Economic Optimisation of Sprinkler Irrigation Considering Uncertainty of Spatial Water Distribution*

Abstract

The sNdy is focused on the development and the application of a stochastic economic optimisation model by which optimal levels of applied water and sprinkler spacing are determined. Data on cropwater production function and uniformity of water application are taken from a sprinkler irrigation plot of sweet corn. It was found that a saving of irrigation water can be achieved not only by raising water prices but also by increasing application uniformity. The spatial variability of applied irrigation water has been well recognised by both agricultural researchers and growers for many years. The level of appiication uniformity is highly dependent on the type and performance of the irrigation method. The yield of a given crop, grown during a specific season in a certain field and under certain management and cultivation conditions. is also spatially variable and is assumed to be dependent directly on the spatially variable water application. It was generally noticed that the variation of the applied water as well as of the yield is not completely disordered in space but can be analysed within the frame of stochastic modelling, that is, regarding the applied water and the resulting yield of a given field as random functions of space coordinates characterised by their probability density function (pdf) and correlation structure, rather than by their deterministic values. Most economic studies of efficient water use under non-uniform irrigation focus on optimisation with respect to the quantity of irrigation water and tend to ignore the optimisation with respect to the uniformity level (for example, Seginer 1978; Feinerman, Letey and Vaux 1983: Feinerman. Bresler and Dagan 1985). in a few previous economic studies (for example, Hill and Keller 1980: Chen and Wallender 1984; Gohring and Wallender 1987). the joint effects of uniformity and quantity of applied water on irrigation system selection or on economical sprinkler spacing were investigated. The dependence of the irrigation system cost on the uniformity was derived by varying the sprinkler spacing and calculating the resulting changes in the uniformity and in the cost. However, the spatial variation of the irrigation water was regarded as deterministic. uncertainty was not accounted for in the economic application. and the attitude of the decision maker' toward risk was ignored. Seginer (1 987) presented a comprehensive review describing a general approach to economic optimisation of the irrigation system considering the quantity of T h i s research has been financed in part by the United States Agency for International Development. in concert with the US Department of Agriculture. Office of International Cooperation and Development.

Surface Runoff, Uniformity of Water Distribution, and Yield of Peanut Irrigated with a Moving Sprinkler System

“…92 and 12%, respectively, parallel to the MSIS spans, and 0.89 and 14%, respectively, perpendicular to the MSIS (Table 1). Feinerman et al (1989) found that nonuniform water application with CV < 15% had negligible effect on crop yield.…”