Estimation of soybean water-nitrogen production function

Due to the limited water resources, the deficit irrigation would be one of the most relevant methods in this situation. The purpose of this study was to optimize the water consumption and nitrogen level simultaneously. In this research, two different irrigation strategies of 75% (I2), 50% (I3) and 25% (I4) of water requirement and full irrigation (I1) and different nitrogen treatments with application of 150 (N1), 112.5 (N2) and 75 (N3) Kg/ha was investigated on yield production. Optimization of water and nitrogen showed that the proper yield function of soybean is the transcendental model among linear, Cobb-Douglas, quadratic and transcendental models. The optimum water and nitrogen levels of soybeans under water-nitrogen stress conditions was estimated 230 and 216.5 mm of water and 150 kg of nitrogen in two years. The results showed that the yield production was increased by 33.28% in N3 with deficit irrigation treatment (I2) as compared with full irrigation method.