Quantifying the Uncertainty Associated with Estimating Sediment Concentrations in Open Channel Flows Using the Stochastic Particle Tracking Method
Publication: Journal of Hydraulic Engineering
Volume 141, Issue 12
Abstract
Suspended sediment concentrations are typically estimated using either the advection-diffusion equation or sediment rating curves in a deterministic manner. This study attempts to develop a stochastic approach for quantifying the probabilistic characteristics of sediment concentrations that can account for the uncertainty associated with flow randomness. Turbulence is a primary cause of particle diffusion in a flow. Impacts from such flow randomness on particle diffusion can be observed from two aspects: (1) the degree of spreading of a particle cloud, and (2) variability in concentration curves observed in different releases of particles under the same turbulence intensity. While the former diffusion has been extensively studied, the latter has not been fully investigated, in spite of its significance in terms of identifying the uncertainty associated with estimating concentrations. Herein, the effect of probabilistic characteristics attributed to turbulence on sediment concentrations is evaluated through multiple realizations of a Lagrangian-based stochastic differential equation for particle trajectory. Both the resuspension and deposition of particles are considered in the transport processes. Sediment concentrations can then be estimated from the spatial distribution of particles. As a result of the ensemble standard deviation, it is found that estimating higher-concentration regions is subject to a higher uncertainty. The coefficient of variation representing the extent of variability relative to their mean in lower-concentration regions is found to be more variable than that in higher-concentration regions. It is observed that when the ensemble standard deviation of the concentration is normalized by the square root of the particle number, the magnitude of the variability of concentration curves tends to approach asymptotically to one single curve.
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Acknowledgments
The authors gratefully acknowledge the financial support from the National Science Foundation under grant contract number EAR-0748787.
References
Ancey, C. (2010). “Stochastic modeling in sediment dynamics: Exner equation for planar bed incipient bed load transport conditions.” J. Geophys. Res. Earth Surf., 115(F2), F00A11.
Arabi, M., Govindaraju, R. S., and Hantush, M. M. (2007). “A probabilistic approach for analysis of uncertainty in the evaluation of watershed management practices.” J. Hydrol., 333(2–4), 459–471.
Arnold, L. (1974). Stochastic differential equations: Theory and applications, Wiley, London.
Chien, N., and Wan, Z. (1999). Mechanics of sediment transport, J. S. Mcnown, ed., ASCE, Reston, VA.
Coleman, N. L. (1986). “Effects of suspended sediment on the open-channel velocity distribution.” Water Resour. Res., 22(10), 1377–1384.
Cuthbertson, A. J. S., and Ervine, D. A. (2007). “Experimental study of fine sand particle settling in turbulent open channel flows over rough porous beds.” J. Hydraul. Eng., 905–916.
Fang, H.-W., and Wang, G.-Q. (2000). “Three-dimensional mathematical model of suspended-sediment transport.” J. Hydraul. Eng., 578–592.
Franceschini, S., and Tsai, C. W. (2010). “Assessment of uncertainty sources in water quality modeling in the Niagara River.” Adv. Water Resour., 33(4), 493–503.
Furbish, D. J., Ball, A. E., and Schmeeckle, M. W. (2012). “A probabilistic description of the bed load sediment flux: 4. Fickian diffusion at low transport rates.” J. Geophys. Res., 117(F3), F03034.
Gardiner, C. W. (1985). Handbook of stochastic methods: For physics, chemistry, and the natural sciences, Springer, New York.
Gyr, A., and Hoyer, K. (2006). Sediment transport: A geophysical phenomenon, Springer, Netherlands.
Hanson, F. B. (2007). Applied stochastic processes and control for jump diffusions: Modeling, analysis, and computation, Society for Industrial & Applied Mathematics, PA.
Harris, A. R., and Davidson, C. I. (2009). “A Monte Carlo model for soil particle resuspension including saltation and turbulent fluctuations.” Aerosol Sci. Technol., 43(2), 161–173.
Heemink, A. W. (1990). “Stochastic modelling of dispersion in shallow water.” Stochastic Hydrol. Hydraul., 4(2), 161–174.
Hunter, J. R., Craig, P. D., and Phillips, H. E. (1993). “On the use of random walk models with spatially variable diffusivity.” J. Comput. Phys., 106(2), 366–376.
Iadanza, C., and Napolitano, F. (2006). “Sediment transport time series in the Tiber River.” Phys. Chem. Earth, 31(18), 1212–1227.
Kloeden, P. E., Platen, E., and Schurz, H. (1994). Numerical solution of SDE through computer experiments, Springer, New York City.
Kurashige, Y. (1993). “Mechanism of suspended sediment supply to headwater rivers and its seasonal variation in west central Hokkaido, Japan.” Jpn. J. Limnol., 54(4), 305–315.
Kurashige, Y. (1998). “Process-based estimation of suspended-sediment concentration during the thaw season in a small headwater basin.” Proc., Modelling Soil Erosion, Sediment Transport and Closely Related Hydrological Processes, Vol. 249, IAHS Press, Wallingford, U.K., 415–422.
Lemke, K. A. (1990). “An evaluation of transfer-function/noise models of suspended sediment concentration.” Prof. Geographer, 42(3), 324–336.
Man, C., and Tsai, C. W. (2007). “Stochastic partial differential equation based model for suspended sediment transport in surface water flows.” J. Eng. Mech., 422–430.
Middlekoop, H., and Van der Perk, M. (1998). “Modelling spatial patterns of overbank sedimentation on embanked floodplains.” Geografiska Annaler, 80A(2), 95–109.
Morehead, M. D., Syvitski, J. P., Hutton, E. W. H., and Peckham, S. D. (2003). “Modeling the temporal variability in the flux of sediment from ungauged river basins.” Global Planet. Change, 39(1-2), 95–110.
Nicholas, A. P., and Walling, D. E. (1997). “Modelling flood hydraulics and overbank deposition on river floodplains.” Earth Surf. Process. Landforms, 22(1), 59–77.
Oh, J., and Tsai, C. W. (2010). “A stochastic jump diffusion particle-tracking model (SJD-PTM) for sediment transport in open channel flows.” Water Resour. Res., 46(10), W10508.
Olive, L. J., Rieger, W. A., and Burgess, J. S. (1980). “Estimation of sediment yields in small catchments: A geomorphic guessing game?” Proc., 16th Conf. of the Institute of Australian Geographers, IAG, Campbell, Australia, 279–288.
Osidele, O. O., Zeng, W., and Beck, M. B. (2003). “Coping with uncertainty: A case study in sediment transport and nutrient load analysis.” J. Water Resour. Plann. Manage., 345–355.
Pope, S. B. (2000). Turbulent flows, Cambridge University Press, Cambridge.
Rustomji, P., and Wilkinson, S. N. (2008). “Applying bootstrap resampling to quantify uncertainty in fluvial suspended sediment loads estimated using rating curves.” Water Resour. Res., 44(9), W09434.
Schumm, S. A. (1963). “A tentative classification of alluvial river channels.”, Washington, DC, 10.
Tsujimoto, T., Shimizu, Y., Kitamura, T., and Izumi, N. (1994). “Flow and suspended sediment transport in compound open-channel with vegetation.” Hydraulics Laboratory, Kanazawa Univ., Japan.
Tung, Y. K., and Yen, B. C. (2005). Hydrosystems engineering uncertainty analysis, McGraw-Hill, New York.
VanSickle, J., and Beschta, R. L. (1983). “Supply-based models of suspended sediment transport in streams.” Water Resour. Res., 19(3), 768–778.
Walling, D. E., and Webb, W. B. (1981). “The reliability of suspended sediment load data.” Proc., Florence Symp. Erosion and Sediment Transport Measurement, Vol. 133, IAHS, Wallingford, U.K., 177–194.
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Published In
Journal of Hydraulic Engineering
Volume 141 • Issue 12 • December 2015
Copyright
© 2015 American Society of Civil Engineers.
History
Received: May 22, 2014
Accepted: Apr 2, 2015
Published online: Jun 17, 2015
Discussion open until: Nov 17, 2015
Published in print: Dec 1, 2015
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