Optimal dynamic irrigation schemes

Optimal control methods are employed to derive irrigation management schemes accounting both for the dynamic response of the biomass yield to soil moisture and for the cost of irrigation water. Moisture dynamics depend on the irrigation rate and on the current biomass and moisture states. We find that the optimal irrigation policy has turnpike characteristics: soil moisture in the root zone should be brought to some optimal target level as rapidly as possible and kept at that level until some time prior to harvest, when irrigation should be ceased. The target moisture level and the stopping time vary across crops, soil types, climatic conditions and economic (price) factors, but the turnpike structure of the optimal irrigation policy persists under general circumstances. An empirical example demonstrates that the optimal scheme significantly outperforms the policy of yield maximization in actual practice.