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A simulation model was developed to estimate the effect of deficit irrigation upon crop yield. The model was designed to provide relative yield estimates for numerous combinations of irrigation system, crop growth and irrigation management parameters. A daily soil moisture balance was used to predict evaporation and transpiration from which crop yields were estimated. Gross irrigation water requirements were estimated from net irrigation requirements, irrigation efficiencies, irrigation system limitations, and effective rainfall. Crop production functions that use physically defined parameters were also developed to relate crop yields to gross irrigation requirements. The production functions worked well on a limited test compared to field data. The model and production functions are general since they depend upon readily available information or physical parameters, and can be used to evaluate irrigation management alternatives.

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Knowledge of evapotranspiration‐yield (ET‐Y) relationships is fundamental in evaluating strategies for managing limited irrigation. The work reported here was done to develop ET‐Y functions for grain sorghum [Sorghum bicolor (L.) Moench], to provide base data for a water management improvement study in Nebraska. A field experiment was conducted using a modified line source sprinkler system to establish treatments that resulted in several different ET levels during each growth stage. The system was installed on a Valentine very fine sand (Typic Ustipsament) in west central Nebraska. The specific objectives of the study were: 1) to determine the crop evapotranspiration‐yield relationships for grain sorghum in this location, 2) determine how the timing and intensity of water deficits affect this relationship, 3) compare the evapotranspiration‐yield response of selected genotypes, and 4) to determine whether crop water use efficiency can be increased by judicious limited irrigation. In two seasons the relationship between evapotranspiration (ET) and grain yield (Y) or dry matter was linear. Evapotranspiration reduction under all conditions tested incurred some yield reduction. For a given genotype the slope of the ET‐Y relationship varied greatly depending on the growth period treatment. The lowest slopes were associated with a treatment in which stress built up steadily over the entire growing season. The slope was generally much steeper when irrigation was restricted to varying degrees for only a portion of the growing season. With greater yield reductions per unit of ET deficit, the latter treatments were considered suboptimal irrigation strategies compared to a gradual stress buildup. One hybrid had a lower slope of the ET‐Y relationship than the other genotypes for the treatment that provided water stress of gradually increasing severity. The percentage yield reductions were similar for all hybrids, however. The yield reduction ratios of the genotypes were different for the two growing seasons. Water use efficiency consistently decreased as ET declined below the maximum. It appeared that water stress, regardless of timing, tended to reduce water use efficiency. The reductions were smallest when stress increased gradually throughout the growing season.