A decision model for stochastic optimization of seasonal irrigation-water allocation

Optimal water allocation on a seasonal basis is generally a decision taken with uncertainty regarding seasonal crop needs (unknown yield, precipitation and other environmental factors). Decision criteria, such as “irrigating for the good years of production” and "applying a little extra water just in case it is needed by the plant", are consistent with the rational behaviour of stochastic profit maximization. The motivation behind an increase in water allocation (acquiring water rights or reserving water for certain crops) is that of self-protection: it is better to maintain an extra allocation of water than to face potential yield losses due to water constraints on production in those years when potential yields exceed average levels. The stochastic optimization model presented herein is applied to maize in Spain showing that in current economic and technical conditions, the optimal stochastic water allocation under yield uncertainty is 10% higher than the irrigation dose required under certainty (historical average yield), which leads to an 8% higher expected profit than that obtained for an average-yield water application.