Drying front in a sloping aquifer: Nonlinear effects

The profiles for the water table height h(x, t) in a shallow sloping aquifer are reexamined with a solution of the nonlinear Boussinesq equation. We demonstrate that the previous anomaly first reported by Brutsaert [1994] that the point at which the water table h first becomes zero at x = L at time t = t_c remains fixed at this point for all times t > t_c is actually a result of the linearization of the Boussinesq equation and not, as previously suggested [Brutsaert, 1994; Verhoest and Troch, 2000], a result of the Dupuit assumption. Rather, by examination of the nonlinear Boussinesq equation the drying front, i.e., the point x_f at which h is zero for times t ≥ t_c, actually recedes downslope as physically expected. This points out that the linear Boussinesq equation should be used carefully when a zero depth is obtained as the concept of an "average" depth loses meaning at that time.