The Bredehoeft problem: Evaluating salvage during groundwater pumping in unconfined aquifers

Abstract

During groundwater pumping from unconfined aquifers, evapotranspiration can be reduced as the water table drops, a process known as salvage. This phenomenon must be included in water balance assessments for accurate predictions of groundwater withdrawals. Although the salvage phenomenon has been well understood for a long time, i.e., since Theis’ pioneering studies, the models that were later developed by Bredehoeft always relied on numerical techniques to treat the inherent non-linearity, most commonly using MODFLOW. Analytical methods have been previously used with success for practical evaluation of water balance components such as stream depletion rates. This work presents a novel analytical solution of the Bredehoeft problem. It is a breakthrough in analytical evaluation of transient salvage losses induced by groundwater withdrawals due to declines of water table. We evaluate stream depletion and loss of storage in addition to salvage, using the new model. Detailed analysis of the solution using COMSOL software indicates that the linear approximation used in the analytical solution is accurate for most practical cases. Diagrams for drawdown, water balance and evaluation of solution accuracy are presented, considering a broad range of problem parameters. Results can be used for analyses of watershed-scale water balances.