Projection-based Model Reduction of Unconfined Groundwater Systems

Groundwater management is enhanced by the development and implementation of mathematical models to evaluate the effects on an aquifer system of various management actions. These evaluations often require a large number of simulations to conduct advanced analyses such as optimization of pumping schedules. Such analyses are intractable for complex, highly-discretized, or regional-scale models with large computational requirements. Therefore, reducing the computational burden associated with these models will provide opportunities for the application of optimization tools and other advanced analyses to a wider spectrum of groundwater management problems. Projection-based model reduction techniques have been shown to be very effective for reducing the computational burden of large-scale simulations. This type of model reduction involves construction of a projection matrix that is used to reduce the state dimensionality of a model by applying principal component analysis (PCA) to identify the components of the original model that have the largest impact on its output. It is also referred to as Proper Orthogonal Decomposition (POD). The projection-based reduction technique preserves the underlying physics of the system and removes components that do not provide significant information to the simulation. Previous researchers have reduced the dimensionality of the confined groundwater equation by three orders of magnitude using POD. To date, POD has only been applied to linear models such as the confined groundwater equation. A novel approach is proposed in this paper that combines the Newton formulation of the unconfined groundwater equation with a projection-based model reduction technique similar to POD. The proposed methodology is applied to the Newton formulation of MODFLOW (MODFLOW-NWT). We first validate the proposed methodology on a 1-D, unconfined MODFLOW-NWT model that solves 100 equations per time step (100-node model) and produced equivalent results by solving 10 equations per time step. We then apply the methodology to a 3-D, unconfined MODFLOW-NWT model. The original full-scale model with 500,000 nodes is reduced to 100 nodes, with about 1% error.