Comment on 'Appropriate Boundary Condition for Dupuit-Boussinesq Theory on the Steady Groundwater Flow in an Unconfined Sloping Aquifer With Uniform Recharge' by Wu et al

摘要

By neglecting unsaturated flow, Wu et al. (2018, https://doi.org/10.1029/2018WR023070) claimed that the zero volumetric discharge at the upstream boundary results in two possible boundary conditions of either zero groundwater table or zero seepage velocity based on the original Dupuit-Boussinesq theory. They further concluded that a steeper and/or shallower aquifer has a zero-groundwater table if the downstream groundwater table is shallower. Here we point out that the conceptual model adopted by Wu et al. (2018) not reasonable and the results are quite different from those with unsaturated flow considered in the real hillslope aquifer. Specifically, the water table at the upstream boundary could be positive or negative due to the lateral unsaturated flow effect, and hence, the seepage velocity must be set to zero to satisfy the zero discharge boundary condition at the upstream boundary. In addition, the zero groundwater table cannot ensure a zero discharge at the upstream boundary. Furthermore, we argue that the discharge with respect to the groundwater table is linearly distributed along the slope distance only when both saturated and unsaturated flows are considered. The saturated flow discharge itself is not distributed linearly. Our comment highlights the importance of unsaturated flow in studying steady groundwater flow in an unconfined sloping aquifer with uniform recharge using the Dupuit-Boussinesq theory.