Interannual Variation in Long-Term Center Pivot–Irrigated Maize Evapotranspiration and Various Water Productivity Response Indices. I: Grain Yield, Actual and Basal Evapotranspiration, Irrigation-Yield Production Functions, Evapotranspiration-Yield Production Functions, and Yield Response Factors

Quantification of crop response to the amount of water applied, available, or used is important for decision making to ensure effective, profitable, conservative agricultural production. However, these variables and responses may have interannual attributes and long-term research has rarely quantified interannual variations of irrigation-yield production functions (IYPF), evapotranspiration-yield production functions (ETYPF), and yield response factors (Ky). This long-term research measured grain yield, actual crop evapotranspiration (ETa), increase in ETa attributable to various irrigation levels, basal evapotranspiration (ETb; ET required to establish grain yield), IYPF, ETYPF, and seasonal Ky for maize (Zea mays L.) from 2005 to 2010 growing seasons. Four full and limited irrigation levels [fully irrigated (FIT), 75% FIT, 60% FIT, and 50% FIT] and rainfed treatment were imposed. Seasonal ETa increased linearly with increasing irrigation and the slopes of the ETa versus seasonal irrigation relationships exhibited substantial interannual variation. All-treatment average ETa values were 561, 583, 592, 660, 591, and 628 mm from 2005 to 2010, respectively. Irrigation amounts significantly impacted grain yield in all years with considerable variation among seasons. All-treatment average yield increases attributable to irrigation were 7.7, 4.6, 1.6, 5.8, and 2.7 ton/ha, relative to rainfed treatment, from 2005 through 2010, respectively; six-year average yield increase was $4.5\mathrm{t}/\mathrm{ha}$. Grain yield had a curvilinear relationship with seasonal irrigation amounts ($R^2=0.79$) and yield increased with irrigation up to approximately 180 mm of irrigation water ($15.5\mathrm{t}/\mathrm{ha}$ grain yield); thereafter, irrigation became excessive and diminishing returns occurred. Interannual variation of grain yield produced per unit of irrigation was observed owing to differences in rainfed yield response to precipitation. Totals of 0.92, 1.72, 0.09, 1.06, 1.90, and $0.08\mathrm{t}/\mathrm{ha}$ grain yield were produced per 25.4 mm of irrigation applied (beyond the intercept) from 2005 through 2010, respectively. Based on the pooled (average of all years) curvilinear IYPF equation, 25.4 mm of irrigation produced approximately $1.45\mathrm{t}/\mathrm{ha}$ grain yield [beyond intercept ($9.29\mathrm{t}/\mathrm{ha}$)]. Grain yield had a very strong, linear increase with seasonal ETa ($R^2>0.92$). The ETYPFs exhibited less interannual variation than the IYPFs and the slope of the ETYPFs ranged from 0.0336 in 2008 to 0.0662 in 2010, with the wettest year (2008) having the lowest slope. Six-year average ETYPF had a high $R^2$ (0.93) with an average slope of 0.0409. ETb of individual years also exhibited substantial interannual variation: 263, 319, 314, 209, 319, and 418 mm for the 2005, 2006, 2007, 2008, 2009, and 2010 growing seasons, respectively. Six-year average pooled data indicated that 279 mm of ETb is needed to establish grain yield. Based on the ETYPF data from individual years, 25.4 mm of ETa resulted in 0.96, 1.20, 1.14, 0.85, 1.22, and $1.68\mathrm{t}/\mathrm{ha}$ maize yield (beyond the intercept) from 2005 through 2010. When individual treatments were considered, 25.4 mm of ETa resulted in 0.98, 0.40, 0.62, 1.01, and $0.48\mathrm{t}/\mathrm{ha}$ grain yield (beyond intercept) for rainfed, 50% FIT, 60% FIT, 75% FIT, and FIT, respectively. The climatic conditions in August were the most influential in determining the slope of the ETYPFs. Seasonal average Ky also exhibited interannual variation, which was 1.89, 1.89, 1.39, 1.80, and 2.64 in 2006, 2007, 2008, 2009, and 2010, respectively. This research provides important data, information, and analyses in terms of interannual variation of various parameters on maize response to water.