Abstract
Stream depletion is the reduction in flow rate in a stream due to pumping in an aquifer that is hydraulically connected to the stream. We developed a semianalytical expression for stream depletion for pumping in a homogeneous aquifer, with an infinitely long, straight stream with a streambed conductance, , that varies cosinusoidally in space and time in the range . The wavelength of the spatial variations is equal to twice the distance between adjacent pools in a pool and riffle sequence, and the period of the temporal fluctuations represents alternating high and low flows. These spatiotemporal variations in streambed conductance produce temporal fluctuations of stream depletion superimposed on a trend that increases at a decreasing rate. Certain combinations of streambed and aquifer hydraulic parameters lead to exaggerated stream depletion, in which the temporally fluctuating stream depletion is not bracketed by the amount that would be obtained with steady, homogeneous streambed conductance of and . After sufficient time has passed, the same parameter sets produce excessive stream depletion, in which stream depletion exceeds the pumping rate at certain times. The degree of exaggerated stream depletion increases with the distance between pools, and is high if the temporal period of fluctuation matches the times of high rate of change of stream depletion.
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Data Availability Statement
All codes used in the solution of Eqs. (6) and (7) are available at ceae.colorado.edu/∼neupauer/stream_depletion_exaggeration. All other data can be reproduced using information provided in the document.
Acknowledgments
The authors thank David Grant for suggesting the conductance model that could be solved analytically in the Laplace domain, and Illés Horváth for providing the MATLAB code for the inverse Laplace transform. Funding for this project was provided by the United States Geological Survey under the Water Resources Research Institute Program, Project No. 2009CO195G.
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Published In
Journal of Hydrologic Engineering
Volume 26 • Issue 2 • February 2021
Copyright
© 2020 American Society of Civil Engineers.
History
Received: Jun 9, 2020
Accepted: Oct 9, 2020
Published online: Dec 7, 2020
Published in print: Feb 1, 2021
Discussion open until: May 7, 2021
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