Spatially variable water table recharge and the hillslope hydrologic response: Analytical solutions to the linearized hillslope Boussinesq equation

Abstract

The linearized hillslope Boussinesq equation, introduced by Brutsaert (1994), describes the dynamics of saturated, subsurface flow from hillslopes with shallow, unconfined aquifers. In this paper, we use a new analytical technique to solve the linearized hillslope Boussinesq equation to predict water table dynamics and hillslope discharge to channels. The new solutions extend previous analytical treatments of the linearized hillslope Boussinesq equation to account for the impact of spatiotemporal heterogeneity in water table recharge. The results indicate that the spatial character of recharge may significantly alter both steady state subsurface storage characteristics and the transient hillslope hydrologic response, depending strongly on similarity measures of controls on the subsurface flow dynamics. Additionally, we derive new analytical solutions for the linearized hillslope-storage Boussinesq equation and explore the interaction effects of recharge structure and hillslope morphology on water storage and base flow recession characteristics. A theoretical recession analysis, for example, demonstrates that decreasing the relative amount of downslope recharge has a similar effect as increasing hillslope convergence. In general, the theory suggests that recharge heterogeneity can serve to diminish or enhance the hydrologic impacts of hillslope morphology.