Real Time Irrigation Scheduling via “Reaching” Dynamic Programming

A dynamic programming model is formulated for determining surface irrigation schedules over the short term that minimize irrigation labor costs while meeting crop requirements under a limited water supply. This is a relevant problem for a large number of farm operations on the High Plains served by wells tapping the Ogallala Aquifer. The model is capable of solving high‐dimensional problems by a “reaching” forward algorithm that defines a surrogate state space by using binary decision policies rather than by discretization of the actual state variables. Real time use of the short‐term model was simulated for two irrigation seasons, using data from the Northern Colorado Research Demonstration Center near Greeley, Colorado. The model optimized the scheduling of nine field groups divided into a total of 24 fields. An 8% savings in irrigation costs resulted for both years, as compared with conventional scheduling, while maintaining acceptable soil moisture levels.