Approximating Water-Table Aquifers Using Confined Models to Reduce Execution Time and Avoid Numerical Instability

Simulating a water-table aquifer can be difficult because the effective hydraulic properties of the aquifer change as the water table moves and the saturated thickness of the aquifer changes.  This imposes a computational burden associated with continually recalculating the hydraulic properties and introduces nonlinearity that can cause convergence problems. The resulting long execution times and numerical instability can make forward modeling, and especially inverse modeling and evaluation of model uncertainty, impractical or even impossible for some ground-water systems. Fortunately, the difficulties sometimes can be avoided by approximating the unconfined system using a confined model, with little loss of accuracy in the solution. This work describes the theoretical basis for the approximation and explores practical aspects of its application in a series of synthetic test cases. The approximation works best when the saturated thickness of the aquifer changes by a modest fraction over the course of the simulation, and it is particularly useful in situations that otherwise would require repeated updating of aquifer properties, such as transient runs and inverse modeling.