Prediction of Sediment Concentration in Rivers by Recursive Least-Squares and Linear Minimum Variance Estimators
Publication: Journal of Hydrologic Engineering
Volume 17, Issue 8
Abstract
Peaks of suspended sediment concentration in rivers appear before peak discharge appears. The observation of discharge is usually done in many rivers for river management, but the suspended sediment concentration is not always observed. The suspended sediment concentration is expressed by a sediment-rating curve over a long period of time. Coefficients in the sediment-rating curve are time varying. The time variation of the suspended sediment concentration is predicted by the sediment-rating curve with the recursive least-squares and the linear minimum variance estimators. Because the sediment-rating curve is linearized by the logarithmic transformation, we can apply the simple linear models such as recursive least-squares and linear minimum variance estimators for the prediction of the suspended sediment concentration. These methods indicate that the coefficients in the sediment-rating curve are time varying. These methods can estimate sediment discharge by identifying the coefficients in the sediment-rating curve. Nash-Sutcliffe model efficiency coefficients indicate that the three-day ahead prediction is possible with accuracy. The recursive linear minimum variance estimator is compared with the recursive least-squares estimator. As a result, the recursive linear minimum variance estimator is not always better than the recursive least-squares estimator, although the former is theoretically superior to the latter as long as the assumption of the linear minimum variance estimator holds. The application of these methods to the prediction of the suspended sediment concentration is found to be possible because discharges are assumed to be observed daily in many rivers.
Get full access to this article
View all available purchase options and get full access to this article.
References
Bhowmik, N. G., Bonini, A. P., Bogner, W. C., and Byrne, R. P. (1980). Hydraulics of flow and sediment transport in the Kankakee River in IL, Illinois State Water Survey, Champaign, IL.
Chiu, C. L., ed., (1978). Application of Kalman filter to hydrology, hydraulics, and water resources, Univ. Pittsburgh, Pennsylvania.
Chiu, C. L., Matalas, N. C., Dawdy, D. R., and Mizumura, K. (1976). “Applications of estimation theory to hydraulic problems.” Proc., 2nd Int. Symp. Stochastic Hydraulics, 20.1–20.16.
Ferguson, R. I. (1986). “River loads underestimated by rating curves.” Water Resour. Res.WRERAQ, 22(1), 74–76.
Gelb, A. (1974). Applied optimal estimation, MIT Press, Cambridge, MA.
Graf, W. H. (1984). Hydraulics of sediment transport, Water Resources Publications, Littleton, CO.
Jain, S. K. (2001). “Development of integrated sediment rating curves using ANNs.” J. Hydraul. Eng.JHEND8, 127(1), 30–37.
Jazwinski, A. H. (1970). Stochastic processes and filtering theory, Academic Press, New York.
Karim, M. F., and Kennedy, J. F. (1990). “Menu of coupled velocity and sediment-discharge relations for rivers.” J. Hydraul. Eng.JHEND8, 116(8), 978–996.
McBean, E. A., and Al-Nassri, S. (1988). “Uncertainty in suspended sediment transport curves.” J. Hydraul. Eng.JHEND8, 114(1), 63–74.
Mizumura, K. (1982). “Prediction of water level in tidal inlet.” J. Waterway, Port, Coastal, Ocean Eng.JWPED5, 6(3), 217–231.
Mizumura, K. (1984). “Applications of Kalman filter to oceanic data.” J. Waterway, Port, Coastal, Ocean Eng.JWPED5, 110, 334–443.
Mizumura, K. (1985). “Estimation of hydraulic data by spline functions.” J. Hydraul. Eng.JHEND8, 111(9), 1219–1225.
Mizumura, K. (1989). “Hydrologic approach to prediction of sediment yield.” J. Hydraul. Eng.JHEND8, 115(4), 529–535.
Mizumura, K. (1990). “Closure to “Hydrologic approach to prediction of sediment yield” by Kazumasa Mizumura.” J. Hydraul. Eng.JHEND8, 116(12), 1554–1555.
Mizumura, K. (1993). “Applications of Kalman filter to inverse problem.” Computational stochastic mechanics, Cheng, A. H-D. and Yang, C. Y-W., eds., Computational Mechanics Publications, Southampton, UK, 545–568.
Mizumura, K. (1994). “Prediction of land subsidence due to groundwater use in snow country.” J. Hydraul. Eng.JHEND8, 120(4), 448–460.
Mizumura, K., and Chiu, C. L. (1985). “Prediction of combined snowmelt and rainfall runoff.” J. Hydraul. Eng.JHEND8, 111(2), 179–193.
Nash, J. E., and Sutcliffe, J. V. (1970). “River flow forecasting through conceptual model part 1-A discussion of principles.” J. Hydrol. (Amsterdam)JHYDA7, 10(3), 282–290.
Neal, J. C., Atkinson, P. M., and Hutton, C. W. (2007). “Flood inundation model updating using an ensemble Kalman filter and spatially distributed measurements.” J. Hydrol. (Amsterdam)JHYDA7, 336(3–4), 401–415.
Ozaki, T. (1980). “On a model of a nonlinear feedback system for river flow prediction.” Water Resour. Res.WRERAQ, 16(1), 225–231.
Porterfield, G. (1972). Techniques of water-resources investigations of the United States Geological Survey, USGS, Washington, DC.
Sage, A. P., and Melsa, J. L. (1971). Estimation theory with applications to communications and control, McGraw-Hill, New York.
Sen, Z., Altunkaynak, A., and Ozger, M. (2004). “Sediment concentration and its prediction by perceptron Kalman filtering procedure.” J. Hydraul. Eng.JHEND8, 130(8), 816–826.
Simon, D. (2006). Optimal state estimation: Kalman, H infinity, and nonlinear approaches, Wiley, Hoboken, NJ.
Simons, D. B., Duong, N., and Li, R. M. (1978). “An approach to short-term water and sed-iment discharge prediction using Kalman filter.” Application of Kalman filter to hydrology, hydraulics, and water resources, Chiu, C. L., ed., Univ. of Pittsburgh, Pittsburgh, 473–481.
Sivakumar, B. (2002). “A phase-space reconstruction approach to prediction of suspended sediment concentration in rivers.” J. Hydrol. (Amsterdam)JHYDA7, 258(1–4), 149–162.
Wang, C. H., and Bai, Y. L. (2008). “Algorithm for real time correction of stream flow concentration based on Kalman filter.” J. Hydrol. Eng.JHYEFF, 13(5), 290–296.
Yang, C. T. (1996). Sediment transport, theory and practice, McGraw-Hill, New York.
Information & Authors
Information
Published In
Journal of Hydrologic Engineering
Volume 17 • Issue 8 • August 2012
Pages: 851 - 857
Copyright
© 2012. American Society of Civil Engineers.
History
Received: Sep 3, 2010
Accepted: Oct 20, 2011
Published online: Oct 24, 2011
Published in print: Aug 1, 2012
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.