Planning Model for Optimal Control of Saltwater Intrusion
Publication: Journal of Water Resources Planning and Management
Volume 114, Issue 2
Abstract
A planning model is presented for the control of seawater intrusion in regional groundwater systems. The management model is structured as a problem in optimal control. The hydraulic response equations, which are developed from continuity principles, relate the movement of the interface to the magnitude and location of groundwater pumping and recharge. Finite difference methods are used to approximate the solution of the aquifer's response to management strategies. The control problem is solved using: (1) The influence‐coefficient method allied with quadratic programming; and (2) reduced‐gradient methods in conjunction with a quasi‐Newton algorithm. The planning model is applied to the Yun Lin groundwater basin in southwestern Taiwan where excessive pumping has produced declining water levels, localized land subsidence, and saltwater intrusion. The optimal groundwater pumping and recharge schedules for the Peikang area of the basin are presented. The computational efficiency of the algorithms is also discussed.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Aguado, E., and Remson, I. (1974). “Groundwater hydraulics in aquifer management.” J. Hydr. Div., ASCE, 100(1), 103–118.
2.
Bear, J. (1979). Dynamics of fluids in porous media. American Elsevier, New York, N.Y.
3.
Bear, J. (1979). Hydraulics of groundwater. McGraw‐Hill, New York, N.Y.
4.
Bear, J., and Dagan, G. (1964). “Moving interface in coastal aquifers.” J. Hydr. Div., ASCE, 90(4), 193–216.
5.
Becker, L., and Yen, W. W.‐G. (1972). “Identification of parameters in unsteady open channel flow.” Water Resourc. Res., 8(4), 956–965.
6.
Collins, M. A., and Gelhar, L. W. (1977). “Seawater intrusion in layered aquifers.” Water Resourc. Res., 794, 971–979.
7.
Collins, M. A., and Gelhar, L. W. (1970). “Groundwater hydrology of the long island aquifer system.” Hydrodynamic Lab. Report No. 122, Dept. of Civil. Engineering, M.I.T., Cambridge, Mass.
8.
Dagan, G., and Bear, J. (1968). “Solving the problem of interface upconing in a coastal aquifer by the method of small perturbation,” J. Hydr. Div., ASCE, 6(1), 15–44.
9.
Fletcher, R. (1975). “An ideal penalty function for constrained optimization.” J. Inst. Math. Applies., 15, 319–342.
10.
Fox, R. L. (1971). Optimization methods for engineering design. Addison‐Wesley, New York, N.Y.
11.
Gill, P. E., et al. (1984). User's guide for QPSOL (version 3.2): Package for quadratic programming. Department of Operations Research, Stanford University, Palo Alto, Calif.
12.
Gorelick, S. M. (1983). “A review of distributed parameter groundwater management modeling methods.” Water Resourc. Res., 19(2), 305–319.
13.
Heidari, M. (1982). “Application of linear systems theory and linear programming to groundwater management in Kansas.” Water Resourc. Bull., 18(6), 1003–1012.
14.
Mercer, J. W., Larson, S. P., and Faust, C. R. (1980a). “Finite difference model to simulate the areal flow of saltwater and freshwater separated by an interface.” U.S.G.S. Open File Report 80‐407, Reston, Va.
15.
Mercer, J. W., Larson, S. P., and Faust, C. R. (1980b). “Simulation of saltwater interface motion.” Groundwater, 18(4), 374–385.
16.
Mualem, Y., and Bear, J. (1974). “The shape of the interface in steady flow in a stratified aquifer.” Water Resourc. Res., 10(6), 1207–1215.
17.
Murtagh, B. A., and Saunders, M. A. (1982). “A projected Lagrangian algorithm and its implementation for sparse nonlinear constraints.” Math. Prog. Study, 16, 84–117.
18.
Murtagh, B. A., and Saunders, M. A. (1983). MINOS 5.0 user's guide. Technical Report 83‐20, Systems Optimization Laboratory, Department of Operations Research, Stanford University, Stanford, Calif.
19.
Noel, J. E., and Howitt, R. E. (1982). “Conjunctive multibasin management: An optimal control approach.” Water Resourc. Res., 18(4), 753–763.
20.
Pinder, G. F., and Page, R. H. (1977). “Finite element simulation of saltwater intrusion on the South Fork of Long Island.” Proc. Int. Conf. Finite Elements, Pentech Press, London, England.
21.
Putty, R. G. (1987). “Simulation analysis of pumping and recharge for the control of saltwater intrusion in the Yun Lin Basin, Taiwan.” Thesis presented to Humboldt State Univ., at Areata, Calif., in partial fulfillment of the requirements for the degree of Bachelor of Science.
22.
Sá da Costa, A. A. G., and Wilson, J. L. (1979). “A numerical model of seawater intrusion in aquifers.” Tech. Rep. No. 247, Ralph M. Parsons Lab., Dept. of Civil Engineering, M.I.T., Cambridge, Mass.
23.
Sá da Costa, A. A. G., and Wilson, J. L. (1980). “Coastal seawater intrusion: A moving boundary problem.” Proc. 13th Int. Conf. Finite Elements Water Res., Oxford, Miss.
24.
Shamir, U., Bear, J., and Gamliel, A. (1984). “Optimal annual operation of a coastal aquifer.” Water Resourc. Res., 20(4), 435–444.
25.
Strack, O. D. L. (1976). “Single‐potential solution for regional interface problems in coastal aquifers.” Water Resourc. Res., 12(6), 1165–1174.
26.
Tsao, Y.‐S. (1983). “Seawater intrusion in the Yun Lin coastal aquifer system.” Agricultural Engrg. Res. Ctr. Report No. 83‐RR‐03, Chung Li, Taiwan.
27.
Tsao, Y.‐S., and Yao, C.‐G. (1984). “A study of seawater intrusion and water quality dispersion mathematical model for the Yun Lin aquifer system.” Thesis presented to the National Taiwan University at Taipei, Taiwan, in partial fulfillment of the requirements for the degree of Master of Science.
28.
Willis, R., and Newman, B. A. (1977). “Management model for groundwater development.” J. Water Resourc. Plng. and Mgmt. Div., ASCE, 103(1), 159–171.
29.
Willis, R., and Liu, P. L.‐F. (1984). “Optimization model for groundwater planning.” J. Water Resourc. Plng. and Mgmt. Div., ASCE, 110(3), 333–347.
30.
Willis, R., and Finney, B. A. (1985). “Optimal control of nonlinear groundwater hydraulics: Theoretical development and numerical experiments.” Water Resourc. Res., 21(10), 1476–1482.
Information & Authors
Information
Published In
Copyright
Copyright © 1988 ASCE.
History
Published online: Mar 1, 1988
Published in print: Mar 1988
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.