Sampling Interval Analysis and CDF Generation for Grain-Scale Gravel Bed Topography
Publication: Journal of Hydraulic Engineering
Volume 144, Issue 10
Abstract
In river hydraulics, there is a continuing need for characterizing bed elevations to arrive at quantitative roughness measures that can be used in flow depth calculations and for improved prediction of fine-sediment transport over and through coarse beds. Recently published prediction methods require a method for estimating the cumulative distribution function (CDF) of bed elevations. Representing the distribution of elevations for rough beds requires a correct choice for the number and spacing of measurement locations. Laboratory experiments over a screeded flat gravel bed with sand having median diameter were used to determine the number and spatial coverage of measurements needed to define the elevation field for a range of uncertainty levels. Approximately 1,000–5,000 randomly collected single elevation measurements were needed to quantify the distribution of elevations for the gravel bed. Relative error in estimating the standard deviation of elevations was insensitive to the number and spacing of elevation measurements when the spacing exceeded (35 mm). The standard deviation of bed elevations was found to be proportional to the median bed material size for several different gravel beds. A method is presented for generating a CDF for bed elevations using the elevation-distribution standard deviation with a randomly sampled distribution function.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
This work was supported by base funding from the United States Department of Agriculture Agricultural Research Service. Mick Ursic, a Support Scientist at the National Sedimentation Laboratory, collected the data that were presented.
References
Aberle, J., and V. I. Nikora. 2006. “Statistical properties of armored gravel bed surfaces.” Water Resour. Res. 42 (11): W11414. https://doi.org/10.1029/2005WR004674.
Bertin, S., and H. Friedrich. 2014. “Measurement of gravel-bed topography: Evaluation study applying statistical roughness analysis.” J. Hydraul. Eng. 140 (3): 269–279. https://doi.org/10.1061/(ASCE)HY.1943-7900.0000823.
Bertin, S., J. Groom, and H. Friedrich. 2017. “Isolating roughness scales of gravel-bed patches.” Water Resour. Res. 53 (8): 6814–6856.
Butler, J. B., S. N. Lane, and J. H. Chandler. 2001. “Characterization of the structure of river-bed gravels using two-dimensional fractal analysis.” Math. Geol. 33 (3): 301–330. https://doi.org/10.1023/A:1007686206695.
Cooper, J. R., and S. J. Tait. 2009. “Water-worked gravel beds in laboratory flumes—A natural analogue?” Earth Surf. Processes Landforms 34 (3): 384–397. https://doi.org/10.1002/esp.1743.
Garcia, M. H. 2008. Sedimentation engineering, processes, measurements, modeling, and practice. Reston, VA: ASCE.
Grams, P. E., and P. R. Wilcock. 2007. “Equilibrium entrainment of fine sediment over a coarse immobile bed.” Water Resour. Res. 43 (10): W10420. https://doi.org/10.1029/2006WR005129.
Heritage, G. L., and D. J. Milan. 2009. “Terrestrial laser scanning of grain roughness in a gravel-bed river.” Geomorphology 113 (1–2): 4–11. https://doi.org/10.1016/j.geomorph.2009.03.021.
Kuhnle, R. A., E. J. Langendoen, and D. G. Wren. 2017. “Prediction of sand transport over immobile gravel from supply limited to capacity conditions.” J. Hydraul. Eng. 143 (7): 04017010. https://doi.org/10.1061/(ASCE)HY.1943-7900.0001292.
Kuhnle, R. A., D. G. Wren, and E. L. Langendoen. 2013. “Sand transport over an immobile gravel substrate.” J. Hydraul. Eng. 139 (2): 167–176. https://doi.org/10.1061/(ASCE)HY.1943-7900.0000615.
Mignot, E., E. Barthelemy, and D. Hurther. 2009. “Double-averaging analysis and local flow characterization of near-bed turbulence in gravel-bed channel flows.” J. Fluid Mech. 618: 279–303. https://doi.org/10.1017/S0022112008004643.
Mohajeri, S. H., S. Grizzi, M. Righetti, G. P. Romano, and V. I. Nikora. 2015. “The structure of gravel-bed flow with intermediate submergence: A laboratory study.” Water Resour. Res. 51 (11): 9232–9255. https://doi.org/10.1002/2015WR017272.
Nikora, V., D. Goring, I. McEwan, and G. Griffiths. 2001. “Spatially averaged open-channel flow over rough beds.” J. Hydraul. Eng. 127 (2): 123–133. https://doi.org/10.1061/(ASCE)0733-9429(2001)127:2(123).
Nikora, V., D. G. Goring, and B. Biggs. 1998. “On gravel-bed roughness characterization.” Water Resour. Res. 34 (3): 517–527. https://doi.org/10.1029/97WR02886.
Nikora, V., S. McLean, S. Coleman, D. Pokrajac, I. McEwan, L. Campbell, J. Aberle, D. Clunie, and K. Koll. 2007. “Double-averaging concept for rough-bed open-channel and overland flows: Applications.” J. Hydraul. Eng. 133 (8): 884–895. https://doi.org/10.1061/(ASCE)0733-9429(2007)133:8(884).
Papanicolaou, A. N., D. C. Dermisis, and M. Elhakeem. 2011. “Investigating the role of clasts on the movement of sand in gravel bed rivers.” J. Hydraul. Eng. 137 (9): 871–883. https://doi.org/10.1061/(ASCE)HY.1943-7900.0000381.
Pearson, E., M. W. Smith, M. J. Klaar, and L. E. Brown. 2017. “Can high resolution 3D topographic surveys provide reliable grain size estimates in gravel bed rivers?” Geomorphology 293 (Part A): 143–155. https://doi.org/10.1016/j.geomorph.2017.05.015.
Powell, D. M., A. Ockelford, S. P. Rice, J. K. Hillier, T. Nguyen, I. Reid, and D. Ackerley. 2016. “Structural properties of mobile armors formed at different flow strengths in gravel-bed rivers.” J. Geophys. Res. Earth Surf. 121 (8): 1494–1515. https://doi.org/10.1002/2015JF003794.
Robert, A. 1988. “Statistical properties of sediment bed profiles in alluvial channels.” Math. Geol. 20 (3): 205–225. https://doi.org/10.1007/BF00890254.
Stoesser, T. 2010. “Physically realistic roughness closure scheme to simulate turbulent channel flow over rough beds within the framework of LES.” J. Hydraul. Eng. 136 (10): 812–819. https://doi.org/10.1061/(ASCE)HY.1943-7900.0000236.
Tuijnder, A. P. 2010. “Sand in short supply, modelling of bedforms, roughness, and sediment transport in rivers under supply-limited conditions.” Ph.D. thesis, Univ. of Twente.
Ursic, M., E. J. Langendoen, H. Momm, D. G. Wren, and R. A. Kuhnle. 2012. “Using terrestrial lidar to characterize morphology and texture of a sand and gravel bed in a laboratory flume.” In Proc., Hydraulic Measurements and Experimental Methods Conf., 6. Reston, VA: ASCE.
Vázquez-Tarrío, D., L. Borgniet, F. Liebault, and A. Recking. 2017. “Using UAS optical imagery and SfM photogrammetry to characterize the surface grain size of gravel bars in a braided river (Veneon River, French Alps).” Geomorphology 285 (C): 94–105.
Venditti, J. G., P. A. Nelson, R. W. Bradley, D. Haught, and A. B. Gitto. 2017. “Bedforms, structures, patches, and sediment supply in gravel-bed rivers.” In Gravel-bed rivers: Process and disasters, edited by D. Tsutsumi and J. B. Laronne. 439–466. Oxford, UK: Wiley-Blackwell.
Wren, D. G., R. A. Kuhnle, E. J. Langendoen, and J. R. Rigby. 2014. “Turbulent flow and sand transport over a cobble bed in a laboratory flume.” J. Hydraul. Eng. 140 (4): 04014001. https://doi.org/10.1061/(ASCE)HY.1943-7900.0000838.
Information & Authors
Information
Published In
Journal of Hydraulic Engineering
Volume 144 • Issue 10 • October 2018
Copyright
©2018 American Society of Civil Engineers.
History
Received: Sep 26, 2017
Accepted: Apr 26, 2018
Published online: Jul 24, 2018
Published in print: Oct 1, 2018
Discussion open until: Dec 24, 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.