Water Science and Engineering 2017, 10(1) 25-35 DOI:   http://dx.doi.org/10.1016/j.wse.2017.03.009  ISSN: 1674-2370 CN: 32-1785/TV

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Keywords
Data assimilation
Hydraulic parameter estimation
Ensemble H-infinity filter
Ensemble Kalman filter
Hydraulic conductivity
Robustness
Authors
Tong-chao Nan
Ji-chun Wu
PubMed
Article by Tong-chao Nan
Article by Ji-chun Wu

Application of ensemble H-infinity filter in aquifer characterization and comparison to ensemble Kalman filter

Tong-chao Nan a,b, Ji-chun Wu a,b,*

aState Key Laboratory of Pollution Control and Resources Reuse, Nanjing University, Nanjing 210093, China
bDepartment of Hydrosciences, School of Earth Sciences and Engineering, Nanjing University, Nanjing 210093, China

Abstract

Though the ensemble Kalman filter (EnKF) has been successfully applied in many areas, it requires explicit and accurate model and measurement error information, leading to difficulties in practice when only limited information on error mechanisms of observational instruments for subsurface systems is accessible. To handle the uncertain errors, we applied a robust data assimilation algorithm, the ensemble H-infinity filter (EnHF), to estimation of aquifer hydraulic heads and conductivities in a flow model with uncertain/correlated observational errors. The impacts of spatial and temporal correlations in measurements were analyzed, and the performance of EnHF was compared with that of the EnKF. The results show that both EnHF and EnKF are able to estimate hydraulic conductivities properly when observations are free of error; EnHF can provide robust estimates of hydraulic conductivities even when no observational error information is provided. In contrast, the estimates of EnKF seem noticeably undermined because of correlated errors and inaccurate error statistics, and filter divergence was observed. It is concluded that EnHF is an efficient assimilation algorithm when observational errors are unknown or error statistics are inaccurate.

Keywords Data assimilation   Hydraulic parameter estimation   Ensemble H-infinity filter   Ensemble Kalman filter   Hydraulic conductivity   Robustness  
Received 2016-10-11 Revised 2017-01-02 Online: 2017-01-31 
DOI: http://dx.doi.org/10.1016/j.wse.2017.03.009
Fund:

This work was supported by the National Natural Science Foundation of China (Grant No. 41602250), and the Project of Hydrogeological Investigation at a 1:50 000 Scale in the Lake-Concentrated Areas of the Northern Ordos Basin of the China Geological Survey (Grant No. DD20160293).

Corresponding Authors: Ji-chun Wu
Email: jcwu@nju.edu.cn
About author:

References:

Assumaning, G.A., Chang, S.Y., 2016. Application of sequential data-assimilation techniques in groundwater contaminant transport modeling. Journal of Environmental Engineering 142(2), 01015073. http://dx.doi.org/10.1061/(ASCE)EE.1943-7870.0001034.
Carrera, J., Neuman, S.P., 1986.Estimation of aquifer parameters under transient and steady state conditions: 2. Uniqueness, stability, and solution algorithms. Water Resources Research 22(2), 211−227. http://dx.doi.org/10.1029/WR022i002p00211.
Chen, L., Kang, Q.J., Mu, Y.T., He, Y.L., Tao, W.Q., 2014. A critical review of the pseudopotential multiphase lattice Boltzmann model: Methods and applications. International Journal of Heat and Mass Transfer 76, 210−236. http://dx.doi.org/10.1016/j.ijheatmasstransfer.2014.04.032.
Chen, Y., Zhang, D.X., 2006. Data assimilation for transient flow in geologic formations via ensemble Kalman filter. Advances in Water Resources 29(8), 1107−1122. http://dx.doi.org/10.1016/j.advwatres.2005.09.007.
Chung, C.C., Lin, C.P., 2009. Apparent dielectric constant and effective frequency of TDR measurements: Influencing factors and comparison. Vadose Zone Journal 8(3), 548−556. http://dx.doi.org/10.2136/vzj2008.0089.
Deng, Z.H., 2013. Robust finite-time H-infinity filtering for uncertain systems subject to missing measurements. Journal of Inequalities and Applications 236. http://dx.doi.org/10.1186/1029-242X-2013-236.
Deutsch, C., Journel, A., 1998. GSLIB: Geostatistical Software LIBrary and User’s Guide, Second ed. Oxford University Press, New York.
Dou, Z., Zhou, Z.F., 2014. Lattice Boltzmann simulation of solute transport in a single rough fracture. Water Science and Engineering 7(3), 277−287. http://dx.doi.org/10.3882/j.issn.1674-2370.2014.03.004.
Essaid, H.I., Bekins, B.A., Cozzarelli, I.M., 2015. Organic contaminant transport and fate in the subsurface: Evolution of knowledge and understanding. Water Resources Research 51(7), 4861–4902. http://dx.doi.org/10.1002/2015WR017121.
Evensen, G., 2003. The ensemble Kalman filter: Theoretical formulation and practical implementation. Ocean Dynamics 53(4), 343−367. http://dx.doi.org/10.1007/s10236-003-0036-9.
Franssen, H.J.H., Kinzelbach, W., 2008. Real-time groundwater flow modeling with the ensemble Kalman filter: Joint estimation of states and parameters and the filter inbreeding problem. Water Resources Research 44(9), W09408. http://dx.doi.org/10.1029/2007WR006505.
Han, Y.Q., Zhang, Y.C., Wang, Y.F., Ye, S., Fang, H.X., 2009. A new sequential data assimilation method. Science in China Series E: Technological Sciences 52(4), 1027−1038. http://dx.doi.org/10.1007/s11431-008-0189-3.
Harbaugh, A.W., Banta, E.R., Hill, M.C., McDonald, M.G., 2000. MODFLOW-2000, the U.S. Geological Survey Modular Ground-water Model: User Guide to Modularization Concepts and the Ground-water Flow Process, Open-File Rep 00-92. U.S. Geological Survey, Reston.
Hassibi, B., Kailath, T., Sayed, A.H., 2000. Array algorithms for H∞ estimation. IEEE Transactions on Automatic Control 45(4), 702−706. http://dx.doi.org/10.1109/9.847105.
Khargonekar, P.P., Nagpal, K.M., 1991. Filtering and smoothing in an H∞ setting. IEEE Transactions on Automatic Control 36(2), 152−166. http://dx.doi.org/10.1109/9.67291.
Lü, H.S., Li, X.L., Yu, Z.B., Horton, R., Zhu, Y.H, Hao, Z.C., Xiang, L., 2010. Using a H-infinity filter assimilation procedure to estimate root zone soil water content. Hydrological Processes 24(25), 3648−3660. http://dx.doi.org/10.1002/hyp.7778.
Luo, X.D., Hoteit, I., 2011. Robust ensemble filtering and its relation to covariance inflation in the ensemble Kalmanfilter. Monthly Weather Review 139, 3938−3953. http://dx.doi.org/10.1175/MWR-D-10-05068.1.
McLaughlin, D., Townley, L.R., 1996. A reassessment of the groundwater inverse problem. Water Resources Research 32(5), 1131−1161. http://dx.doi.org/10.1029/2006WR005144.
Nan, T.C., Wu, J.C., 2011. Groundwater parameter estimation using the ensemble Kalman filter with localization. Hydrogeology Journal 19(3), 547−561. http://dx.doi.org/10.1007/s10040-010-0679-9.
National Research Council, 2013. Alternatives for Managing the Nation's Complex Contaminated Groundwater Sites. The National Academies Press, Washington, D.C.
Panzeri, M., Riva, M., Guadagnini, A., Neuman, S.P., 2013. Data assimilation and parameter estimation via ensemble Kalman filter coupled with stochastic moment equations of transient groundwater flow. Water Resources Research 49(3), 1334−1344. http://dx.doi.org/10.1002/wrcr.20113.
Rubin, Y., Hubbard, S.S., 2007. Hydrogeophysics. Springer, Dordrecht.
Shaked, U., 1990. H∞ minimum error state estimation of linear stationary processes. IEEE Transactions on Automatic Control 35(5), 554−558. http://dx.doi.org/10.1109/9.53521.
Shaked, U., Theodor, Y., 1992. H∞ optimal estimation: A tutorial. In: Proceedings of the 31st IEEE Conference on Decision and Control, IEEE, Tucson, pp. 2278-2286.
Sun, A.Y., Morris, A.P., Mohanty, S., 2009. Comparison of deterministic ensemble Kalman filters for assimilating hydrogeological data. Advances in Water Resources 32(2), 280−292. http://dx.doi.org/10.1016/j.advwatres.2008.11.006.
Tian, Z.C., Li, Z.Z., Liu, G., Li, B.G, Ren, T.S., 2016. Soil water content determination with cosmic-ray neutron sensor: Correcting aboveground hydrogen effects with thermal/fast neutron ratio. Journal of Hydrology 540, 923−933. http://dx.doi.org/10.1016/j.jhydrol.2016.07.004.
Tong, J.X., Yang, J.Z., Hu, B.X., 2015. Analysis of soluble chemical transfer from soil to surface runoff and incomplete mixing parameter identification. Water Science and Engineering 8(3), 217−225. http://dx.doi.org/10.1016/j.wse.2015.04.011.
Wang, Y.F, Wang, B., Han, Y.Q., Zhu, M., Hou, Z.M., Zhou, Y., Liu, Y.D., Kou, Z., 2004. Variational data assimilation experiments of mei-yu front rainstorms in China. Advances in Atmospheric Sciences 21(4), 587−596. http://dx.doi.org/10.1007/BF02915726.
Yeh, T.J., Mao, D.Q, Zha, Y.Y, Wen, J.C, Wan, L., Hsu, K.C., Lee, C.H, 2015. Uniqueness, scale, and resolution issues in groundwater model parameter identification. Water Science and Engineering 8(3), 175−194. http://dx.doi.org/ 10.1016/j.wse.2015.08.002.
Yoneyama, J., 2013. Robust H-infinity filtering for sampled-data fuzzy systems. Fuzzy Sets and Systems, 217, 110−129. http://dx.doi.org/10.1016/j.fss.2012.08.014.
Yu, Z.B., Yang, T., Schwartz, F.W., 2014. Water issues and prospects for hydrological science in China. Water Science and Engineering 7(1), 1−4. http://dx.doi.org/10.3882/j.issn.1674-2370.2014.01.001.
Zhang, W.A., Dong, H., Guo, G., Yu, L., 2014. Distributed sampled-data H-infinity filtering for sensor networks with nonuniform sampling periods. IEEE Transactions on Industrial Informatics, 10(2), 871−881. http://dx.doi.org/10.1109/TII.2014.2299897.

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