Two-step dynamic programming approach for optimal irrigation water allocation

A two-step (deterministic and stochastic) dynamic programming approach has been introduced in this study to solve the complex problem of optimal water allocation in a run-of-the-river-type irrigation project. The complexity of a real-world situation is represented by incorporating in the optimization model the stochasticity of water supply and the nonlinearity of crop production functions. A nonlinear, dated, and multiplicative production function is transformed into a sequentially additive type to replace the usual method of creating an additional ‘state of the plant variable’ which only increases the dimension of the problem. As compared to the explicit stochastic dynamic programming which necessitates, along with its use, an enormous computational complexity due to the so-called ‘curse of dimensionality’, the present model can approximate the theoretical global optimum, at least for the present case study, with a dramatic reduction in computer processing time. It also eliminates the rigidity of the policy derived by the explicit approach, since it provides irrigation planners with alternative decision policies which incorporate intangibles and other nonengineering factors. The traditional method of fixing the cropping pattern based on deterministic estimates of a dependable water supply can likewise be evaluated by the use of the present model. The results of the model's application appear to be practically acceptable.

[1]  F. T. Corbin,et al.  Application of modeling to irrigation management of soybean. , 1980 .

[2]  Jon M. Conrad,et al.  Kennedy, John O. S. Dynamic Programming Applications to Agriculture and Natural Resources. London: Elsevier Applied Science Publishers, 1986, xv + 341 pp., $76.00 , 1987 .

[3]  S. Nairizi,et al.  Effects of Dated Soil Moisture Stress on Crop Yields , 1977, Experimental Agriculture.

[4]  J. Doorenbos,et al.  Yield response to water , 1979 .

[5]  Derrel L. Martin,et al.  Model and production function for irrigation management , 1984 .

[6]  Subhash Chander,et al.  A simple dated water-production function for use in irrigated agriculture , 1988 .

[7]  T. A. Howell,et al.  Optimization of Water Use Efficiency under High Frequency Irrigation — I. Evapotranspiration and Yield Relationship , 1975 .

[8]  R. J. Hanks.  Model for Predicting Plant Yield as Influenced by Water Use1 , 1974 .

[9]  Norman J. Dudley,et al.  Irrigation Planning 2: Choosing Optimal Acreages within a Season , 1971 .

[10]  A. Dinar,et al.  Optimal Allocation of Farm Irrigation Water during Peak Seasons , 1982 .

[11]  Norman J. Dudley,et al.  Optimal Intraseasonal Irrigation Water Allocation , 1971 .

[12]  William S. Butcher,et al.  Optimal Timing of Irrigation , 1968 .

[13]  Subhash Chander,et al.  Irrigation scheduling under a limited water supply , 1988 .

[14]  Marvin E. Jensen,et al.  Water consumption by agricultural plants , 1968 .

[15]  Norman J. Dudley,et al.  Irrigation planning: 4. Optimal interseasonal water allocation , 1972 .

[16]  Rafael L. Bras,et al.  The irrigation scheduling problem and evapotranspiration uncertainty , 1981 .

[17]  T. N. Srinivasan,et al.  Toward the structure of a production function for wheat yields with dated inputs of irrigation water , 1974 .