Optimal groundwater management models are based on the hydraulic equations of the aquifer system. These equations relate the state variables of the groundwater system, the head, and the decision variables that control the magnitude, location, and timing of pumping, or artificial recharge. For the unconfined aquifer these management models are large‐scale, nonlinear programming problems. A differential dynamic programming (DDP) algorithm is used for unsteady, nonlinear, groundwater management problems. Due to the stagewise decomposition of DDP, the dimensionality problems associated with embedding the hydraulic equations as constraints in the management model are significantly reduced. In addition, DDP shows a linear growth in computing effort with respect to the number of stages or planning periods, and quadratic convergence. Several example problems illustrate the application of DDP to the optimal control of nonlinear groundwater hydraulics.

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A dynamic planning model is presented for the optimal management of groundwater quality in regional aquifer systems. The groundwater system is conjunctively managed as a water supply resource and as a storage reservoir for waste water residuals. The waste waters are discharged to the groundwater basin through injection wells. Within the groundwater system, constituents are assumed to follow first‐order chemical or biochemical reactions and linear equilibrium adsorption. The Galerkin finite element method is used to transform the flow and mass transport equations of the aquifer system into systems of ordinary differential equations which are imbedded as constraint equations in the planning model. The mathematical model, which is structured as a nonconvex programing problem, allows the planner or resource manager to determine (1) the optimal pumping and injection schedules (rates and locations) required to satisfy an exogenous water target and waste load demand and (2) the maximum injection concentrations that can be discharged to the basin without degrading the quality of the aquifer. Operational policies are developed for a 480‐day operational cycle for a hypothetical groundwater basin, where it is assumed that groundwater extraction represents the principal resource of the aquifer system. Linear programing is used to identify the optimal planning policies. The important parameters affecting the optimal decisions are discussed.

Nonlinear optimization models are presented for the optimal operation of an unconfined aquifer system. The aquifer's response equations are developed using finite difference methods, quasilinearization, and matrix calculus. The optimization model, which is structured as a discrete time optimal control problem, identifies the optimal pumping pattern necessary to satisfy an exogenous water demand. A quasilinearization optimization algorithm and projected Lagrangian methods are used for the solution of the planning model. Example problems are presented which demonstrate the viability of the approach for nonlinear, nonconvex groundwater management problems.