ABSTRACT

The overriding objective of this proposal is to develop parameter-independent reduced models for flow and transport equations in groundwater modeling. The reduced model is valid for the entire parameter space in the original full-scale model and is three orders of magnitude smaller than the full-scale model. The proposed methodology 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. Model reduction is based on the Galerkin projection of the high-dimensional model equations onto a subspace, approximated by a small number of optimally chosen basis functions (principal components). Algorithms will be developed to optimize the snapshot selection in the parameter space and time for the construction of the parameter-independent principal components. The reduced model captures the dominating characteristics of the original full-scale model and outputs within a desired degree of accuracy. Additionally, procedures will be developed whereby the reduced model is utilized for optimal experimental design for parameter estimation, Monte Carlo simulation, Bayesian inversion, data assimilation, and groundwater management. Numerical experiments and real case studies will be conducted to show how the proposed parameter-independent reduced models can be used to drastically reduce the computational requirements associated with large-scale groundwater flow and transport models, while satisfying the specified level of error tolerance for meeting the stipulated goal.

Groundwater models are used as decision-making tools for the planning and management of water resources systems. In many instances, the groundwater model has to be run a large number of times. A typical model uncertainty analysis requires tens of thousands of model runs to evaluate the uncertainty of the model outputs given the statistical characteristics of the model inputs. It would not be feasible or practical to use a computationally demanding and expensive full-scale model to perform such tasks. The project will develop new algorithms for constructing robust reduced models for groundwater flow and contaminant transport. The new algorithms can be used to perform various critically important hydrological analyses as the reduced models run 1,000 faster than the original full-scale model. The proposed model reduction methodology will be validated and applied to a selected groundwater basin in Southern California. Note that almost 40% of water supply in Southern California is from groundwater pumping. Arrangements have been made with the United States Geological Survey (USGS) office in San Diego for collaborative research participation in order to maximize the immediate applicability of the developed methodology for conjunctive planning of surface water and groundwater in Southern California. However, the proposed methodology is very general and can be applied to other groundwater basins in the country.

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