An Analytical Tool for Estimating Pumping-Induced Drawdown and Stream Depletion Nearby Complex Meandering Stream Networks.

Quantifying the location, magnitude and timing of streamflow depletion is critical for conjunctive water management; however, direct measurements are not available and thus depletion must be estimated. Analytical models are generally rapid and cost-effective but are limited by assumptions that typically include oversimplified representation of streams and stream-aquifer-well hydraulics. Numerical models require considerably more data and intensive computation to improve upon analytical estimates.

SSP&A developed the Distributed Drawdown Function (DDF), a Fortran-based analytical tool which simultaneously estimates drawdown and stream depletion induced by pumping near complex, meandering 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 output includes time series and contours of drawdown as well as time series of estimated stream depletion.

DDF has flexible user inputs, is easy to use, and is computationally efficient which makes DDF particularly suitable for screening applications, reproducible assessment frameworks, or sensitivity analysis. DDF is subject to limitations 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.

For improved accessibility to water resource decision makers, SSP&A has also integrated the DDF program into workflows underlying customized map-based graphical user interfaces.

Contact SSP&A for more information on running DDF with map-based interfaces.

DDF Numerical Model Comparison

Validation tests show that DDF reproduces analytical results and accurately captures spatial variations in drawdown for complex networks where the hydrogeologic setting can be reasonably approximated by homogeneous transmissivity and a perennial stream that is fully connected to the water table. A comparison of DDF with an analogous numerical simulation demonstrates close agreement in both drawdown and stream depletion magnitude and spatial distribution, with DDF- generated stream depletion ratios within six percent of numerical estimates, while significantly reducing computation time. These results indicate that DDF effectively expands simplified analytical solutions to include complex stream geometry without the necessary input data and computation effort of numerical models, offering water resource managers a rapid and accessible method to assess pumping effects on connected surface waters.
DDF Depletion Estimates
REFERENCE

Ou, G., Rogers, J.D., Sandoe, L. and Barth, G. 2026. A Rapid Analytical Tool for Estimating Pumping Effects on Complex Stream Networks. Groundwater. doi: 10.1111/gwat.70113

Distributed Drawdown Function (DDF)

DDF is freely available as a standalone command line tool from the DDF Repository on GitHub at: https://github.com/sspa-inc/DDF. The DDF Repository includes detailed input instructions, example input files, and an example case.

CAPABILITIES

  • Estimates pumping-induced drawdown and stream depletion adjacent to complex stream networks
  • Generates time series of estimated stream depletion and both time series and contours of estimated drawdown
  • Extension of the Theis equation constant head boundary condition to meandering stream geometry
  • Rapid and computationally efficient analytical estimates

COMPATIBILITY

  • DOS command line or DOS-based batch scripting
  • Comma delimited and geoJSON output format for ready integration into post-processing scripts and/or spatial visualization software

DEVELOPMENT LEADS

Gallery

Analytical and numerical predicted drawdown contours generated by DDF.
Panel A shows a nodefac value of 0.5 (midpoint), while panel B shows a nodefac of 1 (endpoint). This example river is coarsely discretized to better show the difference between nodefac values.
DDF estimates spatially-distributed drawdown and streamflow from pumping adjacent to a real river network.
DDF Depletion Estimates

DISCLAIMER: SSP&A’s software is provided “AS IS”, without warranty of any kind, including, without limitation, the warranties of merchantability, fitness for a particular purpose and non-infringement. We request only that application of the software and production of results using the code is accompanied by a suitable acknowledgment. The entire risk and responsibility as to the quality and performance of the Software is borne by the user. SSP&A disclaims all other warranties.

Environmental and Water Resource Solutions

S.S. Papadopulos & Associates is a multi-disciplinary consulting firm focused on delivering solutions for groundwater and hydrogeology, environmental engineering, contaminant studies, remediation, geochemistry, and surface-water hydrology.