An interval multistage water allocation model for crop different growth stages under inputs uncertainty

Due to different responses of crop growth stages to the water deficit, it is necessary to optimize water allocation between different growth stages to obtain the maximum food production in reservoir irrigation systems which are widely distributed throughout Southern China and India. In order to address the inputs uncertainties and dynamics existing in the above agricultural water management, an interval multistage water allocation model is developed. By incorporating multistage stochastic programming and interval parameter programming, the developed model can deal with uncertain inputs both expressed as interval parameters and probability distributions, and realize a dynamic irrigation among different growth stages from a reservoir. In the model, water requirement targets are first treated as first-stage decision variables to tackle the unique problem of agricultural water management. Additionally, given that net benefit and penalty of each growth stage are key parameters due to their determinative roles for allocation between different growth stages, a crop water production function is introduced into the calculation to make them factually reflect the competition among different growth stages. The model is then applied to the Yangshudang Irrigation District to plan rice irrigation and demonstrate its applicability. Rainfall has been divided into five levels with probability distributions in each growth stage and parameters have been characterized as interval numbers to show system uncertainty. Five scenarios that represent different initial active storage levels of the reservoir are set to acquire more detailed results. Through the parameter estimation, net benefits are [1.08, 1.29], [5.04, 6.01], [11.79, 14.08] and [1.61, 1.92] RMB/m3, and penalties are [2.39, 2.48], [11.13, 11.54], [26.05, 27.01] and [3.55, 3.68] RMB/m3 for tillering stage, booting stage, heading stage and milky stage respectively. Through the model simulation, water requirement targets in booting stage and heading stage under all scenarios are set at their upper bound, while this figure in tillering stage reaches its upper bound only when initial active storage is under high or very high level. The results show that irrigation water can be optimally allocated between different growth stages of a single crop in a single reservoir system under inputs uncertainty. Although there is a limitation to regard rainfall as to be uniform in the whole area, the solutions of water requirement targets under different scenarios, as well as water allocation patterns among different growth stages, are valuable for optimizing irrigation water use in meso- and micro-scale agricultural system under inputs uncertainty.