Algorithm for Real Time Correction of Stream Flow Concentration Based on Kalman Filter
Publication: Journal of Hydrologic Engineering
Volume 13, Issue 5
Abstract
This paper develops an algorithm for real-time correction of stream flow concentration based on a Kalman filter to improve the performance of real-time forecasting of river discharge under circumstances in which the nonlinearity of stream flow concentration is significant. The Muskingum matrix equation expresses the system of stream flow concentration as a time-varying linear system and satisfies the state-space expression of the Kalman filter. Updating of the parameter matrices of the system impair the influence of the nonlinearity of stream flow concentration on the linear filtering. The advantage of the algorithm is that predictions of every subbasin can be corrected twice by getting “remote” and “local” correction values and can achieve rational updating. Furthermore, to prevent the occurrence of filter divergence and to reach better filtering accuracy, a new real-time statistical method is proposed to estimate the process noise covariance matrix and measurement noise covariance matrix. The algorithm proves reasonable and effective by its application in the example of the Three Gorges Basin.
Get full access to this article
View all available purchase options and get full access to this article.
References
Ahsan, M., and O’Connor, K. M. (1994). “A reappraisal of the Kalman filtering technique, as applied in river flow forecasting.” J. Hydrol., 161, 197–226.
Carlos, E. P., and Bras, R. L. (1987). “Application of nonlinear filtering in the real-time forecasting of river flows.” Water Resour. Res., 23(4), 675–682.
Chen, S. L. (1992). “Deferential Newton iteration method of nonlinear Muskingum model.” Hydrology, 1, 30–33.
Chen, X. H., and Chen, J. H. (1995). “Research on the on-line real-time flood forecasting for the Three River in Jialingjiang River Basin.” SHUI WEN, 4, 6–12.
Cooper, D. M., and Wood, E. F. (1980a). “Parameter estimation of hydrologic state-space models with unknown system and measurement noise.” National Science Foundation Grant ENG 77-11841, National Science Foundation, Arlington, Va.
Cooper, D. M., and Wood, E. F. (1980b). “Maximum likelihood estimation of unknown parameters and innovation covariances for hydrologic state-space models.” National Science Foundation Grant ENG 77-11841, National Science Foundation. Arlington, Va.
Ding, J., and Deng, Y. R. (1988). Stochastic hydrology, University of Science and Technology of Chengdu, Chengdu, China.
Ge, S. X. (1985). “Discussion of real-time forecasting technique of linear concentration model.” J. Hydraul. Eng., 4, 1–9.
Ge, S. X. (2002). Modern flood forecasting techniques, Water Conservancy Publishing Firm, Beijing.
Hino, M. (1970). “Runoff forecasts by linear predictive filter.” J. Hydr. Div., 96(3), 681–702.
Hino, M. (1973). “On-line prediction of a hydrologic system.” Proc., XV Congress of the International Association of Hydraulic Engineering and Research, Istanbul.
Moradkhani, H., Sorooshian, S., and Gupta, V. H. (2005). “Dual-state-parameter estimation of hydrological models using ensemble Kalman filter.” Adv. Water Resour., 28, 135–147.
Posada, P. J., and Bras, R. L. (1982). “Automatic parameter estimation of a large conceptual rainfall–runoff model: A maximum likelihood approach.” Rep. No. 267, MIT, Cambridge, Mass.
Song, W. Y., and Zhang, Y. (1991). Kalman filtering, Science Publishing, Beijing.
Szilagyi, J. (2004). “Comment on ‘A reappraisal of Kalman filtering technique as applied in river flow forecasting.’ ” J. Hydrol., 285, 286–289.
Todini, E., and Bouillot, D. (1975). “A rainfall–runoff Kalman filter model.” System simulation in water resources, G. C. Vanteenkiste, ed., North-Holland, Amsterdam, The Netherlands.
Todini, E., O’ Connell, P. E., and Jones, D. A. (1977). “Kalman filter estimation problems, real-time hydrological forecasting and control.” Proc., 1st Int. Workshop, Inst. of Hydrology, Wallingford, U.K.
Todini, E., Szollosi-Nagy, A., and Wood, E. (1976). “Adaptive state/parameter estimation algorithm for real-time hydrological forecasting: A case study presented at workshop on recent development in forecasting and control of water resource systems.” Proc., International Institute for Applied Systems Analysis, Laxenburg, Austria.
Wang, C. H., Guo, L. J., Rui, X. F., and Kong, F. Z. (2003). “Study on real-time flood forecasting system for the Three Gorges Reservoir.” Adv. Water Sci., 14(6), 677–681.
Wang, Y. S., and Wang, S. Y. (1985). “Application of adaptive Kalman filter in hydrologic forecast.” Hydrology, 1, 16–21.
Zhang, J. M. (1997). “Real-time correction of water tank model.” J. Hydraul. Eng., 3, 58–64.
Zhao, R. J. (1984). Watershed hydrologic simulation—Xinanjiang model and Shanbei model, Water Conservancy and Electric Power Publishing Firm, Beijing.
Zhu, H. (1992). Automatic measuring and forecasting system for flood information, Water Conservancy and Electric Power Publishing Firm, Beijing.
Information & Authors
Information
Published In
Journal of Hydrologic Engineering
Volume 13 • Issue 5 • May 2008
Pages: 290 - 296
Copyright
© 2008 ASCE.
History
Received: Nov 13, 2006
Accepted: May 22, 2007
Published online: May 1, 2008
Published in print: May 2008
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.