A new stochastic optimization model for deficit irrigation

Deficit irrigation has been suggested as a way to increase system benefits, at the cost of individual benefits, by decreasing the crop water allocation and increasing the total irrigated land. Deterministic methods are common for determining optimal irrigation schedules with deficit irrigation because considering the inherent uncertainty in crop water demands while including the lower and upper bounds on soil moisture availability is a hard problem. To deal with this, a constraint state formulation for stochastic control of the weekly deficit irrigation strategy is proposed. This stochastic formulation is based on the first and second moment analysis of the stochastic soil moisture state variable, considering soil moisture as bounded between a maximum value and a minimum value. As a result, an optimal deficit irrigation scheduling is determined using this explicit stochastic model that does not require discretization of system variables. According to the results, if irrigation strategy is based on deterministic predictions, achievement of high, long-term expected relative net benefits by decreased crop water allocation and increased irrigated land may have a higher failure probability.