Water Science and Engineering 2020, 13(3) 243-252 DOI:   https://doi.org/10.1016/j.wse.2020.09.004  ISSN: 1674-2370 CN: 32-1785/TV

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Hydraulic conductivity
Parameter inversion
Successive linear estimator
Correlation scale error
Observation well number
Pumping test number

Influence of correlation scale errors on aquifer hydraulic conductivity inversion precision

Yun-xiao Mu a,b, Lei Zhu a,b,*, Tong-qing Shen a,b, Meng Zhang a,b, Yuan-yuan Zha c  

a School of Civil Engineering and Water Conservancy, Ningxia University, Yinchuan 750021, China
b Engineering Research Center for Efficient Utilization of Modern Agricultural Water Resources in Arid Regions, Ministry of Education, Yinchuan 750021, China
c State Key Laboratory of Water Resources and Hydropower Engineering Science, Wuhan University, Wuhan 430072, China


In order to investigate the influence of correlation scale error on the inversion precision of the hydraulic conductivity of the aquifer, the successive linear estimator (SLE) was used to invert the hydraulic conductivity field of a heterogeneous aquifer based on synthetic experiments. By increasing the numbers of observation wells and pumping tests, we analyzed the difference between the estimated and true values of hydraulic conductivity with different correlation scale errors. The relationships between the observation well number and the error in inversion results, and between the pumping test number and the error in inversion results were investigated. The results show that, if the amount of observed head data is insufficient, there will be errors in inversion results with changing correlation scale. Due to the existence of correlation scale error, the improvement of inversion precision gradually slows down with the increase of the amount of observed head data, which indicates that too much observed head data causes data redundancy. Therefore, for the synthetic experiments described in this paper, the observation well number should be less than 41, the pumping test number should be less than 17, and a more suitable method should be selected according to the precision requirements of specific situations in practical engineering.

Keywords Hydraulic conductivity   Parameter inversion   Successive linear estimator   Correlation scale error   Observation well number   Pumping test number  
Received 2019-07-11 Revised 2020-02-16 Online: 2020-09-30 
DOI: https://doi.org/10.1016/j.wse.2020.09.004

This work was supported by the National Natural Science Foundation of China (Grants No. 51879134 and 51569023) and the First-class Discipline Construction Funding Project for the Ningxia University of China (Hydraulic Engineering) (Grant No. NXYLXK2017A03).

Corresponding Authors: Lei Zhu
Email: nxuzhulei@163.com
About author:


Bohling, G.C., Zhan, X.Y., Butler Jr., J., Zheng, L., 2002. Steady shape analysis of tomographic pumping tests for characterization of aquifer heterogeneities. Water Resources Research. 38(12), 60-1-60-15. https://doi.org/10.1029/2001WR001176.

Cardiff, M., Barrash, W., 2011. 3-D transient hydraulic tomography in unconfined aquifers with fast drainage response. Water Resources Research. 47(12), W12518. https://doi.org/10.1029/2010WR010367.

Chen, X.L., Dong, H.Z., Chang, P., 2014. The heterogeneity of aquifer is characterized by steady flow hydraulic tomography. Frozen Ground and Foundation. 36(11), 83-85 (in Chinese). https://doi.org/10.13905/j.cnki.dwjz.2014.11.030.

Dong, Y.H., Li, G.M., Zhao, C.H., Ye, S.D., 2009. The heterogeneity of aquifer is characterized by hydraulic tomography. Engineering Investigation. 39(12), 58-61 (in Chinese).

Hanna, S., Yeh, T.-C.J., 1998. Estimation of co-conditional moments of transmissivity head and velocity fields. Advances in Water Resources. 22(1), 87-93. https:// doi.org/10.1016/s0309-1708(97)00033-x.

Hao, Y.H., Ye, T.Q., Han, B.P., Xiang, J.W., Zhu, F., Ni, C.F., 2008. The fracture zone of the aquifer is imaged by hydraulic tomography. Hydrogeology Engineering Geology. 35(6), 6-11 (in Chinese). https://doi.org/10.16030/j.cnki.issn. 1000-3665.2008.06.003.

Hoeksema, R.J., Kitanidis, P.K., 1984. An application of the geostatistical approach to the inverse problem in two dimensional groundwater modeling. Water Resources Research. 20(7), 1003-1020. https://doi.org/10.1029/WR020i007p01003.

Hughson, D.L., Yeh, T.-C.J., 2000. An inverse model for three-dimensional flow in variably saturated porous media. Water Resources Research. 36(4), 829-839. https://doi.org/10.1029/2000wr900001.

Illman, W.A., Liu, X., Craig, A., 2007. Steady-state hydraulic tomography in a laboratory aquifer with deterministic heterogeneity: Multimethod and multiscale validation of hydraulic conductivity tomography. Journal of Hydrology. 341(3), 222-234. https://doi.org/10.1016/j.jhydrol.2007.05.011.

Jiang, L.Q., Sun, R.L., Wang, W.M., Wang, J.S., 2017. Comparison of permeability field between hydraulic chromatography and kriging method for estimating heterogeneous aquifer. Earth Science. 42(2), 307-314 (in Chinese). https://doi.org/10.3799/dqkx.2017.023.

Jimenez, S., Brauchler, R., Bayer, P., 2013. A new sequential procedure for hydraulic tomographic inversion. Advances in Water Resources. 62, 59-70. https://doi.org/10.1016/j.advwatres.2013.10.002.

Kitanidis, P.K., Vomvoris, E.G.., 1983. A geostatistical approach to the inverse problem in groundwater modeling (steady state) and one-dimensional simulations. Water Resources Research. 19(3), 677-690. https://doi.org/10.1029/WR019i003p00677.

Liu, S.Y., Yeh, T.-C.J., Gardiner, R., 2002. Effectiveness of hydraulic tomography: Sandbox experiments. Water Resources Research. 38(4). 5-15-9. https://doi.org/10.1029/2001WR000338.

Tang, Y.Q., Shi, L.S., Yang, J.Z., 2012. Simulation of saturated and unsaturated water flow based on random collocation method. Journal of Sichuan University. 44(5), 30-37 (in Chinese). https://doi.org/10.15961/j.jsuese.2012. 05.006.

Xiang, J.W., Yeh, T.-C.J., Lee, C.H., Hsu, K.C., Wen, J.C., 2009. A simultaneous successive linear estimator and a guide for hydraulic tomography analysis. Water Resources Research. 45(2), W02432. https://doi.org/10.1029/2008WR007180.

Ye, T.Q., 2017. Advanced Groundwater Hydraulics. Geological Press, Beijing (in Chinese).

Yeh, T.-C.J., Srivastava, R., Guzman, A., Harter, T.,1993. A numerical model for water flow and chemical transport in variably saturated porous media. Ground Water. 31(4),634-644. https://doi.org/10.1111/j.1745-6584.1993.tb00597.x.

Yeh, T.-C.J., Gutjahr, A.L., Jin, M.H., 1995. An iterative cokriging-like technique for groundwater flow modeling. Ground Water. 33(1), 33-41. https://doi.org/10.1111/j.1745-6584.1995.tb00260.x.

Yeh, T.-C.J., Jin, M., Hanna, S., 1996. An iterative stochastic inverse method: Conditional effective transmissivity and head fields. Water Resources Research. 32(1), 85-92. https://doi.org/10.1029/95wr02869.

Yeh, T.-C.J., Liu, S.Y., 2000. Hydraulic tomography: Development of a new aquifer test method. Water Resources Research. 36(8), 2095-2105. https://doi.org/10.1029/2000wr900114.

Yeh, T.-C.J., Liu, S., Glass, R.J., Baker, K., Brainard, J.R., Alumbaugh, D., Labrecque, D., 2002. A geostatistically based inverse model for electrical resistivity surveys and its applications to vadose zone hydrology. Water Resources Research. 38(12), 1278. https://doi.org/10.1029/ 2001WR001204.

Zhang, J.Q., Yeh, T.-C.J., 1997. An iterative geostatistical inverse method for steady flow in the vadose zone. Water Resources Research. 33(1), 63-71. https://doi.org/10.1029/96wr02589.

Zha, Y., Yeh, T.-C. J., Illman, W.A., Tanaka, T., Bruines, P., Onoe, H., Saegusa, H., 2015. What does hydraulic tomography tell us about fractured geological media? A field study and synthetic experiments. Journal of Hydrology, 531(1), 17-30. https://doi.org/10.1016/j.jhydrol.2015.06.013.

Zha, Y., Yeh, T.-C. J., Illman, W. A., Tanaka, T., Bruines, P., Onoe, H., Saegusa, H., Mao, D., Takeuchi, S., Wen, J.-C., 2016. An application of hydraulic tomography to a large-scale fractured granite site, Mizunami, Japan. Groundwater, 54(6), 793-804. https://doi.org/10.1111/gwat.12421.

Zhao, Z.F., Illman, W.A., Yeh, T.-C.J., Berg, S.J., Mao, D.Q., 2015. Validation of hydraulic tomography in an unconfined aquifer: A controlled sandbox study. Water Resources Research. 51, 4137–4155. https://doi.org/10.1002/2015WR016910.

Zhu, J.F., Yeh, T.-C.J., 2005. Characterization of aquifer heterogeneity using transient hydraulic tomography. Water Resources Research. 41(7), W07028. https://doi.org/10.1029/2004WR003790.

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