Rapid and accurate estimates of streamflow depletion caused by groundwater pumping using analytical depletion functions

Abstract

Reductions in streamflow due to groundwater pumping (streamflow depletion) can negatively impact water users and aquatic ecosystems but are challenging to estimate due to the time and expertise required to develop numerical models often used for water management. Here, we develop analytical depletion functions, which are simpler approaches consisting of (i) stream proximity criteria which determine the stream segments impacted by a well; (ii) a depletion apportionment equation which distributes depletion among impacted stream segments; and (iii) an analytical model to estimate streamflow depletion in each segment. We evaluate 50 analytical depletion functions via comparison to an archetypal numerical model and find that analytical depletion functions predict streamflow depletion more accurately than analytical models alone. The choice of a depletion apportionment equation has the largest impact on analytical depletion function performance, and equations that consider stream network geometry perform best. The best-performing analytical depletion function combines stream proximity criteria which expand through time to account for the increasing size of the capture zone, a web squared depletion apportionment equation which considers stream geometry, and the Hunt analytical model which includes streambed resistance to flow. This analytical depletion function correctly identifies the stream segment most affected by a well textgreater70% of the time with mean absolute error textless 15% of predicted depletion and performs best for wells in relatively flat settings within 3 km of streams. Our results indicate that analytical depletion functions may be useful water management decision support tools in locations where calibrated numerical models are not available.