The Stream Depletion Model Paradox and a First Solution
Abstract
Hitherto, stream depletion models available in the hydrogeology literature use the xed head Dirichletboundary condition at the stream, and as such do not account for groundwater pumping induced streamdrawdown. They simply treat stream depletion as the decrease in stream discharge due capture by pumping,the groundwater that would discharge to the stream without pumping. We refer to this model predictedstream depletion without stream drawdown as the depletion paradox. It is intuitively clear, however, thatadverse impacts of long-term groundwater abstraction in the neighborhood of a stream include streamdrawdown, which has led to many a dry streambed in the American west and other arid regions. Streamdrawdown is especially acute for low stream ows. A mathematical model that allows for transient streamdrawdown is proposed by introducing the concept of stream storage. The model simply extends the constanthead model at the stream by including a mass-balance condition. The model is developed for a fullypenetrating stream and groundwater abstraction in a conned aquifer. The dependence of model predictedstream depletion and drawdown on stream storage, streambed conductance, aquifer anisotropy, and radialdistance to the pumping well is evaluated. The model is shown to reduce to that of Hantush in the limitas stream storage becomes innitely large, and to the Theis solution with a no- ow boundary at the streamlocation when stream storage gets vanishingly small. The results suggest that using xed stream stage modelsleads to an underestimation the late-time aquifer drawdwon response to pumping in the neighborhood of astream because it correspond to innite stream storage. This is especially critical for management of surfacewater and groundwater resources in systems subjected to prolonged groundwater abstraction and measurablestream drawdown. The model also shows a maximum stream depletion rate, beyond which stream ow to thewell diminishes and eventually vanishes. This suggests that models with xed stream stage overestimate theavailable groundwater supply from streams to pumping wells because of the inherent assumption of innitestream storage. This has implications for sustainable management of groundwater resources near streams.
- Publication:
-
AGU Fall Meeting Abstracts
- Pub Date:
- December 2017
- Bibcode:
- 2017AGUFM.H23D1684M
- Keywords:
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- 0414 Biogeochemical cycles;
- processes;
- and modeling;
- BIOGEOSCIENCES;
- 0496 Water quality;
- BIOGEOSCIENCES;
- 1830 Groundwater/surface water interaction;
- HYDROLOGY;
- 1839 Hydrologic scaling;
- HYDROLOGY