Optimal amounts of water and nitrogen applied to sugar beet when crop price depends on its sugar content

Aim of study: To derive mathematical formulas to determine the optimum amounts of applied water and N at variable crop prices and rainfall conditions for sugar beet.Area of study: Karaj Research Center, Alborz Province, IranMaterial and methods: At first, mathematical formulas were derived to determine optimum applied water and nitrogen for sugar beet under rainfall occurrence, land limited (in cases that arable land area is limited and the farmer can not put more land area under irrigation) and water limited conditions when crop price depends on sugar content. Second, this theory was applied to analyze the relevant experimental data. The experiment was a split-plot design with irrigation treatments as the main plots (40%, 80%, 120% and 160% of evaporation from the surface of class A evaporation pan) and N fertilizer rates (0, 90, 180 and 270 kg N/ha) as subplots.Main results: Under land and water limiting conditions, deficit irrigation of 27% and 48% led to 6.4% and 25.4% decrease in yield and 21.4% and 96.2% increase in total net income, respectively, compared with full irrigation. Under water limiting conditions, cultivated land area increased by 93.7, 108 and 128% for 0, 60 and 120 mm rainfall, respectively. Under land limiting conditions, amounts of optimum irrigation water were 12381.2, 11781.2 and 11181.2 m3/ha, for 0, 60 and 120 mm rainfalls, respectively. The corresponding values for N were 262.5 kg/ha in all three rainfall quantities. Besides, under water limiting conditions, optimum amounts of irrigation water were 8708.1, 7828.8 and 6882.1 m3/ha for 0, 60 and 120 mm rainfalls, respectively. The corresponding values for N were 301.1, 299.5 and 295.5 kg/ha, respectively. Optimum amounts of irrigation water and N decreased by increase in rainfall amount.Research highlights: Under limited irrigation water conditions, if the rainfall, residual N, water cost and base crop price increases, the value of optimum applied water should be decreased