Shallow Unconfined Flow on a Sloping Base Redux

When is the impact of a sloping base large enough to justify more complex models for an unconfined aquifer? The intuitive answer that “it depends on the magnitude of the slope” is not wholly correct. Using recent mathematical results (the Lambert W function), we explicitly solve the simple sloping base problem. This explicit solution offers insights beyond those possible using Dupuit's, Polubarinov-Kochina's, Harr's, Child's, and others' implicit solutions. Specifically, it shows that the impact of the sloping base is best characterized by the saturated thickness divided by the change in base elevation, not by the slope.