Groundwater management using model reduction via empirical orthogonal functions

Abstract

This work presents a novel approach for solving groundwater management problems with reduced computational effort. We replace a groundwater flow model governed by a partial differential equation with a simple model governed by an ordinary differential equation. Model reduction is achieved with empirical orthogonal functions, i.e., principal components. Replacement of the full-scale model by a reduced model allows implementation of the embedding approach for optimal groundwater management. Comparing the results obtained with the full-scale simulation model, preliminary analyses show that the reduced model is able to reproduce head variations in the flow domain with good accuracy and, to a certain degree, the sensitivities of head with respect to pumping. A key advantage of the reduced model is that it is simple and easy to solve, and in many instances captures the dominating characteristics of the original model. In view of the many sources of uncertainty influencing groundwater simulation, the accuracy provided by a reduced model may be sufficient for planning purposes. As with other examples of model reduction presented in recent research efforts, the methodology shows promise in presenting general trends, but does not eliminate the need for the original model when more detailed analyses are needed.