Articles | Volume 25, issue 4
https://doi.org/10.5194/hess-25-1689-2021
© Author(s) 2021. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/hess-25-1689-2021
© Author(s) 2021. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Data assimilation with multiple types of observation boreholes via the ensemble Kalman filter embedded within stochastic moment equations
Chuan-An Xia
Institute of Groundwater and Earth Science, Jinan University,
Guangzhou, China
Dipartimento di Ingegneria Civile e Ambientale, Politecnico di Milano, Milan, Italy
Xiaodong Luo
Norwegian Research Centre (NORCE), Bergen, Norway
Bill X. Hu
CORRESPONDING AUTHOR
Institute of Groundwater and Earth Science, Jinan University,
Guangzhou, China
Monica Riva
Dipartimento di Ingegneria Civile e Ambientale, Politecnico di Milano, Milan, Italy
Department of Hydrology and Atmospheric Sciences, The University of
Arizona, Tucson, USA
Alberto Guadagnini
CORRESPONDING AUTHOR
Dipartimento di Ingegneria Civile e Ambientale, Politecnico di Milano, Milan, Italy
Department of Hydrology and Atmospheric Sciences, The University of
Arizona, Tucson, USA
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Cited articles
Alfonzo, M. and Oliver, D. S.: Seismic data assimilation with an imperfect
model, Comput. Geosci., 24, 889–905, https://doi.org/10.1007/s10596-019-09849-0, 2020.
Bauser, H. H., Berg, D., Klein, O., and Roth, K.: Inflation method for ensemble Kalman filter in soil hydrology, Hydrol. Earth Syst. Sci., 22, 4921–4934, https://doi.org/10.5194/hess-22-4921-2018, 2018.
Bianchi Janetti, E., Riva, M., Straface, S., and Guadagnini, A.: Stochastic
characterization of the Montalto Uffugo research site (Italy) by geostatistical inversion of moment equations of groundwater flow, J. Hydrol., 381, 42–51, 2010.
Bianchi Janetti, E., Guadagnini, L., Riva, M., Guadagnini, A.: Global
sensitivity analyses of multiple conceptual models with uncertain parameters
driving groundwater flow in a regional-scale sedimentary aquifer, J. Hydrol., 574, 544–556, 2019.
Bocquet, M. and Sakov, P.: An iterative ensemble Kalman smoother, Q. J. Roy. Meteorol. Soc., 140, 1521–1535, 2014.
Botto, A., Belluco, E., and Camporese, M.: Multi-source data assimilation for physically based hydrological modeling of an experimental hillslope, Hydrol. Earth Syst. Sci., 22, 4251–4266, https://doi.org/10.5194/hess-22-4251-2018, 2018.
Chen, Y. and Oliver, D. S.: Levenberg–Marquardt forms of the iterative ensemble smoother for efficient history matching and uncertainty quantification, Comput. Geosci., 17, 689–703, 2013.
Chen, Z. and Zhang, Y.: Well flow models for various numerical methods, Int.
J. Numer. Anal. Mod., 6, 375–388, 2009.
Chen, Z., Gomez-Hernandez, J. J., Xu, T., and Zanini, A.: Joint identification of contaminant source and aquifer geometry in a sandbox experiment with the restart ensemble Kalman filter, J. Hydrol., 564, 1074–1084, 2018.
Chang, H., Liao, Q., and Zhang, D.: Surrogate model based iterative ensemble
smoother for subsurface flow data assimilation, Adv. Water Resour., 100,
96–108, 2017.
Deutsch, C. V. and Journel, A. G.: GSLIB: Geostatistical Software Library and User's Guide, 2nd Edn., Oxford University Press, New York, p. 369, 1998.
Elci, A., Molz, F. J., and Waldrop, W. R.: Implications of Observed and
Simulated Ambient Flow in Monitoring Wells, Ground Water, 39, 853–862, 2001.
Elci, A., Flach, G. P., and Molz, F. J.: Detrimental effects of natural
vertical head gradients on chemical and water level measurements in
observation wells: identification and control, J. Hydrol., 281, 70–81, 2003.
Emerick, A. A. and Reynolds, A. C.: Ensemble Smoother with Multiple Data
Assimilation, Comput. Geosci., 55, 3–15, 2013.
Evensen, G.: Sequential data assimilation with a nonlinear quasi-geostrophic
model using Monte Carlo methods to forecast error statistics, J. Geophys.
Res., 99, 10143–10162, 1994.
Evensen, G.: Accounting for model errors in iterative ensemble smoothers,
Comput. Geosci., 23, 761–775, 2019.
Gu, Y. and Oliver, D. S.: An Iterative Ensemble Kalman Filter for Multiphase
Fluid Flow Data Assimilation, SPE J., 12, 438–446, 2007.
Guadagnini, L., Guadagnini, A., and Tartakovsky, D. M.: Probabilistic
Reconstruction of geologic facies, J. Hydrol., 294, 57–67, 2004.
Hendricks Franssen, H. J. and Kinzelbach, W.: Real-time groundwater flow
modeling with the Ensemble Kalman Filter: Joint estimation of states and
parameters and the filter inbreeding problem, Water Resour. Res., 44, W09408, https://doi.org/10.1029/2007WR006505, 2008.
Hendricks Franssen, H. J., Kaiser, H. P., Kuhlmann, U., Bauser, G., Stauffer, F., Mueller, R., and Kinzelbach, W.: Operational real-time modeling with ensemble Kalman filter of variably saturated subsurface flow including stream-aquifer interaction and parameter updating, Water Resour. Res., 47, W02532, https://doi.org/10.1029/2010WR009480, 2011.
Hernandez, A. F., Neuman, S. P., Guadagnini, A., and Carrera, J.: Conditioning mean steady state flow on hydraulic head and conductivity through geostatistical inversion, Stoch. Env. Res. Risk A., 17, 329–338, 2003.
Jazwinski, A. H.: Stochastic processes and filtering theory, Academic Press, New York, 1967.
Konikow, L. F., Hornberger, G. Z., Halford, K. J., Hanson, R. T., and Harbaugh, A. W.: Revised multi-node well (MNW2) package for MODFLOW
ground-water flow model, Report 6-A30, US Geological Survey, available at: http://pubs.er.usgs.gov/publication/tm6A30 (last access: 29 March 2021), 2009.
Kurtz, W., Hendricks Franssen, H. J., Kaiser, H. P., and Vereecken, H.: Joint assimilation of piezometric heads and groundwater temperatures for improved modeling of river-aquifer interactions, Water Resour. Res., 50, 1665–1688, 2014.
Li, L. and Tchelepi, H. A.: Conditional statistical moment equations for
dynamic data integration in heterogeneous reservoirs, SPE Reserv. Eval. Eng., 9, 280–288, 2006.
Li, L., Zhou, H., Gomez-Hernandez, J. J., and Hendricks Franssen, H.-J.:
Jointly mapping hydraulic conductivity and porosity by assimilating concentration data via ensemble Kalman filter, J. Hydrol., 428, 152–169, 2012.
Li, L., Stetler, L., Cao, Z., and Davis, A.: An iterative normal-score ensemble smoother for dealing with non-Gaussianity in data assimilation, J.
Hydrol., 567, 759–766, 2018.
Li, P., Zha, Y., Shi, L., Tso, C.-H. M., Zhang, Y., and Zeng, W.: Comparison
of the use of a physical-based model with data assimilation and machine
learning methods for simulating soil water dynamics, J. Hydrol., 584, 124692, https://doi.org/10.1016/j.jhydrol.2020.124692, 2020.
Liu, G., Chen, Y., and Zhang, D.: Investigation of flow and transport processes at the MADE site using ensemble Kalman filter, Adv. Water Resour.,
31, 975–986, 2008.
Luo, X.: Ensemble-based kernel learning for a class of data assimilation
problems with imperfect forward simulators, PLoS ONE, 14, e0219247, https://doi.org/10.1371/journal.pone.0219247, 2019.
Luo, X., Stordal, A. S., Lorentzen, R. J., and Nævdal, G.: Iterative
Ensemble Smoother as an Approximate Solution to a Regularized Minimum-Average-Cost Problem: Theory and Applications, SPE J., 20, 962–982, 2015.
Luo, X., Lorentzen, R., Valestrand, R., and Evensen, G.: Correlation-Based
Adaptive Localization for Ensemble-Based History Matching: Applied to the Norne Field Case Study, SPE Reserv. Eval. Eng., 22, 1084–1109, 2019.
Mo, S., Zabaras, N., Shi, X., and Wu, J.: Deep Autoregressive Neural Networks for High-Dimensional Inverse Problems in Groundwater Contaminant Source Identification, Water Resour. Res., 55, 3856–3881, 2019.
Neuman, S. P., Guadagnini, A., and Riva, M.: Type-curve estimation of
statistical heterogeneity, Water Resour. Res., 40, W04201, https://doi.org/10.1029/2003WR002405, 2004.
Neuman, S. P., Blattstein, A., Riva, M., Tartakovsky, D. M., Guadagnini, A.,
and Ptak, T.: Type curve interpretation of late-time pumping test data in
randomly heterogeneous aquifers, Water Resour. Res., 43, W10421, https://doi.org/10.1029/2007WR005871, 2007.
Nowak, W.: Measures of parameter uncertainty in geostatistical estimation and geostatistical optimal design, Math. Geosci., 42, 199–221, 2010.
Panzeri, M., Riva, M., Guadagnini, A., and Neuman, S. P.: Data assimilation
and parameter estimation via ensemble Kalman filter coupled with stochastic
moment equations of transient groundwater flow, Water Resour. Res., 49,
1334–1344, 2013.
Panzeri, M., Riva, M., Guadagnini, A., and Neuman, S. P.: Comparison of Ensemble Kalman Filter groundwater-data assimilation methods based on stochastic moment equations and Monte Carlo simulation, Adv. Water Resour.,
66, 8–18, 2014.
Panzeri, M., Riva, M., Guadagnini, A., and Neuman, S. P.: EnKF coupled with
groundwater flow moment equations applied to Lauswiesen aquifer, Germany, J.
Hydrol., 521, 205–216, 2015.
Perulero Serrano, R., Guadagnini, L., Riva, M., Giudici, M., and Guadagnini, A.: Impact of two geostatistical hydro-facies simulation strategies on head
statistics under nonuniform groundwater flow, J. Hydrol., 508, 343–355, 2014.
Post, V., Kooi, H., and Simmons, C.: Using hydraulic head measurements in
variable-density ground water flow analyses, Ground Water, 45, 664–671, 2007.
Riva, M., Guadagnini, A., Neuman, S. P., Janetti, E. B., and Malama, B.:
Inverse analysis of stochastic moment equations for transient flow in randomly heterogeneous media, Adv. Water Resour., 32, 1495–1507, 2009.
Sakov, P. and Bocquet, M.: Asynchronous data assimilation with the EnKF in
presence of additive model error, Tellus A, 70, 1–7, https://doi.org/10.1080/16000870.2017.1414545, 2018.
Sakov, P., Oliver, D. S., and Bertino, L.: An Iterative EnKF for Strongly
Nonlinear Systems, Mon. Weather Rev., 140, 1988–2004, 2012.
Short, M., Guadagnini, L., Guadagnini, A., Tartakovsky, D. M., and Higdon, D.: Predicting vertical connectivity within an aquifer system, Bayesian Anal., 5, 557–582, 2010.
Skjervheim, J.-A., Evensen, G., Hove, J., and Vabø, J. G.: An ensemble smoother for assisted history matching, in: Proceedings of the SPE Reservoir Simulation Symposium, 21–23 February 2011, The Woodlands, TX, USA, SPE 141929, 2011.
Soares, R. V., Maschio, C., and Schiozer, D. J.: A novel localization scheme
for scalar uncertainties in ensemble-based data assimilation methods, J. Petrol. Explor. Product. Technol., 9, 2497–2510, https://doi.org/10.1007/s13202-019-0727-5, 2019.
Song, X., Shi, L., Ye, M., Yang, J., and Navon, I. M.: Numerical Comparison
of Iterative Ensemble Kalman Filters for Unsaturated Flow Inverse Modeling,
Vadose Zone J., 13, 1–12, https://doi.org/10.2136/vzj2013.05.0083, 2014.
Tartakovsky, D. M. and Neuman, S. P.: Transient flow in bounded randomly
heterogeneous domains: 1. Exact conditional moment equations and recursive
approximations, Water Resour. Res., 34, 1–12, https://doi.org/10.1029/97WR02118, 1998a.
Tartakovsky, D. M. and Neuman, S. P.: Transient flow in bounded randomly
heterogeneous domains: 2. Localization of conditional moment equations and
temporal nonlocality effects, Water Resour. Res., 34, 13–20, 1998b.
Thiem, G.: Hydrologische methoden, J. M. Gebhart, Leipzig, Germany, p. 56, 1906.
Van Leeuwen, P. J. and Evensen, G.: Data assimilation and inverse methods in
terms of a probabilistic formulation, Mon. Weather Rev., 124, 2898–2913, 1996.
Wen, X.-H. and Chen, W. H.: Real-time reservoir model updating using ensemble Kalman Filter with confirming option, SPE J., 11, 431–442, 2006.
Winter, C. L. and Tartakovsky, D. M.: Mean flow in composite porous media,
Geophys. Res. Lett., 27, 1759–1762, 2000.
Winter, C. L. and Tartakovsky, D. M.: Groundwater flow in heterogeneous
composite aquifers, Water Resour. Res., 38, 1148, https://doi.org/10.1029/2001WR000450, 2002.
Winter, C. L., Tartakovsky, D. M., and Guadagnini, A.: Numerical solutions of moment equations for flow in heterogeneous composite aquifers, Water Resour. Res., 38, 13-1–13-8, https://doi.org/10.1029/2001WR000222, 2002.
Winter, C. L., Tartakovsky, D. M., and Guadagnini, A.: Moment Differential
Equations for Flow in Highly Heterogeneous Porous Media, Surv. Geophys., 24,
81–106, 2003.
Xia, C.-A., Hu, B. X., Tong, J., and Guadagnini, A.: Data Assimilation in
Density-Dependent Subsurface Flows via Localized Iterative Ensemble Kalman
Filter, Water Resour. Res., 54, 6259–6281, 2018.
Xia, C.-A., Guadagnini, A., Hu, B. X., Riva, M., and Ackerer, P.: Grid
convergence for numerical solutions of stochastic moment equations of
groundwater flow, Stoch. Env. Res. Risk A., 33, 1565–1579, https://doi.org/10.1007/s00477-019-01719-6, 2019.
Xia, C.-A., Pasetto, D., Hu, B. X., Putti, M., and Guadagnini, A.: Integration of moment equations in a reduced-order modeling strategy for Monte Carlo simulations of groundwater flow, J. Hydrol., 590, 125257, https://doi.org/10.1016/j.jhydrol.2020.125257, 2020.
Xu, T. and Gomez-Hernandez, J. J.: Simultaneous identification of a contaminant source and hydraulic conductivity via the restart normal-score
ensemble Kalman filter, Adv. Water Resour., 112, 106–123, 2018.
Ye, M., Neuman, S. P., Guadagnini, A., and Tartakovsky, D. M.: Nonlocal and
localized analyses of conditional mean transient flow in bounded, randomly
heterogeneous porous media, Water Resour. Res., 40, W05104,
https://doi.org/10.1029/2003WR002099, 2004.
Zha, Y. Y., Zhu, P. H., Zhang, Q. R., Mao, W., and Shi, L. S.: Investigation
of Data Assimilation Methods for Soil Parameter Estimation with Different
Types of Data, Vadose Zone J., 18, 190013, https://doi.org/10.2136/vzj2019.01.0013, 2019.
Zhang, D. X.: Stochastic methods for flow in porous media: Coping with
uncertainties, Academic Press, San Diego, CA, 2002.
Zhang, Z. Y., Jiang, X. W., Wang, X. S., Wan, L., and Wang, J. Z.: Why mixed
groundwater at the outlet of open flowing wells in unconfined-aquifer basins
can represent deep groundwater: implications for sampling in long-screen wells, Hydrogeol. J., 27, 409–421, 2019.
Zheng, Q., Zhang, J., Xu, W., Wu, L., and Zeng, L.: Adaptive Multifidelity
Data Assimilation for Nonlinear Subsurface Flow Problems, Water Resour. Res., 55, 203–217, 2019.
Zhou, H., Gomez-Hernandez, J. J., Hendricks Franssen, H.-J., and Li, L.: An
approach to handling non-Gaussianity of parameters and state variables in
ensemble Kalman filtering, Adv. Water Resour., 34, 844–864, 2011.
Zovi, F., Camporese, M., Franssen, H.-J. H., Huisman, J. A., and Salandin, P.: Identification of high-permeability subsurface structures with multiple
point geostatistics and normal score ensemble Kalman filter, J. Hydrol., 548, 208–224, 2017.
Short summary
Our study shows that (i) monitoring wells installed with packers provide the (overall) best conductivity estimates; (ii) conductivity estimates anchored on information from partially and fully screened wells are of similar quality; (iii) inflation of the measurement-error covariance matrix can improve conductivity estimates when a simplified flow model is adopted; and (iv) when compared to the MC-based EnKF, the MEs-based EnKF can efficiently and accurately estimate conductivity and head fields.
Our study shows that (i) monitoring wells installed with packers provide the (overall) best...