Stochastic Control of Groundwater Systems

In groundwater management, uncertainty mainly stems from imprecise parameters and boundary conditions. This paper first formulates a stochastic groundwater management problem and subsequently proposes an appropriate solution approach. The equations of flow are converted to a dynamical state-space system using finite element and difference techniques. Parameter and boundary condition uncertainty is incorporated using the small perturbation method. Management objectives are expressed as a composite performance index which may be used to minimize pumping costs, maintain hydraulic heads and pumping rates in the vicinity of target sequences, or optimally compromise among various system goals. This problem is solved via a numerical optimal control method which exhibits good computational properties. The approach is applied to the management of a two-layer aquifer system with various boundary conditions and uncertainty levels and sources. The results provide useful insights of the system response under uncertainty and quantify the trade-offs between accomplishing average system goals and minimizing uncertainty.