| 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 in practical stochastic modeling. These bottlenecks must be removed or substantially relaxed before stochastic modeling methods can be routinely applied in practice. Motivated by these critical assessments, this research addresses the issue of Gaussianity and issues of data limitations in stochastic modeling. The issue of Gaussianity is addressed by Monte Carlo Simulation (MCS). Data limitations issues are addressed using new source of Geographic Information Systems (GIS) database.;My first application considers a comprehensive study of synthetic scenarios to investigate the probabilistic structure of basic hydrogeological variables such as hydraulic head, groundwater velocity, concentration, seepage flux and solute flux. Results indicate that the statistical structure of 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 we can not always use variance as a good measure of uncertainty. Actual probability distribution from more accurate and generalized method such as MCS is a better way to characterize the structure of hydrogeological variables. This research represents the first systematic analysis of the probabilistic structure of basic hydrogeological variables and findings from this work have significant implications on theoretical and practical stochastic subsurface hydrology.;My second application involves probabilistic delineation of well capture zones. In this paper, we explore the use of a recently-developed statewide GIS database in Michigan. We are particularly interested in exploring if the relatively crude, but detailed datasets can be used to characterize aquifer heterogeneity with sufficient details to enable practical stochastic modeling. We consider three approaches such as deterministic, stochastic macrodispersion, stochastic Monte Carlo, to delineate well capture zones, each representing a different way to conceptualize aquifer heterogeneity. Results show deterministic approach that accounts only for the effect of large-scale trend leads to capture zones that are significantly smaller than its stochastic counterpart. Stochastic Monte Carlo approach that models large-scale trends deterministically and small-scale heterogeneity as random field provides a probability map of well capture zone which is useful for risk-based decision making processes. Stochastic macrodispersion approach that models large-scale trends deterministically and small-scale heterogeneity as effective macrodispersion, provides a computationally efficient alternative to delineate well capture zones. A probability map of well capture zone has important implications for environmental policy on source water protection, risk management and sampling design. |
