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New Analytical Expressions for Two-Dimensional Aquifer Adjoining with Streams of Varying Water Level

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Abstract

This research presents new analytical expressions to analyze interactions between streams of varying water level and a confined aquifer. The stream water level is assumed to vary exponentially with time. The expressions are obtained by means of Laplace and Fourier transform methods and the results are verified with those obtained from MODFLOW. In fact, we derive a new analytical expression for predicting of the groundwater level and flow rate in a confined aquifer between two streams of varying water level at the north and the right boundaries and two constant head boundaries at the left and the south ends. Also, a numerical example is used to investigate about the aquifer response to stream water level changes. Therefore the effects of variation water level of each stream on the flow rate at the left and the south boundaries and also at four points of the aquifer are discussed. Finally, some other new analytical expressions are also deduced for other types of boundary conditions.

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References

  • Bansal RK (2012) Groundwater fluctuations in sloping aquifers induced by time-varying replenishment and seepage from a uniformly rising stream. Transp Porous Media 94:817–836. doi:10.1007/s11242-012-0026-9

    Article  Google Scholar 

  • Bansal R, Das S (2009a) Analytical solution for transient hydraulic head, flow rate and volumetric exchange in an aquifer under recharge condition. J Hydrol Hydromech 57:113–120. doi:10.2478/v10098-009-0010-4

    Article  Google Scholar 

  • Bansal RK, Das SK (2009b) Effects of bed slope on water head and flow rate at the interfaces between the stream and groundwater: analytical study. J Hydrol Eng 14:832–838. doi:10.1061/(ASCE)HE.1943-5584.0000048

    Article  Google Scholar 

  • Bansal RK, Das SK (2010a) Analytical study of water table fluctuation in unconfined aquifers due to varying bed slopes and spatial location of the recharge basin. J Hydrol Eng 15:909–917. doi:10.1061/(ASCE)HE.1943-5584.0000267

    Article  Google Scholar 

  • Bansal RK, Das SK (2010b) Water table fluctuations in a sloping aquifer: analytical expressions for water exchange between stream and groundwater. J Porous Media 13:365–374

    Article  Google Scholar 

  • Bansal RK, Das SK (2011) Response of an unconfined sloping aquifer to constant recharge and seepage from the stream of varying water level. Water Resour Manag 25:893–911. doi:10.1007/s11269-010-9732-7

    Article  Google Scholar 

  • Bansal RK, Lande CK, Warke A (2016) Unsteady groundwater flow over sloping beds: analytical quantification of stream–aquifer interaction in presence of thin vertical clogging layer. J Hydrol Eng 04016017:1–15. doi:10.1061/(ASCE)HE.1943-5584.0001362

    Google Scholar 

  • Barthel R, Banzhaf S (2016) Groundwater and surface water interaction at the regional-scale–A review with focus on regional integrated models. Water Resour Manag 30:1–32. doi:10.1007/s11269-015-1163-z

    Article  Google Scholar 

  • Benedini M, Tsakiris G (2013) Progress in numerical modelling: the finite difference method. In: Water Quality Modelling for Rivers and Streams. Springer, pp 125–148

  • Bobba AG (2012) Ground Water-Surface Water Interface (GWSWI) modeling: recent advances and future challenges. Water Resour Manag 26:4105–4131. doi:10.1007/s11269-012-0134-x

    Article  Google Scholar 

  • Boufadel MC, Peridier V (2002) Exact analytical expressions for the piezometric profile and water exchange between stream and groundwater during and after a uniform rise of the stream level. Water Resour Res 38:27.1–27.6. doi:10.1029/2001WR000780

    Article  Google Scholar 

  • Brown JW, Churchill RV, Lapidus M (1996) Complex variables and applications, vol 7. McGraw-Hill New York

  • Chen X, Chen X (2003) Stream water infiltration, bank storage, and storage zone changes due to stream-stage fluctuations. J Hydrol 280:246–264. doi:10.1016/S0022-1694(03)00232-4

    Article  Google Scholar 

  • Cooper HH, Rorabaugh MI (1963) Ground-water movements and bank storage due to flood stages in surface streams. US Government Printing Office

  • Dever RJ, Cleary RW (1979) Unsteady-state, two-dimensional response of leaky aquifers to stream stage fluctuations. Adv Water Resour 2:13–18. doi:10.1016/0309-1708(79)90002-2

    Article  Google Scholar 

  • Fen C-S, Yeh H-D (2012) Effect of well radius on drawdown solutions obtained with Laplace transform and Green’s function. Water Resour Manag 26:377–390. doi:10.1007/s11269-011-9922-y

    Article  Google Scholar 

  • Ferris JG (1952) Cyclic fluctuations of water level as a basis for determining aquifer transmissibility. US Geol Surv. doi:10.3133/70133368

    Google Scholar 

  • Ghosh NC et al (2015) Semi-analytical model for estimation of unsteady seepage from a large water body influenced by variable flows. Water Resour Manag 29:3111–3129. doi:10.1007/s11269-015-0985-z

    Article  Google Scholar 

  • Gill MA (1985) Bank storage characteristics of a finite aquifer due to sudden rise and fall of river level. J Hydrol 76:133–142. doi:10.1016/0022-1694(85)90094-0

    Article  Google Scholar 

  • Hall FR, Moench AF (1972) Application of the convolution equation to stream‐aquifer relationships. Water Resour Res 8:487–493. doi:10.1029/WR008i002p00487

    Article  Google Scholar 

  • Hantush MS (1967) Flow of groundwater in relatively thick leaky aquifers. Water Resour Res 3:583–590. doi:10.1029/WR003i002p00583

    Article  Google Scholar 

  • Intaraprasong T (2007) Stream aquifer interactions: analytical solution to estimate stream depletions caused by stream stage fluctuations and pumping wells near streams. Dissertation, Texas A&M University

  • Kalin L, Govindaraju R, Parlange J-Y (2000) Steady-state analysis of water movement in a semi-infinite unconfined aquifer under constant accretion. Transp Porous Media 40:165–169. doi:10.1023/A:1006652007287

    Article  Google Scholar 

  • Katsifarakis K (2008) Groundwater pumping cost minimization–an analytical approach. Water Resour Manag 22:1089–1099. doi:10.1007/s11269-007-9212-x

    Article  Google Scholar 

  • Kim KY, Kim T, Kim Y, Woo NC (2007) A semi‐analytical solution for groundwater responses to stream‐stage variations and tidal fluctuations in a coastal aquifer. Hydrol Process 21:665–674. doi:10.1002/hyp.6255

    Article  Google Scholar 

  • Lal AW (2001) Modification of canal flow due to stream-aquifer interaction. J Hydraul Eng 127:567–576. doi:10.1061/(ASCE)0733-9429(2001)127:7(567)

    Article  Google Scholar 

  • Liang X, Zhang Y-K (2012) A new analytical method for groundwater recharge and discharge estimation. J Hydrol 450:17–24. doi:10.1016/j.jhydrol.2012.05.036

    Article  Google Scholar 

  • Mahdavi A (2015) Transient-state analytical solution for groundwater recharge in anisotropic sloping aquifer. Water Resour Manag 29:3735–3748. doi:10.1007/s11269-015-1026-7

    Article  Google Scholar 

  • Mahdavi A, Seyyedian H (2013) Transient-state analytical solution for groundwater recharge in triangular-shaped aquifers using the concept of expanded domain. Water Resour Manag 27:2785–2806. doi:10.1007/s11269-013-0315-2

    Article  Google Scholar 

  • Manglik A, Rai S (2015) Modeling water table fluctuations in anisotropic unconfined aquifer due to time varying recharge from multiple heterogeneous basins and pumping from multiple wells. Water Resour Manag 29:1019–1030. doi:10.1007/s11269-014-0857-y

    Article  Google Scholar 

  • Manglik A, Rai S, Singh V (2013) A generalized predictive model of water table fluctuations in anisotropic aquifer due to intermittently applied time-varying recharge from multiple basins. Water Resour Manag 27:25–36. doi:10.1007/s11269-012-0136-8

    Article  Google Scholar 

  • Mas-Pla J, Menció A, Marsiñach A (2013) Basement groundwater as a complementary resource for overexploited stream-connected alluvial aquifers. Water Resour Manag 27:293–308. doi:10.1007/s11269-012-0186-y

    Article  Google Scholar 

  • Moench A, Barlow P (2000) Aquifer response to stream-stage and recharge variations. I. Analytical step-response functions. J Hydrol 230:192–210. doi:10.1016/S0022-1694(00)00175-X

    Article  Google Scholar 

  • Moutsopoulos KN (2013) Solutions of the Boussinesq equation subject to a nonlinear Robin boundary condition. Water Resour Res 49:7–18. doi:10.1029/2012WR012221

    Article  Google Scholar 

  • Mylopoulos N, Mylopoulos Y, Tolikas D, Veranis N (2007) Groundwater modeling and management in a complex lake-aquifer system. Water Resour Manag 21:469–494. doi:10.1007/s11269-006-9025-3

    Article  Google Scholar 

  • Pérez-Martín MA, Estrela T, Andreu J, Ferrer J (2014) Modeling water resources and river-aquifer interaction in the Júcar River Basin, Spain. Water Resour Manag 28:4337–4358. doi:10.1007/s11269-014-0755-3

    Article  Google Scholar 

  • Pistiner A (2008) Similarity solution to unconfined flow in an aquifer. Transp Porous Media 71:265–272. doi:10.1007/s11242-007-9124-5

    Article  Google Scholar 

  • Pistiner A (2011) An analytical solution for unsteady flow in a phreatic aquifer in the case of continuous rise. Transp Porous Media 86:815–825. doi:10.1007/s11242-010-9655-z

    Article  Google Scholar 

  • Pulido‐Velazquez D, Sahuquillo A, Andreu J, Pulido‐Velazquez M (2007) An efficient conceptual model to simulate surface water body‐aquifer interaction in conjunctive use management models. Water Resour Res 43, W07407. doi:10.1029/2006WR005064

    Google Scholar 

  • Pulido‐Velazquez D, Sahuquillo A, Andreu J (2012) A conceptual–numerical model to simulate hydraulic head in aquifers that are hydraulically connected to surface water bodies. Hydrol Process 26:1435–1448. doi:10.1002/hyp.8214

    Article  Google Scholar 

  • Rai S, Manglik A (2012) An analytical solution of Boussinesq equation to predict water table fluctuations due to time varying recharge and withdrawal from multiple basins, wells and leakage sites. Water Resour Manag 26:243–252. doi:10.1007/s11269-011-9915-x

    Article  Google Scholar 

  • Saeedpanah I, Jabbari E, Shayanfar M (2011) Numerical simulation of ground water flow via a new approach to the local radial point interpolation meshless method. Int J Comput Fluid D 25:17–30. doi:10.1080/10618562.2010.545772

    Article  Google Scholar 

  • Safavi HR, Esmikhani M (2013) Conjunctive use of surface water and groundwater: application of support vector machines (SVMs) and genetic algorithms. Water Resour Manag 27:2623–2644. doi:10.1007/s11269-013-0307-2

    Article  Google Scholar 

  • Sophocleous M (2002) Interactions between groundwater and surface water: the state of the science. Hydrogeol J 10:52–67. doi:10.1007/s10040-001-0170-8

    Article  Google Scholar 

  • Sparks TD, Bockelmann-Evans BN, Falconer RA (2013) Development and analytical verification of an integrated 2-D surface water—Groundwater model. Water Resour Manag 27:2989–3004. doi:10.1007/s11269-013-0327-y

    Article  Google Scholar 

  • Teloglou IS, Bansal RK (2012) Transient solution for stream–unconfined aquifer interaction due to time varying stream head and in the presence of leakage. J Hydrol 428:68–79. doi:10.1016/j.jhydrol.2012.01.024

    Article  Google Scholar 

  • Tsakiris G, Alexakis D (2014) Karstic spring water quality: the effect of groundwater abstraction from the recharge area. Desalin Water Treat 52:2494–2501. doi:10.1080/19443994.2013.800253

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Civil Engineering, Faculty of Engineering, University of Zanjan, University Blvd., Zip Code 45371-38791, Zanjan, Iran

    Iraj Saeedpanah & Ramin Golmohamadi Azar

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  1. Iraj Saeedpanah
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  2. Ramin Golmohamadi Azar
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Correspondence to Iraj Saeedpanah.

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Saeedpanah, I., Golmohamadi Azar, R. New Analytical Expressions for Two-Dimensional Aquifer Adjoining with Streams of Varying Water Level. Water Resour Manage 31, 403–424 (2017). https://doi.org/10.1007/s11269-016-1533-1

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  • DOI: https://doi.org/10.1007/s11269-016-1533-1

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