Comparison of Calibrated Empirical and Semi-Empirical Methods for Bedload Transport Rate Prediction in Gravel Bed Streams
Publication: Journal of Hydraulic Engineering
Volume 144, Issue 7
Abstract
The performance of seven sediment transport equations for bedload transport is compared using almost 2,600 of more than 8,000 measurements from a recent compilation. Named equations tested include the Meyer-Peter Muller, Barry, Pagosa good condition, Wilcock, Parker (both calibrated and uncalibrated), Recking, and that of Elhakeem and Imran. The purpose of the tests was to evaluate the performance of several empirical and semiempirical formulae using a single calibration point relative to three uncalibrated equations. The seven equations were included because they either have a calibration procedure already developed, are used frequently in practice, are historically foundational in the field, or have recently been proposed. Results are expressed in the root mean square error of the logarithms (RMSEL) and the relative mean error (RME) and show that the Pagosa good and Barry equations best predict bedload sediment transport (RMSEL of 0.02 and 0.02, respectively). The Pagosa good equation requires a data point for bankfull discharge and the corresponding bedload transport. The uncalibrated Recking (2013) equation resulted in lower errors than two of the calibrated formulae (Wilcock 2001 and Parker 1990) and was not far behind the calibrated Elhakeem and Imran (2016) formula. The Meyer-Peter Muller and uncalibrated Parker (1990) equations performed the worst (RMSEL of up to 0.85 and 0.86, respectively). The results herein demonstrate: (1) empirical formulae were more successful at predicting bedload transport than semiempirical alternatives, (2) a single calibration point significantly improves the predictive accuracy of any formula, and (3) calibration cannot compensate for all the shortcomings of a model.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
This research was jointly funded by the USDA Forest Service, Rocky Mountain Research Station, and the US Fish and Wildlife Service. We are grateful to numerous researchers who contributed to the current work. We appreciate the thoughtful insight and initial direction from an advisory committee consisting of John Buffington, Yantao Cui, Marwan Hassan, Gary Parker, and Tim Randle. Peter Wilcock’s advice and encouragement were also enormously helpful.
References
Ackers, P., and W. White. 1973. “Sediment transport: New approach and analysis.” J. Hydraul. Div. 99 (11): 2041–2060.
Almedeij, J. H., and P. Diplas. 2003. “Bedload transport in gravel-bed streams with unimodal sediment.” J. Hydraul. Eng. 129 (11): 896–904. https://doi.org/10.1061/(ASCE)0733-9429(2003)129:11(896).
Bakke, P. D., P. O. Basdekas, D. R. Dawdy, and P. C. Klingeman. 1999. “Calibrated Parker-Klingeman model for gravel transport.” J. Hydraul. Eng. 125 (6): 657–660. https://doi.org/10.1061/(ASCE)0733-9429(1999)125:6(657).
Barry, J. J., J. M. Buffington, and J. G. King. 2004. “A general power equation for predicting bed load transport rates in gravel bed rivers.” Water Resour. Res. 40 (10): W10401. https://doi.org/10.1029/2004WR003190.
Bravo-Espinosa, M., W. 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).
Brownlie, W. R. 1983. “Flow depth in sand-bed channels.” J. Hydraul. Eng. 109 (7): 959–990. https://doi.org/10.1061/(ASCE)0733-9429(1983)109:7(959).
Bunte, K., S. R. Abt, K. W. Swingle, and J. P. Potyondy. 2010. “Functions to adjust transport rates from a Helley-Smith Sampler to bedload traps in coarse gravel-bed streams (rating curve approach).” In Paper Presented at 2nd Joint Federal Interagency Conf. Las Vegas.
Chien, N. 1956. “The present status of research on sediment transport.” Trans. Am. Soc. Civ. Eng. 121: 833–884.
Crowder, D. W., and H. V. Knapp. 2005. “Effective discharge recurrence intervals of Illinois streams.” Geomorphology 64 (3–4): 167–184. https://doi.org/10.1016/j.geomorph.2004.06.006.
Doyle, M. W., D. Shields, K. F. Boyd, P. B. Skidmore, and D. W. Dominick. 2007. “Channel-forming discharge selection in river restoration design.” J. Hydraul. Eng. 133 (7): 831–837. https://doi.org/10.1061/(ASCE)0733-9429(2007)133:7(831).
Duan, J. G., L. Chen, and S. Scott. 2006. “Application of surface-based bed load transport equations to a desert gravel-bed stream.” J. Hydraul. Res. 44 (5): 624–630. https://doi.org/10.1080/00221686.2006.9521712.
Einstein, H. A. 1950. “The bed-load function for sediment transportation in open channel flows.”. Washington DC: US Dept. of Agriculture.
Elhakeem, M., and J. Imran. 2016. “Bedload model for nonuniform sediment.” J. Hydraul. Eng. 142 (6): 06016004. https://doi.org/10.1061/(ASCE)HY.1943-7900.0001139.
Emmett, W. W. 1980. A field calibration of the sediment-trapping characteristics of the Helley-Smith bedload sampler. US Geological Survey Professional Paper 1139. Washington, DC: US Government Publishing Office.
Gomez, B., and M. Church. 1989. “An assessment of bed load sediment transport formulae for gravel bed rivers.” Water Resour. Res. 25 (6): 1161–1186. https://doi.org/10.1029/WR025i006p01161.
Hinton, D., R. H. Hotchkiss, and D. P. Ames. 2017. “Comprehensive and quality-controlled bedload transport database.” J. Hydraul. Eng. 143 (2): 06016024. https://doi.org/10.1061/(ASCE)HY.1943-7900.0001221.
Karamisheva, R. D., J. F. Lyness, W. R. C. Myers, and J. O’sullivan. 2006. “Sediment discharge prediction in meandering compound channels.” J. Hydraul. Res. 44 (5): 603–613. https://doi.org/10.1080/00221686.2006.9521710.
King, J. G., W. W. Emmett, P. J. Whiting, R. P. Kenworthy, and J. J. Barry. 2004. “Sediment transport data and related information for selected coarse-bed streams and rivers in Idaho.”, Fort Collins, CO: US Dept. of Agriculture, Forest Service, Rocky Mountain Research Station.
King, J. G., W. W. Emmett, P. J. Whiting, R. P. Kenworthy, and J. J. Barry. 2012. “Sediment transport data for rivers in Idaho and Nevada.” Accessed October 21, 2010. https://www.fs.fed.us/rm/boise/AWAE/projects/sediment_transport/sediment_transport_BAT.shtml.
Lave, R. A. 2008. “The Rosgen wars and the shifting political economy of expertise.” Ph.D. dissertation, Univ. of California.
Lisle, T. E. 1995. “Particle size variations between bed load and bed material in natural gravel bed channels.” Water Resour. Res. 31 (4): 1107–1118. https://doi.org/10.1029/94WR02526.
Martin, Y. 2003. “Evaluation of bed load transport formulae using field evidence from the Vedder River, British Columbia.” Geomorphology 53 (1): 75–95. https://doi.org/10.1016/S0169-555X(02)00348-3.
McLean, D. G. 1980. “Flood control and sediment transport study of the Vedder River.” Ph.D. thesis, Univ. of British Columbia.
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.
Pacheco-Ceballos, R. 1989. “Transport of sediments: Analytical solution.” J. Hydraul. Res. 27 (4): 501–518. https://doi.org/10.1080/00221688909499126.
Parker, G. 1979. “Hydraulic geometry of active gravel rivers.” J. Hydraul. Div. 105 (9): 1185–1201.
Parker, G. 1990. “Surface-based bedload transport relation for gravel rivers.” J. Hydraul. Res. 28 (4): 417–436. https://doi.org/10.1080/00221689009499058.
Parker, G., and P. C. Klingeman. 1982. “On why gravel bed streams are paved.” Water Resour. Res. 18 (5): 1409–1423. https://doi.org/10.1029/WR018i005p01409.
Pitlick, J., Y. Cui, P. R. Wilcock, and R. M. R. Station. 2009. Manual for computing bed load transport using BAGS (Bedload Assessment for Gravel-bed Streams) Software. Fort Collins, CO: US Dept. of Agriculture, Forest Service, Rocky Mountain Research Station.
Recking, A. 2013. “Simple method for calculating reach-averaged bed-load transport.” J. Hydraul. Eng. 139 (1): 70–75. https://doi.org/10.1061/(ASCE)HY.1943-7900.0000653.
Recking, A., P. Frey, A. Paquier, P. Belleudy, and J. Y. Champagne. 2008. “Feedback between bed load transport and flow resistance in gravel and cobble bed rivers.” Water Resour. Res. 44 (5): W05412. https://doi.org/10.1029/2007WR006219.
Reid, I., D. M. Powell, and J. B. Laronne. 1996. “Prediction of bed-load transport by desert flash floods.” J. Hydraul. Eng. 122 (3): 170–173. https://doi.org/10.1061/(ASCE)0733-9429(1996)122:3(170).
Rosgen, D. L., H. L. Silvey, and D. Frantila. 2006. Watershed assessment of river stability and sediment supply (WARSSS). Fort Collins, CO: Wildland Hydrology.
Ryan, S. E., and W. W. Emmett. 2002. The nature of flow and sediment movement in Little Granite Creek near Bondurant, Wyoming. Fort Collins, CO: US Dept. of Agriculture, Forest Service, Rocky Mountain Research Station.
Ryan, S. E., and L. S. Porth. 1999. “A field comparison of three pressure-difference bedload samplers.” Geomorphology 30 (4): 307–322. https://doi.org/10.1016/S0169-555X(99)00059-8.
Ryan, S. E., L. S. Porth, and C. Troendle. 2002. “Defining phases of bedload transport using piecewise regression.” Earth Surf. Processes Landforms 27 (9): 971–990. https://doi.org/10.1002/esp.387.
Simon, A., W. Dickerson, and A. Heins. 2004. “Suspended-sediment transport rates at the 1.5-year recurrence interval for ecoregions of the United States: Transport conditions at the bankfull and effective discharge?” Geomorphology 58 (1–4): 243–262. https://doi.org/10.1016/j.geomorph.2003.07.003.
Simon, A., M. Doyle, M. Kondolf, F. Shields Jr., B. Rhoads, G. Grant, F. Fitzpatrick, K. Juracek, M. McPhillips, and J. MacBroom. 2005. “How well do the Rosgen classification and associated ‘Natural Channel Design’ methods integrate and quantify fluvial processes and channel response.” In Impacts of Global Climate Change, 1–12. Reston, VA: ASCE.
Simon, A., M. Doyle, M. Kondolf, F. Shields Jr., B. Rhoads, and M. McPhillips. 2007. “Critical evaluation of how the Rosgen classification and associated ‘natural channel design’ methods fail to integrate and quantify fluvial processes and channel response.” J. Am. Water Resour. Assoc. 43 (5): 1117–1131. https://doi.org/10.1111/j.1752-1688.2007.00091.x.
Van Rijn, L. C. 1984. “Sediment transport. I: Bed load transport.” J. Hydraul. Eng. 110 (10): 1431–1456. https://doi.org/10.1061/(ASCE)0733-9429(1984)110:10(1431).
Wilcock, P. R. 2001. “Toward a practical method for estimating sediment transport rates in gravel bed rivers.” Earth Surf. Processes Landforms 26 (13): 1395–1408. https://doi.org/10.1002/esp.301.
Wilcock, P. R., J. Pitlick, Y. Cui, and R. M. R. Station. 2009. Sediment transport primer: Estimating bed-material transport in gravel-bed rivers. Fort Collins, CO: US Dept. of Agriculture, Forest Service, Rocky Mountain Research Station.
Wong, M., and G. Parker. 2006. “Reanalysis and correction of bed-load relation of Meyer-Peter and Mueller using their own database.” J. Hydraul. Eng. 132 (11): 1159–1168. https://doi.org/10.1061/(ASCE)0733-9429(2006)132:11(1159).
Wu, W., S. Wang, and Y. Jia. 2000. “Nonuniform sediment transport in alluvial rivers.” J. Hydraul. Res. 38 (6): 427–434. https://doi.org/10.1080/00221680009498296.
Yang, C. T., and C. Huang. 2001. “Applicability of sediment transport formulas.” Int. J. Sediment Res. 16 (3): 335–353.
Yang, C. T., and A. Molinas. 1982. “Sediment transport and unit stream power function.” J. Hydraul. Div. 108 (6): 774–793.
Information & Authors
Information
Published In
Journal of Hydraulic Engineering
Volume 144 • Issue 7 • July 2018
Copyright
©2018 American Society of Civil Engineers.
History
Received: Dec 15, 2016
Accepted: Dec 11, 2017
Published online: Apr 30, 2018
Published in print: Jul 1, 2018
Discussion open until: Sep 30, 2018
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.