Stochastically Optimal Groundwater Management Considering Land Subsidence
Publication: Journal of Water Resources Planning and Management
Volume 133, Issue 6
Abstract
This paper presents a stochastic groundwater management model explicitly considering land subsidence. Through the use of response matrix technique and one-dimensional consolidation equation, a deterministic management model is first developed. By Latin hypercube sampling technique, along with numerical subsurface flow simulation, statistical features of unit response coefficients due to random hydrogeologic parameters, including hydraulic conductivity and Lame constants ( and ), are quantified. The first-order-variance-estimation method is adopted to analyze the uncertainties of drawdown and land subsidence based on which the concept of chance-constrained programming is applied to transfer the original deterministic management model into its stochastic form. The stochastic management model enables the determination of optimal total pumpage subject to the constraints that drawdown and land subsidence do not exceed the allowable values with a specified reliability. A hypothetical example is utilized to demonstrate the applicability of the stochastic model to five cases in which various levels of parameter uncertainty are considered. The results indicate that joint consideration of drawdown and land subsidence is essential, and the proposed stochastic management model can be generally applied for regional groundwater resources management in conjunction with controlling land subsidence.
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Acknowledgments
This study was funded by the Water Resources Agency (WRA), Ministry of Economic Affairs, R.O.C., under Grant No. UNSPECIFIEDMOEA/WRA/ST-920020V3. The writers wish to thank Professor L. H. Huang of National Taiwan University, R.O.C., and Dr. K. C. Chang of the WRA for being instrumental at the initial stage of this study. The writers are also grateful to the reviewers for their constructive comments that greatly improve the contents and presentation of the manuscript.
References
Ahlfeld, D. P., and Heidari, M. (1994). “Applications of optimal hydraulic control to ground-water systems.” J. Water Resour. Plann. Manage., 120(3), 350–365.
Ahlfeld, D. P., and Mulligan, A. E. (2000). Optimal management of flow in groundwater systems, Academic, San Diego.
Anderson, M. P., and Woessner, W. W. (1991). “Applied groundwater modeling: Simulation of flow and advective transport.” Equations and numerical methods, Academic, London, 12.
Bear, J., and Verruijt, A. (1987). “Modeling groundwater flow and pollution.” Modeling three-dimensional flow, Reidel, Taiwan, 78–83.
Biot, M. A. (1941). “General theory of three-dimensional consolidation.” J. Appl. Phys., 12, 155–164.
Bredehoeft, J. D., and Pinder, G. F. (1970). “Digital analysis of areal flow in multiaquifer groundwater systems: A quasi three-dimensional model.” Water Resour. Res., 6(3), 883–888.
Chan, N. (1993). “Robustness of the multiple realization method for stochastic hydraulic aquifer management.” Water Resour. Res., 29(9), 3159–3167.
Chan, N. (1994). “Partial infeasibility method for chance-constrained aquifer management.” J. Water Resour. Plann. Manage., 120(1), 70–89.
Christiaens, K., and Feyen, J. (2001). “Analysis of uncertainties associated with different methods to determine soil hydraulic properties and their propagation in the distributed hydrological MIKE SHE model.” J. Hydrol., 246(1–4), 63–81.
Das, B. M. (1983). “Advanced soil mechanics.” Evaluation of soil settlement, McGraw-Hill, Singapore, 356.
Datta, B., and Dhiman, S. D. (1996). “Chance-constrained optimal monitoring network design for pollutants in ground water.” J. Water Resour. Plann. Manage., 122(3), 180–188.
Feyen, L., and Gorelick, S. M. (2004). “Reliable groundwater management in hydroecologically sensitive areas.” Water Resour. Res., 40(7), 1–14.
Floquet, P., Pibouleau, L., and Domenech, S. (1993). “Recent trends in process optimization.” Desalination, 92(1–3), 1–20.
Floudas, C. A. (1995). Nonlinear and mixed-integer optimization, Oxford University Press, New York.
Freeze, R. A., and Gorelick, S. M. (1999). “Convergence of stochastic optimization and decision analysis in the engineering design of aquifer remediation.” Ground Water, 37(6), 934–954.
Gelhar, L. W. (1993). Stochastic subsurface hydrology, Prentice-Hall, Englewood, Cliffs, N.J.
Gorelick, S. M. (1983). “A review of distributed parameter groundwater management modeling methods.” Water Resour. Res., 19(2), 305–319.
Gutierrez, M. S., and Lewis, R. W. (2002). “Coupling of fluid flow and deformation in underground formations.” J. Eng. Mech., 128(7), 779–787.
Gwo, J. P., Toran, L. E., Morris, M. D., and Wilson, G. V. (1996). “Subsurface stormflow modeling with sensitivity analysis using a Latin-hypercube sampling technique.” Ground Water, 34(5), 811–818.
Helm, D. C. (1987). “Three-dimensional consolidation theory in terms of the velocity of soil.” Geotechnique, 37, 369–392.
Larson, K. J., Basagaoglu, H., and Marino, M. A. (2001). “Prediction of optimal safe groundwater yield and land subsidence in the Los Banos-Kettleman City area, California, using a calibrated numerical simulation model.” J. Hydrol., 242(1–2), 79–102.
McKay, M. D. (1988). “Sensitivity and uncertainty analysis using a statistical sample of input values.” Uncertainty analysis, Y. Ronen, ed., CRC, Boca Raton, Fla., 145–186.
McKay, M. D., Beckman, R. J., and Conover, W. J. (2000). “A comparison of three methods for selecting values of input variables in the analysis of output from a computer code.” Technometrics, 42(1), 55–61.
Morgan, D. R., Eheart, J. W., and Valocchi, A. J. (1993). “Aquifer remediation design under uncertainty using a new chance constrained programming technique.” Water Resour. Res., 29(3), 551–561.
Mylopoulos, Y. A., Theodosiou, N., and Mylopoulos, N. A. (1999). “A stochastic optimization approach in the design of an aquifer remediation under hydrogeologic uncertainty.” Water Resour. Manage., 13(5), 335–351.
Nguyen, V. N., and Chowdhury, R. N. (1985). “Simulation for risk analysis with correlated variables.” Geotechnique, 35(1), 47–58.
Onta, P. R., and Gupta, A. D. (1995). “Regional management modeling of a complex groundwater system for land subsidence control.” Water Resour. Manage., 9(1), 1–25.
Phillips, S. P., Carlson, C. S., Metzger, L. F., Howle, J. F., Galloway, D. L., Sneed, M., Ikehara, M. E., Hudnut, K. W., and King, N. E. (2003). “Analysis of tests of subsurface injection, storage, and recovery of freshwater in Lancaster, Antelope Valley, California.” Rep. No. 03-4061, Development of a Simulation/Optimization Model, U.S. Geological Survey Water–Resources Investigations, Washington, D.C., 93–100.
Reismann, H., and Pawlik, P. S. (1980). “Elasticity: Theory and applications.” Elasticity and its limits, Wiley, New York, 128–135.
Ricardo, D. D., and Keith, L. (2000). “Regional-scale leaching assessment for tenerife: Effect of data uncertainties.” J. Environ. Qual., 29(3), 835–847.
Ricardo, D. D., Keith, L., and Jesus, S. N. (1999). “An assessment of agrochemical leaching potentials for Tenerife.” J. Contam. Hydrol., 36(1–2), 1–30.
Sawyer, C. S., and Lin, Y.-F. (1998). “Mixed-integer chance-constrained models for ground-water remediation.” J. Water Resour. Plann. Manage., 124(5), 285–294.
Tsai, T. L. (2001). “The development and application of model of regional land subsidence due to groundwater overpumping.” Ph.D. thesis, National Chiao Tung Univ., Hsinchu, Taiwan.
Tung, Y.-K. (1986). “Groundwater management by chance-constrained model.” J. Water Resour. Plann. Manage., 112(1), 1–19.
Uryas’ev, S. P. (1991). “New variable-metric algorithms for nondifferentiable optimization problems.” J. Optim. Theory Appl., 71(2), 359–388.
Wagner, B. J. (1995). “Recent advances in simulation-optimization groundwater management modeling.” Rev. Geophys., 33(S1), 1021–1028.
Wagner, B. J., and Gorelick, S. M. (1987). “Optimal groundwater quality management under parameter uncertainty.” Water Resour. Res., 23(7), 1162–1174.
Wagner, B. J., and Gorelick, S. M. (1989). “Reliable aquifer remediation in the presence of spatially variable hydraulic conductivity: From data to design.” Water Resour. Res., 25(10), 2211–2225.
Wagner, J. M., Shamir, U., and Nemati, H. R. (1992). “Groundwater quality management under uncertainty: Stochastic programming approaches and the value of information.” Water Resour. Res., 28(5), 1233–1246.
Whittaker, B. N., and Reddish, D. J. (1989). “Subsidence occurrence, prediction and control.” Natural subsidence and influence of geological processes, Elsevier Science, Amsterdam, The Netherlands, 1–13.
Yang, Y. F., and Dong, H. L. (2001). “A trust region algorithm for constrained nonsmooth optimization problems.” J. Comput. Math., 19(4), 357–364.
Yeh, W. W.-G. (1992). “Systems analysis in ground-water planning and management.” J. Water Resour. Plann. Manage., 118(3), 224–237.
Information & Authors
Information
Published In
Journal of Water Resources Planning and Management
Volume 133 • Issue 6 • November 2007
Pages: 486 - 498
Copyright
© 2007 ASCE.
History
Received: Aug 17, 2004
Accepted: Aug 7, 2006
Published online: Nov 1, 2007
Published in print: Nov 2007
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