Kalman Filtering with Regional Noise to Improve Accuracy of Contaminant Transport Models
Publication: Journal of Environmental Engineering
Volume 131, Issue 6
Abstract
Spatially independent Gaussian noise has been widely assumed in examining the Kalman filter (KF) properties in different areas of engineering practice. However, for subsurface modeling, it is more reasonable to consider both data and noise as regional. In this study, regional noises are employed in KF and finite-difference schemes in solving the subsurface transport problem. A KF is constructed as a data assimilation scheme for a subsurface numeric model. Also, a regional random field simulation scheme is proposed and employed to examine the impact on effectiveness of KF correction processes. The results indicate that the prediction error of the KF data assimilation scheme is 30% smaller than the error from the deterministic model. Furthermore, by applying a correct regional noise structure, the KF data assimilation scheme reduces the prediction error from 25 to 10 ppm in our model, indicating an improvement of 60% in prediction accuracy.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
This work was sponsored by the Department of Energy Samuel Massie Chair of Excellence Program under Grant No. DF-FG01-94EW11425. The views and conclusions contained herein are those of the writers and should not be interpreted as necessarily representing the official policies or endorsements, either expressed or implied, of the funding agency.
References
Bowles, D. S., and Greney, W. J. (1978). “Steady state river quality modeling by sequential extended Kalman filters.” Water Resour. Res., 12, 3281–3291.
Brooker, P. I. (2001). “Modelling spatial variability using soil profiles in the Riverland of South Australia.” Environ. Int., 27, 121–126.
Conwell, P. M., Silliman, S. E., and Zheng, L. (1997). “Design of a piezometer network for estimation of the variogram of the hydraulic gradient: The role of the instrument.” Water Resour. Res., 33(11), 2489–2492.
Ferraresi, M., and Marinelli, A. (1996). “An extended formulation of the integrated finite difference method for groundwater flow and transport.” J. Hydrol., 175(1–4), 453–471.
Ferreyra, R. A., Apezteguia, H. P., Sereno, R., and Jones, J. W. (2002). “Reduction of soil sampling density using scaled semivariograms and simulated annealing.” Geoderma, 110, 265–289.
Ghil, M., Cohn, S. E., Tavantzis, J., Bube, K., and Isaacson, E. (1981). “Applications of estimation theory to numerical weather prediction.” Dynamic meteorology: Data assimilation methods., L. Bengtsson, M. Ghil, and E. Kallen, eds., Springer, New York, 139–224.
Goovaerts, P. (1999). “Geostatistics in soil science: state-of-the-art and perspectives.” Geoderma, 89, 1–45.
Heuvelink, G. B. M., and Webster, R. (2001). “Modelling soil variation: past, present, and future.” Geoderma, 100, 269–301.
Harrouni, K. El., Ouazar, D., Wrobel, L. C., and Cheng, A. H.-D. (1997). “Aquifer parameter estimation by extended Kalman filtering and boundary elements.” Eng. Anal. Boundary Elem., 19(3), 231–237.
Hunt, B. (1978). “Dispersive sources in uniform groundwater flow.” J. Hydraul. Div., Am. Soc. Civ. Eng., 104(1), 75–85.
Kalman, R. E., and Bucy, R. S. (1961). “New results in linear filtering and prediction theory.” J. Basic Eng., 83, 95–108.
Ngan, P., and Russel, S. O. (1986). “Example of flow forecasting with Kalman filter.” J. Hydraul. Eng., 112(9), 818–832.
Stednick, J. D., and Roig, L. C. (1989). “Kalman filter calculation of sampling frequency when determine annual mean solution concentrations.” Water Resour. Bull., 25(3), 672–682.
Van Geer, F. C. (1982). “An equation based theoretical approach to network design for groundwater levels using Kalman filters.” Int. Assoc. Hydrol. Sci., 136, 241–250.
Webster, R., and Oliver, M. A. (1992). “Sample adequately to estimate variograms for soil properties.” J. Soil Sci., 43, 177–192.
Yu, Y. S., Heidari, M., and Guang-Te, W. (1989). “Optimal estimation of contaminant transport in ground water.” Water Resour. Bull., 25(2), 295–300.
Zou, S., and Parr, A. (1995). “Optimal estimation of two-dimensional contaminant transport.” Ground Water, 33(2), 319–325.
Information & Authors
Information
Published In
Journal of Environmental Engineering
Volume 131 • Issue 6 • June 2005
Pages: 971 - 982
Copyright
© 2005 ASCE.
History
Received: Jul 22, 2003
Accepted: Jul 26, 2004
Published online: Jun 1, 2005
Published in print: Jun 2005
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.