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Large-scale quantification and mapping of crop water use efficiency (CWUE), evapotranspiration water use efficiency (ETWUE), and crop yield production functions, especially on a long-term and large-scale basis, are important to effectively evaluate and manage freshwater resources in relation to agricultural production. The overall objectives of this study were to quantify and map the long-term (1986-2009) magnitudes, trends, and frequency distributions of CWUE and ETWUE on a county and statewide scale and develop yield production functions on a county, zonal, and statewide scale for irrigated and rainfed maize and soybean in Nebraska. From 1986 to 2009, total increases of 31%, 37%, 29%, and 33% were observed for irrigated maize, rainfed maize, irrigated soybean, and rainfed soybean yields, respectively. During that period, grain yields increased annually by 166 kg ha(-1) for irrigated maize and by 84 kg ha(-1) for rainfed maize. The yield increases on an annual basis for irrigated and rainfed soybean were about 50 and 30 kg ha(-1), respectively. Irrigated and rainfed maize ETc peak frequency occurred at 600 and 400 mm, respectively, and irrigated and rainfed soybean ETc peaks were at 500 and 400 mm, respectively. On average, irrigated maize ETc was 52%, 46%, 35%, and 25% greater than rainfed maize ETc in zone 1 (semi-arid), zone 2, zone 3, and zone 4 (sub-humid), respectively. For soybean, irrigated ETc was 41%, 29%, and 15% higher than rainfed soybean ETc in zones 2, 3, and 4, respectively (soybean is not grown in zone 1, the driest zone in western Nebraska). Irrigated CWUE for maize for all counties (90 counties for a 24-year period) had a mean value of 1.74 kg m(-3) [standard deviation (SD) = 0.37 kg m(-3)] and ranged from 2.07 kg m(-3) in sub-humid zone 4 to 1.33 kg m(-3) in semi-arid zone 1. For soybean, the statewide average (78 counties for a 24-year period) irrigated CWUE was 0.64 kg m(-3) (SD = 0.14 kg m(-3)) and ranged from 0.81 to 0.54 kg m(-3). The ETWUE had a mean of 2.32 kg m(-3) (SD = 0.52 kg m(-3)) for maize and a mean of 1.01 kg m(-3) (SD = 0.55 kg m(-3)) for soybean. On a statewide average basis, about 74% and 3% of the variability in rainfed and irrigated maize yields, respectively, was explained by ETc alone. For rainfed soybean, ETc explained about 44% of the variability in yield; however, no strong relationship was observed between irrigated soybean yield and ETc. Maize CWUE showed substantial increases (from 1986 to 2009) of 35% and 36% in zones 1 and 2, and lesser increases of 17% and 15% were observed in zones 3 and 4, indicating that zones with smaller yields could increase CWUE more effectively by proper irrigation, soil, and crop management. These wide variations in CWUE and ETWUE indicate that there is a significant potential to increase the efficiency of current Nebraska crop production systems. The CWUE and ETWUE maps and the zonal and statewide average yield production function data presented in this study can be useful for evaluating the differences in these variables across the state for close monitoring, assessment, resource allocation, and management decisions.