Stochastic Approximation Applied to Optimal Irrigation and Drainage Planning
Publication: Journal of Irrigation and Drainage Engineering
Volume 115, Issue 3
Abstract
Parameter uncertainty in modeling complex hydrologic systems has resulted in development of stochastically based water management models. Optimal solutions to such models, particularly those having parameters with large variance, may be difficult, if at all possible, to obtain, due to intensive computational requirements. This paper discusses application of a stochastic quasigradient (SQG) approximation method to a management model. The model describes the effects of regional irrigation and drainage system planning on shallow saline groundwater behavior and net economic returns to farmers. Due to the complexity of the model, Monte Carlo simulation techniques were used. Despite model complexity and large parameter variance originating from spatial variability in soil hydraulic properties, the SQG method obtained near‐optimal solutions in about 15% of the CPU time required to obtain such solutions using response surface methodology.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Colorni, A., and Fronza, G. (1976). “Reservoir management via reliability programming.” Water Resour. Res., 12(1), 85–88.
2.
Cornell, C. A. (1972). “First order analysis of model and parameter uncertainty.” Presentation at the Int. Symp. on Uncertainties in Hydrologic and Water Resour. Systems, Univ. of Arizona, Tucson, Ariz.
3.
Dagan, G. (1982a). “Stochastic modeling of groundwater flow by unconditional and conditional probabilities, 1. Conditional simulation and the direct problem.” Water Resour. Res., 18(4), 813–833.
4.
Dagan, G. (1982b). “Stochastic modeling of groundwater flow by unconditional and conditional probabilities, 2. The solute transport.” Water Resour. Res., 18(4), 835–848.
5.
Dagan, G. (1986). “Statistical theory of groundwater flow and transport: Pore to laboratory, laboratory to formation, and formation to regional scale.” Water Resour. Res., 22(9), 1205–1245.
6.
Dettinger, M. D., and Wilson, J. L. (1981). “First order analysis of uncertainty in numerical models of groundwater flow, Part 1. Mathematical development.” Water Resour. Res., 17(1), 149–161.
7.
El Kadi, A. L. (1984). Modeling variability in groundwater flow. GWMI 84‐10, Int. Ground Water Modeling Ctr., Indianapolis, Ind.
8.
Ermoliev, Y. (1983). “Stochastic quasigradient methods and their application to system optimization.” Stochastics, 9, 1–36.
9.
Ermoliev, Y., and Gaivoronski, A. (1984). “Stochastic quasigradient methods and their implementation.” Working Paper WP 84–55, Int. Inst. for Appl. Systems Analysis. Laxenburg, Austria.
10.
Ermoliev, Y., and Wets, R. J‐B (1988). Numerical techniques for stochastic optimization. Springer‐Verlag, Berlin, West Germany.
11.
Gates, T. K., and Grismer, M. E. (1989a). “Irrigation and drainage strategies in salinity‐affected regions.” J. Irrig. Drain. Engrg., ASCE, 115(2), 255–284.
12.
Gates, T. K., and Grismer, M. E. (1989b). “Stochastic optimal management of perched saline aquifers in irrigated regions.” Proc., Int. Conf. on Groundwater Contamination: Use of Numerical Models in Decision‐Making, Oct., 1987, Amsterdam, The Netherlands.
13.
Grismer, M. E., Gates, T. K., and Hanson, B. R. (1988). “Irrigation and drainage strategies in salinity problem areas,” Cal. Ag., 42(5), 23–24.
14.
Gupta, R. K., and Chauhan, H. S. (1986). “Stochastic modeling of irrigation water requirements.” J. Irrig. Drain. Engrg., ASCE, 112(1), 65–76.
15.
Karlsson, M., and Yakowitz, S. (1987). “Rainfall‐runoff forecasting methods, old and new.” Stochastic Hydrology and Hydraulics, 1, 303–318.
16.
Kavvas, M. L., and Herd, K. R. (1985). “A radar‐based stochastic model for shorttime‐increment rainfall.” Water Resour. Res., 21(9), 1437–1455.
17.
Kavvas, M. L., Saquib, M. N., and Puri, P. S. (1987). “On a stochastic description of the time‐space behaviour of extra‐tropical cyclonic precipitation fields.” Stochastic Hydrology and Hydraulics, 1, 37–52.
18.
Kitanidis, P. K. (1987). “A first order approximation to stochastic optimal control of reservoirs.” Stochastic Hydrology and Hydraulics, 1, 169–184.
19.
Kleijnen, J. P. C. (1987). Statistical tools for simulation practitioners. Marcel Dekker, New York, N.Y.
20.
Letey, J., et al. (1986). An agricultural dilema: Drainage water and toxics disposal in the San Joaquin Valley. Pub. 3319, Agric. Exp. Sta., Div. of Agric. and Nat. Resour., Univ. of California, Oakland, Calif.
21.
Loucks, D. P. (1968). “Computer models for reservoir regulation.” J. Sanit. Engrg. Div., ASCE, 94(4), 657–669.
22.
Myers, R. H. (1971). Response surface methodology. Allyn and Bacon, Boston, Mass.
23.
Rockafellar, R. T., and Wets, R. J‐B (1987). “Scenarios and policy aggregation in optimization under uncertainty.” Working Paper WP 87–119, Int. Inst. for Appl. Systems Analysis, Laxenburg, Austria.
24.
Rubinstein, R. Y. (1986). Monte Carlo optimization, simulation and sensitivity of queueing networks. John Wiley and Sons, New York, N.Y.
25.
Simonovic, S. P., and Mariño, M. A. (1980). “Reliability programing in reservoir management. 1. Single multipurpose reservoir.” Water Resour. Res., 16(5), 844–848.
26.
Tung, Y. (1986). Groundwater management by chance‐constrained model.” J. Water Resour. Plng. Mgmt., ASCE, 112(1), 1–19.
27.
Wagner, B. J., and Gorelick, S. M. (1987). “Optimal groundwater quality management under parameter uncertainty.” Water Resour. Res., 23(7), 1162–1174.
28.
Wets, R. J‐B (1983). “Stochastic programming: Solution techniques and approximation schemes.” Mathematical programming The state of the art, A. Bachem et al., eds., Springer Verlag, Berlin, West Germany, 566–602.
29.
Yevjevich, V. (1972). Stochastic processes in hydrology. Water Resources Publications, Ft. Collins, Colo.
Information & Authors
Information
Published In
Journal of Irrigation and Drainage Engineering
Volume 115 • Issue 3 • June 1989
Pages: 488 - 502
Copyright
Copyright © 1989 ASCE.
History
Published online: Jun 1, 1989
Published in print: Jun 1989
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.