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Resolving the Stream Depletion Model Paradox: Theory of Depletion with Stream Drawdown near a Pumping Well
  • Bwalya Malama,
  • Ye-Chen Lin
Bwalya Malama
California Polytechnic State University, California Polytechnic State University

Corresponding Author:bmalama@calpoly.edu

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Ye-Chen Lin
National Chiao Tung University, National Chiao Tung University
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Mathematical models for stream depletion typically use the constant-head Dirichlet boundary condition or the general Robin boundary condition at the stream. Both approaches fix stream stage as constant during pumping. Fixed the stream stage implies the stream acts as an infinite water source with depletion affecting stream discharge but having no impact on stream stage. We refer to this depletion without drawdown as the “depletion paradox.” It is a glaring model limitation, ignoring the most observable adverse effect of long-term groundwater abstraction near a stream – dry streambeds. Our field data demonstrate that stream stage responds to pumping near the stream. This motivates the development of a model considering transient stream drawdown using the concepts of finite stream storage and mass continuity at the stream-aquifer interface. The models include the cases for fully- and non-penetrating the stream. First-order mass transfer is also assumed across the streambed. The proposed model reduces to the fixed-stage model as stream storage becomes infinitely large and the confined flow case with a no-flow boundary at the streambed when stream storage vanishes. Sensitivity analysis for hydraulic properties of the stream-aquifer system is also included. Our results suggest that fixed-stage models (a) underestimate late-time aquifer drawdown to pumping adjacent to a stream and (b) overestimate the available groundwater supply from streams to pumping wells because of the infinite stream storage assumption. This can have significant implications for the sustainable management of water resources in interacting stream-aquifer systems with heavy groundwater abstraction.