Potato (Solanum tuberosum L.) is a heat‐ and drought‐sensitive crop, which in hot climates usually requires large water applications for optimum production. Irrigation water in Israel is both limiting in quantity and high in price; thus it is critical to know the water requirement of the crop, as well as how to improve irrigation efficiency. Field experiments were conducted in the Negev (arid) region of Israel on a Typic Camborthid soil to determine the water production functions of potatoes (‘Desiree’) under drip and sprinkler irrigation. Irrigation treatments were based on Class A pan evaporation. The linear production functions relating total yield in metric ton ha−1 to seasonal water application depth (W) in cm were, for sprinkler irrigation: Y = ‐23.5+1.19W, and for drip irrigation: Y = −12.8+1.14W. Similar total maximum yields were obtained with about 8 % less water with the drip as with the sprinkler method (not statistically significant). A single production function for both methods described the yield of marketable tubers: Y = −40.0+1.28W. These functions apply in the relative water application range (water applied over Class A pan evaporation) of 0.3 to 1.0, at which point the function reaches a plateau. Yield was reduced by 12% as soil water potential in the 0 to 0.6 m depth increment changed from −20 to −29 J kg−1 for sprinkler irrigation. Under drip irrigation the soil could dry to −40 J kg−1 without yield reduction, as long as the water supply was adequate. This was explained by the higher root concentration under drip than under sprinkler irrigation.

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An approach to irrigation decisions for wheat under conditions of unstable rainfall is presented, and a simulation model designed for tracing the variation of moisture in the soil profile during the growing season of wheat is described. Empirical estimates of the response function of wheat yield derived on the basis of 4 years of irrigation experiments are presented. The paper concludes with the simulation and comparison of several irrigation policies for wheat under conditions of stochastic rainfall.

An approach to irrigation decisions for wheat under conditions of unstable rainfall is presented, and a simulation model designed for tracing the variation of moisture in the soil profile during the growing season of wheat is described. Empirical estimates of the response function of wheat yield derived on the basis of 4 years of irrigation experiments are presented. The paper concludes with the simulation and comparison of several irrigation policies for wheat under conditions of stochastic rainfall. An approach is presented to estimating a response function of wheat yield to soil moisture and to determining the optimal irrigation policy under conditions of stochastic rainfall. A necessary condition for the determination of an optimal irrigation policy under unstable rainfall conditions is the availability of information on variation of the soil moisture over time and as a function of depth. Since it is impractical from the cost point of view to conduct measurements of soil moisture before and after each rainfall and/or irrigation, a method designed to reconstruct the soil moisture fluctuations on the basis of the incomplete data available is needed. A computer simulation model designed for this purpose is briefly described in the first section of this paper, and estimates of wheat response functions to soil moisture are given in the second section. An analysis of the optimal irrigation policy is presented in the third section: Considerable data are a•ailable on methods aimed at evaluating evapotranspiration and fluctuations in soil moisture [e.g., Penman, 1949; Blaney and Criddle, 1950; Thornthwaite

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