Two new exact solutions are presented for uniform unconfined groundwat
er flow over a stepped base; one for a step down in the direction of f
low, the other for a step up in the direction of flow. These are two-d
imensional solutions of Laplace's equation in the vertical plane, and
are derived using the hodograph method and conformal mappings on Riema
nn surfaces. The exact solutions are compared with approximate one-dim
ensional solutions which neglect the resistance to vertical flow. For
small horizontal hydraulic gradients typical of regional groundwater f
low, little error is introduced by neglecting the vertical resistance
to flow. This conclusion may be extended to two-dimensional analytical
models in the horizontal plane, which neglect the vertical resistance
to flow and treat the aquifer base as a series of flat steps.