Kacimov (2025) Ephemeral reservoirs of low-head wadi dams drained by seepage, evaporation and pumping: the Pavlovsky/Polubarinova-Kochina/Abel analytical legacy redux

Identification

• Journal: Advances in Water Resources
• Year: 2025
• Date: 2025-12-25
• Authors: A. R. Kacimov
• DOI: 10.1016/j.advwatres.2025.105201

Research Groups

• Department of Soils, Water and Agricultural Engineering, Sultan Qaboos University, Oman
• N.I. Lobachevsky Institute of Mathematics and Mechanics, Kazan Federal University, Kazan, Russia

Short Summary

This paper develops analytical and numerical solutions, based on conformal mappings and ordinary differential equations, to model transient 2-D seepage and reservoir depletion in low-head wadi dams, facilitating optimal design for water management in arid regions.

Objective

• To study transient 2-D seepage through the porous bed of a wadi dam, considering reservoir depletion due to seepage, evaporation, and pumping, and to solve optimal design problems for smart management of reservoir water storage.

Study Configuration

• Spatial Scale: Two-dimensional cross-section of a low-head wadi dam with a vertical cutoff wall, its reservoir, and the underlying porous wadi bed.
• Temporal Scale: Transient analysis of reservoir water storage depletion, from initial conditions to complete depletion, including the determination of a "time front."

Methodology and Data

• Models used:
  • Conformal mappings (Schwarz-Christoffel formula)
  • Analytical solutions based on Pavlovsky and Polubarinova-Kochina's work
  • Ordinary Differential Equations (ODEs), including Abel's ODE
  • Computer algebra routines for numerical integration (Cauchy problem)
  • HYDRUS2D for numerical modeling of saturated-unsaturated seepage
• Data sources: Not applicable; the study is theoretical and computational.

Main Results

• Developed analytical solutions for transient 2-D seepage through a porous wadi bed under a small-head dam, incorporating a vertical cutoff wall.
• Formulated an Ordinary Differential Equation (ODE) describing the mass balance in the headwater, accounting for seepage, evaporation, and pumping/injection.
• Provided exact solutions for the ODE in cases of no pumping or constant rate pumping, leading to linear or Abel's ODE.
• Implemented numerical integration via computer algebra routines to solve the Cauchy problem, determining the "time front" for complete reservoir depletion.
• Solved optimal design problems aimed at smart management of reservoir water storage for irrigation and animal husbandry in arid environments.
• Demonstrated the kinematics of saturated-unsaturated seepage using HYDRUS2D for both unclogged and clogged reservoir beds.
• Discussed the subsurface hydrology of dam cascades, including groundwater-recharged systems, for smart water retention in ephemeral streams.

Contributions

• Revitalizes and extends the analytical legacy of Pavlovsky, Polubarinova-Kochina, and Abel for modern design and operation of low-head wadi dams.
• Integrates seepage, evaporation, and pumping/injection into a comprehensive analytical and numerical framework for reservoir depletion modeling.
• Provides a robust methodology for solving optimal design problems to enhance water management in small community dams in arid zones.
• Offers insights into saturated-unsaturated flow dynamics and the impact of reservoir bed clogging, complementing analytical solutions with numerical simulations.
• Extends the applicability of the framework to complex systems like cascades of dams and groundwater-recharged systems.

Funding

• No specific funding projects or programs were mentioned in the provided text.

Citation

@article{Kacimov2025Ephemeral,
  author = {Kacimov, A. R.},
  title = {Ephemeral reservoirs of low-head wadi dams drained by seepage, evaporation and pumping: the Pavlovsky/Polubarinova-Kochina/Abel analytical legacy redux},
  journal = {Advances in Water Resources},
  year = {2025},
  doi = {10.1016/j.advwatres.2025.105201},
  url = {https://doi.org/10.1016/j.advwatres.2025.105201}
}