A Rapid Analytical Tool for Estimating Pumping Effects on Complex Stream Networks

Understanding how groundwater pumping affects streamflow is critical for conjunctive water management, yet most analytical methods oversimplify stream geometry and the stream-aquifer-well hydraulics, while numerical models require considerably more data and computation to improve upon analytical predictions. This note introduces the distributed drawdown function (DDF), an analytical tool designed to efficiently estimate groundwater drawdown and stream depletion caused by pumping near complex stream networks. DDF extends the Theis solution by discretizing stream networks into multiple nodes and applying the principle of superposition to enforce constant head boundary conditions along meandering stream geometries. The tool solves a system of linear equations to determine the leakage rate at each stream node that results in zero drawdown at the stream boundary. DDF is subject to simplifying assumptions inherent to the drawdown function, which for the Theis equation includes constant transmissivity and a fully penetrating stream with constant stage and no resistance to flow across the streambed. Validation tests show that DDF accurately captures spatial variations in drawdown for complex networks. A comparison of DDF with a numerical simulation for a complex stream network demonstrates close agreement in both drawdown and stream depletion, with DDF-generated stream depletion fractions within 6% of numerical estimates. These results indicate that DDF effectively expands simplified analytical solutions to include complex stream geometry and multiple pumping wells without the necessary input data and computational effort of numerical models, offering water resource managers a rapid and accessible method to assess pumping effects on connected surface waters.