A Class of Exact Solutions of the Boussinesq Equation for Horizontal and Sloping Aquifers. Issue 2 (3rd February 2018) - Bartlett, M. S.; Porporato, A.
Abstract: The nonlinear equation of Boussinesq (1877) is a foundational approach for studying groundwater flow through an unconfined aquifer, but solving the full nonlinear version of the Boussinesq equation remains a challenge. Here, we present an exact solution to the full nonlinear Boussinesq equation that not only applies to sloping aquifers but also accounts for source and sink terms such as bedrock seepage, an often significant flux in headwater catchments. This new solution captures the hysteretic relationship (a loop rating curve) between the groundwater flow rate and the water table height, which may be used to provide a more realistic representation of streamflow and groundwater dynamics in hillslopes. In addition, the solution provides an expression where the flow recession varies based on hillslope parameters such as bedrock slope, bedrock seepage, aquifer recharge, plant transpiration, and other factors that vary across landscape types. Key Points: A class of solutions of the nonlinear Boussinesq equation with source/sink terms is presented, which includes past solutions as special cases The new solution applies to sloping aquifers and may include a head‐dependent rate of water seepage through the soil and bedrock interface The analytical results capture hysteresis between the groundwater level and groundwater flow rate as a function of hillslope characteristics