This is a proposal submitted to both NSF and ARO for joint support, with each agency being asked to fund separate but related facets of the proposal. We propose to develop techniques which can be used for model reduction, whereby a complex full-model is replaced with a smaller simpler approximation that produces outputs within a desired degree of accuracy. Our proposed method combines the data driven and model driven methods in that it makes use of input/output data relationships as well as incorporates the physics of the model. The overriding objective of this proposal is to formulate and generalize model reduction via proper orthogonal decomposition in groundwater modeling in one, two, and three dimensions and to develop a protocol for snapshot selection based on the structure of both the governing equation and the parameters of the model. We will also propose procedures whereby the reduced-model is utilized for groundwater management as well as for solving the inverse problem of parameter estimation. We will use numerical experiments and real case studies to show how this new, robust methodology can be used to drastically reduce the computational demand, while maintaining a significant degree of accuracy. The NSF portion of the work focuses on error analysis of the reduced model, which is a key component of the proposed research. Additionally, we will focus on verification of the proposed methodology using field data for parameter estimation and conjunctive use of surface water and groundwater. We have made arrangements with the Calleguas Municipal Water District (CMWD) in southern California for collaboration.
