Optimal grain sorghum irrigation strategies in a dynamic, stochastic environment

Abstract

Agricultural production and associated economic effects of irrigation on the Texas High Plains are seriously threatened by a rapidly declining groundwater supply and a swift upward trend in energy costs. To optimize the amount of irrigation water to be applied during specified periods of the production process, a stochastic open-loop feedback control policy was built into a grain sorghum growth simulation model. The control policy operated under the basis of constant revision of the expectations generated at every starting point for each of the production periods. If discrepancies between the expected and the realized values existed, then, based on current conditions a reevaluation of the control variable, irrigation water, was made and the decision for the first period adopted. This process continued throughout each period of the growing season. Within the stochastic policy designed, the values for the control variable were obtained by numerical search. The model was applied to estimate optimal irrigation strategies and the impact of fuel curtailments on them. Initially, optimal irrigation strategies were developed under the assumption of perfect knowledge. Under this assumption, the results indicated there was not a unique strategy to be applied at all times. The quantities of irrigation water to apply at each period depended on the initial or starting conditions. Since one of the purposes of building the model was to make it perform under stochastic or real world conditions, the assumption of complete knowledge was relaxed to consider the case where the climatic environment was unknown. As in the deterministic case, the optimal amounts of irrigation water, by period, depended much on the existing initial conditions at each period. It was also observed, that with the open-loop feedback control, the results obtained for yields did not differ substantially from those obtained in the perfect knowledge case. The discrepancies among the two cases were primarily in the optimal amount of water applied and therefore in net returns. In the stochastic case, the use of irrigation water had a mean value approximately 25 percent more than in the case of perfect knowledge..