Analytical solution to linearized groundwater responses in sloping unconfined leaky aquifers under transient surface recharge

Siao-Ya Tang; Ping-Cheng Hsieh; Siao-Ya Tang; Ping-Cheng Hsieh

doi:10.3934/math.20251084

AIMS Mathematics

2025, Volume 10, Issue 10: 24446-24468. doi: 10.3934/math.20251084

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Analytical solution to linearized groundwater responses in sloping unconfined leaky aquifers under transient surface recharge

Siao-Ya Tang ,
Ping-Cheng Hsieh ^,

Department of Soil and Water Conservation, National Chung Hsing University, Taichung 40227, Taiwan

Received: 10 July 2025 Revised: 01 October 2025 Accepted: 13 October 2025 Published: 24 October 2025
MSC : 76S05

The increasing frequency of extreme climate events due to global warming has intensified water scarcity during prolonged droughts, highlighting the urgent need for effective water resource management. In Taiwan, where land availability is limited and population density is high, reservoirs serve as the primary storage mechanism; however, groundwater still accounts for approximately one-third of the total water supply. This study investigates groundwater level responses in a sloping, unconfined, leaky aquifer subjected to transient surface recharge and temporally varying boundary conditions, represented using Heaviside step functions. The governing Boussinesq equation is linearized through a time-dependent averaging strategy to enable analytical tractability, and then solved using the generalized integral transform technique (GITT). A convergence and validity analysis of the linearization is provided to justify this approximation. Model validation is conducted by comparing the analytical results under uniform recharge and horizontal slope conditions with prior benchmark studies. The proposed method demonstrates improved computational efficiency compared with Laplace-transform-based approaches. The findings indicate that steeper aquifer slopes shift peak water levels downslope, hydraulic conductivity controls the drawdown rate, and even small leakage rates exert a significant influence on groundwater dynamics.
- sloping aquifer,
- recharge,
- boundary water level,
- integral transform,
- leaky layer
Citation: Siao-Ya Tang, Ping-Cheng Hsieh. Analytical solution to linearized groundwater responses in sloping unconfined leaky aquifers under transient surface recharge[J]. AIMS Mathematics, 2025, 10(10): 24446-24468. doi: 10.3934/math.20251084

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Abstract

The increasing frequency of extreme climate events due to global warming has intensified water scarcity during prolonged droughts, highlighting the urgent need for effective water resource management. In Taiwan, where land availability is limited and population density is high, reservoirs serve as the primary storage mechanism; however, groundwater still accounts for approximately one-third of the total water supply. This study investigates groundwater level responses in a sloping, unconfined, leaky aquifer subjected to transient surface recharge and temporally varying boundary conditions, represented using Heaviside step functions. The governing Boussinesq equation is linearized through a time-dependent averaging strategy to enable analytical tractability, and then solved using the generalized integral transform technique (GITT). A convergence and validity analysis of the linearization is provided to justify this approximation. Model validation is conducted by comparing the analytical results under uniform recharge and horizontal slope conditions with prior benchmark studies. The proposed method demonstrates improved computational efficiency compared with Laplace-transform-based approaches. The findings indicate that steeper aquifer slopes shift peak water levels downslope, hydraulic conductivity controls the drawdown rate, and even small leakage rates exert a significant influence on groundwater dynamics.

References

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