Too many streams and not enough time or money? New analytical depletion functions for rapid and accurate streamflow depletion estimates

Groundwater pumping can cause streamflow depletion by reducing groundwater discharge to streams and/or inducing surface water infiltration. Analytical and numerical models are two standard methods to predict streamflow depletion. Numerical models require extensive data and efforts to develop robust estimates, while analytical models are easy to implement with low data and experience requirements but are limited by numerous simplifying assumptions. We have pioneered a new approach that balances the shortcomings of analytical and numerical models: analytical depletion functions, which include more empirical functions expanding the applicability of analytical models for real-world settings with complex hydrogeologic landscapes and stream networks. Specifically, analytical depletion functions combine analytical models with stream proximity criteria used to determine which stream segments are most likely to be affected by a pumping well and a depletion apportionment equation which is a geometric method to distribute depletion among the affected stream segments. The accuracy of analytical depletion functions has been tested by comparing against a variety of numerical models from simplified, archetypal models to sophisticated, calibrated models in both steady-state to transient conditions. Estimates of streamflow depletion from analytical depletion function generally agree with estimates from numerical models, suggesting analytical depletion functions are an accurate tool for the streamflow depletion assessment over diverse hydrogeological landscapes and scales. Analytical depletion functions are rapidly and easily implemented and have low data requirements like analytical models but have significant advantages of better agreement with numerical models and better representation of complex stream geometries. Relative to numerical models, analytical depletion functions have limited ability to explore non-pumping related impacts and incorporate subsurface heterogeneity. Analytical depletion functions can be used as a stand-alone tool or part of decision-support tools as preliminary screening of potential groundwater pumping impacts when issuing new and existing water licenses while ensuring streamflow meets environmental flow needs.