Stochastic modeling of subsurface flow and transport has become a subject of wide interest and intensive research for last few decades and results evolution of many stochastic theories. These theories, however, have had relatively little impact on practical groundwater modeling. In a recent forum on stochastic subsurface hydrology: from theory to application, a number of leading experts in stochastic modeling stress that data limitation, the assumptions of linearization, stationarity, Gaussianity, and excessive computations required are the bottlenecks and must be removed or substantially relaxed before stochastic methods can be routinely applied in practice.This dissertation, consisting of two papers, addresses the important issues of Gaussianity and data limitations in stochastic modeling. Paper1 investigates systematically the probabilistic structure of basic hydrogeological variables such as hydraulic head, groundwater velocity, concentration, seepage flux and solute flux through an integrated Monte Carlo simulation. Paper2 investigates the use of a statewide groundwater database from practical stochastic groundwater modeling and interested in exploring if the relatively crude, but detailed datasets can be used to characterize aquifer heterogeneity and how they can be best used to enable practical stochastic modeling. Results from Paper1 indicate that the statistical structure for real-world groundwater systems in general non-Gaussian, nonstationary and anisotropic. Some critical state variables are extremely complex, with the probability distribution varying rapidly with locations and directions even for very weak heterogeneity. This study concludes that variance cannot be used as an effective measure of uncertainty and linearized Gaussian-based stochastic methods must be used with extreme caution. This research represents the first systematic analysis of the probabilistic structure of basic hydrogeological variables and findings from this work have implications on theoretical and practical stochastic subsurface hydrology.Results from Paper2 show that the rapidly growing statewide dataset can potentially improve our ability to apply stochastic methods for practical problems. In particular, the study shows the statewide water well database can be used to characterize aquifer heterogeneity at regional scale (on the order of several thousand meters) and, in most cases, local scale (on the order of several hundred meters). The study also shows that the regional scale variability can be best modeled deterministically and the local scale heterogeneity stochastically. Application of the statewide database in conjunction with a seamlessly integrated hierarchical stochastic modeling software system enables probabilistic well capture zone modeling and risk-based source water protection in ways that were previously impractical.
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