Beer, A. R. and Turowski, J. M.: From process to centuries: Upscaling field-calibrated models of fluvial bedrock erosion, Geophys. Res. Lett., 48, 093415, https://doi.org/10.1029/2021GL093415, 2021.
Bhattacharya, B., Price, R. K., and Solomatine, D. P.: Machine Learning
Approach To Modeling Sediment Transport, J. Hydraul. Eng., 133, 776–793, https://doi.org/10.1061/(ASCE)0733-9429(2007)133:4(440), 2007.
Brownlie, W. R.: Compilation of alluvial channel data: Laboratory and field, W. M. Keck Laboratory of Hydraulics and Water Resources Report, 43B, California Institute of Technology,
https://resolver.caltech.edu/CaltechKHR:KH-R-43B (last access: 25 Aprril 2022), 1981.
Buffington, J. M. and Montgomery, D. R.: A systematic analysis of eight
decades of incipient motion studies, with special reference to gravel-bedded
rivers, Water Resour. Res., 33, 1993–2029, https://doi.org/10.1029/96WR03190, 1997.
Bui, V. H., Bui, M. D., and Rutschmann, P.: Combination of Discrete Element
Method and Artificial Neural Network for Predicting Porosity of Gravel-Bed
River, Water, 11, 1461, https://doi.org/10.3390/w11071461, 2019.
Bunte, K. and Abt, S. R.: Effect of sampling time on measured gravel bed load transport rates in a coarse-bedded stream, Water Resour. Res., 41, W11405, https://doi.org/10.1029/2004WR003880, 2005.
Chollet, F.: Keras, Keras [code],
https://keras.io/
(last access: 25 April 2022), 2015.
Church, M., Hassan, M. A., and Wolcott, J. F.: Stabilizing self-organized
structures in gravel-bed stream channels: Field and experimental observations, Water Resour. Res., 34, 3169–3179, https://doi.org/10.1029/98WR00484, 1998.
Cohen, S., Syvitski, J., Ashley, T., Lammers, R., Fekete, B., and Li, H.-Y.:
Spatial trends and drivers of bedload and suspended sediment fluxes in global rivers, Water Resour. Res., 58, 2021 031583, https://doi.org/10.1029/2021WR031583, 2022.
Deal, E., Venditti, J. G., Benavides, S. J., Bradley, R., Zhang, Q., Kamrin,
K., and Perron, J. T.: Grain shape effects in bed load sediment transport,
Nature, 613, 298–302, https://doi.org/10.1038/s41586-022-05564-6, 2023.
Dietrich, W. E., Kirchner, J. W., Ikeda, H., and Iseya, F.: Sediment supply and the development of the coarse surface layer in gravel-bedded rivers, Nature, 340, 215–217, https://doi.org/10.1038/340215a0, 1989.
Dovoedo, Y. H. and Chakraborti, S.: Outlier detection for multivariate
skew-normal data: A comparative study, Stat. Comput. Simul., 83, 773–783, https://doi.org/10.1080/00949655.2011.636364, 2013.
East, A. E., Pess, G. R., Bountry, J. A., Magirl, C. S., Ritchie, A. C., and
Logan, J. B.: Large-scale dam removal on the Elwha River, Geomorphology, 228, 765–786, https://doi.org/10.1016/j.geomorph.2014.08.028, 2015.
Einstein, A. H.: The Bed-Load Function for Sediment Transportation in Open
Channel Flows, Technical Bulletin, Soil Conservation Series, US Dept. of Agriculture,
https://naldc.nal.usda.gov/catalog/43419 (last access: 25 April 2022), 1950.
Einstein, H. A.: Bed load transport as a probability problem, in: Sedimentation: 746 Symposium to Honor Professor H. A. Einstein, 1972 (translation from 747 German of H. A. Einstein doctoral thesis), Originally presented to Federal Institute of Technology, Zurich, Switzerland, C1–C105,
https://lib.ugent.be/catalog/rug01:002054080 (last access: 25 April 2022), 1937.
Ferdowsi, B., Ortiz, C. P., Houssais, M., and Jerolmack, D. J.: River-bed
armouring as a granular segregation phenomenon, Nat. Commun., 8, 1363, https://doi.org/10.1038/s41467-017-01681-3, 2017.
Furbish, D. J., Ball, A. E., and Schmeeckle, M. W.: A probabilistic description of the bed load sediment flux: 4. Fickian diffusion at low
transport rates, J. Geophys. Res.-Earth, 117, F03034, https://doi.org/10.1029/2012JF002356, 2012.
Garcia, M. H. (Ed.): Sedimentation Engineering: Processes, Measurements,
Modeling, and Practice, ASCE, Reston, Virginia, https://doi.org/10.1061/9780784408148.ch02, 2007.
Geron, A.: Hands-on Machine Learning with Scikit-Learn, Keras & TensorFlow, in: 2nd Edn., O'Reilly, Sebastopol, Canada, 2019.
Gilbert, G. K.: The transportation of debris by running water, US Geological Survey Professional Paper 86, US Geological Survey, 263 pp., https://doi.org/10.3133/pp86, 1914.
Goldstein, E. B., Coco, G., and Plant, N. G.: Corresponding Author, Earth-Sci. Rev., 194, 97–108, https://doi.org/10.1016/j.earscirev.2019.04.022, 2019.
Gomez, B. and Church, M.: An assessment of bed load sediment transport formulae for gravel bed rivers, Water Resour. Res., 25, 1161–1186,
https://doi.org/10.1029/WR025i006p01161, 1989.
Gomez, B. and Soar, P. J.: Bedload transport: beyond intractability, Roy. Soc. Open Sci., 9, 211932, https://doi.org/10.1098/rsos.211932, 2022.
Gomez, B., Soar, P. J., and Downs, P. W.: Good vibrations: Big data impact
bedload research, Earth Surf. Proc. Land., 47, 129–142, https://doi.org/10.1002/esp.5304, 2022.
Han, H. and Morrison, R. R.: Data-driven approaches for runoff prediction using distributed data, Stoch. Env. Res. Risk A., 36, 2153–2171, https://doi.org/10.1007/s00477-021-01993-3, 2022.
Hassani, A., Azapagic, A., and Shokri, N.: Global predictions of primary
soil salinization under changing climate in the 21st century, Nat. Commun., 12, 1–17, https://doi.org/10.1038/s41467-021-26907-3, 2021.
Haykin, S.: Kalman Filters, in: Kalman Filtering and Neural Networks, John Wiley & Sons, Ltd, 1–21, https://doi.org/10.1002/0471221546.ch1, 2001.
Haykin, S.: Neural Networks and Learning Machines, Third Edition, Pearson Education, Inc., McMaster University, Hamilton, ISBN 0131471392, 2009.
Hinton, D., Hotchkiss, R., and Ames, D. P.: Comprehensive and Quality-Controlled Bedload Transport Database, J. Hydraul. Eng., 143, 06016024, https://doi.org/10.1061/(asce)hy.1943-7900.0001221, 2017.
Hosseiny, H.: A Deep Learning Model for Predicting River Flood Depth and
Extent, Environ. Model. Softw., 145, 105186, https://doi.org/10.1016/j.envsoft.2021.105186, 2021.
Hosseiny, H., Nazari, F., Smith, V., and Nataraj, C.: A Framework for Modeling Flood Depth Using a Hybrid of Hydraulics and Machine Learning, Sci. Rep., 10, 1–14, https://doi.org/10.1038/s41598-020-65232-5, 2020.
Hosseiny, H., Masteller, C. C., Dale, J. E., and Phillips, C. B.: Development of a machine learning model for river bedload – Data, Model, and Scripts (Version 1), Zenodo [data set], https://doi.org/10.5281/zenodo.7641313, 2023.
Houssais, M., Ortiz, C. P., Durian, D. J., and Jerolmack, D. J.: Onset of
sediment transport is a continuous transition driven by fluid shear and
granular creep, Nat. Commun. 6, 6527, https://doi.org/10.1038/ncomms7527, 2015.
Hsu, K., Gupta, H. V., and Sorooshian, S.: Artificial Neural Network Modeling of the Rainfall-Runoff Process, Water Resour. Res., 31, 2517–2530,
https://doi.org/10.1029/95WR01955, 1995a.
Kennedy, D., Lakonishok, J., and Shaw, W. H.: Accommodating Outliers and
Nonlinearity in Decision Models, J. Account. Audit. Financ., 7, 161–190, https://doi.org/10.1177/0148558X9200700205, 1992.
King, J. G., Emmett, W. W., Whiting, P. J., Kenworthy, R. P., and Barry, J.
J.: Sediment Transport Data and Related Information for Selected Coarse-Bed
Streams and Rivers in Idaho, Gen. Tech. Rep. RMRS-GTR-131. Fort Collins, CO: U.S. Department of Agriculture, Forest Service, Rocky Mountain Research Station, 26 pp., https://doi.org/10.2737/RMRS-GTR-131 2004.
Kitsikoudis, V., Sidiropoulos, E., and Hrissanthou, V.: Assessment of sediment transport approaches for sand-bed rivers by means of machine learning, Hydrolog. Sci. J., 60, 1566–1586, https://doi.org/10.1080/02626667.2014.909599, 2015.
Lai, C. Y., Kingslake, J., Wearing, M. G., Chen, P. H. C., Gentine, P., and
Li, H.: Vulnerability of Antarctica's ice shelves to meltwater-driven
fracture, Nature, 584, 574–578, https://doi.org/10.1038/s41586-020-2627-8, 2020.
Lajeunesse, E., Malverti, L., and Charru, F.: Bed load transport in turbulent flow at the grain scale: Experiments and modeling, J. Geophys. Res.-Earth, 115, F04001, https://doi.org/10.1029/2009JF001628, 2010.
Leopold, L. B., Bagnold, R. A., Wolman, M. G., and Brush Jr., L. M.: Flow
resistance in sinuous or irregular channels, in: Geological Survey Professional Paper, Geological Survey, Washington, DC, https://doi.org/10.3133/pp282D, 1960.
Li, H.-Y., Tan, Z., Ma, H., Zhu, Z., Abeshu, G. W., Zhu, S., Cohen, S., Zhou, T., Xu, D., and Leung, L. R.: A new large-scale suspended sediment model and its application over the United States, Hydrol. Earth Syst. Sci., 26, 665–688, https://doi.org/10.5194/hess-26-665-2022, 2022.
Marquis, G. A. and Roy, A. G.: Using multiple bed load measurements: Toward
the identification of bed dilation and contraction in gravel-bed rivers, J. Geophys. Res.-Earth, 117, F01014, https://doi.org/10.1029/2011JF002120, 2012.
Masteller, C. C. and Finnegan, N. J.: Interplay between grain protrusion and
sediment entrainment in an experimental flume, J. Geophys. Res.-Earth, 122, 274–289, https://doi.org/10.1002/2016JF003943, 2017.
Masteller, C. C., Finnegan, N. J., Turowski, J. M., Yager, E. M., and Rickenmann, D.: History-Dependent Threshold for Motion Revealed by Continuous Bedload Transport Measurements in a Steep Mountain Stream, Geophys. Res. Lett., 46, 2583–2591, https://doi.org/10.1029/2018GL081325, 2019.
Meyer-Peter, E. and Müller, R.: Formulas for Bed-Load transport, in: appendix 2, IAHSR 2nd meeting, Stockholm,
https://repository.tudelft.nl/islandora/object/uuid:4fda9b61-be28-4703-ab06-43cdc2a21bd7?collection=research (last access: 25 April 2022), 1948.
Monsalve, A. and Yager, E. M.: Bed Surface Adjustments to Spatially Variable
Flow in Low Relative Submergence Regimes: Bed Surface Adjustments in LRS,
Water Resour. Res., 53, 9350–9367, https://doi.org/10.1002/2017WR020845, 2017.
Monsalve, A., Yager, E. M., Turowski, J. M., and Rickenmann, D.: A probabilistic formulation of bed load transport to include spatial variability of flow and surface grain size distributions, Water Resour. Res.,
52, 3579–3598, https://doi.org/10.1002/2015WR017694, 2016.
Mueller, E. R., Pitlick, J., and Nelson, J. M.: Variation in the reference
Shields stress for bed load transport in gravel-bed streams and rivers, Water Resour. Res., 41, W04006, https://doi.org/10.1029/2004WR003692, 2005.
Paintal, A. S.: A Stochastic Model Of Bed Load Transport, J. Hydraul. Res., 9, 527–554, https://doi.org/10.1080/00221687109500371, 1971.
Parker, G.: Self-formed straight rivers with equilibrium banks and mobile
bed. Part 2, The gravel river, J. Fluid Mech., 89, 127–146,
https://doi.org/10.1017/S0022112078002505, 1978.
Parker, G.: Surface-based bedload transport relation for gravel rivers, J. Hydraul. Res., 28, 417–436, https://doi.org/10.1080/00221689009499058, 1990.
Phillips, C. B. and Jerolmack, D. J.: Self-organization of river channels as
a critical filter on climate signals, Science, 352, 694–697, https://doi.org/10.1126/science.aad3348, 2016.
Phillips, C. B. and Jerolmack, D. J.: Bankfull Transport Capacity and the
Threshold of Motion in Coarse-Grained Rivers, Water Resour. Res., 55,
11316–11330, https://doi.org/10.1029/2019WR025455, 2019.
Phillips, C. B., Hill, K. M., Paola, C., Singer, M. B., and Jerolmack, D. J.: Effect of Flood Hydrograph Duration, Magnitude, and Shape on Bed Load Transport Dynamics, Geophys. Res. Lett., 45, 8264–8271, https://doi.org/10.1029/2018GL078976, 2018.
Phillips, C. B., Masteller, C. C., Slater, L. J., Dunne, K. B. J., Francalanci, S., Lanzoni, S., Merritts, D. J., Lajeunesse, E., and Jerolmack, D. J.: Threshold constraints on the size, shape and stability of alluvial rivers, Nat. Rev. Earth Environ., 3, 406–419, https://doi.org/10.1038/s43017-022-00282-z, 2022.
Recking, A.: A comparison between flume and field bed load data and consequences for surface-based bed load transport prediction, Water Resour. Res., 46, W03518, https://doi.org/10.1029/2009WR008007, 2010.
Recking, A.: Influence of sediment supply on mountain streams bedload transport, Geomorphology, 175–176, 139–150, https://doi.org/10.1016/j.geomorph.2012.07.005, 2012.
Recking, A.: An analaysis of nonlinearity effects on bed load transport
prediction, J. Geophys. Res.-Earth, 118, 1264–1281, https://doi.org/10.1002/jgrf.20090, 2013a.
Recking, A.: Simple Method for Calculating Reach-Averaged Bed-Load Transport, J. Hydraul. Eng., 139, 70–75, https://doi.org/10.1061/(asce)hy.1943-7900.0000653, 2013b.
Recking, A.: BedloadWeb,
https://en.bedloadweb.com/ (last access: 25 April 2022), 2019.
Recking, A., Liébault, F., Peteuil, C., and Jolimet, T.: Testing bedload
transport equations with consideration of time scales, Earth Surf. Proc. Land., 37, 774–789, https://doi.org/10.1002/esp.3213, 2012.
Rickenmann, D.: Hyperconcentrated Flow and Sediment, Hydraul. Eng., 117, 1419–1439, https://doi.org/10.1061/(ASCE)0733-9429(1991)117:11(1419), 1991.
Rickenmann, D.: Variability of Bed Load Transport During Six Summers of
Continuous Measurements in Two Austrian Mountain Streams (Fischbach and Ruetz, Water Resour. Res., 54, 107–131, https://doi.org/10.1002/2017WR021376, 2018.
Rickenmann, D. and McArdell, B. W.: Continuous measurement of sediment transport in the Erlenbach stream using piezoelectric bedload impact sensors, Earth Surf. Proc. Land., 32, 1362–1378, https://doi.org/10.1002/esp.1478, 2007.
Saravanan, K. and Sasithra, S.: Review on Classification Based on Artificial
Neural Networks, Int. J. Ambient Syst. Appl., 2, 11–18, https://doi.org/10.5121/ijasa.2014.2402, 2014.
Singer, M. B.: Transient response in longitudinal grain size to reduced
gravel supply in a large river, Geophys. Res. Lett., 37, L18403, https://doi.org/10.1029/2010GL044381, 2010.
Singh, A., Fienberg, K., Jerolmack, D. J., Marr, J., and Foufoula-Georgiou,
E.: Experimental evidence for statistical scaling and intermittency in sediment transport rates, J. Geophys. Res.-Earth, 114, F01025, https://doi.org/10.1029/2007JF000963, 2009.
Slater, L. J. and Singer, M. B.: Imprint of climate and climate change in alluvial riverbeds: Continental United States, 1950–2011, Geology, 41, 595–598, https://doi.org/10.1130/G34070.1, 2013.
Tan, Z., Leung, L. R., Li, H.-Y., and Cohen, S.: Representing global soil erosion and sediment flux in Earth System Models, J. Adv. Model. Earth Sy., 14, e2021MS002756, https://doi.org/10.1029/2021MS002756, 2022.
Warrick, J. A., Bountry, J. A., East, A. E., Magirl, C. S., Randle, T. J.,
and Gelfenbaum, G.: Large-scale dam removal on the Elwha River, sediment
budget and synthesis, Geomorphology, 246, 729–750, https://doi.org/10.1016/j.geomorph.2015.01.010, 2015.
Wilcock, P. R.: Two-Fraction Model of Initial Sediment Motion in Gravel-Bed
Rivers, Science, 280, 410–412, https://doi.org/10.1126/science.280.5362.410, 1998.
Wilcock, P. R.: Toward a practical method for estimating sediment-transport
rates in gravel-bed rivers, Earth Surf. Proc. Land., 26, 1395–1408, 2001.
Wilcock, P. R. and Crowe, J. C.: Surface-based Transport Model for Mixed-Size Sediment Surface-based Transport Model for Mixed-Size Sediment, J. Hydraul. Eng., 129, 120–128, https://doi.org/10.1061/(ASCE)0733-9429(2003)129:2(120), 2003.
Willmott, C. J. and Matsuura, K.: Advantages of the mean absolute error (MAE) over the root mean square error (RMSE) in assessing average model performance, Clim. Res., 30, 79–82, https://doi.org/10.3354/cr030079, 2005.
Wong, M. and Parker, G.: Reanalysis and Correction of Bed-Load Relation of
Meyer-Peter and Müller Using Their Own Database, J. Hydraul. Eng., 132, 1159–1168, https://doi.org/10.1061/(asce)0733-9429(2006)132:11(1159), 2006.
Zhao, T. and Nepf, H. M.: Turbulence Dictates Bedload Transport in Vegetated
Channels Without Dependence on Stem Diameter and Arrangement, Geophys. Res. Lett., 48, e2021GL095316, https://doi.org/10.1029/2021GL095316, 2021.
Zhou, X., Wu, W., Qin, Y., and Fu, X.: Geoinformation-based landslide
susceptibility mapping in subtropical area, Sci. Rep., 11, 24325, https://doi.org/10.1038/s41598-021-03743-5, 2021.
