partially penetrating wells.

Observed Time-drawdown Curve
----------------------------

Before the time-dependent solution of @theis1935, distance drawdown was the diagnostic plot for aquifer test data. Detailed distance-drawdown plots require many observation locations (e.g., the 80 observation wells of @wenzel1936TheimTest). Re-analyzing results of the unconfined pumping test in Grand Island, [@wenzel1942] noticed that the [@theis1935] solution gave inconsistent estimates of $S_s$ and $K$, attributed to the delay in the yield of water from storage as the water table fell. The @theis1935 solution corresponds to the Dupuit assumptions for unconfined flow, and can only re-create the a portion of observed unconfined time-drawdown profiles (either late or early). The effect of the water table must be taken into account through a boundary condition or source term in the governing equation to reproduce observed behavior in unconfined pumping tests.

![Drawdown data from Cape Cod [@moenchetal2001], observation well F377-037. Upper dashed curve is confined model of @hantush1961 with $S=S_sb$, lower dotted curve is same with $S=S_sb + S_y$. Solid curve is unconfined model of @neuman1974 using $S_y=0.23$.[]{data-label="fig:capecod"}](cape_cod_F377-037.eps){width="80.00000%"}

[@walton1960] recognized three distinct segments characterizing different release mechanisms on time-drawdown curve under water table conditions (see Figure \[fig:capecod\]). A log-log time-drawdown plot in an unconfined aquifer has a characteristic 