The thesis contains two studies: First is the water budget analysis using the groundwater modeling and next is the groundwater modeling using the MCMC scheme. The case study for the water budget analysis was the Norman Landfill site in Oklahoma with a quite complex hydrology. This site contains a wetland that controls the groundwater-surface water interaction. This study reports a simulation study for better understanding of the local water balance at the landfill site using MODFLOW-2000. Inputs to the model are based on local climate, soil, geology, vegetation and seasonal hydrological dynamics of the system to determine the groundwater-surface water interaction, water balance components in various hydrologic reservoirs, and the complexity and seasonality of local/regional hydrological processes. The model involved a transient two- dimensional hydrogeological simulation of the multi-layered aquifer. In the second part of the thesis, a Markov Chain Monte Carlo (MCMC) method were developed to estimate the hydraulic conductivity field conditioned on the measurements of hydraulic conductivity and hydraulic head for saturated flow in randomly heterogeneous porous media. The groundwater modeling approach was found to be efficient in identifying the dominant hydrological processes at the Norman Landfill site including evapotranspiration, recharge, and regional groundwater flow and groundwater-surface water interaction. The MCMC scheme also proved to be a robust tool for the inverse groundwater modeling but its strength depends on the precision of the prior covariance matrix.