02 Nov 2022
02 Nov 2022
Status: this preprint is currently under review for the journal HESS.

Transient Theory of Pumping Induced Depletion and Drawdown of a Stream with Finite Channel Storage

Bwalya Malama1, Ying-Fan Lin2, Hwa-Lung Yu2, Hua-Ting Tseng2, and Sam Greene1 Bwalya Malama et al.
  • 1Natural Resources Management and Environmental Sciences, California Polytechnic State University, San Luis Obispo, State of California, USA
  • 2Department of Bioenvironmental Systems Engineering, National Taiwan University, Taipei City, Taiwan

Abstract. Mathematical models for stream depletion with stream stage decline or drawdown are developed to overcome the deficiency in existing models that typically use the constant-head (Dirichlet) or general (Robin) boundary condition and source terms at the stream-aquifer interface. Existing approaches assume a fixed stream stage during pumping, implies that the stream is an infinite water source, with depletion defined as a decrease in stream discharge. We refer to this depletion without drawdown as the ``stream depletion paradox.'' It is a glaring model limitation, ignoring the most observable adverse effect of long-term groundwater abstraction near a stream, namely stage declines that eventually lead to dry streambeds. Field data are presented to demonstrate that stream stage responds to pumping near the stream, motivating the development of an alternative theory predicts transient stream drawdown based on the concepts of finite stream storage and mass continuity at the stream-aquifer interface. Based on this alternative theory, models are developed for the cases of a non- and a fully-penetrating stream. The proposed model reduces to the fixed-stage model in the limit as stream storage becomes infinitely large and to the limiting case of confined aquifer flow with a no-flow boundary at the streambed when the stream storage vanishes. The model is applied to field observations of both aquifer and stream drawdown from tests conducted in a confined aquifer over which a shallow stream flows. Model fits and parameter estimates are obtained both aquifer and stream drawdown data. Model predicted and observed transient drawdown behavior indicate that fixed-stage models (a) underestimate late-time aquifer drawdown and (b) overestimate the available recharge from streams to pumping wells. This has significant implications for the sustainable management of water resources in hydraulically connected stream-aquifer systems with heavy groundwater abstraction.

Bwalya Malama et al.

Status: open (until 05 Jan 2023)

Comment types: AC – author | RC – referee | CC – community | EC – editor | CEC – chief editor | : Report abuse

Bwalya Malama et al.

Bwalya Malama et al.


Total article views: 277 (including HTML, PDF, and XML)
HTML PDF XML Total BibTeX EndNote
235 37 5 277 1 2
  • HTML: 235
  • PDF: 37
  • XML: 5
  • Total: 277
  • BibTeX: 1
  • EndNote: 2
Views and downloads (calculated since 02 Nov 2022)
Cumulative views and downloads (calculated since 02 Nov 2022)

Viewed (geographical distribution)

Total article views: 259 (including HTML, PDF, and XML) Thereof 259 with geography defined and 0 with unknown origin.
Country # Views %
  • 1
Latest update: 30 Nov 2022
Short summary
We identify a limitation in existing models for stream depletion due to groundwater pumping. Existing models assume the stream acts as infinite source during groundwater pumping by imposing a constant head condition at a stream. We overcome this by adopting a mass conservation law and a stream storage coefficient to model stream drawdown. The model is applied to field drawdowns of stream and aquifer. The model fit the data well and give hydraulic estimates that compare well to similar sediment.