Optimal Groundwater Management Using Empirical Orthogonal Functions

This research investigates the applicability of model reduction, through empirical orthogonal functions (EOF's) and the Galerkin projection, to groundwater management. In the past, groundwater models have been coupled with optimization algorithms to solve parameter estimation and groundwater management problems. The solution of a groundwater management problem generally involves finding a set of pumping/recharge rates that maximizes some measure of the system performance while satisfying a set of constraints on groundwater heads, velocities or solute concentrations. Solution of the management problem with an optimization algorithm requires repeated calls to a numerical simulation model for objective function and gradient evaluations. In many practical applications the simulation model may include thousands of nodes, and extensive solution times required to run the simulation model may prohibit the applicability of simulation-optimization schemes to large-scale problems or to real-time decision support. The use of a reduced model for simulation permits a dramatic decrease in running times when the EOF's have been computed in advance. As a result, when quick answers are required, fast execution of the reduced model makes it possible to apply simulation and optimization, such as real-time group decision-making and conflict resolution. Results from the proposed methodology are compared with results obtained with the original groundwater model, in order to assess the effect of the necessary loss of accuracy that stems from using the reduced model over the solution of the management problem for a real-world case study.