Open-Loop Stochastic Control of Grain Sorghum Irrigation Levels and Timing

Crop growth simulation models that consider the soil-plant-atmosphere continuum recently have become an important research tool. Examples of growth simulation models include those for corn (Curry and Chen), cotton (Baker, Hesketh, Duncan), alfalfa (Miles et al.), barley (Kallis and Tooming), wheat (Trenbath), and grain sorghum (Arkin, Vanderlip, Ritchie). This article investigates the utility of the grain-sorghum-growth simulation model of Arkin, Vanderlip, and Ritchie as an irrigation management tool on the Texas High Plains with economic criteria guiding decisions. Most water-use studies (e.g., Swanson and Thaxton; Jensen and Musick; Shipley, Regier, Wehrly) emphasize the need for coordinating irrigation with water requirements of the plant during critical stages of plant development. Yield response attributed to a specific irrigation depends upon several factors, including: (a) amount of soil moisture available at the time of irrigation; (b) stage of the plant development; and (c) interaction effect from previous or subsequent irrigations, or both, which reduce or eliminate moisture stress conditions. Normally, three or four irrigations are applied to grain sorghum in the Texas High Plains to meet water use requirements during the growing season. Applications may vary from only one preplant to as many as six postplant waterings (Shipley and Regier). Increasing concern for the declining groundwater supply and energy costs along with potential energy curtailments in the region emphasize the importance of improved irrigation planning and management. Potential fuel curtailments magnify the already existing degree of risk and uncertainty of farming in areas with low and unstable rainfall. This uncertainty results in production practices that depart from the optimal deterministic input-output combinations, even for risk-averse producers. Previous estimates of economically optimal irrigation water application rates, and estimates of the impact of rising energy costs were primarily based on the assumption that the producer knew in advance the state of the different future environments that would surround him (Casey, Jones and Lacewell; Lacewell; Condra and Lacewell). Climatic, institutional, and economic conditions throughout the production year were considered as known at the beginning of the year. To overcome these limitations, the computerized grain sorghum growth model was modified to consider stochastic situations in weather and/or institu-