Multi-dimensional Marching-Jury Backwards Beam Equation Method with uncertainty in transport parameters: Influence of non-Gaussianity and sampling network on pollution event reconstruction

Groundwater contamination in the United States is a growing concern because of the potential risk associated with the contaminants and the extent of the problem. To allocate the cost of remediation activities, forensic techniques (e.g., compositional analysis, tracers, and transport models) are used to identify sources of contaminants. In this thesis a backwards in time transport model is studied. The Marching-Jury Backwards Beam Equation method (MJBBE) for 1D problems, or the Marching-Jury Backwards Plate Equation method (MJBPE) for multidimensional problems, solves the governing equation backwards in time to determine contaminant source location(s) and historical spatial distribution of a plume(s) in fully heterogeneous media. Modified MJBBE (mMJBBE) equations were also developed that are slightly different than the original MJBBE equations. The performance of the mMJBBE is superior in handling uncertainty in heterogeneous fields by recovering the spatial distribution with small sampling densities (10%) while the original MJBBE could successfully handle only sampling densities greater than 50%. For the 2D case, MJBPE was able to recover the historical distribution for two contamination sources when a composite plume at the current time is completely mixed and there are no features to distinguish the two different sources. The performance of the MJBPE and MJBPE methods when non-Gaussian and Gaussian generated fields are used, was compared to correct and incorrect selection of the true dispersion field. The MJBPE was able to capture the spatial distribution and the centroid location at 90% back in time for all cases of non-Gaussianity with very good accuracy. For multi-dimensional problems a Tridiagonal Block Matrix Solver was developed that is not dependent on the number of time steps in the solution; is the most accurate because errors are not compounded over time when compared to the marching methods; and performs better in terms of memory usage.