Development of an optimal control system for maintaining minimum groundwater levels

Abstract

This paper describes the development and application of an optimal control system designed to reduce the deviation of piezometric head from minimum monthly target levels. The control strategy is generated from a Box-Jenkins double input-single output transfer function (SARIMAX) model relating local piezometric head fluctuations at an ecologically vulnerable location to regional rainfall and pumping volumes. The optimal control scheme is developed to minimize head deviations from the minimum target levels while simultaneously satisfying pumping/injection constraints associated with predetermined water resource management preferences. The control action manipulates the control variable (pumping) to compensate for existing and expected deviations of the piezometric head from target levels due to both observed disturbances (i.e., rainfall) and random (i.e., white noise) disturbances. An example applied to a localized region of the Upper Floridan aquifer in northeast Florida shows that the control action reduces the number of deviations below target head levels by 79% and the magnitude of the mean deviation below target by 72%. This improvement was achieved through a 29% reduction in pumping volume. The optimal control system thus provides a useful means of managing groundwater fluctuations at ecologically vulnerable locations by restricting regional pumping to offset regional rainfall deficits.