Abstract
Hantush’s model is widely used for predicting rise in water table in response to groundwater recharge. Several approximate methods of the Hantush mound function, S(α, β) have been developed to overcome the limitations of Hantush’s tabulated values of the S(α, β) function. These approximate methods have their own advantages and disadvantages, and it is difficult to identify the most accurate and computationally efficient S(α, β) estimation method. In this study, performance of four different algebraic approximate S(α, β) estimation methods are compared with the Hantush method using the published data. The four different methods considered are Swamee and Ohja (1997) (SO), Singh (2012) (SI), Vatankhah (2013) (VA) and Gauss-Legendre quadrature (GL) method with various Gaussian points (GP). Seven statistical accuracy and computation efficiency indicators are used to assess the performance of different S(α, β) estimation methods. The GL method with 100 to16 GPs is found to be the most accurate S(α, β) estimation method. This is followed by the SO, GL with 14 to 12 GPs, VA, GL with 10 GP, SI, and GL with 9 to 3 GPs. A good trade off between accuracy and efficiency is found with the SO, VA, and GL method with 14, 12 and 10 GPs. Comprehensive analysis of different S(α, β) estimation methods, and their ranking based on overall performance index will be helpful in modelling water table rise due to groundwater recharge, optimum design of recharge basin, and evaluation of effectiveness of recharge basins in groundwater recharging.
Similar content being viewed by others
References
Abramowitz M, Stegun IA (1972) Handbook of mathematical functions. National Bureau of Standards, Washington, D.C.
Aish AM (2010) Simulation of groundwater mound resulting from proposed artificial recharge of treated sewage effluent case study-Gaza waste water treatment plant, Palestine. Geol Groat 63(1):67–73. https://doi.org/10.4154/GC.2010.04
Ali S (2009) Study of artificial groundwater recharge from a pond in a small watershed. Unpublished Ph. D. Thesis, Indian Institute of Technology Roorkee, Roorkee, India, 173p
Ali S, Ghosh NC, Singh R, Sethy BK (2013) Generalized explicit models for estimation of wetting front length and potential recharge. Water Resour Manag 27:2429–2445. https://doi.org/10.1007/s11269-013-0295-2
Ali S, Islam A, Mishra PK, Sikka AK (2016) Green-Ampt approximations: a comprehensive analysis. J Hydrol 535:340–355. https://doi.org/10.1016/j.hydrol.2016.01.065
Allen EE (1954) Analytical approximations. Math Tables Aids Comp 55(8):162–164
Asano T, Burton F, Leverenz H, Tsuchihashi R, Tchobanoglous G (2006) Water reuse: issues, technologies, and applications. Metcalf and Eddy, New York
Baumann P (1952) Groundwater movement controlled through spreading. Trans ASCE 117(1):1024–1060
Bianchi WC, Haskell JR (1975) Field observations of transient groundwater mounds produced by artificial recharge into an unconfined aquifer. USDA, Agr Res Serv Report No ARS W-27, 27p
Bianchi WC, Muckel DC (1970) Groundwater recharge hydrology. ARS 41–161, USDA, 62 p
Bouwer H (2002) Artificial recharge of groundwater: hydrogeology and engineering. Hydrogeol J 10:121–142. https://doi.org/10.1007/s10040-001-0182-4
Brock RR, Amar AC (1974) Groundwater recharge strip basin experiments. J Hydraul Div ASCE:569–592
Carleton GB (2010) Simulation of groundwater mounding beneath hypothetical storm water infiltration basins. US Geol Surv Sci Investig Rep 2010–5102, 64p. http://store.usgs.gov. Accessed 15 September 2015
Chaudhary M, Chahar B (2007) Recharge seepage from an array of rectangular channels. J Hydrol 343:71–79. https://doi.org/10.1016/j.hydrol.2007.06.009
Chipongo K, Khiadani M (2015) Comparison of simulation methods for recharge mounds under rectangular basins. Water Resour Manag 29:2855–2874. https://doi.org/10.1007/s11269-015-0974-2
Evans G (1993) Practical numerical integration. Wiley, Chichester, p 328p
Finnemore EJ (1995) A program to calculate ground-water mound heights. Ground Water 33(1):139–143. https://doi.org/10.1111/j.1745-6584.1995.tb00269.x
Glover RE (1960) Mathematical derivations pertain to groundwater recharge. Agricultural Research Service, USDA, Colorado
Hantush MS (1967) Growth and decay of groundwater mounds in response to uniform percolation. Water Resour Res 3:227–234. https://doi.org/10.1029/WR003i001p00227
Hastings C Jr (1955) Approximations for digital computers. Princeton, Priceton University Press
Latinopoulos P (1986) Analytical solutions for strip basin recharge to aquifers with Cauchy boundary conditions. J Hydrol 83:197–206. https://doi.org/10.1016/0022-1694(86)90151-4
Legates DR, McCabe GJ (1999) Evaluating the use of “goodness-of-fit” measures in hydrologic and hydroclimatic model validation. Water Resour Res 35(1):233–241. https://doi.org/10.1029/1998WR900018
Marino MA (1967) Hele-Shaw model study of the growth and decay of groundwater ridges. J Geophysics Res 72:1195–1205
Marmion KR (1962) Hydraulics of artificial recharge in non-homogeneous formations. Water Resources Centre Contribution, 48, Univ of California, Berkeley, Calif. 88p
Molden D, Sunada DK, Warner JW (1984) Microcomputer modeling of artificial recharge using Glover’s solution. Ground Water 22(1):73–79. https://doi.org/10.1111/j.1745-6584.1984.tb01478.x
Moriasi DN, Gitau MW, Pai N, Daggupati P (2015) Hydrologic and water quality models: performance measures and evaluation criteria. Trans ASABE 58(6):1763–1785. https://doi.org/10.13031/trans.58.10715
Nash JE, Sutcliffe JE (1970) River flow forecasting through conceptual model. J Hydrol 10:282–290. https://doi.org/10.1016/0022-1694(70)90255-6
Pliakas F, Petalas C, Diamantis I, Kallioras A (2005) Modeling of groundwater artificial recharge by reactivating an old stream bed. Water Resour Manag 19(3):279–294. https://doi.org/10.1007/s11269-005-3472-0
Rao NH, Sarma PBS (1981) Groundwater recharge from rectangular areas. Ground Water 19(3):270–274. https://doi.org/10.1111/j.1745-6584.1981.tb03470.x
Saran S, Swamee PK, Singh KK (1977) Computer programming and numerical models. Saritha Prakashan, New Delhi
Schmidtke KD (1980) Stochastic estimation and prediction of states in unconfined aquifer subject to artificial recharge. M A Sc thesis, Univ of Waterloo, Waterloo, Ont
Schmidtke KD, McBea EA, Sykes J (1982) Stochastic estimation of states in unconfined aquifer subject to artificial recharge. Water Resour Res 18(5):15–19-1530. https://doi.org/10.1029/WR018i005p01519
Singh SK (2012) Groundwater mound due to artificial recharge from rectangular areas. J Irrig Drain Eng 138(5):476–480. https://doi.org/10.1061/(ASCE)IR.1943-4774.0000427
Sumner DM, Rolston DE, Marino MA (1999) Effects of unsaturated zone on ground-water mounding. J Hydrol Eng 4(1):66–69. https://doi.org/10.1061/(ASCE)1084-0699(1999)4:1(65)
Swamee PK, Ohja CSP (1997) Ground-water mound equation for rectangular recharge area. J Irrig Drain Eng 123(3):215–218. https://doi.org/10.1061/(ASCE)0733-9437(1997)123:3(215)
Todd DK (1980) Groundwater hydrology, 2nd edn. Wiley, New York, p 535p
Vatankhah A (2013) Discussion of groundwater mound due to artificial recharge from rectangular areas. by Sunil K. Singh. J Irrig Drain Eng 10.1061 /(ASCE) IR. 1943–4774.0000555
Warner JW, Molden D, Chehata M, Sunada DK (1989) Mathematical analysis of artificial recharge. Water Resour Res 25:401–411. https://doi.org/10.1111/j.1752-1688.1989.tb03077.x
Welton WC (1970) Groundwater resources evaluation. McGraw hill Book Co, Inc, New York, p 664p
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Ali, S., Islam, A. Evaluation of Hantush’s S Function Estimation Methods for Predicting Rise in Water Table. Water Resour Manage 33, 2239–2260 (2019). https://doi.org/10.1007/s11269-019-02272-1
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11269-019-02272-1