and the effects of the unsaturated zone.

Unsaturated Flow Without Confined Aquifer Storage
-------------------------------------------------

[@kroszynskidagan1975] were the first to account analytically for the effect of the unsaturated zone on aquifer drawdown. They extended the solution of [@dagan1967] by accounting for unsaturated flow above the water table. They used Richards’ equation for axis-symmetric unsaturated flow in a vadose zone of thickness $L$ $$\label{richards}
  K_r\frac{1}{r}\frac{\partial}{\partial r}\left( k(\psi
    )r\frac{\partial \sigma}{\partial r}\right)+
  K_z\frac{\partial}{\partial z}\left( k(\psi )\frac{\partial
      \sigma}{\partial z}\right) = C(\psi)\frac{\partial \sigma
  }{\partial t}
  \qquad
  \xi < z <b+L$$ where $\sigma = b + \psi_a - h$ is unsaturated zone drawdown \[L\], $\psi _a$ is air-entry pressure head \[L\], $0 \leq k(\psi )\leq 1$ is dimensionless relative hydraulic conductivity, $C(\psi)=d\theta/d
\psi$ is the moisture retention curve \[1/L\], and $\theta$ is dimensionless volumetric water content (see inset in Figure \[fig:diagram\]). They assumed flow in the underlying saturated zone was governed by the Laplace equation (like @dagan1967). The saturated and unsaturated flow equations were coupled through interface conditions at the water table expressing continuity of hydraulic heads and normal groundwater fluxes, $$\begin{aligned}
  s=\sigma\qquad
  \nabla s \cdot \textbf{n}=\nabla \sigma \cdot \textbf{n} \qquad
  z= \xi\end{aligned}$$ where $\textbf{n}$ is the unit vector perpendicular to the water table.

To solve the 