Imperial College London, Royal School of Mines, South Kensington, London, SW7 2AZ, UK
Related authors
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Gareth G. Roberts
Earth Surf. Dynam., 13, 563–570, https://doi.org/10.5194/esurf-13-563-2025, https://doi.org/10.5194/esurf-13-563-2025, 2025
Short summary
Short summary
The use of new artificial intelligence (AI) techniques to learn how landscapes evolve is demonstrated. A few “snapshots” of an eroding landscape at different stages of its history provide enough information for AI to ascertain rules governing its evolution. Once the rules are known, predicting landscape evolution is extremely rapid and efficient, providing new tools to understand landscape change.
Conor P. B. O'Malley, Gareth G. Roberts, James Panton, Fred D. Richards, J. Huw Davies, Victoria M. Fernandes, and Sia Ghelichkhan
Geosci. Model Dev., 17, 9023–9049, https://doi.org/10.5194/gmd-17-9023-2024, https://doi.org/10.5194/gmd-17-9023-2024, 2024
Short summary
Short summary
We wish to understand how the history of flowing rock within Earth's interior impacts deflection of its surface. Observations exist to address this problem, and mathematics and different computing tools can be used to predict histories of flow. We explore how modeling choices impact calculated vertical deflections. The sensitivity of vertical motions at Earth's surface to deep flow is assessed, demonstrating how surface observations can enlighten flow histories.
Cited articles
Adams, B. A., Hodges, K. V., Whipple, K. X., Ehlers, T. A., van Soest, M. C., and Wartho, J.: Constraints on the tectonic and landscape evolution of the Bhutan Himalaya from thermochronometry, Tectonics, 34, 1329–1347, https://doi.org/10.1002/2015TC003853, 2015. a
Adams, B. A., Whipple, K. X., Forte, A. M., Heimsath, A. M., and Hodges, K. V.: Climate controls on erosion in tectonically active landscapes, Science Advances, 6, https://doi.org/10.1126/sciadv.aaz3166, 2020. a
Ancey, C., Bohorquez, P., and Heyman, J.: Stochastic interpretation of the advection-diffusion equation and its relevance to bed load transport, Journal of Geophysical Research: Earth Surface, 120, 2529–2551, https://doi.org/10.1002/2014JF003421, 2015. a
Anderson, R. S. and Anderson, S. P.: Geomorphology: The Mechanics and Chemistry of Landscapes, Cambridge University Press, https://doi.org/10.1017/CBO9780511794827, 2010. a, b
Attal, M., Tucker, G. E., Whittaker, A. C., Cowie, P. A., and Roberts, G. P.: Modeling fluvial incision and transient landscape evolution: Influence of dynamic channel adjustment, Journal of Geophysical Research: Earth Surface, 113, https://doi.org/10.1029/2007JF000893, 2008. a
Audet, P.: Directional wavelet analysis on the sphere: Application to gravity and topography of the terrestrial planets, Journal of Geophysical Research: Planets, 116, https://doi.org/10.1029/2010JE003710, 2011. a
Baldwin, J. A., Whipple, K. X., and Tucker, G. E.: Implications of the shear stress river incision model for the timescale of postorogenic decay of topography, Journal of Geophysical Research: Solid Earth, 108, https://doi.org/10.1029/2001JB000550, 2003. a
Balmino, G.: The Spectra of the topography of the Earth, Venus and Mars, Geophysical Research Letters, 20, 1063–1066, https://doi.org/10.1029/93GL01214, 1993. a
Barnes, R., Lehman, C., and Mulla, D.: Priority-flood: An optimal depression-filling and watershed-labeling algorithm for digital elevation models, Computers & Geosciences, 62, 117–127, https://doi.org/10.1016/j.cageo.2013.04.024, 2014. a
Barnhart, K. R., Hutton, E. W. H., Tucker, G. E., Gasparini, N. M., Istanbulluoglu, E., Hobley, D. E. J., Lyons, N. J., Mouchene, M., Nudurupati, S. S., Adams, J. M., and Bandaragoda, C.: Short communication: Landlab v2.0: a software package for Earth surface dynamics, Earth Surf. Dynam., 8, 379 – 397, https://doi.org/10.5194/esurf-8-379-2020, 2020a. a, b
Barnhart, K. R., Tucker, G. E., Doty, S. G., Shobe, C. M., Glade, R. C., Rossi, M. W., and Hill, M. C.: Inverting Topography for Landscape Evolution Model Process Representation: 1. Conceptualization and Sensitivity Analysis, Journal of Geophysical Research: Earth Surface, 125, https://doi.org/10.1029/2018JF004961, 2020b. a, b
Barnhart, K. R., Tucker, G. E., Doty, S. G., Shobe, C. M., Glade, R. C., Rossi, M. W., and Hill, M. C.: Inverting Topography for Landscape Evolution Model Process Representation: 3. Determining Parameter Ranges for Select Mature Geomorphic Transport Laws and Connecting Changes in Fluvial Erodibility to Changes in Climate, Journal of Geophysical Research: Earth Surface, 125, https://doi.org/10.1029/2019JF005287, 2020c. a, b
Beaumont, C., Fullsack, P., and Hamilton, J.: Erosional control of active compressional orogens, in: Thrust Tectonics, edited by: McClay, K. R., Springer Netherlands, 1–18, https://doi.org/10.1007/978-94-011-3066-0_1, 1992. a
Bell, T. H.: Statistical features of sea-floor topography, Deep Sea Research and Oceanographic Abstracts, 22, 883–892, https://doi.org/10.1016/0011-7471(75)90090-X, 1975. a
Booth, A. M., Roering, J. J., and Perron, J. T.: Automated landslide mapping using spectral analysis and high-resolution topographic data: Puget Sound lowlands, Washington, and Portland Hills, Oregon, Geomorphology, 109, 132–147, https://doi.org/10.1016/j.geomorph.2009.02.027, 2009. a
Bovy, B.: fastscape-lem/fastscape: Release v0.1.0beta3, Zenodo [code], https://doi.org/10.5281/zenodo.4435110, 2021. a
Braun, J. and Sambridge, M.: Modelling landscape evolution on geological time scales: a new method based on irregular spatial discretization, Basin Research, 9, 27–52, https://doi.org/10.1046/j.1365-2117.1997.00030.x, 1997. a, b, c
Braun, J. and van der Beek, P.: Evolution of passive margin escarpments: What can we learn from low-temperature thermochronology?, Journal of Geophysical Research: Earth Surface, 109, https://doi.org/10.1029/2004JF000147, 2004. a
Braun, J. and Willett, S. D.: A very efficient O(n), implicit and parallel method to solve the stream power equation governing fluvial incision and landscape evolution, Geomorphology, 180–181, 170–179, https://doi.org/10.1016/j.geomorph.2012.10.008, 2013. a, b
Braun, J., Robert, X., and Simon-Labric, T.: Eroding dynamic topography, Geophysical Research Letters, 40, 1494–1499, https://doi.org/10.1002/grl.50310, 2013. a
Campforts, B., Vanacker, V., Herman, F., Vanmaercke, M., Schwanghart, W., Tenorio, G. E., Willems, P., and Govers, G.: Parameterization of river incision models requires accounting for environmental heterogeneity: insights from the tropical Andes, Earth Surf. Dynam., 8, 447 – 470, https://doi.org/10.5194/esurf-8-447-2020, 2020. a, b
Castelltort, S. and Yamato, P.: The influence of surface slope on the shape of river basins: Comparison between nature and numerical landscape simulations, Geomorphology, 192, 71–79, https://doi.org/10.1016/j.geomorph.2013.03.022, 2013. a, b
Chen, T.-Y. K., Hung, C.-Y., Chiang, Y.-C., Hsieh, M.-L., and Capart, H.: A stochastic model of geomorphic risk due to episodic river aggradation and degradation, Engineering Geology, 309, 106845, https://doi.org/10.1016/j.enggeo.2022.106845, 2022. a
Clubb, F. J., Mudd, S. M., Schildgen, T. F., van der Beek, P. A., Devrani, R., and Sinclair, H. D.: Himalayan valley-floor widths controlled by tectonically driven exhumation, Nature Geoscience, 16, 739–746, https://doi.org/10.1038/s41561-023-01238-8, 2023. a
Cooley, J. W. and Tukey, J. W.: An Algorithm for the Machine Calculation of Complex Fourier Series, Mathematics of Computation, 19, 297–301, https://doi.org/10.1090/S0025-5718-1965-0178586-1, 1965. a
Coulthard, T. J., Ramirez, J., Fowler, H. J., and Glenis, V.: Using the UKCP09 probabilistic scenarios to model the amplified impact of climate change on drainage basin sediment yield, Hydrol. Earth Syst. Sci., 16, 4401 – 4416, https://doi.org/10.5194/hess-16-4401-2012, 2012. a
Croissant, T. and Braun, J.: Constraining the stream power law: a novel approach combining a landscape evolution model and an inversion method, Earth Surf. Dynam., 2, 155 – 166, https://doi.org/10.5194/esurf-2-155-2014, 2014. a, b, c
Cullen, C., Anders, A. M., Lai, J., and Druhan, J. L.: Numerical modeling of groundwater-driven stream network evolution in low-relief post-glacial landscapes, Earth Surface Processes and Landforms, 47, 658–671, https://doi.org/10.1002/esp.5278, 2022. a
DeLisle, C. and Yanites, B. J.: Modeling Climate and Tectonic Controls on Bias in Measured River Incision Rates, Geophysical Research Letters, 51, e2024GL109339, https://doi.org/10.1029/2024GL109339, 2024. a
Etherington, T. R.: Perlin noise as a hierarchical neutral landscape model, Web Ecol., 22, 1 – 6, https://doi.org/10.5194/we-22-1-2022, 2022. a
Ferrier, K. L., Huppert, K. L., and Perron, J. T.: Climatic control of bedrock river incision, Nature, 496, 206–209, https://doi.org/10.1038/nature11982, 2013. a
Fisher, J. A., Pazzaglia, F. J., Anastasio, D. J., and Gallen, S. F.: Linear Inversion of Fluvial Topography in the Northern Apennines: Comparison of Base-Level Fall to Crustal Shortening, Tectonics, 41, https://doi.org/10.1029/2022TC007379, 2022. a
Flint, J. J.: Stream gradient as a function of order, magnitude, and discharge, Water Resources Research, 10, 969–973, https://doi.org/10.1029/WR010i005p00969, 1974. a
Forte, A. M., Yanites, B. J., and Whipple, K. X.: Complexities of landscape evolution during incision through layered stratigraphy with contrasts in rock strength, Earth Surface Processes and Landforms, 41, 1736–1757, https://doi.org/10.1002/esp.3947, 2016. a, b, c
Fournier, A., Fussell, D., and Carpenter, L.: Computer rendering of stochastic models, Commun. ACM, 25, 371–384, https://doi.org/10.1145/358523.358553, 1982. a
Gailleton, B., Mudd, S. M., Clubb, F. J., Grieve, S. W. D., and Hurst, M. D.: Impact of Changing Concavity Indices on Channel Steepness and Divide Migration Metrics, Journal of Geophysical Research: Earth Surface, 126, https://doi.org/10.1029/2020JF006060, 2021. a, b
Gilbert, G. K.: Report on the geology of the Henry Mountains (Technical Report), Tech. rep., Geographical and Geological Survey of the Rocky Mountain Region, Government Printing Office, https://doi.org/10.3133/70039916, 1877. a
Goren, L., Willett, S. D., Herman, F., and Braun, J.: Coupled numerical – analytical approach to landscape evolution modeling, Earth Surface Processes and Landforms, 39, 522–545, https://doi.org/10.1002/esp.3514, 2014. a, b, c
Gray, H. J., Shobe, C. M., Hobley, D. E., Tucker, G. E., Duvall, A. R., Harbert, S. A., and Owen, L. A.: Off-fault deformation rate along the southern San Andreas fault at Mecca Hills, southern California, inferred from landscape modeling of curved drainages, Geology, 46, 59–62, https://doi.org/10.1130/G39820.1, 2017. a, b, c
Hack, J. T.: Studies of Longitudinal Stream Profiles in Virginia and Maryland, in: Geological Survey Professional Paper 294-B USGS, United States Government Printing Office, Washington (1957), 45–80, https://doi.org/10.3133/pp294B, 1957. a, b, c, d
Hancock, G. R., Coulthard, T. J., and Lowry, J. B. C.: Predicting uncertainty in sediment transport and landscape evolution – the influence of initial surface conditions, Computers & Geosciences, 90, 117–130, https://doi.org/10.1016/j.cageo.2015.08.014, 2016. a
Harel, M. A., Mudd, S. M., and Attal, M.: Global analysis of the stream power law parameters based on worldwide 10Be denudation rates, Geomorphology, 268, 184–196, https://doi.org/10.1016/j.geomorph.2016.05.035, 2016. a
Harkins, N., Kirby, E., Heimsath, A., Robinson, R., and Reiser, U.: Transient fluvial incision in the headwaters of the Yellow River, northeastern Tibet, China, China, J. Geophys. Res, 112, 3–04, https://doi.org/10.1029/2006JF000570, 2007. a, b
Harrison, C. G. A., Miskell, K. J., Brass, G. W., Saltzman, E. S., and Sloan, J. L.: Continental hypsography, Tectonics, 2, 357–377, https://doi.org/10.1029/TC002i004p00357, 1983. a
Hasbargen, L. E. and Paola, C.: Landscape instability in an experimental drainage basin, Geology, 28, 1067–1070, https://doi.org/10.1130/0091-7613(2000)28<1067:LIIAED>2.0.CO;2, 2000. a
Haviv, I., Enzel, Y., Whipple, K. X., Zilberman, E., Matmon, A., Stone, J., and Fifield, K. L.: Evolution of vertical knickpoints (waterfalls) with resistant caprock: Insights from numerical modeling, Journal of Geophysical Research: Earth Surface, 115, https://doi.org/10.1029/2008JF001187, 2010. a
He, C., Yang, C.-J., Turowski, J. M., Ott, R. F., Braun, J., Tang, H., Ghantous, S., Yuan, X., and Stucky de Quay, G.: A global dataset of the shape of drainage systems, Earth Syst. Sci. Data, 16, 1151–1166, https://doi.org/10.5194/essd-16-1151-2024, 2024. a
Hergarten, S., Robl, J., and Stüwe, K.: Tectonic geomorphology at small catchment sizes – extensions of the stream-power approach and the χ method, Earth Surf. Dynam., 4, 1–9, https://doi.org/10.5194/esurf-4-1-2016, 2016. a, b
Hobley, D. E. J., Adams, J. M., Nudurupati, S. S., Hutton, E. W. H., Gasparini, N. M., Istanbulluoglu, E., and Tucker, G. E.: Creative computing with Landlab: an open-source toolkit for building, coupling, and exploring two-dimensional numerical models of Earth-surface dynamics, Earth Surf. Dynam., 5, 21–46, https://doi.org/10.5194/esurf-5-21-2017, 2017. a, b, c, d
Holdt, M. C., White, N. J., Stephenson, S. N., and Conway-Jones, B. W.: Densely Sampled Global Dynamic Topographic Observations and Their Significance, Journal of Geophysical Research: Solid Earth, 127, e2022JB024391, https://doi.org/10.1029/2022JB024391, 2022. a
Hoskins, A. M., Attal, M., Mudd, S. M., and Castillo, M.: Topographic Response to Horizontal Advection in Normal Fault-Bound Mountain Ranges, Journal of Geophysical Research: Earth Surface, 128, e2023JF007126, https://doi.org/10.1029/2023JF007126, 2023. a
Howard, A. D.: A detachment-limited model of drainage basin evolution, Water Resources Research, 30, 2261–2285, https://doi.org/10.1029/94WR00757, 1994. a, b, c, d
Hurtrez, J.-E., Sol, C., and Lucazeau, F.: Effect of drainage area on hypsometry from an analysis of small-scale drainage basins in the Siwalik Hills (Central Nepal), Earth Surface Processes and Landforms, 24, 799–808, https://doi.org/10.1002/(SICI)1096-9837(199908)24:9<799::AID-ESP12>3.0.CO;2-4, 1999. a
Hutton, E., Barnhart, K., Hobley, D., Tucker, G., Nudurupati, S., Adams, J., Gasparini, N., Shobe, C., Strauch, R., Knuth, J., Mouchene, M., Lyons, N., Litwin, D., Glade, R., Giuseppecipolla95, Manaster, A., Abby, L., Thyng, K., and Rengers, F.: Landlab, Zenodo [code], https://doi.org/10.5281/zenodo.595872, 2020. a, b
Ijjasz-Vasquez, E. J., Bras, R. L., and Rodriguez-Iturbe, I.: Hack's relation and optimal channel networks: The elongation of river basins as a consequence of energy minimization, Geophysical Research Letters, 20, 1583–1586, https://doi.org/10.1029/93GL01517, 1993. a
Ijjász-Vásquez, E. J., Bras, R. L., and Moglen, G. E.: Sensitivity of a basin evolution model to the nature of runoff production and to initial conditions, Water Resources Research, 28, 2733–2741, https://doi.org/10.1029/92WR01561, 1992. a, b
Ijjász-Vásquez, E. J., Bras, R. L., Rodríguez-Iturbe, I., Rigon, R., and Rinaldo, A.: Are river basins optimal channel networks?, Advances in Water Resources, 16, 69–79, https://doi.org/10.1016/0309-1708(93)90030-J, 1993. a
Imperial College Research Computing Service: https://doi.org/10.14469/hpc/2232, 2025. a
Istanbulluoglu, E. and Bras, R. L.: Vegetation-modulated landscape evolution: Effects of vegetation on landscape processes, drainage density, and topography, Journal of Geophysical Research: Earth Surface, 110, https://doi.org/10.1029/2004JF000249, 2005. a
Karlstrom, K. E., Crow, R. S., Peters, L., McIntosh, W., Raucci, J., Crossey, L. J., Umhoefer, P., and Dunbar, N.: 40Ar/39Ar and field studies of Quaternary basalts in Grand Canyon and model for carving Grand Canyon: Quantifying the interaction of river incision and normal faulting across the western edge of the Colorado Plateau, GSA Bulletin, 119, 1283–1312, https://doi.org/10.1130/0016-7606(2007)119[1283:AAFSOQ]2.0.CO;2, 2007. a
Kirby, E. and Whipple, K.: Quantifying differential rock-uplift rates via stream profile analysis, Geology, 29, 415–418, https://doi.org/10.1130/0091-7613(2001)029<0415:QDRURV>2.0.CO;2, 2001. a
Kirby, E. and Whipple, K. X.: Expression of active tectonics in erosional landscapes, Journal of Structural Geology, 44, 54–75, https://doi.org/10.1016/j.jsg.2012.07.009, 2012. a
Kirchner, J. W. and Weil, A.: No fractals in fossil extinction statistics, Nature, 395, 337–338, https://doi.org/10.1038/26384, 1998. a
Kooi, H. and Beaumont, C.: Escarpment evolution on high-elevation rifted margins: Insights derived from a surface processes model that combines diffusion, advection, and reaction, Journal of Geophysical Research: Solid Earth, 99, 12191–12209, https://doi.org/10.1029/94JB00047, 1994. a
Kwang, J. S. and Parker, G.: Extreme Memory of Initial Conditions in Numerical Landscape Evolution Models, Geophysical Research Letters, 46, 6563–6573, https://doi.org/10.1029/2019GL083305, 2019. a, b, c, d
Kwang, J. S., Langston, A. L., and Parker, G.: The role of lateral erosion in the evolution of nondendritic drainage networks to dendricity and the persistence of dynamic networks, Proceedings of the National Academy of Sciences, 118, e2015770118, https://doi.org/10.1073/pnas.2015770118, 2021. a
Lague, D.: The stream power river incision model: evidence, theory and beyond, Earth Surface Processes and Landforms, 39, 38–61, https://doi.org/10.1002/esp.3462, 2014. a, b, c
Langbein, W. B.: Topographic Characteristics of Drainage Basins, USGS Numbered Series 968-C, USGS, https://doi.org/10.3133/wsp968C, 1947. a, b
Leonard, J. S. and Whipple, K. X.: Influence of Spatial Rainfall Gradients on River Longitudinal Profiles and the Topographic Expression of Spatially and Temporally Variable Climates in Mountain Landscapes, Journal of Geophysical Research: Earth Surface, 126, e2021JF006183, https://doi.org/10.1029/2021JF006183, 2021. a
Lifton, N. A. and Chase, C. G.: Tectonic, climatic and lithologic influences on landscape fractal dimension and hypsometry: implications for landscape evolution in the San Gabriel Mountains, California, Geomorphology, 5, 77–114, https://doi.org/10.1016/0169-555X(92)90059-W, 1992. a
Lipp, A. G. and Roberts, G. G.: Scale-Dependent Flow Directions of Rivers and the Importance of Subplate Support, Geophysical Research Letters, 48, e2020GL091107, https://doi.org/10.1029/2020GL091107, 2021. a
Lipp, A. G., Roberts, G. G., Whittaker, A. C., Gowing, C. J. B., and Fernandes, V. M.: River Sediment Geochemistry as a Conservative Mixture of Source Regions: Observations and Predictions From the Cairngorms, UK, Journal of Geophysical Research: Earth Surface, 125, e2020JF005700, https://doi.org/10.1029/2020JF005700, 2020. a
Lipp, A. G., Roberts, G. G., Whittaker, A. C., Gowing, C. J. B., and Fernandes, V. M.: Source Region Geochemistry From Unmixing Downstream Sedimentary Elemental Compositions, Geochemistry, Geophysics, Geosystems, 22, e2021GC009838, https://doi.org/10.1029/2021GC009838, 2021. a
Lyons, N. J., Val, P., Albert, J. S., Willenbring, J. K., and Gasparini, N. M.: Topographic controls on divide migration, stream capture, and diversification in riverine life, Earth Surf. Dynam., 8, 893–912, https://doi.org/10.5194/esurf-8-893-2020, 2020. a, b, c
Malatesta, L. C., Finnegan, N. J., Huppert, K. L., and Carreño, E. I.: The influence of rock uplift rate on the formation and preservation of individual marine terraces during multiple sea-level stands, Geology, 50, 101–105, https://doi.org/10.1130/G49245.1, 2022. a
Mandelbrot, B. B. and Wheeler, J. A.: The Fractal Geometry of Nature, American Journal of Physics, 51, 286–287, https://doi.org/10.1119/1.13295, 1983. a
Marder, E. and Gallen, S. F.: Climate control on the relationship between erosion rate and fluvial topography, Geology, 51, 424–427, https://doi.org/10.1130/G50832.1, 2023. a
Marder, E., Gallen, S. F., and Pazzaglia, F. J.: Late Cenozoic deformation in the U.S. southern Colorado Front Range revealed by river profile analysis and fluvial terraces, GSA Bulletin, 136, 1067–1085, https://doi.org/10.1130/B36440.1, 2023. a
McKenzie, D. and Bowin, C.: The relationship between bathymetry and gravity in the Atlantic Ocean, Journal of Geophysical Research, 81, 1903–1915, https://doi.org/10.1029/JB081i011p01903, 1976. a, b
McKenzie, D. and Fairhead, D.: Estimates of the effective elastic thickness of the continental lithosphere from Bouguer and free air gravity anomalies, Journal of Geophysical Research: Solid Earth, 102, 27523–27552, https://doi.org/10.1029/97JB02481, 1997. a
Mitchell, N. A. and Yanites, B. J.: Spatially Variable Increase in Rock Uplift in the Northern U.S. Cordillera Recorded in the Distribution of River Knickpoints and Incision Depths, Journal of Geophysical Research: Earth Surface, 124, 1238–1260, https://doi.org/10.1029/2018JF004880, 2019. a
Montgomery, D. R. and Dietrich, W. E.: Channel Initiation and the Problem of Landscape Scale, Science, 255, 826–830, https://doi.org/10.1126/science.255.5046.826, 1992. a
Montgomery, D. R. and Foufoula-Georgiou, E.: Channel network source representation using digital elevation models, Water Resources Research, 29, 3925–3934, https://doi.org/10.1029/93WR02463, 1993. a
Montgomery, D. R., Balco, G., and Willett, S. D.: Climate, tectonics, and the morphology of the Andes, Geology, 29, 579–582, https://doi.org/10.1130/0091-7613(2001)029<0579:CTATMO>2.0.CO;2, 2001. a
Morisawa, M. E.: Quantitative Geomorphology of Some Watersheds in the Appalachian Plateau, GSA Bulletin, 73, 1025–1046, https://doi.org/10.1130/0016-7606(1962)73[1025:QGOSWI]2.0.CO;2, 1962. a
Morris, M.: noisy_initial_conditions (1.1.0), Zenodo [code], https://doi.org/10.5281/zenodo.16926470, 2025. a
Morris, M. J., Lipp, A. G., and Roberts, G. G.: Towards Inverse Modeling of Landscapes Using the Wasserstein Distance, Geophysical Research Letters, 50, e2023GL103880, https://doi.org/10.1029/2023GL103880, 2023. a, b, c
Mudd, S. M., Attal, M., Milodowski, D. T., Grieve, S. W. D., and Valters, D. A.: A statistical framework to quantify spatial variation in channel gradients using the integral method of channel profile analysis, Journal of Geophysical Research: Earth Surface, 119, 138–152, https://doi.org/10.1002/2013JF002981, 2014. a, b, c
Mueller, J. E.: Re-evaluation of the Relationship of Master Streams and Drainage Basins, GSA Bulletin, 83, 3471–3474, https://doi.org/10.1130/0016-7606(1972)83[3471:ROTROM]2.0.CO;2, 1972. a, b
O'Callaghan, J. F. and Mark, D. M.: The extraction of drainage networks from digital elevation data, Computer Vision, Graphics, and Image Processing, 28, 323–344, https://doi.org/10.1016/S0734-189X(84)80011-0, 1984. a
O'Hara, D., Goren, L., van Wees, R. M. J., Campforts, B., Grosse, P., Lahitte, P., Kereszturi, G., and Kervyn, M.: Time-varying drainage basin development and erosion on volcanic edifices, Earth Surf. Dynam., 12, 709–726, https://doi.org/10.5194/esurf-12-709-2024, 2024. a
O'Malley, C. P. B.: Quantitative analysis of river profiles and fluvial landscapes, Ph.D. thesis, University of Cambridge, https://doi.org/10.17863/CAM.51663, 2020. a, b
O’Malley, C. P. B., White, N. J., Stephenson, S. N., and Roberts, G. G.: Large-Scale Tectonic Forcing of the African Landscape, Journal of Geophysical Research: Earth Surface, 126, https://doi.org/10.1029/2021JF006345, 2021. a, b
Paul, J. D., Roberts, G. G., and White, N.: The African landscape through space and time, Tectonics, 33, 898–935, https://doi.org/10.1002/2013TC003479, 2014. a
Paxman, G. J. G., Jamieson, S. S. R., Hochmuth, K., Gohl, K., Bentley, M. J., Leitchenkov, G., and Ferraccioli, F.: Reconstructions of Antarctic topography since the Eocene – Oligocene boundary, Palaeogeography, Palaeoclimatology, Palaeoecology, 535, 109 346, https://doi.org/10.1016/j.palaeo.2019.109346, 2019. a
Pelletier, J. D.: The power spectral density of atmospheric temperature from time scales of 10−2 to 106 yr, Earth and Planetary Science Letters, 158, 157–164, https://doi.org/10.1016/S0012-821X(98)00051-X, 1998. a
Pelletier, J. D.: Self-organization and scaling relationships of evolving river networks, Journal of Geophysical Research: Solid Earth, 104, 7359–7375, https://doi.org/10.1029/1998JB900110, 1999. a
Pelletier, J. D.: Numerical modeling of the Cenozoic geomorphic evolution of the southern Sierra Nevada, California, Earth and Planetary Science Letters, 259, 85–96, https://doi.org/10.1016/j.epsl.2007.04.030, 2007. a
Perlin, K.: An image synthesizer, SIGGRAPH Comput. Graph., 19, 287–296, https://doi.org/10.1145/325165.325247, 1985. a
Perlin, K.: Improving noise, in: Proceedings of the 29th Annual Conference on Computer Graphics and Interactive Techniques, SIGGRAPH '02, Association for Computing Machinery, New York, NY, USA, 681–682, ISBN 1581135211, https://doi.org/10.1145/566570.566636, 2002. a, b
Pritchard, D., Roberts, G. G., White, N. J., and Richardson, C. N.: Uplift histories from river profiles, Geophysical Research Letters, 36, https://doi.org/10.1029/2009GL040928, 2009. a, b
Pulkkinen, S., Nerini, D., Pérez Hortal, A. A., Velasco-Forero, C., Seed, A., Germann, U., and Foresti, L.: Pysteps: an open-source Python library for probabilistic precipitation nowcasting (v1.0), Geosci. Model Dev., 12, 4185–4219, https://doi.org/10.5194/gmd-12-4185-2019, 2019. a
Racano, S., Jara-Muñoz, J., Cosentino, D., and Melnick, D.: Variable Quaternary Uplift Along the Southern Margin of the Central Anatolian Plateau Inferred From Modeling Marine Terrace Sequences, Tectonics, 39, https://doi.org/10.1029/2019TC005921, 2020. a
Rapp, R. H.: The decay of the spectrum of the gravitational potential and the topography for the Earth, Geophysical Journal International, 99, 449–455, https://doi.org/10.1111/j.1365-246X.1989.tb02031.x, 1989. a
Rigon, R., Rodriguez-Iturbe, I., Maritan, A., Giacometti, A., Tarboton, D. G., and Rinaldo, A.: On Hack's Law, Water Resources Research, 32, 3367–3374, https://doi.org/10.1029/96WR02397, 1996. a
Robert, A. and Roy, A. G.: On the fractal interpretation of the mainstream length-drainage area relationship, Water Resources Research, 26, 839–842, https://doi.org/10.1029/WR026i005p00839, 1990. a, b
Roberts, G. G. and Wani, O.: A theory of stochastic fluvial landscape evolution, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 480, 20230456, https://doi.org/10.1098/rspa.2023.0456, 2024. a, b, c, d
Roberts, G. G. and White, N.: Estimating uplift rate histories from river profiles using African examples, Journal of Geophysical Research: Solid Earth, 115, https://doi.org/10.1029/2009JB006692, 2010. a, b, c, d
Roberts, G. G., Paul, J. D., White, N., and Winterbourne, J.: Temporal and spatial evolution of dynamic support from river profiles: A framework for Madagascar, Geochemistry, Geophysics, Geosystems, 13, https://doi.org/10.1029/2012GC004040, 2012a. a, b
Roberts, G. G., White, N. J., Martin-Brandis, G. L., and Crosby, A. G.: An uplift history of the Colorado Plateau and its surroundings from inverse modeling of longitudinal river profiles, Tectonics, 31, https://doi.org/10.1029/2012TC003107, 2012b. a, b, c, d
Roberts, G. G., White, N., and Lodhia, B. H.: The Generation and Scaling of Longitudinal River Profiles, Journal of Geophysical Research: Earth Surface, 124, 137–153, https://doi.org/10.1029/2018JF004796, 2019. a, b, c
Roberts, L. N. R. and Kirschbaum, M. A.: Paleogeography and the Late Cretaceous of the Western Interior of middle North America; coal distribution and sediment accumulation, Professional Paper, number: 1561, https://doi.org/10.3133/pp1561, 1995. a
Rosenbloom, N. A. and Anderson, R. S.: Hillslope and channel evolution in a marine terraced landscape, Santa Cruz, California, Journal of Geophysical Research: Solid Earth, 99, 14013–14029, https://doi.org/10.1029/94JB00048, 1994. a, b
Royden, L. H., Clark, M. K., and Whipple, K. X.: Evolution of river elevation profiles by bedrock incision: Analytical solutions for transient river profiles related to changing uplift and precipitation rates, in: Eos Trans. AGU, 81(48), Fall Meet. Suppl. Abstract T62F-09, 2000. a
Rudge, J. F., Roberts, G. G., White, N. J., and Richardson, C. N.: Uplift histories of Africa and Australia from linear inverse modeling of drainage inventories, Journal of Geophysical Research: Earth Surface, 120, 894–914, https://doi.org/10.1002/2014JF003297, 2015. a
Ruiz Sánchez-Oro, M., Mudd, S. M., and Gailleton, B.: Using Disorder Metrics to Distinguish Discharge-Driven From Drainage Area-Driven Incision and Quantify Deviations in Channel Steepness, Journal of Geophysical Research: Earth Surface, 129, e2023JF007 553, https://doi.org/10.1029/2023JF007553, 2024. a
Rust, D. J. and Summerfield, M. A.: Isopach and borehole data as indicators of rifted margin evolution in southwestern Africa, Marine and Petroleum Geology, 7, 277–287, https://doi.org/10.1016/0264-8172(90)90005-2, 1990. a
Salles, T.: Badlands: A parallel basin and landscape dynamics model, SoftwareX, 5, 195–202, https://doi.org/10.1016/j.softx.2016.08.005, 2016. a, b, c
Salles, T. and Hardiman, L.: Badlands: An open-source, flexible and parallel framework to study landscape dynamics, Computers & Geosciences, 91, 77–89, https://doi.org/10.1016/j.cageo.2016.03.011, 2016. a, b
Salles, T., Husson, L., Lorcery, M., and Hadler Boggiani, B.: Landscape dynamics and the Phanerozoic diversification of the biosphere, Nature, 624, 115–121, https://doi.org/10.1038/s41586-023-06777-z, 2023. a
Sassolas-Serrayet, T., Cattin, R., and Ferry, M.: The shape of watersheds, Nature Communications, 9, 3791, https://doi.org/10.1038/s41467-018-06210-4, 2018. a
Schoenbohm, L., Whipple, K., Burchfiel, B., and Chen, L.: Geomorphic constraints on surface uplift, exhumation, and plateau growth in the Red River region, Yunnan Province, China, GSA Bulletin, 116, 895–909, https://doi.org/10.1130/B25364.1, 2004. a
Shen, H., Lynch, B., Poulsen, C. J., and Yanites, B. J.: A modeling framework (WRF-Landlab) for simulating orogen-scale climate-erosion coupling, Computers & Geosciences, 146, 104625, https://doi.org/10.1016/j.cageo.2020.104625, 2021. a
Singer, M. B., Grieve, S. W. D., Chen, S.-A., and Michaelides, K.: Climatic Controls on the Length and Shape of the World's Drainage Basins, Geophysical Research Letters, 51, e2024GL111220, https://doi.org/10.1029/2024GL111220, 2024. a, b
Singh, A., Lanzoni, S., Wilcock, P. R., and Foufoula-Georgiou, E.: Multiscale statistical characterization of migrating bed forms in gravel and sand bed rivers, Water Resources Research, 47, https://doi.org/10.1029/2010WR010122, 2011. a
Sklar, L. S. and Dietrich, W. E.: Sediment and rock strength controls on river incision into bedrock, Geology, 29, 1087–1090, https://doi.org/10.1130/0091-7613(2001)029<1087:SARSCO>2.0.CO;2, 2001. a
Smith, A. G., Fox, M., Schwanghart, W., and Carter, A.: Comparing methods for calculating channel steepness index, Earth-Science Reviews, 227, 103970, https://doi.org/10.1016/j.earscirev.2022.103970, 2022. a, b, c, d
Smith, T. R., Merchant, G. E., and Birnir, B.: Towards an elementary theory of drainage basin evolution: II. A computational evaluation, Computers & Geosciences, 23, 823–849, https://doi.org/10.1016/S0098-3004(97)00067-8, 1997. a, b
Snyder, N. P., Whipple, K. X., Tucker, G. E., and Merritts, D. J.: Landscape response to tectonic forcing: Digital elevation model analysis of stream profiles in the Mendocino triple junction region, northern California, GSA Bulletin, 112, 1250–1263, https://doi.org/10.1130/0016-7606(2000)112<1250:LRTTFD>2.0.CO;2, 2000. a
Stephenson, S. N., White, N. J., Li, T., and Robinson, L. F.: Disentangling interglacial sea level and global dynamic topography: Analysis of Madagascar, Earth and Planetary Science Letters, 519, 61–69, https://doi.org/10.1016/J.EPSL.2019.04.029, 2019. a
Strahler, A.: Quantitative analysis of watershed geomorphology, Eos, Transactions American Geophysical Union, 38, 913–920, https://doi.org/10.1029/TR038i006p00913, 1957. a
Strahler, A. N.: Hypsometric (Area-Altitude) Analysis of Erosional Topography, GSA Bulletin, 63, 1117–1142, https://doi.org/10.1130/0016-7606(1952)63[1117:HAAOET]2.0.CO;2, 1952. a
Tarboton, D., Bras, R., and Rodriguez-Iturbe, I.: Scale and elevation in river networks, Water Resources Research, 25, 2037–2051, https://doi.org/10.1029/WR025i009p02037, 1989. a
Theodoratos, N., Seybold, H., and Kirchner, J. W.: Scaling and similarity of a stream-power incision and linear diffusion landscape evolution model, Earth Surf. Dynam., 6, 779–808, https://doi.org/10.5194/esurf-6-779-2018, 2018. a
Thompson Jobe, J. A. and Reitman, N. G.: Timescales of Surface Faulting Preservation in Low-Strain Intraplate Regions From Landscape Evolution Modeling and the Geomorphic and Historical Record, Journal of Geophysical Research: Solid Earth, 130, e2024JB029 966, https://doi.org/10.1029/2024JB029966, 2025. a
Tian, D., Uieda, L., Leong, W. J., Fröhlich, Y., Schlitzer, W., Grund, M., Jones, M., Toney, L., Yao, J., Magen, Y., Tong, J.-H., Materna, K., Belem, A., Newton, T., Anant, A., Ziebarth, M., Quinn, J., and Wessel, P.: PyGMT: A Python interface for the Generic Mapping Tools, Zenodo [code], https://doi.org/10.5281/zenodo.13679420, 2024. a
Tucker, G., Gasparini, N., Bras, R., and Lancaster, S.: The Channel-Hillslope Integrated Landscape Development Model (CHILD), in: Landscape Erosion and Evolution Modeling, edited by: Harmon, R. S. and Doe III, W. W., Springer US, 349–388, ISBN 978-1-4615-0575-4, https://doi.org/10.1007/978-1-4615-0575-4_12, 2001. a, b, c, d
Tucker, G. E. and Hancock, G. R.: Modelling landscape evolution, Earth Surface Processes and Landforms, 35, 28–50, https://doi.org/10.1002/esp.1952, 2010. a
Tucker, G. E. and Slingerland, R. L.: Erosional dynamics, flexural isostasy, and long-lived escarpments: A numerical modeling study, Journal of Geophysical Research: Solid Earth, 99, 12229–12243, https://doi.org/10.1029/94JB00320, 1994. a, b
Turcotte, D. L.: Self-organized complexity in geomorphology: Observations and models, Geomorphology, 91, 302–310, https://doi.org/10.1016/j.geomorph.2007.04.016, 2007. a
Turcotte, D. L. D. L.: Fractals and chaos in geology and geophysics., Cambridge University Press, Cambridge, 2nd Edn., ISBN 978-0-521-56164-8, 1997. a
Valentine, A. P. and Davies, D. R.: Global Models From Sparse Data: A Robust Estimate of Earth's Residual Topography Spectrum, Geochemistry, Geophysics, Geosystems, 21, e2020GC009240, https://doi.org/10.1029/2020GC009240, 2020. a
Wang, Y., Zhang, H., Zheng, D., Yu, J., Pang, J., and Ma, Y.: Coupling slope–area analysis, integral approach and statistic tests to steady-state bedrock river profile analysis, Earth Surf. Dynam., 5, 145–160, https://doi.org/10.5194/esurf-5-145-2017, 2017. a
Wang, Y., Goren, L., Zheng, D., and Zhang, H.: Short communication: Forward and inverse analytic models relating river long profile to tectonic uplift history, assuming a nonlinear slope–erosion dependency, Earth Surf. Dynam., 10, 833–849, https://doi.org/10.5194/esurf-10-833-2022, 2022. a
Watts, A. B. and Moore, J. D. P.: Flexural Isostasy: Constraints From Gravity and Topography Power Spectra, Journal of Geophysical Research: Solid Earth, 122, 8417–8430, https://doi.org/10.1002/2017JB014571, 2017. a, b
Wessel, P., Luis, J. F., Uieda, L., Scharroo, R., Wobbe, F., Smith, W. H. F., and Tian, D.: The Generic Mapping Tools Version 6, Geochemistry, Geophysics, Geosystems, 20, 5556–5564, https://doi.org/10.1029/2019GC008515, 2019. a
Whipple, K. X. and Tucker, G. E.: Dynamics of the stream-power river incision model: Implications for height limits of mountain ranges, landscape response timescales, and research needs, Journal of Geophysical Research: Solid Earth, 104, 17661–17674, https://doi.org/10.1029/1999JB900120, 1999. a, b, c
Willemin, J. H.: Hack's Law: Sinuosity, convexity, elongation, Water Resources Research, 36, 3365–3374, https://doi.org/10.1029/2000WR900229, 2000. a
Willett, S. D. and Brandon, M. T.: On steady states in mountain belts, Geology, 30, 175–178, https://doi.org/10.1130/0091-7613(2002)030<0175:OSSIMB>2.0.CO;2, 2002. a, b, c
Willgoose, G. and Hancock, G.: Revisiting the hypsometric curve as an indicator of form and process in transport-limited catchment, Earth Surface Processes and Landforms, 23, 611–623, https://doi.org/10.1002/(SICI)1096-9837(199807)23:7<611::AID-ESP872>3.0.CO;2-Y, 1998. a
Willgoose, G., Bras, R. L., and Rodriguez-Iturbe, I.: Results from a new model of river basin evolution, Earth Surface Processes and Landforms, 16, 237–254, https://doi.org/10.1002/esp.3290160305, 1991. a
Willgoose, G. R., Hancock, G. R., and Kuczera, G.: A Framework for the Quantitative Testing of Landform Evolution Models, in: Prediction in Geomorphology, American Geophysical Union (AGU), 195–216, ISBN 978-1-118-66855-9, https://doi.org/10.1029/135GM14, 2003. a, b, c, d
Yacobucci, M. M.: Multifractal and white noise evolutionary dynamics in Jurassic – Cretaceous Ammonoidea, Geology, 33, 97–100, https://doi.org/10.1130/G20906.1, 2005. a
Yi, R. S., Arredondo, Á., Stansifer, E., Seybold, H., and Rothman, D. H.: Shapes of river networks, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 474, 20180081, https://doi.org/10.1098/rspa.2018.0081, 2018. a
Young, R. and McDougall, I.: Long-Term Landscape Evolution: Early Miocene and Modern Rivers in Southern New South Wales, Australia, The Journal of Geology, 101, 35–49, https://doi.org/10.1086/648195, 1993. a
Zaprowski, B. J., Pazzaglia, F. J., and Evenson, E. B.: Climatic influences on profile concavity and river incision, Journal of Geophysical Research: Earth Surface, 110, https://doi.org/10.1029/2004JF000138, 2005. a
Zhou, Z., Whittaker, A. C., Bell, R. E., and Hampson, G. J.: Unravelling tectonic and lithological effects on transient landscapes in the Gulf of Corinth, Greece, Basin Research, 36, e12901, https://doi.org/10.1111/bre.12901, 2024. a
Short summary
We run many computer models that describe how landscapes evolve through time. We change how randomness (noise) is added to the models to explore how it affects the shapes and properties of the final landscape. We add different types of noise at the start, during, and at the end of models, aiming to mimic reality. The range of shapes and properties produced from different noises can be as large as ranges possibly caused by climate, but running many models can help with measuring this uncertainty.
We run many computer models that describe how landscapes evolve through time. We change how...
