An approximate analytical solution for groundwater variation in unconfined aquifers subject to variable boundary water levels and groundwater recharge

An-Ping Wang; Ming-Chang Wu; Ping-Cheng Hsieh; An-Ping Wang; Ming-Chang Wu; Ping-Cheng Hsieh

doi:10.3934/math.20241393

AIMS Mathematics

2024, Volume 9, Issue 10: 28722-28740. doi: 10.3934/math.20241393

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An approximate analytical solution for groundwater variation in unconfined aquifers subject to variable boundary water levels and groundwater recharge

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

Received: 10 July 2024 Revised: 18 September 2024 Accepted: 29 September 2024 Published: 10 October 2024
MSC : 76S05

This study investigated the effects of fluctuating boundary water levels and surface recharge on groundwater flow within unconfined aquifers. We aimed to understand how changes in recharge patterns and variable boundary water levels, such as those from rivers or canals, affect groundwater levels over time and space. To achieve this, we solved the linearized Boussinesq equation using the time-marching method alongside the generalized integral transformation method. Our analysis focused on how different types of recharge affect groundwater level variations and flow dynamics. We found that boundary effects on groundwater level change propagate from the edges toward the aquifer's center, becoming more pronounced with increased boundary water levels. Over time, the system stabilizes, leading to a steady water table height and flow rate, which depend on the disparity between the boundary water levels. Our analytical model demonstrated flexibility and practical applicability by allowing for the consideration or omission of various influencing factors, thus facilitating complete knowledge about groundwater variations and offering future strategic insights for sustainable groundwater resource management.
- groundwater table,
- unconfined aquifer,
- varying boundary water level,
- recharge,
- generalized integral transform method
Citation: An-Ping Wang, Ming-Chang Wu, Ping-Cheng Hsieh. An approximate analytical solution for groundwater variation in unconfined aquifers subject to variable boundary water levels and groundwater recharge[J]. AIMS Mathematics, 2024, 9(10): 28722-28740. doi: 10.3934/math.20241393

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Abstract

This study investigated the effects of fluctuating boundary water levels and surface recharge on groundwater flow within unconfined aquifers. We aimed to understand how changes in recharge patterns and variable boundary water levels, such as those from rivers or canals, affect groundwater levels over time and space. To achieve this, we solved the linearized Boussinesq equation using the time-marching method alongside the generalized integral transformation method. Our analysis focused on how different types of recharge affect groundwater level variations and flow dynamics. We found that boundary effects on groundwater level change propagate from the edges toward the aquifer's center, becoming more pronounced with increased boundary water levels. Over time, the system stabilizes, leading to a steady water table height and flow rate, which depend on the disparity between the boundary water levels. Our analytical model demonstrated flexibility and practical applicability by allowing for the consideration or omission of various influencing factors, thus facilitating complete knowledge about groundwater variations and offering future strategic insights for sustainable groundwater resource management.

References

[1]	P. Döll, Vulnerability to the impact of climate change on renewable groundwater resources: a global-scale assessment, Environ. Res. Lett., 4 (2009), 035006. https://doi.org/10.1088/1748-9326/4/3/035006 doi: 10.1088/1748-9326/4/3/035006
[2]	Y. Zhou, F. Zwahlen, Y. Wang, Y. Li, Impact of climate change on irrigation requirements in terms of groundwater resources, Hydrogeo. J., 18 (2010), 1571–1582. https://doi.org/10.1007/s10040-010-0627-8 doi: 10.1007/s10040-010-0627-8
[3]	S. M. Gorelick, C. Zheng, Global change and the groundwater management challenge, Water Res. Res., 51 (2018), 3031–3051. https://doi.org/10.1002/2014WR016825 doi: 10.1002/2014WR016825
[4]	Z. Huo, S. Feng, S. Kang, X. Mao, F. Wang, Numerically modelling groundwater in an arid area with ANN‐generated dynamic boundary conditions, Hydrol. Process., 25 (2011), 705–713. https://doi.org/10.1002/hyp.7858 doi: 10.1002/hyp.7858
[5]	P. Zhou, G. Li, Y. Lu, Numerical modeling of tidal effects on groundwater dynamics in a multi-layered estuary aquifer system using equivalent tidal loading boundary condition: case study in Zhanjiang, China, Environ. Earth Sci., 75 (2016), 117. https://doi.org/10.1007/s12665-015-5034-y doi: 10.1007/s12665-015-5034-y
[6]	P. C. Hsieh, H. T. Hsu, C. B. Liao, P. T. Chiueh, Groundwater response to tidal fluctuation and rainfall in a coastal aquifer, J. Hydrol., 521 (2015), 132–140. https://doi.org/10.1016/j.jhydrol.2014.11.069 doi: 10.1016/j.jhydrol.2014.11.069
[7]	P. C. Hsieh, J. L. Huang, M. C. Wu, Response of groundwater levels in a coastal aquifer to tidal waves and rainfall recharge, Water, 12 (2020), 625. https://doi.org/10.3390/w12030625 doi: 10.3390/w12030625
[8]	W. D. Welsh, Groundwater balance modelling with Darcy's Law, Ph.D. Thesis, Canberra: The Australian National University, 2007.
[9]	H. A. Basha, Traveling wave solution of the Boussinesq equation for groundwater flow in horizontal aquifers, Water Res. Res., 49 (2013), 1668–1679. https://doi.org/10.1002/wrcr.20168 doi: 10.1002/wrcr.20168
[10]	S. N. Rai, Modeling groundwater flow in unconfined aquifers, In: S. Basu, N. Kumar, Modelling and simulation of diffusive processes: methods and applications, Cham: Springer, 2014,187–210. https://doi.org/10.1007/978-3-319-05657-9_9
[11]	Q. Jiang, Y. Tang, A general approximate method for the groundwater response problem caused by water level variation, J. Hydrol., 529 (2015), 398–409. https://doi.org/10.1016/j.jhydrol.2015.07.030 doi: 10.1016/j.jhydrol.2015.07.030
[12]	S. Mohan, K. Sangeeta, Recharge estimation using infiltration models, ISH J. Hydraul. Eng., 11 (2005), 1–10. https://doi.org/10.1080/09715010.2005.10514796 doi: 10.1080/09715010.2005.10514796
[13]	D. Bui, A. Kawamura, T. Tong, H. Amaguchi, N. Nakagawa, Spatio-temporal analysis of recent groundwater-level trends in the Red River Delta, Vietnam, Hydrogeol. J., 20 (2012), 1635–1650. https://doi.org/10.1007/s10040-012-0889-4 doi: 10.1007/s10040-012-0889-4
[14]	H. Wang, J. E. Gao, M. J. Zhang, X. H. Li, S. L. Zhang, L. Z. Jia, Effects of rainfall intensity on groundwater recharge based on simulated rainfall experiments and a groundwater flow model, Catena, 127 (2015), 80–91. https://doi.org/10.1016/j.catena.2014.12.014 doi: 10.1016/j.catena.2014.12.014
[15]	M. C. Wu, P. C. Hsieh, Improved solutions to the linearized Boussinesq equation with temporally varied rainfall recharge for a sloping aquifer, Water, 11 (2019), 826. https://doi.org/10.3390/w11040826 doi: 10.3390/w11040826
[16]	M. C. Wu, P. C. Hsieh, Variation of groundwater flow caused by any spatiotemporally varied recharge, Water, 12 (2020), 287. https://doi.org/10.3390/w12010287 doi: 10.3390/w12010287
[17]	P. C. Hsieh, M. C. Wu, Changes in groundwater flow in an unconfined aquifer adjacent to a river under surface recharge, Hydrol. Sci. J., (2023) 920–937. https://doi.org/10.1080/02626667.2023.2193295 doi: 10.1080/02626667.2023.2193295
[18]	A. Upadhyaya, H. S. Chauhan, Interaction of stream and sloping aquifer receiving constant recharge, J. Irrig. Drain., 127 (2001), 295–301. https://doi.org/10.1061/(ASCE)0733-9437(2001)127:5(295) doi: 10.1061/(ASCE)0733-9437(2001)127:5(295)
[19]	P. W. Werner, On non-artesian groundwater flow, Geofis. Pura Appl., 25 (1953), 37–43. https://doi.org/10.1007/BF02014053 doi: 10.1007/BF02014053
[20]	P. W. Werner, Some problems in non‐artesian ground‐water flow, Eos Trans. Am. Geophy., 38, (1957), 511–518. https://doi.org/10.1029/TR038i004p00511 doi: 10.1029/TR038i004p00511
[21]	T. S. Zissis, I. S. Teloglou, G. A. Terzidis, Response of a sloping aquifer to constant replenishment and to stream varying water level, J. Hydrol., 243 (2001), 180–191. https://doi.org/10.1016/S0022-1694(00)00415-7 doi: 10.1016/S0022-1694(00)00415-7
[22]	A. Upadhyaya, H. S. Chauhan, Falling water tables in horizontal/sloping aquifer, J. Irrig. Drain. Eng., 127 (2001), 378–384. https://doi.org/10.1061/(ASCE)0733-9437(2001)127:6(378) doi: 10.1061/(ASCE)0733-9437(2001)127:6(378)
[23]	A. Upadhyaya, H. S. Chauhan, Water table rise in sloping aquifer due to canal seepage and constant recharge, J. Irrig. Drain. Eng., 128 (2002), 160–167. https://doi.org/10.1061/(ASCE)0733-9437(2002)128:3(160) doi: 10.1061/(ASCE)0733-9437(2002)128:3(160)
[24]	E. A. Sudicky, The Laplace transform Galerkin technique: a time‐continuous finite element theory and application to mass transport in groundwater, Water Res. Res., 25 (1989), 1833–1846. https://doi.org/10.1029/WR025i008p01833 doi: 10.1029/WR025i008p01833
[25]	E. A. Sudicky, R. G. McLaren, The Laplace transform Galerkin technique for large‐scale simulation of mass transport in discretely fractured porous formations, Water Res. Res., 28 (1992), 499–514. https://doi.org/10.1029/91WR02560 doi: 10.1029/91WR02560
[26]	K. Y. Kim, T. Kim, Y. Kim, N. C. Woo, A semi‐analytical solution for groundwater responses to stream‐stage variations and tidal fluctuations in a coastal aquifer, Hydrol. Process., 21 (2007), 665–674. https://doi.org/10.1002/hyp.6255 doi: 10.1002/hyp.6255
[27]	K. A. R. Kpegli, S. E. van der Zee, A. Alassane, G. Bier, M. Boukari, A. Leijnse, et al., Impact of hydraulic and storage properties on river leakage estimates: A numerical groundwater flow model case study from southern Benin, J. Hydrol., 19 (2018), 136–163. https://doi.org/10.1016/j.ejrh.2018.07.004 doi: 10.1016/j.ejrh.2018.07.004
[28]	L. Min, P. Y. Vasilevskiy, P. Wang, S. P. Pozdniakov, J. Yu, Numerical approaches for estimating daily river leakage from arid ephemeral streams, Water, 12 (2020), 499. https://doi.org/10.3390/w12020499 doi: 10.3390/w12020499
[29]	J. Bear, C. Braester, On the flow of two immscible fluids in fractured porous media, Dev. Soil Sci., 2 (1972), 177–202. https://doi.org/10.1016/S0166-2481(08)70538-5 doi: 10.1016/S0166-2481(08)70538-5
[30]	M. N. Özisik, Boundary value problems of heat conduction, New York: Dover Publications Inc., 1968.
[31]	A. Upadhyaya, H. S. Chauhan, Water table fluctuations due to canal seepage and time varying recharge, J. Hydrol., 244 (2001), 1–8. https://doi.org/10.1016/S0022-1694(00)00328-0 doi: 10.1016/S0022-1694(00)00328-0

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