Dynamic programming model for quasi-real time reservoir operation and irrigation scheduling

A forward dynamic programming (FDP) model designed to solve the problem of reservoir operation and irrigation scheduling was developed and tested. The typical scenario for application of the model is composed of a system of one or two reservoirs in parallel supplying water to as many as three irrigation districts. The complexity of the problem was reduced by breaking the problem into two models: interseasonal and intraseasonal models. The interseasonal model defines seasonal deliveries from the reservoir system. The objective function is to maximize the net benefit for the entire system. Constraints are imposed on the maximum and minimum releases, water allocations and reservoir storage, and the maximum and minimum cultivated areas. The intraseasonal model uses area and water allocations generated from the interseasonal model to produce an irrigation scheduling for the individual farms in one of the irrigation districts in the reservoir system. It uses a FDP model to maximize the net benefits for the irrigation district within a cropping season. The best solution is constrained by the capacity of the water conveyance system and the soil water storage capacity. Multiple planting dates can be assigned for all crops within the district. Crop evapotranspiration, reservoir evaporation, and inflows are fitted using seasonal multiplicative ARIMA models. The latter are applied to forecast the input parameters for the planning horizon under consideration (typically, four seasons for the interseasonal model and six months per season for the intraseasonal model). Upon availability of the current values, the forecast of the input variables is updated and the intraseasonal model runs to generate a more precise irrigation schedule. This feature permits the application of the model for real-time operation of the irrigation district. At the end of the season, the intraseasonal model is updated to generate more realistic area and water allocations. The FDP model was applied to a watershed in northeast Brazil.