Nonlinear Inversion of an Unconfined Aquifer: Simultaneous Estimation of Heterogeneous Hydraulic Conductivities,Recharge Rates,and Boundary Conditions

A new inverse method is developed to simultaneously estimate heterogeneous hydraulic conductivities, source/sink rates, and unknown boundary conditions for steady-state flow in an unconfined aquifer. Unlike objective function-based techniques, the new method does not optimize any data-model misfits. Instead, its formulation is developed by honoring physical flow principles as well as observation data at sampled locations. Under the Dupuit–Forchheimer assumption of negligible vertical flow, accuracy and stability of the new method are demonstrated using synthetic heterogeneous aquifer problems with increasingly complex flow: (1) aquifer domains without source/sink effects; (2) aquifer domains with a point sink (a pumping well operating under a constant discharge rate); (3) aquifer domains with constant or spatially variable recharge; (4) aquifer domains with constant or spatially variable recharge undergoing single-well pumping. For all problems, inversion yields stable solutions under increasing head measurement errors (up to $pm $ 10 % of the total head variation in a problem), although accuracy of the estimated parameters degrades with the increasing errors. The inverse method is successfully tested on problems with high hydraulic conductivity contrasts—up to 10,000 times between the maximum and minimum values. In inverting several heterogeneous problems, if the aquifer is assumed homogeneous with a constant recharge rate, physically meaningful parameter estimates (i.e., equivalent conductivities and mean recharge rates) can be determined. Alternatively, if the inverse parameterization contains spurious parameters, inversion can identify such parameters, while the simultaneous estimation of non-spurious parameters is not affected. The method obviates the well-known issues associated with model “structure errors”, when inverse parameterization either simplifies or complexifies the true parameter field.