AbstractsMathematics

Playa lakes usually occur in arid or semiarid regions where lands are flat and there is an absence of well-developed surface drainage nets. They are usually filled by surface runoff from highly erratic precipitation patterns. There are about 20,000 of them in the high plains of Texas and their volume of storage is an estimated 2.5-3 maf. As such, they represent a major underutilized water source. The major drawbacks to their utilization are high evaporation losses, questionable depth-area relations and the stochastic nature of the rainfall source. This paper assumes that the water is available and presents a dynamic programming model useful in determining the optimal utilization of the water for irrigation. If irrigation is the major use, its timing of application is of paramount importance. A deterministic dynamic programming model, utilizing the state variables of antecedent soil moisture and amount of available water, is presented, and provides the time and amount of irrigation required to maximize crop response. A better stochastic model is also presented which considers rainfall probability and resulting lake filling. The models are only first attempts and do not incorporate all possible variables.