Preprints
https://doi.org/10.5194/hess-2021-50
https://doi.org/10.5194/hess-2021-50

  23 Feb 2021

23 Feb 2021

Status: this preprint has been withdrawn by the authors.

Evaluation of hillslope storage with variable width under temporally varied rainfall recharge

Ping-Cheng Hsieh1 and Tzu-Ting Huang2 Ping-Cheng Hsieh and Tzu-Ting Huang
  • 1Department of Soil and Water Conservation, National Chung Hsing University, Taichung 40227, Taiwan
  • 2Department of Water Resources, Taoyuan City Government, Taoyuan 330, Taiwan

Abstract. This study discussed water storage in aquifers of hillslopes under temporally varied rainfall recharge by employing a hillslope-storage equation to simulate groundwater flow. The hillslope width was assumed to vary exponentially to denote the following complex hillslope types: uniform, convergent, and divergent. Both analytical and numerical solutions were acquired for the storage equation with a recharge source. The analytical solution was obtained using an integral transform technique. The numerical solution was obtained using a finite difference method in which the upwind scheme was used for space derivatives and the third-order Runge–Kutta scheme was used for time discretization. The results revealed that hillslope type significantly influences the drains of hillslope storage. Drainage was the fastest for divergent hillslopes and the slowest for convergent hillslopes. The results obtained from analytical solutions require the tuning of a fitting parameter to better describe the groundwater flow. However, a gap existed between the analytical and numerical solutions under the same scenario owing to the different versions of the hillslope-storage equation. The study findings implied that numerical solutions are superior to analytical solutions for the nonlinear hillslope-storage equation, whereas the analytical solutions are better for the linearized hillslope-storage equation. The findings thus can benefit research on and have application in soil and water conservation.

This preprint has been withdrawn.

Ping-Cheng Hsieh and Tzu-Ting Huang

Interactive discussion

Status: closed

Comment types: AC – author | RC – referee | CC – community | EC – editor | CEC – chief editor | : Report abuse
  • RC1: 'Comment on hess-2021-50', Anonymous Referee #1, 01 Mar 2021
    • AC1: 'Reply on RC1', Ping-Cheng Hsieh, 08 Mar 2021
  • RC2: 'Comment on hess-2021-50', Anonymous Referee #2, 16 Apr 2021
    • AC2: 'Reply on RC2', Ping-Cheng Hsieh, 27 Apr 2021

Interactive discussion

Status: closed

Comment types: AC – author | RC – referee | CC – community | EC – editor | CEC – chief editor | : Report abuse
  • RC1: 'Comment on hess-2021-50', Anonymous Referee #1, 01 Mar 2021
    • AC1: 'Reply on RC1', Ping-Cheng Hsieh, 08 Mar 2021
  • RC2: 'Comment on hess-2021-50', Anonymous Referee #2, 16 Apr 2021
    • AC2: 'Reply on RC2', Ping-Cheng Hsieh, 27 Apr 2021

Ping-Cheng Hsieh and Tzu-Ting Huang

Ping-Cheng Hsieh and Tzu-Ting Huang

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This preprint has been withdrawn.

Short summary
This study discussed water storage in aquifers of hillslopes with variable width under temporally varied rainfall recharge by employing a hillslope-storage equation to simulate groundwater flow. Both analytical and numerical solutions were acquired. The analytical solution was obtained using an integral transform technique. The numerical one was obtained using a finite difference method with the upwind scheme for space derivatives and the Runge–Kuttta scheme for time discretization.