The role of recharge/discharge and hydraulic conductivity in gravitational groundwater flow systems

This study introduces a new formulation for solving Tóth's unit basin groundwater flow problem by using Neumann boundary conditions at the water table. This enables considering the impacts of hydraulic conductivity and groundwater recharge, in contrast to the earlier model, which assumed that the water table shape and location was known. The original Tóth problem was represented numerically to obtain the equivalent recharge/discharge boundary, which then was used for new analytical formulation of the problem. The results show that the likely changes in hydraulic conductivity and recharge significantly affect the magnitude of hydraulic head, but not the shape of the contour lines. Basin dimensions (i.e. basin depth to length aspect ratio (b/a)) affect both the hydraulic head magnitude and the shape of the resulting contours. As the aspect ratio decreases, the flow becomes more horizontal, and equipotential lines tend to become more vertical. Results reveal that the head gradient is higher for lower aspect ratios and exponentially decreases as the basin becomes square. These results enable understand the relationship between basin geometry and hydrological parameters, and their relation to water table shape and gradient.