Preprints
https://doi.org/10.5194/hess-2022-353
https://doi.org/10.5194/hess-2022-353
02 Nov 2022
 | 02 Nov 2022
Status: this preprint was under review for the journal HESS but the revision was not accepted.

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

Bwalya Malama, Ying-Fan Lin, Hwa-Lung Yu, Hua-Ting Tseng, and Sam Greene

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.

Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims made in the text, published maps, institutional affiliations, or any other geographical representation in this preprint. The responsibility to include appropriate place names lies with the authors.
Bwalya Malama, Ying-Fan Lin, Hwa-Lung Yu, Hua-Ting Tseng, and Sam Greene

Status: closed

Comment types: AC – author | RC – referee | CC – community | EC – editor | CEC – chief editor | : Report abuse
  • RC1: 'Comment on hess-2022-353', Anonymous Referee #1, 01 Dec 2022
    • AC1: 'Reply on RC1', Bwalya Malama, 10 Dec 2022
      • RC3: 'Reply on AC1', Anonymous Referee #1, 02 Jan 2023
        • AC4: 'Reply on RC3', Bwalya Malama, 29 Jan 2023
    • CC1: 'Reply on RC1', Ying-Fan Lin, 29 Dec 2022
      • RC2: 'Reply on CC1', Anonymous Referee #1, 02 Jan 2023
        • CC2: 'Reply on RC2', Ying-Fan Lin, 02 Jan 2023
          • RC4: 'Reply on CC2', Anonymous Referee #1, 02 Jan 2023
            • AC6: 'Reply on RC4', Bwalya Malama, 29 Jan 2023
        • CC3: 'Reply on RC2 (Marked manuscript)', Ying-Fan Lin, 02 Jan 2023
          • RC5: 'Reply on CC3', Anonymous Referee #1, 02 Jan 2023
            • AC7: 'Reply on RC5', Bwalya Malama, 29 Jan 2023
        • AC5: 'Reply on RC2', Bwalya Malama, 29 Jan 2023
  • RC6: 'Comment on hess-2022-353', Anonymous Referee #2, 08 Jan 2023
    • AC2: 'Reply on RC6', Bwalya Malama, 23 Jan 2023
    • AC3: 'Reply on RC6', Bwalya Malama, 23 Jan 2023

Status: closed

Comment types: AC – author | RC – referee | CC – community | EC – editor | CEC – chief editor | : Report abuse
  • RC1: 'Comment on hess-2022-353', Anonymous Referee #1, 01 Dec 2022
    • AC1: 'Reply on RC1', Bwalya Malama, 10 Dec 2022
      • RC3: 'Reply on AC1', Anonymous Referee #1, 02 Jan 2023
        • AC4: 'Reply on RC3', Bwalya Malama, 29 Jan 2023
    • CC1: 'Reply on RC1', Ying-Fan Lin, 29 Dec 2022
      • RC2: 'Reply on CC1', Anonymous Referee #1, 02 Jan 2023
        • CC2: 'Reply on RC2', Ying-Fan Lin, 02 Jan 2023
          • RC4: 'Reply on CC2', Anonymous Referee #1, 02 Jan 2023
            • AC6: 'Reply on RC4', Bwalya Malama, 29 Jan 2023
        • CC3: 'Reply on RC2 (Marked manuscript)', Ying-Fan Lin, 02 Jan 2023
          • RC5: 'Reply on CC3', Anonymous Referee #1, 02 Jan 2023
            • AC7: 'Reply on RC5', Bwalya Malama, 29 Jan 2023
        • AC5: 'Reply on RC2', Bwalya Malama, 29 Jan 2023
  • RC6: 'Comment on hess-2022-353', Anonymous Referee #2, 08 Jan 2023
    • AC2: 'Reply on RC6', Bwalya Malama, 23 Jan 2023
    • AC3: 'Reply on RC6', Bwalya Malama, 23 Jan 2023
Bwalya Malama, Ying-Fan Lin, Hwa-Lung Yu, Hua-Ting Tseng, and Sam Greene
Bwalya Malama, Ying-Fan Lin, Hwa-Lung Yu, Hua-Ting Tseng, and Sam Greene

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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.