A single-period model for conjunctive use of ground and surface water under severe overdrafts and water deficit

We develop a model for a multi-reservoir system, where the inflow to the main reservoir and the demand for irrigation water at local areas are stochastic. The controlled releases from the main reservoir to local ones can be supplemented by groundwater from an aquifer suffering from severe overdrafts. We consider high penalty costs for pumping groundwater in order to reduce the risk of total depletion of the aquifer as well as quality degradation and seawater intrusion. We analyze the problem for a single period with a single decision-maker approach. We allow deficit irrigation in the problem of maximizing expected total profit for the entire region. We show that the formulated non-linear stochastic problem is concave with linear constraints and propose an iterative procedure that generates an optimal operating policy. We illustrate the model through a hypothetical example.