A Linear Dynamic Programming Approach to Irrigation System Management with Depleting Groundwater

A model for measuring the economic benefits of irrigation system development over a depleting aquifer is presented, along with related methodology for detailed long-range farm planning. The paper considers management issues, such as distribution system configuration, drilling policy, area developed for irrigation, and crop production. A Linear Dynamic Programming (LDP) method is developed and applied to derive optimal temporal investments in the use of stock resources and long-term cropping plans. First, parametric linear programming (PLP) is used to maximize periodic profits subject to specified values of state variables related to annual water use and irrigation system capacity. The PLP results are then used in a dynamic programming model to determine the optimal allocation of water and irrigation resources over time. The impact of aquifer depletion on the profitability of furrow and pivot irrigation systems is illustrated for a typical farm situation in the Texas High Plains. Results indicate that the economic benefits of modern water and energy efficient irrigation systems may come from the expansion of current irrigation intensity rather than from an extended period of irrigation when water is initially scarce relative to land. Several conditions are identified where economic depletion may occur before the point of physical exhaustion is reached.