Data assimilation and parameter estimation via ensemble Kalman filter coupled with stochastic moment equations of transient groundwater flow

Water Resources Research

Volumn 49, Issue 3, 2013, Pages 1334-1344

  Panzeri, M ^a   Riva, M ^a   Guadagnini, A ^a   Neuman, S P ^b  

^a POLITECNICO DI MILANO   (Italy)

^b UNIVERSITY OF ARIZONA   (United States)

Author keywords

conditioning; data assimilation; ensemble Kalman filter; moment equations; stochastic models; transient groundwater flow

Indexed keywords

AQUIFERS; GROUNDWATER FLOW; GROUNDWATER RESOURCES; HYDRAULIC CONDUCTIVITY; INTEGRODIFFERENTIAL EQUATIONS; KALMAN FILTERS; MONTE CARLO METHODS; NATURAL GAS CONDITIONING; STOCHASTIC SYSTEMS; WELL PUMPS;

COMPUTATIONAL FEASIBILITY; DATA ASSIMILATION; ENSEMBLE KALMAN FILTER; FLUX BOUNDARY CONDITIONS; HETEROGENEOUS AQUIFERS; MOMENT EQUATIONS; SPACE-TIME EVOLUTION; TRANSIENT GROUNDWATER FLOW;

STOCHASTIC MODELS;

BAYESIAN ANALYSIS; DATA ASSIMILATION; GROUNDWATER FLOW; HYDRAULIC CONDUCTIVITY; KALMAN FILTER; STOCHASTICITY; TRANSIENT FLOW; TWO-DIMENSIONAL FLOW;

EID: 84876720538     PISSN: 00431397     EISSN: 19447973     Source Type: Journal    
DOI: 10.1002/wrcr.20113     Document Type: Article

References (43)

1. Aanonsen, S. I., G. Nævdal, D. S. Oliver, A. C. Reynolds, and, B. Vallès, (2009), Ensemble Kalman filter in reservoir engineering - A review, SPE J., 14 (3), 393-412, doi: 10.2118/117274-PA.
2. Alcolea, A., J. Carrera, and, A. Medina, (2006), Pilot points method incorporating prior information for solving the groundwater flow inverse problem, Adv. Water Resour., 29, 1678-1689. (Pubitemid 44341083)
3. Bertino, L., G. Evensen, and, H. Wackemagel, (2003), Sequential data assimilation techniques in oceanography, Int. Stat. Rev., 71 (2), 223-241, doi: 10.1111/j.1751-5823.2003.tb00194.x. (Pubitemid 37052980)
4. Burgers, G., P. J. van Leeuwen, and, G. Evensen, (1998), Analysis scheme in the ensemble Kalman filter, Mon. Weather Rev., 126 (6), 1719-1724, doi: 10.1175/1520-0493(1998)126<1719:ASITEK>2.0.CO;2. (Pubitemid 128597660)
5. Butler, T., and, M. Juntunen, (2012), Reparameterization for statistical state estimation applied to differential equations, J. Comput. Phys., 231 (6), 2641-2654, doi: 10.1016/j.jcp.2011.12.019.
6. Chen, Y., and, D. Zhang, (2006), Data assimilation for transient flow in geologic formations via ensemble Kalman filter, Adv. Water Res., 29 (8), 1107-1122, doi: 10.1016/j.advwatres.2005.09.007. (Pubitemid 44089284)
7. Chen, Y., D. S. Oliver, and, D. Zhang, (2009), Data assimilation for nonlinear problems by ensemble Kalman filter with reparameterization, J. Pet. Sci. Eng., 66 (1-2), 1-14, doi: 10.1016/j.petrol.2008.12.002.
8. De Hoog, F. R., J. H. Knight, and, A. N. Stokes, (1982), An improved method for numerical inversion of Laplace transform, SIAM J. Sci. Stat. Comput., 3 (3), 357-366.
9. Evensen, G., (1994), Sequential data assimilation with a nonlinear quasi-geostrophic model using Monte Carlo methods to forecast error statistics, J. Geophys. Res., 99 (C 5), 10143-10162, doi: 10.1029/94JC00572.
10. Evensen, G., (2003), The ensemble Kalman filter: Theoretical formulation and practical implementation, Ocean Dyn., 53 (4), 343-367. doi: 10.1007/s10236-003-0036-9.
11. Evensen, G., (2007), Data Assimilation: The Ensemble Kalman Filter, Springer, Berlin.
12. Furrer, R., and, T. Bengtsson, (2007), Estimation of high-dimensional prior and posterior covariance matrices in Kalman filter variants, J. Multivariate Anal., 98 (2), 227-255, doi: 10.1016/j.jmva.2006.08.003. (Pubitemid 44660963)
13. Gelb, A., (1974), Applied Optimal Estimation, MIT Press, Cambridge, Mass.
14. Gõmez-Hernández, J. J., and, A. G. Journel, (1993), Joint sequential simulation of multi-Gaussian field, in Geostatitics Troia'92, vol. 1, edited by, Soares, pp. 85-94, Kluwer Acad., Dordrecht, Neth.
15. Gu, Y., and, D. S. Oliver, (2006), The ensemble Kalman filter for continuous updating of reservoir simulation models, J. Energy Resour. Technol., 128 (1), 79-87, doi: 10.1115/1.2134735. (Pubitemid 44058071)
16. Gu, Y., and, D. S. Oliver, (2007), An iterative ensemble Kalman filter for multiphase fluid flow data assimilation, SPE J., 12 (4), 438-446, doi: 10.2118/108438-PA.
17. Guadagnini, A., and, S. P. Neuman, (1999), Nonlocal and localized analyses of conditional mean steady state flow in bounded, randomly nonuniform domains: 2. Computational examples, Water Resour. Res., 35 (10), 3019-3039, doi: 10.1029/1999WR900159. (Pubitemid 29461967)
18. Haugen, V., G. Nævdal, L.-J. Natvik, G. Evensen, A. M. Berg, and, K. M. Flornes, (2008), History matching using the ensemble Kalman filter on a north sea field case, SPE J., 13 (4), 382-391, doi: 10.2118/102430-PA.
19. Hendricks Franssen, H.-J., and, W. Kinzelbach, (2008), Real-time groundwater flow modeling with the Ensemble Kalman Filter: Joint estimation of states and parameters and the filter imbreeding problem, Water Resour. Res., 44, W09408, doi: 10.1029/2007WR006505.
20. Hernandez, A. F., S. P. Neuman, A. Guadagnini, and, J. Carrera, (2006), Inverse stochastic moment analysis of steady state flow in randomly heterogeneous media, Water Resour. Res., 42, W05425, doi: 10.1029/2005WR004449.
21. Houtekamer, P. L., and, H. L. Mitchell, (1998), Data assimilation using an ensemble Kalman filter technique, Mon. Weather Rev., 126 (3), 796-811, doi: 10.1175/1520-0493(1998)126<0796:DAUAEK>2.0.CO;2. (Pubitemid 128581567)
22. Kalman, R. E., (1960), A new approach to linear filtering and prediction problems, J. Basic Eng., 82, 35-45.
23. Li, J., and, D. Xiu, (2009), A generalized polynomial chaos based ensemble Kalman filter with high accuracy, J. Comput. Phys., 228 (15), 5454-5469, doi: 10.1016/j.jcp.2009.04.029.
24. Li, L., and, H. A. Tchelepi, (2006), Conditional statistical moment equations for dynamic data integration in heterogeneous reservoirs, SPE Reservoir Eval. Eng., 9 (3), 280-288. (Pubitemid 43984855)
25. Li, L., H. Zhou, J. J. Gõmez-Hernández, and, H.-J. Hendricks Franssen, (2012), Jointly mapping hydraulic conductivity and porosity by assimilating concentration data via ensemble Kalman filter, J. Hydrol., 428-429, 152-169, doi: 10.1016/j.jhydrol.2012.01.037.
26. Likanapaisal, P., L. Li, and, H. A. Tchelepi, (2012), Dynamic data integration and quantification of prediction uncertainty using statistical-moment equations, SPE J., 17 (1), 98-111, doi: 10.2118/119138-PA.
27. Liu, G., Y. Chen, and, D. Zhang, (2008), Investigation of flow and transport processes at the MADE site using ensemble Kalman filter, Adv. Water Resour., 31, 975-986, doi: 10.1016/j.advwatres.2008.03.006.
28. McLaughlin, D. B., (2002), An integrated approach to hydrologic data assimilation: interpolation, smoothing, and filtering, Adv. Water Resour., 25 (8-12), 1275-1286, doi: 10.1016/S0309-1708(02)00055-6.
29. Oliver, D. S., and, Y. Chen, (2011), Recent progress on reservoir history matching: a review, Comput. Geosci. 15 (1), 185-221, doi: 10.1007/s10596-010- 9194-2.
30. Pasetto, D., A. Guadagnini, and, M. Putti, (2011), POD-based Monte Carlo approach for the solution of regional scale groundwater flow driven by randomly distributed recharge, Adv. Water Resour., 34 (11), 1450-1463, doi: 10.1016/j.advwatres.2011.07.003.
31. Reichle, R. H., D. B. McLaughlin, and, D. Entekhabi, (2002a), Hydrological data assimilation with the ensemble Kalman filter, Mon. Weather Rev., 130 (1), 103-114, doi: 10.1175/1520-0493(2002)130<0103:HDAWTE>2.0. CO;2. (Pubitemid 34838242)
32. Reichle, R. H., J. P. Walker, R. D. Koster, and, P. R. Houser, (2002b), Extended versus ensemble Kalman filtering for land data assimilation, J. Hydrometeorol., 3 (6), 728-740, doi: 10.1175/1525-7541(2002)003<0728: EVEKFF>2.0.CO;2. (Pubitemid 36122408)
33. Riva, M., A. Guadagnini, S. P. Neuman, E. Bianchi Janetti, and, B. Malama, (2009), Inverse analysis of stochastic moment equations for transient flow in randomly heterogeneous media, Adv. Water Resour., 32 (10), 1495-1507, doi: 10.1016/j.advwatres.2009.07.003.
34. Riva, M., A. Guadagnini, F. De Gaspari, and, A. Alcolea, (2010), Exact sensitivity matrix and influence of the number of pilot points in the geostatistical inversion of moment equations of groundwater flow, Water Resour. Res., 46, W11513, doi: 10.1029/2009WR008476.
35. Riva, M., M. Panzeri, A. Guadagnini, and, S. P. Neuman, (2011), Role of model selection criteria in geostatistical inverse estimation of statistical data- and model-parameters, Water Resour. Res., 47, W07502, doi: 10.1029/2011WR010480.
36. Schöniger, A., W. Nowak, and, H.-J. Hendricks Franssen, (2012), Parameter estimation by ensemble Kalman filters with transformed data: Approach and application to hydraulic tomography, Water Resour. Res., 48, W04502, doi: 10.1029/2011WR010462.
37. Tartakovsky, D. M., and, S. P. Neuman, (1998), Transient flow in bounded randomly heterogeneous domains: 1. Exact conditional moment equations and recursive approximations, Water Resour. Res., 34 (1), 1-12, doi: 10.1029/97WR02118. (Pubitemid 28031183)
38. Vrugt, J., C. G. H. Diks, H. V. Gupta, W. Bouten, and, J. M. Verstraten, (2005), Improved treatment of uncertainty in hydrologic modeling: Combining the strengths of global optimization and data assimilation, Water Resour. Res., 41, W01017, doi: 10.1029/2004WR003059.
39. Wen, X.-H., and, W. H. Chen, (2006), Real-time reservoir model updating using ensemble Kalman filter with confirming option, SPE J., 11 (4), 431-442, doi: 10.2118/92991-PA. (Pubitemid 46099492)
40. Ye, M., S. P. Neuman, A. Guadagnini, and, D. M. Tartakovsky, (2004), Nonlocal and localized analyses of conditional mean transient flow in bounded, randomly heterogeneous porous media, Water Resour. Res., 40, W05104, doi: 10.1029/2003WR00209.
41. Zeng, L., H. Chang, and, D. Zhang, (2011), A probabilistic collocation-based Kalman filter for history matching, SPE J., 16 (2), 294-306, doi: 10.2118/140737-PA.
42. Zeng, L., L. Shi, D. Zhang, and, L. Wu, (2012), A sparse grid Bayesian method for contaminant source identification, Adv. Water Resour., 37, 1-9, doi: 10.1016/j.advwatres.2011.09.011.
43. Zhang, D., Z. Lu, and, Y. Chen, (2007), Dynamic reservoir data assimilation with an efficient, dimension-reduced Kalman filter, SPE J., 12 (1), 108-117, doi: 10.2118/95277-PA. (Pubitemid 46620636)