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Value of Information as a Context-Specific Measure of Uncertainty in Groundwater Remediation

Water Resources Management volume 26, pages1513–1535(2012)Cite this article

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Abstract

The remediation of groundwater sites has been recognized as a difficult and expensive task for years. One of the challenges is that the success of remediation is usually contingent upon an appropriate level of characterization of the physical, chemical, and biological site properties. For example, thermal treatment cannot be economically applied if the location of a non-aqueous phase liquid (NAPL) source is unknown. Both characterization and remediation are expensive. Thus, efforts need to be prioritized and optimized taking effects of uncertainty into consideration. Traditional measures of uncertainty, such as variance and correlation coefficients, do not fully depict the significance of uncertainty. For example, a small error in a parameter to which performance is sensitive may affect the prospect for remediation success much more than a large error in a parameter that has minor influence. In this paper, we quantify uncertainty as the expected increase in the cost of achieving clean-up objectives that is associated with uncertainty in performance prediction models, i.e., the minimum expected cost attainable with the present state of uncertainty minus the expected cost achievable if uncertainty were fully or partially removed. This measure, a.k.a., the value of information (VOI), is context-specific, i.e., it is dependent on site conditions and remediation strategies as well as specific remediation objectives and unit costs. We consider clean-up objectives, cost formulations, and sensitivity of costs to uncertainty in parameters, measurements, and the model itself and seek to minimize expected cost under conditions of incomplete information. We present results from a synthetic case study of dense non-aqueous phase liquid (DNAPL) plume treatment. The results quantify the cost attributable to uncertainty, thus setting an upper limit on how much one should pay for characterization, and helping decision makers to decide whether the data should be collected or not.

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References

  1. Abriola LM (2005) Contaminant source zones: remediation or perpetual stewardship? Environ Health Perspect, 113(7):A438–A439. ISSN 0091-6765. http://www.jstor.org/stable/3436174

  2. Ades AE, Lu G, Claxton K (2004) Expected value of sample information calculations in medical decision modeling. Med Decis Mak 24(2):207–227. ISSN 0272-989X. doi:10.1177/0272989X04263162

  3. Basu NB, Fure AD, Jawitz JW (2008) Predicting dense nonaqueous phase liquid dissolution using a simplified source depletion model parameterized with partitioning tracers. Water Resour Res 44(7):W07414, 2008. doi:10.1029/2007WR006008

  4. Ben-Zvi M, Berkowitz B, Kesler S (1988) Pre-posterior analysis as a tool for data evaluation: application to aquifer contamination. Water Resour Manag 2(1):11–20. doi:10.1007/BF00421927

  5. Borisova T, Shortle J, Horan RD, Abler David (2005) Value of information for water quality management. Water Resour Res 41:W06004. doi:10.1029/2004WR003576. http://www.agu.org/journals/wr/wr0506/2004WR003576/0.shtml

  6. Bratvold RB, Bickel JE, Lohne HP (2009) Value of information in the oil and gas industry: Past, present, and future. SPE Reserv Evalu Eng 12(4):630–638. ISSN 1094-6470. doi:10.2118/110378-PA

  7. Cachon GP, Fisher M (2000) Supply chain inventory management and the value of shared information. Manage Sci 46(8):1032–1048. ISSN 0025-1909. doi:10.1287/mnsc.46.8.1032.12029

  8. Cardiff M, Liu X, Kitanidis PK, Parker J, Kim U (2010) Cost optimization of DNAPL source and plume remediation under uncertainty using a semi-analytic model. J Contam Hydrol, 113(1–4):5–43. ISSN 0169-7722. doi:10.1016/j.jconhyd.2009.11.004

  9. Christ JA, Ramsburg CA, Pennell KD, Abriola LM (2006) Estimating mass discharge from dense nonaqueous phase liquid source zones using upscaled mass transfer coefficients: an evaluation using multiphase numerical simulations. Water Resour Res 42(11):W11420

  10. Dawdy DR (1979) The worth of hydrologic data. Water Resour Res 15(6):1726–1732. URL http://www.agu.org/journals/wr/v015/i006/WR015i006p01726/

  11. Domenico PA (1987) An analytical model for multidimensional transport of a decaying contaminant species. J Hydrol 91(1-2):49–58

  12. Dridi L, Pollet I, Razakarisoa O, Schafer G (2009) Characterisation of a DNAPL source zone in a porous aquifer using the partitioning interwell tracer test and an inverse modelling approach. J Contam Hydrol 107(1–2):22–44

  13. EPA (2004) Site characterization technologies for DNAPL investigations (EPA 542-r-04-017). Technical report EPA 542-R-04-017. EPA, Office of solid waste and emergency response

  14. Falta RW, Basu N, Rao PS (2005a) 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

  15. Falta RW, Rao PS, Basu N (2005b) Assessing the impacts of partial mass depletion in DNAPL source zones—i. analytical modeling of source strength functions and plume response. J Contam Hydrol 78(4):259–280

  16. Felli JC, Hazen GB (1998) Sensitivity analysis and the expected value of perfect information. Med Decis Mak 18(1):95–109. ISSN 0272-989X

  17. Feyen L, Gorelick SM (2005) Framework to evaluate the worth of hydraulic conductivity data for optimal groundwater resources management in ecologically sensitive areas. Water Resour Res 41(3):W03019

  18. Gavirneni S, Kapuscinski R, Tayur S (1999) Value of information in capacitated supply chains. Manage Sci 45(1):16–24. ISSN 0025-1909

  19. Gill PE, Murray W, Saunders MA (2002) Snopt: an SQP algorithm for large-scale constrained optimization. SIAM J Optim 12(4):979–1006. ISSN 1052-6234

  20. Gordon NJ, Salmond DJ, SmithAFM (1993) Novel-approach to nonlinear non-gaussian bayesian state estimation. IEE Proc F Radar Signal Process 140(2):107–113. ISSN 0956-375X

  21. Gorelick SM (1990) Large scale nonlinear deterministic and stochastic optimization: formulations involving simulation of subsurface contamination. Math Program 48(1):19–39. doi:10.1007/BF01582250

  22. Gould JP (1974) Risk, stochastic preference, and the value of information. J Econ Theory 8(1):64–84. ISSN 0022-0531. doi:10.1016/0022-0531(74)90006-4

  23. Griffin TW, Watson KW (2002) A comparison of field techniques for confirming dense nonaqueous phase liquids. Ground Water Monit Remediat 22(2):48–59

  24. Hanemann WM (1989) Information and the concept of option value. J Environ Econ Manage 16(1):23–37. ISSN 0095-0696. doi:10.1016/0095-0696(89)90042-9

  25. Hayden N, Diebold J, Farrell C, Laible J, Stacey R (2006) Characterization and removal of DNAPL from sand and clay layered media. J Contam Hydrol 86(1-2):53–71

  26. Howard RA (1966) Information value theory. IEEE Trans Syst Sci Cybern SSC2(1):22–26

  27. Hsu N-S, William W-G (1989) Yeh. Optimum experimental design for parameter identification in groundwater hydrology. Water Resour Res 25(5):1025–1040. ISSN 0043-1397. doi:10.1029/WR025i005p01025

  28. James BR, Gorelick SM (1994) When enough is enough: The worth of monitoring data in aquifer remediation design. Water Resour Res 30(12):3499–3513. ISSN 0043-1397. doi:10.1029/94WR01972

  29. Kagan A, Shepp LA (1998) Why the variance? Stat Probab Lett 38(4):329–333. ISSN 0167-7152. doi:10.1016/S0167-7152(98)00041-8

  30. Kitanidis PK (1996) On the geostatistical approach to the inverse problem. Adv Water Resour 19(6):333–342

  31. Klemeš V (1977) Value of information in reservoir optimization. Water Resour Res 13(5):837–850. URL http://www.agu.org/journals/wr/v013/i005/WR013i005p00837/

  32. Lee J, Liu X, Kitanidis PK, Kim U, Parker J, Bloom A, Lyon R (2012) Cost optimization of dnapl remediation at dover air force base site. Ground Water Monit Remediat (2012, in press)

  33. Liu JS (2008) Monte Carlo strategies in scientific computing. Springer. ISBN 0387763694

  34. Liu X, Cardiff M, Kitanidis PK (2010) Parameter estimation in nonlinear environmental problems. Stoch Environ Res Risk Assess 24(7):1003–1022. doi:10.1007/s00477-010-0395-y

  35. Maddock T III (1973) Management model as a tool for studying the worth of data. Water Resour Res 9(2):270–280. ISSN 0043-1397. doi:10.1029/WR009i002p00270

  36. Mantoglou A, Kourakos G (2007) Optimal groundwater remediation under uncertainty using multi-objective optimization. Water Resour Res 21:835–847. ISSN 0920-4741. doi:10.1007/s11269-006-9109-0

  37. McCarthy J (1956) Measures of the value of information. Proc Natl Acad Sci USA 42(9):654–655. ISSN 00278424. URL http://www.jstor.org/stable/89735

  38. Mylopoulos YA, Theodosiou N, Mylopoulos NA (1999) A stochastic optimization approach in the design of an aquifer remediation under hydrogeologic uncertainty. Water Resour Manag 13:335–351. ISSN 0920-4741. doi:10.1023/A:1008182906373

  39. Newman MA, Hatfield K, Hayworth J, Rao PSC, Stauffer T (2006) Inverse characterization of napl source zones. Environ Sci Technol 40(19):6044–6050

  40. Park E, Parker JC (2005) Evaluation of an upscaled model for DNAPL dissolution kinetics in heterogeneous aquifers. Adv Water Resour 28(12):1280–1291

  41. Parker J, Kim U, Kitanidis PK, Cardiff M, Liu X (2010) Stochastic cost optimization of multistrategy DNAPL site remediation. Ground Water Monit Remediat 30(3):65–78. doi:10.1111/j.1745-6592.2010.01287.x

  42. Parker JC, Park E, Tang G (2008) Dissolved plume attenuation with DNAPL source remediation, aqueous decay and volatilization—analytical solution, model calibration and prediction uncertainty. J Contam Hydrol 102(1-2):61–71. ISSN 0169-7722. doi:10.1016/j.jconhyd.2008.03.009

  43. Powell K, Silfer B (2005) In-situ techniques for napl characterization. Environ Claims J 17(2):223–230. ISSN 1040-6026. URL http://www.informaworld.com/10.1080/10406020500240202.

  44. Rao PSC, Annable MD, Kim H (2000) Napl source zone characterization and remediation technology performance assessment: recent developments and applications of tracer techniques. J Contam Hydrol 45(1–2):63–78 (IAH groundwater quality 1998 conference (GQ98) 1998 Tubingen, Germany)

  45. Reichard EG, Evans JS (1989) Assessing the value of hydrogeologic information for Risk-Based remedial action decisions. Water Resour Res 25(7):1451–1460. http://www.agu.org/journals/wr/v025/i007/WR025i007p01451/

  46. Rubin DB (1987) The calculation of posterior distributions by data augmentation: Comment: A noniterative Sampling/Importance resampling alternative to the data augmentation algorithm for creating a few imputations when fractions of missing information are modest: the SIR algorithm. J Am Stat Assoc 82(398):543–546. ISSN 01621459. http://www.jstor.org/stable/2289460

  47. Slack JR, Wallis JR, Matalas NC (1975) On the value of information to flood frequency analysis. Water Resour Res 11(5):629–647. http://www.agu.org/journals/wr/v011/i005/WR011i005p00629/

  48. Steinberg DM, Hunter WG (1984) Experimental design: review and comment. Technometrics 26(2):71–97. ISSN 00401706. http://www.jstor.org/stable/1268097

  49. Stephens DW (1989) Variance and the value of information. Am Nat 134(1):128–140. ISSN 0003-0147

  50. Wagner BJ (1995) Sampling design methods for groundwater modeling under uncertainty. Water Resour Res 31(10):2581–2591. ISSN 0043-1397. doi:10.1029/95WR02107

  51. Wagner JM, Shamir U, Nemati HR (1992) Groundwater quality management under uncertainty—stochastic-programming approaches and the value of information. Water Resour Res 28(5):1233–1246. ISSN 0043-1397

  52. Walter AI, Steven JB, Liu X, Massi A (2010) Hydraulic/partitioning tracer tomography for dnapl source zone characterization: small-scale sandbox experiments. Environ Sci Technol 44(22):8609–8614. ISSN 0013-936X. doi:10.1021/es101654j

  53. Yeh TCJ, Zhu JF (2007) Hydraulic/partitioning tracer tomography for characterization of dense nonaqueous phase liquid source zones. Water Resour Res 43(6):W06435

  54. Yokota F, Thompson KM (2004) Value of information analysis in environmental health risk management decisions: Past, present, and future. Risk Anal 24(3):635–650. ISSN 1539-6924. doi:10.1111/j.0272-4332.2004.00464.x

  55. Zelt CA, Azaria A, Levander A (2006) 3d seismic refraction traveltime tomography at a groundwater contamination site. Geophysics 71(5):H67–H78

  56. Zhu JF, Cai X, Yeh TCJ (2009) Analysis of tracer tomography using temporal moments of tracer breakthrough curves. Adv Water Resour 32(3):391–400

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Acknowledgements

This research was funded by the U.S. Department of Defense Strategic Environmental Research and Development Program (SERDP) Environmental Restoration Focus Area managed by Andrea Leeson under project ER-1611 entitled “Practical Cost Optimization of Characterization and Remediation Decisions at DNAPL sites with Consideration of Prediction Uncertainty”.

Author information

Author notes
    • Xiaoyi Liu

    Present address: Lawrence Berkeley National Laboratory, Earth Science Division, Berkeley, CA, 94720, USA

Affiliations

  1. Department of Civil and Environmental Engineering, Stanford University, Stanford, CA, USA
    • Xiaoyi Liu
    • , Jonghyun Lee
    •  & Peter K. Kitanidis
  2. Department of Civil and Environmental Engineering, University of Tennessee, Knoxville, TN, USA
    • Jack Parker
    •  & Ungtae Kim
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Correspondence to Xiaoyi Liu.

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Liu, X., Lee, J., Kitanidis, P.K. et al. Value of Information as a Context-Specific Measure of Uncertainty in Groundwater Remediation. Water Resour Manage 26, 1513–1535 (2012). https://doi.org/10.1007/s11269-011-9970-3

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Keywords

  • Groundwater remediation
  • Optimization
  • Value of information
  • Calibration
  • Uncertainty quantification