Performance of Bedload Sediment Transport Formulas Applied to the Lower Minnesota River
Publication: Journal of Hydrologic Engineering
Volume 26, Issue 7
Abstract
Despite limitations in reproducing complex bedload sediment transport processes in rivers, formulas have been preferred over collection and analysis of field data due to the high cost and time-consuming nature of bedload discharge measurements. However, the performance of such formulas depends on the hydraulic and sedimentological conditions they attempt to describe. The availability of field measurements provides a unique opportunity to test bedload transport formulas to better guide formula selection. Hydraulic parameters and bedload discharge data from the Lower Minnesota River and two of its tributaries were used to evaluate nine bedload transport formulas using three different indices. The bedload data for the different sites were collected by the United States Geological Survey (USGS) from 2011 through 2014, with bed material varying from very coarse to medium sand. The formulas calculated higher bedload rates than were measured due to a combination of site-specific physical characteristics, including the presence of bed forms (dunes), and sampling uncertainties. Because of the lack of reproducibility of the tested formulas, five power functions, based on the relation between the specific unit power (independent hydraulic variable) and the USGS measured data (dependent variable), were derived as provisional equations to estimate the bedload discharge on the Lower Minnesota River and tributaries.
Get full access to this article
View all available purchase options and get full access to this article.
Data Availability Statement
All data used during the study are available in a repository online in accordance with funder data retention policies (https://doi.org/10.3133/sir20165174).
Acknowledgments
The authors acknowledge CNPq-Brazil for their financial support to Elisa Armijos (Post-Doctoral Grant project number 405759/2015) and extend deep gratitude to Peter R. Wright (USGS-Wyoming-Montana Water Science Center) and Faith A. Fitzpatrick (USGS-Upper Midwest Water Science Center) for their valuable contributions to improving this article. Any use of trade, firm, or product names is for descriptive purposes only and does not imply endorsement by the US Government.
References
Aguirre-Pe, J., A. Moncada, and M. Olivero. 2004. “Transporte de sedimentos en rios y canales.” [In Spanish.] In Proc., XXI Congresso Latinoamericano de Hidráulica. Valencia, Spain: IAHR.
Aguirre-Pe, J., M. L. Olivero, and A. T. Moncada. 2003. “Particle densimetric Froude number for estimating sediment transport.” J. Hydraul. Eng. 129 (6): 428–437. https://doi.org/10.1061/(ASCE)0733-9429(2003)129:6(428).
Ancey, C. 2020. “Bedload transport: A walk between randomness and determinism. Part 2: Challenges and prospects.” J. Hydraul. Res. 58 (1): 18–33. https://doi.org/10.1080/00221686.2019.1702595.
Andrews, E. D., and W. R. White. 1981. “Measurement and computation of the bed material discharge in a shallow sand-bed stream, Muddy Creek, Wyoming.” Water Resour. Res. 17 (1): 131–141. https://doi.org/10.1029/WR017i001p00131.
ASCE. 1982. “Relationships between morphology of small streams and sediment yields.” J. Hydraul. Div. 108 (11): 1328–1365. https://doi.org/10.1061/JYCEAJ.0005936.
Bagnold, R. A. 1966. An approach to the sediment transport problem from general physics. Washington, DC: USGS.
Bagnold, R. A. 1980. “An empirical correlation of bedload transport rates in flumes and natural rivers.” Proc. R. Soc. London. Ser. A. 372 (1751): 453–473. https://doi.org/10.1098/rspa.1980.0122.
Batalla, R. 1997. “Evaluating bed-material transport equations using field measurements in a sandy gravel-bed Stream, Arbucies River, NE Spain.” Earth Surf. Process. Landf. 22 (2): 121–130. https://doi.org/10.1002/(SICI)1096-9837(199702)22:2%3C121::AID-ESP671%3E3.0.CO;2-7.
Belmont, P., et al. 2011. “Large shift in source of fine sediment in the upper Mississippi River.” Environ. Sci. Technol. 45 (20): 8804–8810. https://doi.org/10.1021/es2019109.
Bisantino, T., F. Gentile, P. Milella, and T. Liuzzi. 2010. “Effect of time scale on the performance of different sediment transport formulas in a semiarid region.” J. Hydraul. Eng. 136 (1): 56–61. https://doi.org/10.1061/(ASCE)HY.1943-7900.0000125.
Bravo-Espinosa, M., W. R. Osterkamp, and V. L. Lopes. 2003. “Bedload transport in alluvial channels.” J. Hydraul. Eng. 129 (10): 783–795. https://doi.org/10.1061/(ASCE)0733-9429(2003)129:10(783).
Cheng, N. S. 2002. “Exponential formula for bedload transport.” J. Hydraul. Eng. 128 (10): 942–946. https://doi.org/10.1061/(ASCE)0733-9429(2002)128:10(942).
Childers, D. 1999. Field comparisons of six pressure-difference bedload samplers in high-energy flow. Vancouver, Washington: USGS.
DuBoys. 1879. “Le Rhone et les rivieres a lit affouillable.” [In French.) Ann. Ponts Chaussees 5 (18): 141–195.
Edwards, T. E., and G. D. Glysson. 1999. Book 3, chapter C2: Field methods for measurements of fluvial sediment. Reston, VA: USGS.
Einstein, H. A. 1950. The bedload function for sediment transportation in open channel flows. Washington, DC: USDA Soil Conservation Service.
Emmett, W. W. 1979. A field calibration of the sediment-trapping characteristics of the Helley-Smith bedload sampler. Reston, VA: USGS.
Frings, R. M., and S. Vollmer. 2017. “Guidelines for sampling bedload transport with minimum uncertainty.” Sedimentology 64 (6): 1630–1645. https://doi.org/10.1111/sed.12366.
Gomez, B., and M. Church. 1989. “An assessment of bedload sediment transport formulae for gravel bed rivers.” Water Resour. Res. 25 (6): 1161–1186. https://doi.org/10.1029/WR025i006p01161.
Gomez, B., R. L. Noff, and D. W. Hubbell. 1989. “Temporal variation in bedload transport rates associated with the migration of bedforms.” Earth Surf. Process. 14 (2): 135–156. https://doi.org/10.1002/esp.3290140205.
Gomez, B., and B. M. Troutman. 1997. “Evaluation of process errors in bed load sampling using a dune model.” Water Resour. Res. 33 (10): 2387–2398. https://doi.org/10.1029/97WR01711.
Gran, K. B., P. Belmont, S. S. Day, C. Jennings, A. Johnson, L. Perg, and P. R. Wilcock. 2009. Geomorphic evolution of the Le Sueur River, Minnesota, USA, and implications for current sediment loading. Boulder, CO: Geological Society of America.
Gray, J. R., and F. J. M. Simões. 2008. “Estimating sediment discharge.” In Sedimentation engineering—Processes, measurements, modeling, and practice, edited by M. Garcia. Reston, VA: ASCE.
Gray, J. R., R. H. Webb, and D. W. Hyndman. 1991. “Low-flow sediment transport in the Colorado River.” In Vol. I of Proc., 5th Federal Interagency Sedimentation Conf. Reston, VA: USGS.
Groten, J. T., C. A. Ellison, and J. S. Hendrickson. 2016. Suspended-sediment concentrations, bedload, particle sizes, surrogate measurements, and annual sediment loads for selected sites in the lower Minnesota River Basin, water years 2011 through 2016. Reston, VA: USGS.
Habersack, H., and J. B. Laronne. 2002. “Evaluation and improvement of bed load discharge formulas based on Helley–Smith sampling in an alpine gravel bed river.” J. Hydraul. Eng. 128 (5): 484–499. https://doi.org/10.1061/(ASCE)0733-9429(2002)128:5(484).
Holmes, R. R. 2010. Measurement of bedload transport in sand-bed rivers: A look at two indirect sampling methods. Reston, VA: USGS.
Julien, P. Y., G. J. Klaassen, W. B. M. Ten Brinke, and A. W. E. Wilbers. 2002. “Bed resistance of the Bovenrijn River during the 1998 flood.” J. Hydraul. Eng. 128 (12): 1042–1050. https://doi.org/10.1061/(ASCE)0733-9429(2002)128:12(1042).
Kalinski, A. A. 1947. “Movement of sediment as bed load in rivers.” Am. Geophys. Union 28 (4): 615–620. https://doi.org/10.1029/TR028i004p00615.
Karim, F. 1998. “Bed material discharge prediction for no uniform bed sediments.” J. Hydraul. Eng. 124 (6): 597–604. https://doi.org/10.1061/(ASCE)0733-9429(1998)124:6(597).
Kleinhans, M. G. 2001. “The key role of fluvial dunes in transport and deposition of sand-gravel mixtures, a preliminary note.” Sediment. Geol. 143 (1–2): 7–13. https://doi.org/10.1016/S0037-0738(01)00109-9.
Lenhart, C. F., M. L. Titov, J. S. Ulrich, J. L. Nieber, and B. J. Suppes. 2013. “The role of hydrologic alteration and riparian vegetation dynamic in channel evolution along the lower Minnesota River.” Trans. ASABE 56 (2): 549–561. https://doi.org/10.13031/2013.42686.
Madsen, O. S. 1991. “Mechanics of cohesionless sediment transport.” In Proc., Coastal Sediments ASCE, 91: Proc. of a Special Conf. on Quantitative Approaches to Coastal Sediment Processes, 15–27. Reston, VA: ASCE.
Magner, J. A., and S. C. Alexander. 1993. The Minnesota River Basin: A hydrogeological overview, 21. St Paul, MN: Minnesota Pollution Control Agency.
Martin, Y., and D. Ham. 2005. “Testing bedload transport formulae using morphologic transport estimates and field data: Lower Fraser River, British Columbia.” Earth Surf. Process. Landf. 30 (10): 1265–1282. https://doi.org/10.1002/esp.1200.
McLean, D. G. 1985. “Sensitivity analysis of bedload equations.” In Vol. 18 of Proc., Canadian Society Civil Engineering Annual Conf., 1–15. Pointe Claire, QC: Canadian Society of Civil Engineering.
Meade, R. H. 1985. “Wavelike movement of bedload sediment, East Fork River, Wyoming.” Environ. Geol. Water Sci. 7 (4): 215–225. https://doi.org/10.1007/BF02509922.
Meyer-Peter, E., H. Favre, and A. Einstein. 1934. “Neuere versuchsresultate uber den geschiebetrieb.” [In German.] Schweiz. Bauzeitung 103 (13): 147–150.
Meyer-Peter, E., and R. Müller. 1948. “Formulas for bed-load transport.” In Proc., 2nd Meeting of the Int. Association for Hydraulic Research (IAHR), 39–64. Delft, Netherlands: International Association for Hydraulic Research.
Molinas, A., and B. Wu. 2001. “Transport of sediment in large sand-bed rivers.” J. Hydraul. Res. 39 (2): 135–146. https://doi.org/10.1080/00221680109499814.
MPCA (Minnesota Pollution Control Agency). 2009. “Minnesota’s impaired waters and total maximum daily loads (TMDLs).” Accessed April 29, 2019. http://www.pca.state.mn.us/water/tmdl/index.html.
NCASI (National Council for Air and Stream Improvements). 1999. Scale considerations and the detectability of sedimentary cumulative watershed effects. Research Triangle Park, NC: National Council for Air and Stream Improvements.
Niño, Y., and M. H. Garcia. 1998. “Using Lagrangian particle saltation observations for bedload sediment transport modeling.” Hydrol. Process. 12 (8): 1197–1218. https://doi.org/10.1002/(SICI)1099-1085(19980630)12:8%3C1197::AID-HYP612%3E3.0.CO;2-U.
Nittrouer, J. 2013. “Backwater hydrodynamics and sediment transport in the lowermost Mississippi River Delta: Implications for the development of fluvial-deltaic landform in large lowland river.” In Proc., of the HP1, IAHS-IAPSO-IAEI Assembly, 48–61. Wallingford, UK: International Association of Hydrological Science.
Parker, G., P. C. Klingeman, and D. G. McLean. 1982. “Bedload and size distribution in paved gravel-bed streams.” J. Hydraul. Div. 108 (4): 544–571. https://doi.org/10.1061/JYCEAJ.0005854.
Recking, A., F. Liebault, C. Peteuil, and T. Jolimet. 2012. “Testing bedload transport equations with consideration of time scales.” Earth Surf. Process. Landf. 37 (7): 774–789. https://doi.org/10.1002/esp.3213.
Schoklitsch, A. 1962. Vol. 1 of Handbuch des wasserbaues, 173–177. [In German.] Vienna, Austria: Springer.
Schottler, S. P., J. Ulrich, P. Belmont, R. Moore, J. W. Lauer, D. R. Engstrom, and J. E. Almendinger. 2014. “Twentieth century agricultural drainage creates more erosive rivers.” Hydrol. Process. 28 (4): 1951–1961. https://doi.org/10.1002/hyp.9738.
Shields, A. 1936. Anwendug der Aehnlichkeitsmechanik und der Turbulenzforschung auf die Geschiebebewegung. [In German]. Berlin: Mitteilungen der Preussiischen Versuchsanstalt fur Wasserbau and Schiffhau.
Simons, D. B., E. V. Richardson, M. L. Albertson, and R. J. Kodoatie. 2004. Geomorphic, hydrologic, hydraulic and sediment concepts applied to alluvial rivers. Fort Collins, CO: Colorado State Univ.
Southern Minnesota River Basin Commission. 1977. Minnesota River Basin report. St. Paul, MN: USDA, SCS, ERS and Forest Service.
Toffaleti, F. B. 1968. A procedure for computation of the total river sand discharge and detailed distribution, bed to surface. Vicksburg, MS: Committee on Channel Stabilization, USACE Waterways Experimental Station.
Turowski, J. M. 2011. “Probability distributions for bed form-dominated bed load transport: The Hamamori distribution revised.” J. Geophys. Res. 116 (F2): F02017. https://doi.org/10.1029/2010JF001803.
USACE. 2020. Minnesota River Basin interagency study. St. Paul, MN: USACE.
Vanoni, V. A. 2006. Sedimentation engineering-classic edition. Reston, VA: ASCE.
White, W. R., H. Milli, and A. D. Crabbe. 1975. “Sediment transport theories: A review.” Proc. Inst. Civ. Eng. 59 (2): 265–292. https://doi.org/10.1680/iicep.1975.3740.
Wilcock, P. R. 2009. Identifying sediment sources in the Minnesota River Basin. St. Paul, MN: Minnesota Pollution Control Agency.
World Meteorological Organization. 2003. Manual on sediment management and measurement. Geneva, Switzerland: World Meteorological Organization.
Yalin, M. S. 1963. “An expression for bed-load transportation.” J. Hydraul. Div. 89 (3): 221–250. https://doi.org/10.1061/JYCEAJ.0000874.
Yang, C. T. 1983. “Rate of energy dissipation and river sedimentation.” In Proc., 2nd Int. Symp. on River Sedimentation, 575–585. Beijing: Water Resources and Electric Power Press.
Yang, C. T. 1996. Sediment transport: Theory and practice. Malabar, FL: Krieger Publishing Company.
Information & Authors
Information
Published In
Journal of Hydrologic Engineering
Volume 26 • Issue 7 • July 2021
Copyright
© 2021 American Society of Civil Engineers.
History
Received: Aug 31, 2020
Accepted: Mar 16, 2021
Published online: Apr 26, 2021
Published in print: Jul 1, 2021
Discussion open until: Sep 26, 2021
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.
Cited by
- Seyed Abbas Hosseini, Abbas Abbaszadeh Shahri, Reza Asheghi, Prediction of bedload transport rate using a block combined network structure, Hydrological Sciences Journal, 10.1080/02626667.2021.2003367, 67, 1, (117-128), (2022).