used this concept and through analysis of large amount of field drawdown data with [@boulton1963] solution, he established an empirical relationship between the delay index and physical aquifer properties. Prickett proposed a methodology for estimation of $S$, $S_y$, $K$, and $\alpha$ of unconfined aquifers by analyzing pumping tests with the [@boulton1963] solution.

Although Boulton’s model was able to reproduce all three segment of the unconfined time-drawdown curve, it failed to explain the physical mechanism of the delayed yield process because of the non-physical nature of the “delay index” in the [@boulton1963] solution.

[@streltsova1972a] developed an approximate solution for the decline of the water table and $s^\ast$ in fully penetrating pumping and observation wells. Like @boulton1954b, she treated the water table as a sharp material boundary, writing the two-dimensional depth-averaged flow equation as $$\label{streltsova_equation}
  \frac{\partial ^2 s^\ast}{\partial r^2}+
  \frac{1}{r}\frac{\partial s^\ast}{\partial r}=
  \frac{S}{T}\left(\frac{\partial s^\ast}{\partial t}-
  \frac{\partial \xi}{\partial t} \right).$$ The rate of water table decline was assumed to be linearly proportional to the difference between the water table elevation $\xi$ and the vertically averaged head $b-s^\ast$, $$\label{streltsova_watertable}
  \frac{\partial \xi}{\partial t}=\frac{K_z}{S_yb_z}
  \left( s^\ast-b+\xi \right)$$ where $b_z=b/3$ is an effective aquifer thickness over which water table recharge is distributed into the deep aquifer. Equation 