a synthetic aquifer with unsaturated properties given by the model of [@vangenuchten1980]. They also estimated aquifer parameters from Cape Cod drawdown data [@moenchetal2001], comparing estimated @vangenuchten1980 parameters with laboratory values [@maceetal1998].

[@mishraneuman2011] further extended their [-@mishraneuman2010] solution to include a finite-diameter pumping well with storage. @mishraneuman2010 [@mishraneuman2011] were the first to estimate non-exponential model unsaturated aquifer properties from pumping test data, by curve-fitting the exponential model to the [@vangenuchten1980] model. Analyzing pumping test data of @moenchetal2001 (Cape Cod, Massachusetts) and @nwankwor1984 [@nwankwor1992] (Borden, Canada), they estimated unsaturated flow parameters similar to laboratory-estimated values for the same soils.

Future Challenges
=================

The conceptualization of groundwater flow during unconfined pumping tests has been a challenging task that has spurred substantial theoretical research in the field hydrogeology for decades. Unconfined flow to a well is non-linear in multiple ways, and the application of analytical solutions has required utilization of advanced mathematical tools. There are still many additional challenges to be addressed related to unconfined aquifer pumping tests, including:

-   Hysteretic effects of unsaturated flow. Different exponents and reference pressures are needed during drainage and recharge events, complicating simple superposition needed to handle multiple pumping wells, variable pumping rates, or analysis of recovery data.

