Optimization of Unconfined Groundwater Systems: A Differential Dynamic Programming Algorithm

Groundwater optimization models are predicated on the hydraulic or water quality response equations of the aquifer system. These equations relate the state variables of the groundwater system, the head or mass concentrations, and the decision variables that control the magnitude, location, and timing of pumping, artificial recharge, or waste injection. These management models are large-scale, non-convex programing problems. The objective of this paper is to present a differential dynamic programming (DDP) algorithm for solution of groundwater optimization problems. The effects of state and control variable constraints are discussed. The Jacobian matrices of the algorithm are evaluated analytically using a fully implicit, finite difference model of the aquifer system. DDP is used to identify optimal groundwater pumping schedules for a two-dimensional, unconfined aquifer system. The CPU time and central memory requirements of the algorithm are also presented.