Effects of hydraulic conductivity variability on hillslope-scale shallow subsurface flow response and storage-discharge relations

An important problem in scientific hydrology is accounting for the effect of small-scale heterogeneity in lumped representations of flow through landscapes. In this work we investigate the effect of lateral variations in hydraulic conductivity on saturated subsurface lateral flow through hillslopes using an idealized model based on the Boussinesq equation. The model simulates flow over an impervious planar base through heterogeneous conductivity fields in response to simple recharge inputs and periodic recharge events. The results indicate that the hillslope-scale response depends on the relative importance of topographic and water table potential gradients driving flow. The relative magnitude of these drivers is related to a dimensionless variable (eta) over bar. Where water table gradients dominate, a network of flow paths channel flow through the hillslope toward high-conductivity areas, and the response is primarily dependent on the boundary condition at the toe of the hillslope. Where the topographic gradients dominate, the flow is delayed by low-conductivity areas, producing a power law-like response, suggesting that high exponents in observed storage-discharge relations may be traced to the presence of heterogeneity in the landscape. These observations suggest that the nature of the lumped hillslope-scale hydrologic models depends on the emergent behaviors that arise at that scale as a result of the interactions between hillslope properties (including their variability in space), the relationship between the hillslopes and their surrounding landscape elements (through the boundary conditions), and the temporal variability of the recharge that enters the system.