Estimation of Spatially Variable Aquifer Hydraulic Properties Using Kalman Filtering
Publication: Journal of Hydraulic Engineering
Volume 123, Issue 11
Abstract
Spatial variability of aquifer properties and hydraulic heads are modeled as random fields, and their estimates are achieved by Kalman filtering. The state-space equation is developed from a quasi-analytical solution of a first-order approximation of the governing stochastic flow equation. In the state-space system, the effects of aquifer heterogeneity and uncertainty in recharge are lumped linearly into a random noise vector that is correlated in time. To account for the correlated system noise, we reformulate the problem in terms of an augmented–state-space system and use the resulting Kalman filtering recursions to estimate transmissivities, storativities, and hydraulic heads, simultaneously. The filter is applied to a numerical experiment in which the statistical parameters of log aquifer properties are assumed to be known. The results indicate that under mild head gradients, head measurements alone are of limited value if the objective is to estimate the spatial distribution of aquifer transmissivity and storativity. Ultimately, measurements of the aquifer properties may be required for reliable estimation of their unknown values.
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References
1.
Andricevic, R.(1990). “Cost-effective network design for groundwater flow monitoring.”Stochastic Hydro. and Hydr., 4(1), 27–41.
2.
Bakr, A. A., Gelhar, L. W., Gutjahr, A. L., and McMillan, J. R.(1978). “Stochastic analysis of spatial variability in subsurface flow, 1, comparison of one- and three-dimensional flows.”Water Resour. Res., 14(2), 263–272.
3.
Bear, J. (1979). Hydraulics of groundwater. McGraw-Hill, Inc., New York, N.Y.
4.
Cushman, J. H.(1986). “On measurement, scale, and scaling.”Water Resour. Res., 22(2), 129–134.
5.
Dagan, G.(1985). “Stochastic modeling of groundwater flow by unconditional and conditional probabilities: the inverse problem.”Water Resour. Res., 21(1), 65–72.
6.
Dagan, G., and Rubin, Y.(1988). “Stochastic identification of recharge, transmissivity, and storativity in aquifer transient flow: a quasi-steady approach.”Water Resour. Res., 24(10), 1698–1710.
7.
Graham, W., and McLaughlin, D.(1989). “Stochastic analysis of nonstationary subsurface solute transport, 2, conditional moments.”Water Resour. Res., 25(10), 215–232.
8.
Hantush, M. M., and Mariño, M. A.(1994). “Two-dimensional stochastic analysis and optimal estimation in aquifers: random recharge.”Water Resour. Res., 30(2), 559–569.
9.
Hantush, M. M., and Mariño, M. A.(1995). “Continuous-time stochastic analysis of groundwater flow in heterogeneous aquifers.”Water Resour. Res., 31(3), 565–575.
10.
Hoeksema, R. J., and Kitanidis, P. K.(1984). “An application of the geostatistical approach to the inverse problem in two-dimensional groundwater modeling.”Water Resour. Res., 20(7), 1009–1020.
11.
Jazwinski, A. H. (1970). Stochastic processes and filtering theory. Academic Press, Inc., New York, N.Y.
12.
Kuiper, L. K.(1973). “Analytical solution of spatially discretized groundwater flow equations.”Water Resour. Res., 9(4), 1094–1097.
13.
Loaiciga, H. A., and Mariño, M. A.(1987). “Parameter estimation in groundwater: classical, Bayesian, and deterministic assumptions and their impact on management policies.”Water Resour. Res., 23(6), 1027–1035.
14.
Neuman, S. P.(1982). “Statistical characterization of aquifer heterogeneities: an overview.”Recent Trends in Hydrogeol. Spec. Pap. Geol. Soc. Am., 189, 81–102.
15.
Schmidtke, K. D., McBean, E. A., and Sykes, J. F.(1982). “Stochastic estimation of states in unconfined aquifers subject to artificial recharge.”Water Resour. Res., 18(5), 1519–1530.
16.
Shumway, R. H. (1988). Applied statistical time series analysis. Prentice-Hall, Inc. Englewood Cliffs, N.J.
17.
Sudicky, E. A.(1986). “A natural-gradient experiment on solute transport in a sand aquifer: spatial variability of hydraulic conductivity and its role in the dispersion process.”Water Resour. Res., 22(13), 2069–2082.
18.
Sun, N.-Z., and Yeh, W. W.-G.(1992). “A stochastic inverse solution for transient groundwater flow: parameter identification and reliability analysis.”Water Resour. Res., 28(12), 3269–3280.
19.
Van Geer, F. C., Te Stroet, B. M., and Zhou, Y.(1991). “Using Kalman filtering to improve and quantify the uncertainty of numerical groundwater simulations: 1. the role of system noise and its calibration.”Water Resour. Res., 27(8), 1987–1994.
20.
Van Geer, F. C., and Van Der Kloet, P.(1985). “Two algorithms for parameter estimation in groundwater flow problems.”J. Hydro., Amsterdam, The Netherlands, 77, 361–378.
21.
Wilson, J., Kitanidis, P., and Dettinger, M. (1978). “State and parameter estimation in groundwater models.”Applications of Kalman filter to hydrology, hydraulics and water resources, C. L. Chiu, ed., Dept. of Civ. Engrg., University of Pittsburgh Press, Pittsburgh Pa., 657–679.
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Published In
Journal of Hydraulic Engineering
Volume 123 • Issue 11 • November 1997
Pages: 1027 - 1035
Copyright
Copyright © 1997 American Society of Civil Engineers.
History
Published online: Nov 1, 1997
Published in print: Nov 1997
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