Karst aquifers are vulnerable to contamination, as conduits and fractures in the aquifers are preferential flow paths where contaminants move fast. On the other hand, the presence of conduits and fractures make groundwater modeling for karst aquifer a challenge. This dissertation addresses several important issues related to groundwater contamination, numerical modeling, and equipment development with potential applications in karst. In Chapter 2, I discuss groundwater contamination in the karst aquifer of Yucatan, which is the only source of drinking water for the population of Yucatan but groundwater in the top of the aquifer has been polluted and cannot be used for human consumption. I developed a new statistical method to analyze temporal and spatial variation of groundwater quality in the aquifer. By using this method, I identified the factors that cause temporal and spatial changes in the groundwater quality as well as the zones of influence. The spatial changes are caused by the following factors: interaction between groundwater and matrix rock, distribution of precipitation, seawater intrusion, mixture of water rich in sulfates, and human pollution in two zones within the study area. The temporal variation is caused by changes in the amount and distribution of precipitation. The new method proves to be important for deriving information about the temporal and spatial processes affecting groundwater quality. Chapter 3 is focused on validating the MODFLOW CFP M1 model developed by the U.S. Geological Survey for simulating groundwater flow in karst aquifers. The model validation process is important to build confidence for using the model. I was interested in quantifying to what extent the model can accurately simulate groundwater flow in karst conduit and surrounding porous media, in other words, if the equation used to simulate the flow exchange between karst conduits and surrounding porous media was suitable for this experiment. The model validation was done using results of lab experiments. A sandbox lab device was developed to understand three-dimensional (3-D) groundwater flow in a confined karst aquifer with a conduit in the middle of the aquifer. Thirteen lab experiments were performed. Hydraulic heads and flow rates of the conduit and surrounding sand were measured. I used three experimental results to calibrate the roughness of the conduit, hydraulic conductivity of the sand surrounding the conduit, and a coefficient used by MODFLOW CFP M1 for simulating the flow exchange. Using the calibrated model, I evaluated the estimated errors (the difference between model simulations and the corresponding data) along with the 95% confidence intervals for the true error. The errors were calculated for flow rates at the inflow and outflow of the sandbox and the heads in the porous media. The confidence intervals consider measurement error, model calibration error, parameter uncertainty, and propagation of the measurement error in the boundary conditions. The results of model calibration and validation showed that the magnitude of the error was highly correlated with the magnitude of measured flow exchange, indicating that MODFLOW CFP M1 cannot adequately capture the physics of the flow exchange. Therefore, MODFLOW CFP M1 is valid when the flow exchange is small but invalid otherwise for this sandbox experiment. In Chapter 4, I developed a seepage meter to measure groundwater seepage from groundwater to surface waterbodies such as a lake. I was interested in verifying the accuracy of an analytic solution, which estimates the seepage through the bottom of a lake, using measurements from a sandbox experiment. However, existing methods were not useful in this case because of the small scale. Therefore, I proposed a new seepage meter useful for this case. The proposed seepage meter can be used to estimate the hydraulic conductivity as well. Therefore, I tested: (1) the accuracy of the seepage meter using a Darcy column, and (2) the accuracy of the analytic solution using a MODFLOW model and seepage measurements from a sandbox. This sandbox represents an unconfined aquifer with groundwater discharge into a lake. The new seepage meter consists of a cylinder inserted into the lake bed. The groundwater seepage is directed first to the cylinder and then to an external reservoir where seepage measurements are made. The laboratory results show that the seepage meter can be used to measure seepage for the laboratory experiment. However, more tests are needed to further evaluate the accuracy of the seepage meter. The numerical results show that the analytic solution is a good approximation for seepage estimation. Chapter 5 discusses the conclusions of my dissertation research and the research in future studies.