Model Reduction via Proper Orthogonal Decomposition of Transient Confined and Unconfined Groundwater-Flow
Understanding groundwater resources is enhanced through the application of mathematical models that simulate the dynamics of an aquifer system. Conducting advanced analyses such as inverse problems for parameter estimation or optimization of pumping schedules under different scenarios requires a large number of simulations. Such analyses are intractable for complex, highly-discretized models with large computational requirements. Reducing the computational burden associated with these simulation models provides the opportunity to perform more advanced analyses on a wider spectrum of groundwater management problems. Projection based model reduction via Proper Orthogonal Decomposition (POD) has been shown to reduce the state space dimension by several orders of magnitude and thus reduces the computational burden. Two new POD techniques have been developed that improve the computation of high dimensional groundwater modeled systems. The first method provides a framework for developing parameter independent reduced models for solving inverse problems of confined groundwater models. This methodology is validated using synthetic test cases to solve a traditional inverse problem and Bayesian inverse problem. The second method presents a novel technique that allows for model reduction of unconfined groundwater flow, a nonlinear system of equations, using the Newton formulation of MODFLOW. This method extends POD to nonlinear equations and reduces the computational burden of solving the inverse of the Jacobian required by the Newton formulation. Multiple test cases are presented to illustrate how a POD model is constructed and applied to different groundwater models. These two techniques result in several orders of magnitude of reduction in the state dimension and reduce to the total CPU time. For the case of the Bayesian inverse problem, the synthetic example’s parameter posterior distributions that are described with the Metropolis-Hastings Markov chain Monte Carlo method results in a time savings of 48 days when using the reduced model.