Rapid and Accurate Estimates of Streamflow Depletion Caused by Groundwater Pumping Using Analytical Depletion Functions

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 >= 70% of the time with mean absolute error < 15% of predicted depletion and performs best for wells in relatively flat settings within similar to 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. Plain Language Summary Groundwater pumping can reduce streamflow ("streamflow depletion"), but it is hard to determine which streams will be affected by a well and how much each stream will be depleted. In this study, we develop and test simple tools called analytical depletion functions that can be used to estimate streamflow depletion in real-world settings where more complex models or field estimates are not available. We find that analytical depletion functions accurately predict which stream will be most affected by groundwater pumping for >= 70% of wells and accurately estimate the amount of depletion. Thus, we conclude that analytical depletion functions are a useful tool to provide rapid, screening-level estimates of streamflow depletion for water managers in areas where more complex approaches are unavailable. By integrating analytical depletion functions into online decision support tools, it will be possible for nonexperts to quickly estimate reductions in streamflow caused by groundwater pumping from existing and/or proposed wells.