Sam Zipper , Tom Dallemagne, Tom Gleeson, Thomas Boerman, Andreas Hartmann 

Quantifying reductions in streamflow due to groundwater pumping (‘streamflow depletion’) is essential for conjunctive management of groundwater and surface water resources. Analytical models are widely used to estimate streamflow depletion but include potentially problematic assumptions such as simplified stream-aquifer geometry and rely on largely untested depletion apportionment equations to distribute depletion from a well among different stream reaches. Here, we use archetypal numerical models to evaluate the sensitivity of five depletion apportionment equations to stream networks with varying drainage densities, topographic relief, and groundwater recharge rates; and statistically evaluate the sources of error for each equation. We introduce a new depletion apportionment equation called web squared which considers stream network geometry, and find that it performs the best under most conditions tested. For all depletion apportionment equations, performance decreases with increases in drainage density, relief, or recharge rates, and all equations struggle to estimate depletion in short stream reaches. Poorly performing apportionment equations tend to underestimate streamflow depletion relative to numerical model results, leading to a negative bias and underpredicted variability, while error in the best performing apportionment equations tends to be due to imperfect correlation. From a management perspective, apportionment equations with error due to bias and variability are preferable as they correctly identify which reaches will be affected and can be statistically corrected. Overall, these results indicate that the web squared method introduced here, which explicitly considers stream geometry, performs the best over a range of real-world conditions, and will be most accurate in flatter and drier environments.