Ensemble Kalman filtering versus sequential self-calibration for inverse modelling of dynamic groundwater flow systems

Journal of Hydrology

Volumn 365, Issue 3-4, 2009, Pages 261-274

  Franssen, H J Hendricks ^a   Kinzelbach, W ^a  

^a ETH ZURICH   (Switzerland)

Author keywords

Data assimilation; Ensemble Kalman Filtering; Groundwater hydrology; Inverse modelling; Sequential self calibration; Transient groundwater flow

Indexed keywords

BENCHMARKING; CALIBRATION; CONTROL THEORY; FLOW OF WATER; GROUNDWATER; GROUNDWATER FLOW; HYDRAULIC MODELS; HYDRAULICS; HYDROGEOLOGY; HYDROLOGY; KALMAN FILTERS; PARAMETER ESTIMATION; PUMPS; SEMICONDUCTOR COUNTERS; SOLUTE TRANSPORT; STOCHASTIC MODELS; TIME SERIES; WATER;

DATA ASSIMILATION; ENSEMBLE KALMAN FILTERING; GROUNDWATER HYDROLOGY; INVERSE MODELLING; SEQUENTIAL SELF-CALIBRATION; TRANSIENT GROUNDWATER FLOW;

UNDERGROUND RESERVOIRS;

BENCHMARKING; CALIBRATION; ENSEMBLE FORECASTING; ESTIMATION METHOD; FLOW MODELING; GROUNDWATER FLOW; KALMAN FILTER; MONTE CARLO ANALYSIS;

EID: 58849099486     PISSN: 00221694     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jhydrol.2008.11.033     Document Type: Article

References (62)

1. Aksoy A., Zhang F., and Nielsen-Gammon J.W. Ensemble-based simultaneous state and parameter estimation in a two-dimensional sea-breeze model. Monthly Weather Review 134 (2006) 2951-2970
2. Alcolea A., Carrera J., and Medina A. Pilot points method incorporating prior information for solving the groundwater flow inverse problem. Advances in Water Resources 29 11 (2006) 1678-1689
3. Alcolea A., Carrera J., and Medina A. Regularized pilot points method for reproducing the effect of small scale variability, application to simulations of contaminant transport. Journal of Hydrology (2008) 10.1016/j.jhydrol.2008.03.004
4. Anderson J.L. An ensemble adjustment Kalman filter for data assimilation. Monthly Weather Review 129 (2001) 2884-2903
5. Anderson J.L. An adaptive covariance inflation error correction algorithm for ensemble filters. Tellus 59A (2007) 210-224
6. Bennett A.F. Inverse Methods in Physical Oceanography (1992), Cambridge University Press, New York
7. Bishop C.H., Etherton B.J., and Majumdar S.J. Adaptive sampling with the ensemble transform Kalman filter. Part I: theoretical aspects. Monthly Weather Review 129 (2001) 420-436
8. Blasone R.S., Vrugt J.A., Madsen H., Rosbjerg D., Robinson B.A., and Zyvoloski G.A. Generalized likelihood uncertainty estimation (GLUE) using adaptive Markov chain Monte Carlo sampling. Advances in Water Resources (2008) 10.1016/j.advwatres.2007.12.003
9. Blasone, R.S., Madsen, H., Rosbjerg, D. 2008b. Uncertainty assessment of integrated distributed hydrological models using GLUE with Markov chain Monte Carlo sampling. Journal of Hydrology. doi:10.1016/j.hydrol.2007.12.026.
10. Burgers G., van Leeuwen P.J., and Evensen G. Analysis scheme in the Ensemble Kalman Filter. Monthly Weather Review 126 (1998) 1719-1724
11. Caers J., and Hoffman T. The probability perturbation method: a new look at bayesian inverse modeling. Mathematical Geology 38 1 (2006) 81-100
12. Capilla J.E., Rodrigo J., and Gómez-Hernández J.J. Simulation of non-Gaussian transmissivity fields honoring piezometric data and integrating soft and secondary information. Mathematical Geology 31 7 (1999) 907-927
13. Carrera J., and Neuman S.P. Estimation of aquifer parameters under transient and steady state conditions: 1. Maximum likelihood method incorporating prior information. Water Resources Research 22 2 (1986) 199-210
14. Carrera J., and Neuman S.P. Estimation of aquifer parameters under transient and steady state conditions: 2. Uniqueness, stability, and solution algorithms. Water Resources Research 22 2 (1986) 211-227
15. Carrera J., and Neuman S.P. Estimation of aquifer parameters under transient and steady state conditions: 3. Application to synthetic and field data. Water Resources Research 22 2 (1986) 228-242
16. de Marsily G. 1978. De l'identification des systèmes hydrogéologiques. Thèse, Univ. Paris VI.
17. Doucet A., de Freitas N., and Gordon N.J. Sequential Monte Carlo Methods in Practice (2001), Springer Verlag, New York
18. Evensen G. Sequential data assimilation with a nonlinear quasi-geostrophic model using Monte Carlo methods in forecast error studies. Journal of Geophysical Research 99 C5 (1994) 10143-10162
19. Evensen G. Sampling strategies and square root analysis schemes for the EnKF. Ocean Dynamics 54 (2004) 539-560
20. Foglia L., Mehl S.W., Hill M.C., Perona P., and Burlando P. Testing alternative ground water models using cross validation and other methods. Ground Water 45 5 (2007) 627-641 10.1111/j.1745-6584.2007.00341.x
21. Gómez-Hernández J.J., and Journel A.G. Joint sequential simulation of multi-Gaussian fields. In: Soares A. (Ed). Geostatistics Tróia'92 vol. 1 (1993), Kluwer Academic Publishers 85-94
22. Gómez-Hernández J.J., Sahuquillo A., and Capilla J.E. Stochastic simulation of transmissivity fields conditional to both transmissivity and piezometric data. 1. Theory. Journal of Hydrology 1-4 203 (1997) 162-174
23. Gómez-Hernández J.J., Hendricks Franssen H.J., and Cassiraga E.F. Stochastic analysis of flow response in a three-dimensional fractured block. International Journal of Rock Mechanics & Mining Sciences 38 (2001) 31-44
24. Hendricks Franssen, H.J. 2001. Inverse stochastic modelling of groundwater flow and mass transport. Ph.D. Thesis, Technical University of Valencia.
25. Hendricks Franssen H.J., and Gómez-Hernández J.J. Impact of measurement errors in the sequential self-calibrated approach. Advances in Water Resources 26 5 (2003) 501-511
26. Hendricks Franssen H.J., and Kinzelbach W. Real-time groundwater flow modelling with the Ensemble Kalman Filter: joint estimation of states and parameters and the filter inbreeding problem. Water Resources Research 44 (2008) W09408 10.1029/2007WR006505
27. Hendricks Franssen H.J., Gómez-Hernández J.J., Sahuquillo A., and Capilla J.E. Joint simulation of transmissivity and storativity fields conditional to hydraulic head data. Advances in Water Resources 23 1 (1999) 1-13
28. Hendricks Franssen H.J., Gómez-Hernández J.J., and Sahuquillo A. Coupled inverse modelling of groundwater flow and mass transport and the worth of concentration data. Journal of Hydrology 281 4 (2003) 281-295
29. Hendricks Franssen H.J., Stauffer F., and Kinzelbach W. Joint estimation of transmissivities and recharges-application: stochastic characterization of well capture zones. Journal of Hydrology 294 (2004) 87-102
30. Hendricks Franssen H.J., Brunner P., Makobo P., and Kinzelbach W. Equally likely inverse solutions to a groundwater flow problem including pattern information from remote sensing images. Water Resources Research 44 (2008) W01419 10.1029/2007WR006097
31. Hendricks Franssen, H.J., Alcolea, A., Riva, M., Bakr, M., van de Wiel, N., Stauffer, F., Guadagnini, A. submitted. A comparison of seven methods for the inverse modelling of groundwater flow. Application to the characterisation of well catchments. Advances in Water Resources.
32. Hernandez A.F., Neuman S.P., Guadagnini A., and Carrera J. Conditioning mean steady state flow on hydraulic head and conductivity through geostatistical inversion. Stochastic Environmental Research and Risk Assessment 7 (2003) 329-338 10.1007/s00477-003-0154-4
33. Hernandez A.F., Neuman S.P., Guadagnini A., and Carrera J. Inverse stochastic moment analysis of steady state flow in randomly heterogeneous media. Water Resources Research 42 (2006) W05425 10.1029/2005WR004449
34. Hoeksema R.J., and Kitanidis P.K. An application of the geostatistical approach to the inverse problem in two-dimensional modeling. Water Resources Research 20 7 (1984) 1003-1020
35. Houtekamer P.L., Michell H.L., Pellerin G., Buehner M., Charron M., Spacek L., and Hansen B. Atmospheric data assimilation with an Ensemble Kalman filter: results with real observations. Monthly Weather Review 133 (2005) 604-620
36. Hu L.Y., Blanc G., and Noetinger B. Gradual deformation and iterative calibration of sequential stochastic simulations. Mathematical Geology 33 4 (2001) 475-489
37. Janssen G.M.C.M., Valstar J.R., and van der Zee S.E.A.T.M. Inverse modeling of multimodal conductivity distributions. Water Resources Research 42 (2006) W03410 10.1029/ 2005WR004356
38. Kalnay E. Atmospheric Modeling, Data Assimilation and Predictability (2003), Cambridge University Press, United Kingdom
39. Kalnay E., Li H., Miyoshi T., Yang S.-C., and Ballabrera-Poy J. 4-D-Var or ensemble Kalman filter?. Tellus 59A (2007) 758-773
40. Kerrou J., Renard P., Hendricks Franssen H.J., and Lunati I. Issues in characterizing connectivity and heterogeneity in non-multi-Gaussian media. Advances in Water Resources 31 (2008) 147-159 10.1016/j.advwatres.2007.07.002
41. Kitanidis P.K., and Vomvoris E.G. A geostatistical approach to the inverse modeling in groundwater modeling (steady state) and one-dimensional simulations. Water Resources Research 19 3 (1983) 677-690
42. Lavenue A.M., and de Marsily G. Three-dimensional interference test interpretation in a fractured aquifer using the pilot point inverse method. Water Resources Research 37 11 (2001) 2659-2675
43. LaVenue A.M., RamaRao B.S., de Marsily G., and Marietta M.G. Pilot point methodology for automated calibration of an ensemble of conditionally simulated transmissivity fields. 1. Theory and computational experiments. Water Resources Research 31 3 (1995) 475-494
44. Liu Y., and Gupta H.V. Uncertainty in hydrologic modeling: toward an integrated data assimilation framework. Water Resources Research 43 (2007) W07401 10.1029/2006WR005756
45. Madsen, H., Sörensen, J.T. 2007. Recent advances in data assimilation in large scale hydrodynamic and hydrological forecasting models, International workshop on Advances in Hydroinformatics 4-7 June 2007, Niagara Falls Canada.
46. Moradkhani H., Sorooshian S., Gupta H.V., and Houser P.R. Dual state-parameter estimation of hydrological models using ensemble Kalman filter. Advances in Water Resources 28 (2005) 135-147
47. Naevdal, G., Johnsen, L.V., Aanonsen, S.I., Vefring, E.H. 2003. Reservoir monitoring and continuous model updating using ensemble Kalman filter. Society of Petroleum Engineers 84372.
48. Reichle R.H., Crow W.T., and Keppenne C.L. An adaptive ensemble Kalman filter for soil moisture data assimilation. Water Resources Research 44 (2008) W03423 10.1029/2007WR006357
49. Sahuquillo, A., Capilla, J.E., Gómez-Hernández, J.J., Andreu, J. 1992. Conditional simulation of transmissivity fields honoring piezometric data. In: Blain, W. R., & Cabrera, E. (Eds.), Hydraulic Engineering Software IV, Fluid Flow Modeling, pp. 201-214.
50. Tonkin M., Doherty J., and Moore C. Efficient nonlinear predictive error variance for highly parameterized models. Water Resources Research 43 (2007) W07429 10.1029/2006WR005348
51. Valstar, J.R. 2001. Inverse modeling of groundwater flow and transport, Ph.D. Thesis, Delft University of Technology, the Netherlands.
52. Verlaan M., and Heemink A.W. Tidal flow forecasting using reduced rank square root filters. Stochastic Hydrology and Hydraulics 11 (1997) 349-368
53. Vermeulen P.T.M., Heemink A.W., and Valstar J.R. Inverse modelling of groundwater flow using model reduction. Water Resources Research 41 (2004) W06003 10.1029/2004WR003698
54. Vrugt J., Dirks C.G.H., Gupta H.V., Bouten W., and Verstraten J.M. Improved treatment of uncertainty in hydrologic modeling: combining the strengths of global optimization and data assimilation. Water Resources Research 41 (2005) W01017 10.1029/2004WR003059
55. Wang X., Hamill T.M., Whitaker J.S., and Bishop C.H. A comparison of hybrid ensemble transform Kalman filter-optimum interpolation and ensemble square root filter analysis schemes. Monthly Weather Review 135 (2007) 1055-1076
56. Wen X.-H., and Chen W.H. Real-time reservoir updating using ensemble Kalman filter: the confirming approach. SPEJ 11 4 (2006) 431-442
57. Wen X.-H., and Chen W.H. Practical issues on real-time reservoir updating using ensemble Kalman filter. SPEJ 12 2 (2007) 156-166
58. Whitaker J.S., and Hamill T.M. Ensemble data assimilation without perturbed observations. Monthly Weather Review 130 (2002) 1913-1924
59. Woodbury A., and Ulrych T. A full-Bayesian approach to the groundwater inverse problem for steady state flow. Water Resources Research 36 8 (2000) 2081-2093
60. Xiong X., Navon I.M., and Uzunoglu B. A note on the particle filter with posterior Gaussian resampling. Tellus 58A (2006) 456-460
61. Zhang D., Lu Z., and Chen Y. Dynamic reservoir data assimilation with an efficient, dimension-reduced Kalman filter. SPEJ 12 1 (2007) 108-117
62. Zimmerman D.A., de Marsily G., Gotway C.A., Marietta M.G., Axness C.L., Beauheim R.L., Bras R.L., Carrera J., Dagan G., Davies P.B., Gallegos D.P., Galli A., Gómez-Hernández J.J., Grindrod P., Gutjahr A.L., Kitanidis P.K., Lavenue A.M., McLaughlin D., Neuman S.P., RamaRao B.S., Ravenne C., and Rubin Y. A comparison of seven geostatistically based inverse approaches to estimate transmissivities for modeling advective transport by groundwater flow. Water Resources Research 34 6 (1998) 1373-1413