Uncertainty evaluation of mass discharge estimates from a contaminated site using a fully Bayesian framework

Water Resources Research

Volumn 46, Issue 1, 2010, Pages

  Troldborg, Mads ^a,b   Nowak, Wolfgang ^c   Tuxen, Nina ^d   Bjerg, Poul L ^a   Helmig, Rainer ^c   Binning, Philip J ^a  

^a TECHNICAL UNIVERSITY OF DENMARK   (Denmark)

^b SCOTTISH CROP RESEARCH INSTITUTE   (United Kingdom)

^c UNIVERSITY OF STUTTGART   (Germany)

^d OOrbicon A/S   (Denmark)

Author keywords

[No Author keywords available]

Indexed keywords

BAYESIAN; BAYESIAN FRAMEWORKS; BAYESIAN MODEL AVERAGING; CONCEPTUAL MODEL; CONTAMINATED SITES; CONTROL PLANES; COPENHAGEN; DATA SETS; DATA TYPE; GEO-STATISTICS; GEOLOGICAL MODELS; GEOSTATISTICAL MODELS; MASS-DISCHARGE; MEASURED DATA; MEASUREMENT UNCERTAINTY; MONTE CARLO SIMULATION; MULTILEVEL CONTROL; NATURAL ATTENUATION; POTENTIAL RISKS; RIGOROUS APPROACH; SITE CONDITIONS; SITE REMEDIATION; STEADY STATE; TWO SOURCES; UNCERTAINTY EVALUATION;

BAYESIAN NETWORKS; COMPUTER SIMULATION; ESTIMATION; GEOLOGIC MODELS; MONTE CARLO METHODS; PROBABILITY DISTRIBUTIONS; RISK PERCEPTION; TRICHLOROETHYLENE; UNCERTAINTY ANALYSIS;

DISCHARGE (FLUID MECHANICS);

BAYESIAN ANALYSIS; CONCEPTUAL FRAMEWORK; DATA SET; DISCHARGE; GEOSTATISTICS; MONTE CARLO ANALYSIS; PROBABILITY; STEADY-STATE EQUILIBRIUM; TRICHLOROETHYLENE; UNCERTAINTY ANALYSIS;

COPENHAGEN [(CTY) HOVEDSTADEN]; DENMARK; HOVEDSTADEN;

EID: 79551503155     PISSN: 00431397     EISSN: None     Source Type: Journal    
DOI: 10.1029/2010WR009227     Document Type: Article

References (72)

1. Ajami, N. K., Q. Y. Duan, and S. Sorooshian (2007), An integrated hydrologic Bayesian multimodel combination framework: Confronting input, parameter, and model structural uncertainty in hydrologic prediction, Water Resour. Res., 43, W01403, doi:10.1029/2005WR004745. (Pubitemid 46364281)
2. Annable, M. D., K. Hatfield, J. Cho, H. Klammler, B. L. Parker, J. A. Cherry, and P. S. C. Rao (2005), Field-scale evaluation of the passive flux meter for simultaneous measurement of groundwater and contaminant fluxes, Environ. Sci. Technol., 39(18), 7194-7201, doi:10.1021/es050074g.
3. Basu, N. B., P. S. C. Rao, I. C. Poyer, M. D. Annable, and K. Hatfield (2006), Flux-based assessment at a manufacturing site contaminated with trichloroethylene, J. Contam. Hydrol., 86(1-2), 105-127, doi:10.1016/j.jconhyd. 2006.02.011.
4. Bjerg, P., K. Hinsby, T. Christensen, and P. Gravesen (1992), Spatial variability of hydraulic conductivity of an unconfined sandy aquifer determined by a mini slug test, J. Hydrol., 136(1-4), 107-122, doi:10.1016/ 0022-1694(92)90007-I. (Pubitemid 23373176)
5. Bockelmann, A., T. Ptak, and G. Teutsch (2001), An analytical quantification of mass fluxes and natural attenuation rate constants at a former gasworks site, J. Contam. Hydrol., 53(3-4), 429-453, doi:10.1016/S0169-7722(01) 00177-2.
6. Chen, Y., and D. X. Zhang (2006), Data assimilation for transient flow in geologic formations via ensemble Kalman filter, Adv. Water Resour., 29(8), 1107-1122, doi:10.1016/j.advwatres.2005.09.007. (Pubitemid 44089284)
7. Christiansen, J. S., P. Engesgaard, and P. L. Bjerg (1998), A physically and chemically heterogeneous aquifer: Field study and reactive transport modelling, IAHS Publ., 250, 329-336.
8. Cirpka, O. A., and W. Nowak (2003), Dispersion on kriged hydraulic conductivity fields, Water Resour. Res., 39(2), 1027, doi:10.1029/ 2001WR000598.
9. Cypher, J. A., and L. D. Lemke (2009), Multiple working transport hypotheses in a heterogeneous glacial aquifer system, Ground Water Monit. Rem., 29(3), 105-119, doi:10.1111/j.1745-6592.2009.01245.x.
10. de Barros, F. P. J., and W. Nowak (2010), On the link between contaminant source release conditions and plume prediction uncertainty, J. Contam. Hydrol., 116(1-4), 24-34, doi:10.1016/j.jconhyd.2010.05.004.
11. Dietrich, C. R., and G. N. Newsam (1993), A fast and exact method for multidimensional Gaussian stochastic simulations, Water Resour. Res., 29(8), 2861-2869, doi:10.1029/93WR01070.
12. Diggle, P. J., and P. J. Ribeiro (2007), Model-Based Geostatistics, Springer, New York.
13. Draper, D. (1995), Assessment and propagation of model uncertainty, J. R. Stat. Soc., Ser. B, 57(1), 45-97.
14. Einarson, M. D., and D. M. Mackay (2001), Predicting impacts of groundwater contamination, Environ. Sci. Technol., 35(3), 66A-73A, doi:10.1021/es0122647.
15. Evensen, G. (2007), Data Assimilation-The Ensemble Kalman Filter, Springer, Berlin.
16. Falta, R. W., N. Basu, and P. S. Rao (2005), Assessing impacts of partial mass depletion in DNAPL source zones: II. Coupling source strength functions to plume evolution, J. Contam. Hydrol., 79(1-2), 45-66, doi:10.1016/j.jconhyd. 2005.05.012. (Pubitemid 41191128)
17. Feenstra, S., J. A. Cherry, and B. L. Parker (1996), Conceptual models for the behaviour of dense non-aqueous phase liquids (DNAPLs) in the subsurface, in Dense Chlorinated Solvents and other DNAPLs in Groundwater, edited by J. F. Pankow and J. A. Cherry, pp. 53-88, Waterloo, Hove, U. K.
18. Foglia, L., S. W. Mehl, M. C. Hill, P. Perona, and P. Burlando (2007), Testing alternative ground water models using cross-validation and other methods, Ground Water, 45(5), 627-641, doi:10.1111/j.1745-6584. 2007.00341.x.
19. Franssen, H. J. H., and W. Kinzelbach (2009), Ensemble Kalman filtering versus sequential self-calibration for inverse modelling of dynamic groundwater flow systems, J. Hydrol., 365(3-4), 261-274, doi:10.1016/j.jhydrol.2008.11.033.
20. Gelhar, L. W. (1993), Stochastic Subsurface Hydrology, Prentice Hall, Englewood Cliffs, N. J.
21. Guilbeault, M. A., B. L. Parker, and J. A. Cherry (2005), Mass and flux distributions from DNAPL zones in sandy aquifers, Ground Water, 43(1), 70-86, doi:10.1111/j.1745-6584.2005.tb02287.x. (Pubitemid 41672676)
22. Handcock, M. S., and M. L. Stein (1993), A Bayesian analysis of kriging, Technometrics, 35(4), 403-410, doi:10.2307/1270273.
23. Harbaugh, A. W., E. R. Banta, M. C. Hill, and M. G. McDonald (2000), MODFLOW-2000, the U.S. Geological Survey modular ground-water model-User guide to modularization concepts and the ground-water flow process, U.S. Geol. Surv. Open File Rep., 00-92.
24. Harrar, W. G., T. O. Sonnenborg, and H. J. Henriksen (2003), Capture zone, travel time, and solute-transport predictions using inverse modeling and different geological models, Hydrogeol. J., 11(5), 536-548, doi:10.1007/s10040- 003-0276-2. (Pubitemid 37450483)
25. Hatfield, K., M. Annable, J. Cho, P. S. C. Rao, and H. Klammler (2004), A direct passive method for measuring water and contaminant fluxes in porous media, J. Contam. Hydrol., 75(3-4), 155-181, doi:10.1016/j.jconhyd.2004.06.005.
26. Herold, M., T. Ptak, M. Bayer-Raich, T. Wendel, and P. Grathwohl (2009), Integral quantification of contaminant mass flow rates in a contaminated aquifer: Conditioning of the numerical inversion of concentration-time series, J. Contam. Hydrol., 106(1-2), 29-38, doi:10.1016/j.jconhyd.2008.12.006.
27. Hoeting, J. A., D. Madigan, A. E. Raftery, and C. T. Volinsky (1999), Bayesian model averaging: A tutorial, Stat. Sci., 14(4), 382-401.
28. Hojberg, A. L., and J. C. Refsgaard (2005), Model uncertainty-parameter uncertainty versus conceptual models, Water Sci. Technol., 52(6), 177-186.
29. Huang, C. L., B. X. Hu, X. Li, and M. Ye (2009), Using data assimilation method to calibrate a heterogeneous conductivity field and improve solute transport prediction with an unknown contamination source, Stochastic Environ. Res. Risk Assess., 23(8), 1155-1167, doi:10.1007/s00477-008-0289-4.
30. Intergovernmental Panel on Climate Change (2007), Climate Change 2007: The Physical Science Basis, Contribution of Working Group I to the Fourth Assessment Report of the Intergovernmental Panel of Climate Change, edited by S. Solomon et al., Cambridge Univ. Press, Cambridge, U. K.
31. Jawitz, J. W., A. D. Fure, G. G. Demmy, S. Berglund, and P. S. C. Rao (2005), Groundwater contaminant flux reduction resulting from nonaqueous phase liquid mass reduction, Water Resour. Res., 41, W10408, doi:10.1029/2004WR003825. (Pubitemid 41705693)
32. Jaynes, E. T. (1982), On the rationale of maximum-entropy methods, Proc. IEEE, 70(9), 939-952, doi:10.1109/PROC.1982.12425.
33. Kalbus, E., C. Schmidt, M. Bayer-Raich, S. Leschik, F. Reinstorf, G. U. Balcke, and M. Schirmer (2007), New methodology to investigate potential contaminant mass fluxes at the stream-aquifer interface by combining integral pumping tests and streambed temperatures, Environ. Pollut., 148(3), 808-816, doi:10.1016/j.envpol.2007.01.042. (Pubitemid 46891648)
34. Kao, C. M., and Y. S. Wang (2001), Field investigation of the natural attenuation and intrinsic biodegradation rates at an underground storage tank site, Environ. Geol., 40(4-5), 622-631, doi:10.1007/s002540000226.
35. Kitanidis, P. K. (1986), Parameter uncertainty in estimation of spatial functions: Bayesian analysis, Water Resour. Res., 22(4), 499-507, doi:10.1029/WR022i004p00499.
36. Kitanidis, P. K. (1993), Generalized covariance functions in estimation, Math. Geol., 25(5), 525-540, doi:10.1007/BF00890244.
37. Kitanidis, P. K. (1995), Quasi-linear geostatistical theory for inversing, Water Resour. Res., 31(10), 2411-2419, doi:10.1029/95WR01945.
38. Konikow, L. F., and J. D. Bredehoeft (1992), Groundwater models cannot be validated, Adv. Water Resour., 15(1), 75-83, doi:10.1016/0309-1708 (92)90033-X.
39. Kübert, M., and M. Finkel (2006), Contaminant mass discharge estimation in groundwater based on multi-level point measurements: A numerical evaluation of expected errors, J. Contam. Hydrol., 84(1-2), 55-80, doi:10.1016/j.jconhyd.2005.12.003.
40. Lee, S. Y., S. F. Carle, and G. E. Fogg (2007), Geologic heterogeneity and a comparison of two geostatistical models: Sequential Gaussian and transition probability-based geostatistical simulation, Adv. Water Resour., 30(9), 1914-1932, doi:10.1016/j.advwatres.2007.03.005. (Pubitemid 46939642)
41. Li, K. B., P. Goovaerts, and L. M. Abriola (2007), A geostatistical approach for quantification of contaminant mass discharge uncertainty using multilevel sampler measurements, Water Resour. Res., 43, W06436, doi:10.1029/2006WR005427. (Pubitemid 47134704)
42. Li, X. B., and F. T. C. Tsai (2009), Bayesian model averaging for groundwater head prediction and uncertainty analysis using multimodel and multimethod, Water Resour. Res., 45, W09403, doi:10.1029/2008WR007488.
43. Liu, G. S., Y. Chen, and D. X. Zhang (2008), Investigation of flow and transport processes at the MADE site using ensemble Kalman filter, Adv. Water Resour., 31(7), 975-986, doi:10.1016/j.advwatres.2008.03.006.
44. Matérn, B. (1986), Spatial Variation, Springer, Berlin.
45. Neuman, S. P. (2003), Maximum likelihood Bayesian averaging of uncertain model predictions, Stochastic Environ. Res. Risk Assess., 17(5), 291-305, doi:10.1007/s00477-003-0151-7.
46. Neuman, S. P., and P. J. Wierenga (2003), A comprehensive strategy of hydrogeologic modeling and analysis for nuclear facilities and sites, Rep. NUREG/CR-6805, Univ. of Ariz., Tucson.
47. Nowak, W. (2009), Best unbiased ensemble linearization and the quasilinear Kalman ensemble generator, Water Resour. Res., 45, W04431, doi:10.1029/2008WR007328.
48. Nowak, W., and O. A. Cirpka (2004), A modified Levenberg-Marquardt algorithm for quasi-linear geostatistical inversing, Adv. Water Resour., 27(7), 737-750, doi:10.1016/j.advwatres.2004.03.004.
49. Nowak, W., F. P. J. de Barros, and Y. Rubin (2010), Bayesian geostatistical design: Task-driven optimal site investigation when the geostatistical model is uncertain, Water Resour. Res., 46, W03535, doi:10.1029/2009WR008312.
50. Pardo-Igúzquiza, E., M. Chica-Olmo, M. J. Garcia-Soldado, and J. A. Luque-Espinar (2009), Using semivariogram parameter uncertainty in hydrogeological applications, Ground Water, 47(1), 25-34, doi:10.1111/j.1745- 6584.2008.00494.x.
51. Poeter, E., and D. Anderson (2005), Multimodel ranking and inference in ground water modeling, Ground Water, 43(4), 597-605, doi:10.1111/j.1745-6584. 2005.0061.x.
52. Raftery, A. E., T. Gneiting, F. Balabdaoui, and M. Polakowski (2005), Using Bayesian model averaging to calibrate forecast ensembles, Mon. Weather Rev., 133(5), 1155-1174, doi:10.1175/MWR2906.1. (Pubitemid 40829946)
53. Refsgaard, J. C., J. P. van der Sluijs, J. Brown, and P. van der Keur (2006), A framework for dealing with uncertainty due to model structure error, Adv. Water Resour., 29(11), 1586-1597, doi:10.1016/j.advwatres.2005. 11.013.
54. Rein, A., S. Bauer, P. Dietrich, and C. Beyer (2009), Influence of temporally variable groundwater flow conditions on point measurements and contaminant mass flux estimations, J. Contam. Hydrol., 108(3-4),118-133, doi:10.1016/j.jconhyd.2009.06.005.
55. Riva, M., L. Guadagnini, A. Guadagnini, T. Ptak, and E. Martac (2006), Probabilistic study of well capture zones distribution at the Lauswiesen field site, J. Contam. Hydrol., 88(1-2), 92-118, doi:10.1016/j.jconhyd. 2006.06.005.
56. Rojas, R., L. Feyen, and A. Dassargues (2008), Conceptual model uncertainty in groundwater modeling: Combining generalized likelihood uncertainty estimation and Bayesian model averaging, Water Resour. Res., 44, W12418, doi:10.1029/2008WR006908.
57. Schwede, R. L., and O. A. Cirpka (2010a), Interpolation of steady-state concentration data by inverse modeling, Ground Water, 48(4), 569-579, doi:10.1111/j.1745-6584.2009.00668.x.
58. Schwede, R. L., and O. A. Cirpka (2010b), Stochastic evaluation of mass discharge from pointlike concentration measurements, J. Contam. Hydrol., 111(1-4), 36-47, doi:10.1016/j.jconhyd.2009.10.011.
59. Snyder, C., T. Bengtsson, P. Bickel, and J. Anderson (2008), Obstacles to high-dimensional particle filtering, Mon. Weather Rev., 136(12), 4629-4640, doi:10.1175/2008MWR2529.1.
60. Soga, K., J. W. E. Page, and T. H. Illangasekare (2004), A review of NAPL source zone remediation efficiency and the mass flux approach, J. Hazard. Mater., 110(1-3), 13-27, doi:10.1016/j.jhazmat.2004.02.034.
61. Sohn, M. D., M. J. Small, and M. Pantazidou (2000), Reducing uncertainty in site characterization using Bayes Monte Carlo methods, J. Environ. Eng., 126(10), 893-902, doi:10.1061/(ASCE)0733-9372(2000)126:10(893).
62. Srivastava, R. M. (1992), Reservoir characterization with probability field simulation, paper presented at Annual Technical Conference and Exhibition, Soc. of Pet. Eng., Washington, D. C.
63. Troldborg, L., J. C. Refsgaard, K. H. Jensen, and P. Engesgaard (2007), The importance of alternative conceptual models for simulation of concentrations in a multi-aquifer system, Hydrogeol. J., 15(5), 843-860, doi:10.1007/s10040- 007-0192-y.
64. Troldborg, M., G. Lemming, P. J. Binning, N. Tuxen, and P. L. Bjerg (2008), Risk assessment and prioritisation of contaminated sites on the catchment scale, J. Contam. Hydrol., 101(1-4), 14-28, doi:10.1016/j. jconhyd.2008.07.006.
65. Tuxen, N., L. C. Larsen, M. Troldborg, P. J. Binning, and P. L. Bjerg (2008), Re-evaluation of existing investigations, Rundforbivej 176 (in Danish), Reg. Hovedstaden, Orbicon, Roskilde, Denmark.
66. Vrugt, J. A., and B. A. Robinson (2007), Treatment of uncertainty using ensemble methods: Comparison of sequential data assimilation and Bayesian model averaging, Water Resour. Res., 43, W01411, doi:10.1029/2005WR004838.
67. Woodbury, A. D., and T. J. Ulrych (1993), Minimum relative entropy: Forward probabilistic modeling, Water Resour. Res., 29(8), 2847-2860, doi:10.1029/93WR00923.
68. Woodbury, A. D., and T. J. Ulrych (2000), A full-Bayesian approach to the groundwater inverse problem for steady state flow, Water Resour. Res., 36(8), 2081-2093, doi:10.1029/2000WR900086.
69. Ye, M., S. P. Neuman, and P. D. Meyer (2004), Maximum likelihood Bayesian averaging of spatial variability models in unsaturated fractured tuff, Water Resour. Res., 40, W05113, doi:10.1029/2003WR002557.
70. Ye, M., K. F. Pohlmann, and J. B. Chapman (2008), Expert elicitation of recharge model probabilities for the Death Valley regional flow system, J. Hydrol., 354(1-4), 102-115, doi:10.1016/j.jhydrol.2008.03.001.
71. Ye, M., K. F. Pohlmann, J. B. Chapman, G. M. Pohll, and D. M. Reeves (2009), A model-averaging method for assessing groundwater conceptual model uncertainty, Ground Water, 48(5), 716-728, doi:10.1111/j.1745- 6584.2009.00633.x.
72. Zheng, C., and P. P. Wang (1999), MT3DMS, A modular three-dimensional multi-species transport model for simulation of advection, dispersion and chemical reactions of contaminant in groundwater systems; documenta- tion and user's guide, Contract Rep. SERDP-99-1, U.S. Army Eng. Res. and Dev. Cent., Vicksburg, Miss.