A linear dynamic programming approach to modeling the effects of producer interaction on optimal groundwater use in the southern high plains of Texas
A model is presented for measuring the degree to which incentives to agricultural producers under current groundwater laws may result in the long-run misallocation of groundwater. This study focuses on the interaction between producers as they compete for a common groundwater supply. A linear dynamic programming method (LDP) is applied to derive optimal intertemporal use of the stock resource 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 for agricultural producers over time, subject to water use policies followed by other producers. A finite difference groundwater model is used to simulate water table elevation in the aquifer after uniform periods of time. A finite difference grid is superimposed onto a study area in the Southern High Plains to replace the continuous aquifer with an equivalent set of discrete elements. Various pumping schemes are then duplicated to show the effect on water table elevation. A relationship between water use by a representative producer with that of other producers in the area is arrived at by regression analysis. This relationship is inserted into the dynamic model to determine the optimal use of groundwater by the representative producer given various strategies followed by other producers over a 45-year time horizon. Results of this study indicate the degree to which competitive producer interactions could affect the optimal long-term use of groundwater.