Articles | Volume 8, issue 3
https://doi.org/10.5194/esurf-8-825-2020
© Author(s) 2020. 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-8-825-2020
© Author(s) 2020. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
A bed load transport equation based on the spatial distribution of shear stress – Oak Creek revisited
Angel Monsalve
CORRESPONDING AUTHOR
Departamento de Ingeniería de Obras Civiles, Universidad de la Frontera, Francisco Salazar 1145, Temuco, Chile
Catalina Segura
Forest Engineering, Resources & Management, Oregon State
University, 201 Peavy Hall, Corvallis, OR 97331, USA
Nicole Hucke
Departamento de Ingeniería de Obras Civiles, Universidad de la Frontera, Francisco Salazar 1145, Temuco, Chile
Scott Katz
Forest Engineering, Resources & Management, Oregon State
University, 201 Peavy Hall, Corvallis, OR 97331, USA
Natural Systems Design, Bellingham, WA 98225, USA
Related authors
Angel D. Monsalve, Samuel R. Anderson, Nicole M. Gasparini, and Elowyn M. Yager
Geosci. Model Dev., 18, 3427–3451, https://doi.org/10.5194/gmd-18-3427-2025, https://doi.org/10.5194/gmd-18-3427-2025, 2025
Short summary
Short summary
Rivers shape landscapes by moving sediments and changing their beds, but existing computer models oversimplify these processes by only considering erosion. We developed new software that simulates how rivers transport sediments and change over time through both erosion and deposition. This helps scientists and engineers better predict river behavior for water management, flood prevention, and ecosystem protection.
Angel D. Monsalve, Samuel R. Anderson, Nicole M. Gasparini, and Elowyn M. Yager
Geosci. Model Dev., 18, 3427–3451, https://doi.org/10.5194/gmd-18-3427-2025, https://doi.org/10.5194/gmd-18-3427-2025, 2025
Short summary
Short summary
Rivers shape landscapes by moving sediments and changing their beds, but existing computer models oversimplify these processes by only considering erosion. We developed new software that simulates how rivers transport sediments and change over time through both erosion and deposition. This helps scientists and engineers better predict river behavior for water management, flood prevention, and ecosystem protection.
Mortimer L. Bacher, Julian Klaus, Adam S. Ward, Jasmine Krause, Catalina Segura, and Clarissa Glaser
EGUsphere, https://doi.org/10.5194/egusphere-2025-1625, https://doi.org/10.5194/egusphere-2025-1625, 2025
Short summary
Short summary
Slug tracer experiments are biased toward faster flow paths, underscoring the need for tracers that reveal temporally longer timescales. We explore integrating solute tracers with naturally occurring radon to quantify flow paths of different timescales at the reach scale. Joint calibration of a transient storage model with both tracers better constrains model parameters, highlighting that this approach is critical for improving solute transport estimates in future studies.
Cited articles
Barry, J. J., Buffington, J. M., and King, J. G.: A general power equation for predicting bed load transport rates in gravel bed rivers, Water Resour.
Res., 40, 1–22, https://doi.org/10.1029/2004WR003190, 2004.
Barton, G. J., McDonald, R. R., Nelson, J. M., and Dinehart, R. R.:
Simulation of flow and sediment mobility using a multidimensional flow model
for the white sturgeon critical-habitat reach, Kootenai River near Bonners
Ferry, Idaho, US Geological Survey Scientific Investigations Report 2005-5230, US Geological Survey, Reston, Virginia, p. 54, 2005.
Beschta, R. L.: Increased bag size improves Helley-Smith bed load sampler
for use in streams with high sand and organic matter transport, in: Erosion
and sediment transport measurement, Proceedings of the Florence symposium
IAHS, June 1981, Florence, 17–25, 1981.
Bevington, P. R. and Robinson, D. K.: Data reduction and error analysis for
the physical sciences, 3rd Edition, McGraw-Hill, New York, NY, USA, 2003.
Bradley, D. N. and Tucker, G. E.: Measuring gravel transport and dispersion in a mountain river using passive radio tracers, Earth Surf. Proc. Land., 37, 1034–1045, https://doi.org/10.1002/esp.3223, 2012.
Bunte, K., Abt, S. R., Potyondy, J. P., and Swingle, K. W.: A comparison of
coarse bedload transport measured with bedload traps and Helley-Smith samplers, Geodin. Acta, 21, 53–66, https://doi.org/10.3166/ga.21.53-66, 2008.
Clayton, J. A. and Pitlick, J.: Spatial and temporal variations in bed load
transport intensity in a gravel bed river bend, Water Resour. Res., 43,
1–13, https://doi.org/10.1029/2006WR005253, 2007.
Conner, J. T. and Tonina, D.: Effect of cross-section interpolated bathymetry on 2D hydrodynamic model results in a large river, Earth Surf. Proc. Land., 39, 463–475, https://doi.org/10.1002/esp.3458, 2014.
Einstein, H. A.: The bed-load function for sediment transportation in open
channel flows, US Soil Conservation Service Technical Report 1026, US Soil Conservation Service, Washington, D.C., https://doi.org/10.22004/ag.econ.156389, 1950.
Emmett, W. W.: A field calibration of the sediment-trapping characteristics
of the Helley-Smith bedload sampler, USGS Professional paper 1139, USGS, Washington, D.C., https://doi.org/10.3133/pp1139, 1980.
Ferguson, R. I.: The missing dimension: Effects of lateral variation on 1-D
calculations of fluvial bedload transport, Geomorphology, 56, 1–14,
https://doi.org/10.1016/S0169-555X(03)00042-4, 2003.
Fernandez Luque, R. and Van Beek, R.: Erosion And transport Of bed-load sediment, J. Hydraul. Res., 14, 127–144, https://doi.org/10.1080/00221687609499677,
1976.
Freedman, D. and Diaconis, P.: On the histogram as a density estimator: L2 theory, Z. Wahrscheinlichkeitstheor. Verw. Gebiet., 57, 453–476, https://doi.org/10.1007/BF01025868, 1981.
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.
Hassan, M. A. and Church, M.: Sensitivity of bed load transport in Harris
Creek: Seasonal and spatial variation over a cobble-gravel bar, Water Resour. Res., 37, 813–825, https://doi.org/10.1029/2000WR900346, 2001.
Katz, S. B., Segura, C., and Warren, D. R.: The influence of channel bed
disturbance on benthic Chlorophyll a: A high resolution perspective,
Geomorphology, 305, 141–153, https://doi.org/10.1016/j.geomorph.2017.11.010, 2018.
Kinzel, P. J., Nelson, J. M., and Heckman, A. K.: Response of sandhill crane
(Grus canadensis) riverine roosting habitat to changes in stage and sandbar
morphology, River Res. Appl., 25, 135–152, https://doi.org/10.1002/rra.1103, 2009.
Lisle, T. E.: Particle size variation between bed load and bed material in
natural gravel beds channel, Water Resour. Res., 31, 1107–1118,
https://doi.org/10.1029/94WR02526, 1995.
Lisle, T. E., Nelson, J. M., Pitlick, J., Madej, M. A., and Barkett, B. L.:
Variability of bed mobility in natural, gravel-bed channels and adjustments to sediment load at local and reach scales, Water Resour. Res., 36, 3743–3755, https://doi.org/10.1029/2000WR900238, 2000.
Maturana, O., Tonina, D., McKean, J. A., Buffington, J. M., Luce, C. H., and
Caamaño, D.: Modeling the effects of pulsed versus chronic sand inputs
on salmonid spawning habitat in a low-gradient gravel-bed river, Earth Surf.
Proc. Land., 39, 877–889, https://doi.org/10.1002/esp.3491, 2014.
May, C. L. and Pryor, B. S.: Initial motion and bedload transport distance
determined by particle tracking in a large regulated river, River Res. Appl., 30, 508–520, https://doi.org/10.1002/rra.2665, 2014.
May, C. L., Pryor, B., Lisle, T. E., and Lang, M.: Coupling hydrodynamic
modeling and empirical measures of bed mobility to predict the risk of scour
and fill of salmon redds in a large regulated river, Water Resour. Res., 45, W05402, https://doi.org/10.1029/2007WR006498, 2009.
McDonald, R., Nelson, J., Paragamian, V., and Barton, G.: Modeling the effect
of flow and sediment transport on white sturgeon spawning habitat in the
Kootenai River, Idaho, J. Hydraul. Eng., 136, 1077–1092,
https://doi.org/10.1061/(ASCE)HY.1943-7900.0000283, 2010.
Mcdonald, R. R., Nelson, J. M., and Bennett, J. P.: Multi-Dimensional Surface-Water Modeling System User's Guide, US Geological Survey Techniques
and Methods 6-B2, US Geological Survey, Reston, VA, 2005.
Meyer-Peter, E. and Müller, R.: Formulas for Bed-Load Transport, in:
Proceedings of the 2nd Meeting of the International Association of Hydraulic
Research, 7–9 June 1948, Stockholm, Sweden, 39–64, 1948.
Milhous, R. T.: Sediment transport in a gravel-bottomed stream, PhD Thesis, Department of Civil Engineering, Oregon State University, Oregon, 1973.
Miller, A. J. and Cluer, B. L.: Modeling Considerations for Simulation of Flow in Bedrock Channels, in: Bedrock Channels, Rivers Over Rock: Fluvial
Processes in Bedrock Channels, edited by: Tinkler, K. J. and Wohl, E. E.,
American Geophysical Union, Washington, D.C., USA, 1998.
Monsalve, A. D., 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. and Pitlick, J.: Sediment supply and channel morphology in
mountain river systems: 2. Single thread to braided transitions, J. Geophys.
Res.-Earth, 119, 1516–1541, https://doi.org/10.1002/2013JF002843.Sediment, 2014.
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, 1–10, https://doi.org/10.1029/2004WR003692, 2005.
Nash, J. E. and Sutcliffe, J. V.: River flow forecasting through conceptual
models part I – A discussion of principles, J. Hydrol., 10, 282–290,
https://doi.org/10.1016/0022-1694(70)90255-6, 1970.
Nelson, J. M. and McDonald, R. R.: Mechanics and modeling of flow and bed
evolution in lateral separation eddies, US Geological Survey, Glen Canyon
Environmental Studies Report, Flagstaff, Arizona, USA, 1995.
Nelson, J. M. and Smith, J. D.: Flow in meandering channels with natural
topography, in: River Meandering, Water Resources Monographs, vol. 12, edited
by: Ikeda, S. and Parker, G., American Geophysical Union, Washington, D.C., USA, 69–102, 1989.
Nelson, J. M., Bennett, J. P., and Wiele, S. M.: Flow and Sediment-Transport
Modeling, in: Tools in Fluvial Geomorphology, edited by: Kondolf, G. M. and
Piegay, H., John Wiley & Sons, Ltd, Chichester, UK, 539–576, 2003.
Nelson, P. A., Dietrich, W. E., and Venditti, J. G.: Bed topography and the
development of forced bed surface patches, J. Geophys. Res.-Earth, 115, F04024, https://doi.org/10.1029/2010JF001747, 2010.
Nicholas, A. P.: Modelling bedload yield braided gravel bed rivers, Geomorphology, 36, 89–106, https://doi.org/10.1016/S0169-555X(00)00050-7, 2000.
Nitsche, M., Rickenmann, D., Turowski, J. M., Badoux, A., and Kirchner, J. W.: Evaluation of bedload transport predictions using flow resistance equations to account for macro-roughness in steep mountain streams, Water
Resour. Res., 47, W08513, https://doi.org/10.1029/2011WR010645, 2011.
Nitsche, M., Rickenmann, D., Kirchner, J. W., Turowski, J. M., and Badoux, A.: Macroroughness and variations in reach-averaged flow resistance in steep
mountain streams, Water Resour. Res., 48, W12518, https://doi.org/10.1029/2012WR012091, 2012.
O'Connor, J. E., Mangano, J. F., Anderson, S. W., Wallick, J. R., Jones, K.
L., and Keith, M. K.: Geologic and physiographic controls on bed-material yield, transport, and channel morphology for alluvial and bedrock rivers,
western Oregon, Bull. Geol. Soc. Am., 126, 377–397, https://doi.org/10.1130/B30831.1, 2014.
O'leary, S. J. and Beschta, R. L.: Bedload transport in an Oregon coast range stream, Water Resour. Bull., 17, 886–894, https://doi.org/10.1111/j.1752-1688.1981.tb01313.x, 1981.
Olinde, L. and Johnson, J. P. L.: Using RFID and accelerometer-embedded
tracers to measure probabilities of bed load transport, step lengths, and
rest times in a mountain stream, Water Resour. Res., 51, 7572–7589,
https://doi.org/10.1002/2014WR016120, 2015.
Paola, C.: Incoherent structure: Turbulence as a metaphor for stream braiding, in: Coherent Flow Structures in Open Channels, edited by: Ashworth, P., Bennett, S. J., Best, J. L., and McLelland, S., John Wiley, Chichester, UK, 706–723, 1996.
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.
Parker, G. and Klingeman, P. C.: On why gravel bed streams are paved, Water
Resour. Res., 18, 1409, https://doi.org/10.1029/WR018i005p01409, 1982.
Parker, G., Klingeman, P. C., and McLean, D. G.: Bedload and size distribution in paved gravel-bed streams, J. Hydraul. Div., 108, 544–571, 1982.
Paustian, S. J. and Beschta, R. L.: The suspended sediment regime of an Oregon coast range stream, J. Am. Water Resour. Assoc., 15, 144–154, https://doi.org/10.1111/j.1752-1688.1979.tb00295.x, 1979.
Pitlick, J.: Variability of bed load measurement, Water Resour. Res., 24, 173–177, https://doi.org/10.1029/WR024i001p00173, 1988.
Pitlick, J., Mueller, E. R., and Segura, C.: Differences in Sediment Supply
to Braided and Single-Thread River Channels: What Do the Data Tell Us?, in:
Gravel-Bed Rivers: Processes, Tools, Environments, edited by: Church, M.,
Biron, P. M., and Roy, A. G., John Wiley & Sons, Ltd., Chichester, UK, 502–511, 2012.
Press, W. H., Teukolsky, S. A., Vetterling, W. T., and Flannery, B. P.: Numerical Recipes: The Art of Scientific Computing, 3rd Edn., Cambridge University Press, Cambridge, 2007.
Recking, A.: A comparison between flume and field bed load transport data and consequences for surface-based bed load transport prediction, Water Resour. Res., 46, 1–16, https://doi.org/10.1029/2009WR008007, 2010.
Recking, A.: An analysis 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.
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.
Schmidt, K.-H. and Ergenzinger, P.: Bedload entrainment, travel lengths, step lengths, rest periods – studied with passive (iron, magnetic) and active (radio) tracer techniques, Earth Surf. Proc. Land., 17, 147–165, https://doi.org/10.1002/esp.3290170204, 1992.
Segura, C. and Katz, S.: FaSTMECH Modelling results for Seven Flow Levels at Oak Creek (Version 1), Oregon State University, Dataset, https://doi.org/10.7267/fn1075623, 2020.
Segura, C. and Pitlick, J.: Coupling fluvial-hydraulic models to predict gravel transport in spatially variable flows, J. Geophys. Res.-Earth, 120, 834–855, https://doi.org/10.1002/2014JF003302, 2015.
Turowski, J. and Rickenmann, D.: Measuring the statistics of bed-load transport using indirect sensors, J. Hydraul. Eng., 137, 116–121,
https://doi.org/10.1061/(ASCE)HY.1943-7900.0000277, 2011.
Vericat, D., Church, M., and Batalla, R. J.: Bed load bias?: Comparison of
measurements obtained using two (76 and 152 mm) Helley-Smith samplers in a
gravel bed river, Water Resour. Res., 42, W01402, https://doi.org/10.1029/2005WR004025,
2006.
Wilcock, P. R. and Crowe, J. C.: 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.
Wilcock, P. R. and Kenworthy, S. T.: A two-fraction model for the transport of sand/gravel mixtures, Water Resour. Res., 38, 1–12,
https://doi.org/10.1029/2001WR000684, 2002.
Wyss, C. R., Rickenmann, D., Fritschi, B., Turowski, J. M., and Weitbrecht,
V.: Laboratory flume experiments with the Swiss plate geophone bed load monitoring system: 1. Impulse counts and particle size identification, Water
Resour. Res., 52, 7744–7759, https://doi.org/10.1002/2015WR018555, 2016a.
Wyss, C. R., Rickenmann, D., Fritschi, B., Turowski, J. M., Weitbrecht, V.,
Travaglini, E., Bardou, E., and Boes, R. M.: Laboratory flume experiments with the Swiss plate geophone bed load monitoring system: 2. Application to
field sites with direct bed load samples, Water Resour. Res., 52, 7760–7778, https://doi.org/10.1002/2016WR019283, 2016b.
Wyss, C. R., Rickenmann, D., Fritschi, B., Turowski, J. M., Weitbrecht, V., and Boes, R. M.: Measuring bed load transport rates by grain-size fraction
using the swiss plate geophone signal at the erlenbach, J. Hydraul. Eng., 142, 1–11, https://doi.org/10.1061/(ASCE)HY.1943-7900.0001090, 2016c.
Yager, E. M., Kirchner, J. W., and Dietrich, W. E.: Calculating bed load
transport in steep boulder bed channels, Water Resour. Res., 43, W07418,
https://doi.org/10.1029/2006WR005432, 2007.
Yager, E. M., Dietrich, W. E., Kirchner, J. W., and McArdell, B. W.: Patch
dynamics and stability in steep, rough streams, J. Geophys. Res.-Earth, 117, 1–16, https://doi.org/10.1029/2011JF002253, 2012a.
Yager, E. M., Dietrich, W. E., Kirchner, J. W., and McArdell, B. W.: Prediction of sediment transport in step-pool channels, Water Resour. Res.,
48, W01541, https://doi.org/10.1029/2011WR010829, 2012b.
Yager, E. M., Venditti, J. G., Smith, H. J., and Schmeeckle, M. W.: The trouble with shear stress, Geomorphology, 323, 41–50,
https://doi.org/10.1016/j.geomorph.2018.09.008, 2018.
Short summary
Part of the inaccuracies when estimating bed load transport in
gravel-bed rivers is because we are not considering the wide distributions of shear stress in these systems. We modified a subsurface-based bed load transport equation to include these distributions. By doing so, our approach accurately predicts bed load transport rates when the pavement layer is still present, while the original one predicts zero transport. For high flows, our method had similar performance to the original equation.
Part of the inaccuracies when estimating bed load transport in
gravel-bed rivers is because we...