Numerical investigation of leakage in sloping aquifers

Abstract

A sloping aquifer resting on impermeable bedrock is a common paradigm in hydrological modeling. The underlying assumption of this paradigm is examined in this study of leaky hillslope systems. Leakage is simulated with a three-dimensional finite element Richards equation model for a 100 m synthetic hillslope composed of an unconfined and a confined aquifer separated by an aquitard. The simulations examine different configurations of aquifer and aquitard properties (hydraulic conductivity, aquitard thickness), hillslope geometry (uniform, convergent, divergent), hillslope inclination (0.2, 5, and 30%), and boundary conditions (Dirichlet, seepage face), as well as the interplay between leakage, water levels, and outflow. The results show that leakage generally percolates in both directions, with downward (positive) leakage in upslope portions of the aquifer and upward (reverse or negative) leakage in downslope regions. Geometry is found to be a main determinant of the partitioning of leakage along a hillslope, with for instance upward leakage in large portions of convergent slopes but only in a restricted downslope region for divergent slopes. In steep hillslopes, the reverse leakage that occurs downslope as a result of quick upslope drying represents a major component of the water budget. Outflow boundary conditions also exert a major control on the volume and direction of leakage, with the placement and extent of Dirichlet or seepage face nodes along the outflow face being particularly important factors. A dimensional analysis is used to synthesize the main findings and to highlight the differences in response between leaky and non-leaky hillslope conceptualizations. Leakage is also examined for a larger scale aquifer system, in a preliminary assessment of the importance of this exchange process for river basin models that are based on extensions of simple hillslope conceptualizations.