The Bredehoeft Problem: Verifying Accuracy of Linearized Salvage Evaluation in Water Table Aquifers due to Groundwater Pumping

In water table aquifers, evapotranspiration can be reduced due to the groundwater pumping. These changes must be evaluated to assess how much water can be used for groundwater withdrawals. Although this salvage phenomenon was well understood a long time ago since pioneering studies of Theis and Bredehoeft, the models always applied numerical techniques to treat their non-linearity, most commonly using MODFLOW. However, in cases of limitations on watershed data properties, analytical methods were used successfully for practical evaluation of water balance components (e.g., stream depletion rates). Previously we made a breakthrough in solving the Bredehoeft problem analytically by linearization. This solution permits evaluating stream depletion and loss of storage in addition to salvage. Using compiled ranges of input parameters, the detailed analysis of solution using the COMSOL software indicates that linear approximation of the problem has good accuracy in practical ranges. Diagrams for evaluation of accuracy for broad ranges of parameters defining stream-aquifer connection and evapotranspiration are presented. Results can be used for analyses of the watershed water balances.