First-order based cumulative distribution function for solute concentration in heterogeneous aquifers: Theoretical analysis and implications for human health risk assessment

Water Resources Research

Volumn 50, Issue 5, 2014, Pages 4018-4037

  De Barros, F P J ^a   Fiori, A ^b  

^a University of Southern California   (United States)

^b ROMA TRE UNIVERSITY   (Italy)

Author keywords

concentration PDF; heterogeneous flow fields; human health risk assessment; probabilistic risk analysis; stochastic hydrogeology; uncertainty quantification

Indexed keywords

ANISOTROPY; AQUIFERS; HYDRAULIC CONDUCTIVITY; RISK ANALYSIS; RISK ASSESSMENT; STOCHASTIC SYSTEMS;

HETEROGENEOUS FLOW; HUMAN HEALTH RISK ASSESSMENT; PROBABILISTIC RISK ANALYSIS; STOCHASTIC HYDROGEOLOGY; UNCERTAINTY QUANTIFICATIONS;

HYDROGEOLOGY;

AQUIFER; CONCENTRATION (COMPOSITION); CORRELATION; DILUTION; HEALTH RISK; HETEROGENEOUS MEDIUM; SOLUTE; UNCERTAINTY ANALYSIS; WATER QUALITY;

EID: 84900934959     PISSN: 00431397     EISSN: 19447973     Source Type: Journal    
DOI: 10.1002/2013WR015024     Document Type: Article

References (61)

1. Andričevic̈, R., (1998), Effects of local dispersion and sampling volume on the evolution of concentration fluctuations in aquifers, Water Resour. Res., 34 (5), 1115-1129. (Pubitemid 28219542)
2. Andricevic, R., (2008), Exposure concentration statistics in the subsurface transport, Adv. Water Resour., 31 (4), 714-725.
3. Bellin, A., and, D. Tonina, (2007), Probability density function of non-reactive solute concentration in heterogeneous porous formations, J. Contam. Hydrol., 94 (1-2), 109-125. (Pubitemid 47505376)
4. Bellin, A., Y. Rubin, and, A. Rinaldo, (1994), Eulerian-Lagrangian approach for modeling of flow and transport in heterogeneous geological formations, Water Resour. Res., 30 (11), 2913-2924. (Pubitemid 292091)
5. Bellin, A., G. Severino, and, A. Fiori, (2011), On the local concentration probability density function of solutes reacting upon mixing, Water Resour. Res., 47, W01514, doi: 10.1029/2010WR009696.
6. Boso, F., F. P. J. de Barros, A. Fiori, and, A. Bellin, (2013), Performance analysis of statistical spatial measures for contaminant plume characterization toward risk-based decision making, Water Resour. Res., 49, 3119-3132, doi: 10.1002/wrcr.20270.
7. Broyda, S., M. Dentz, and, D. Tartakovsky, (2010), Probability density functions for advective-reactive transport in radial flow, Stochastic Environ. Res. Risk Assess., 24 (7), 985-992.
8. Caroni, E., and, V. Fiorotto, (2005), Analysis of concentration as sampled in natural aquifers, Transp. Porous Media, 59 (1), 19-45. (Pubitemid 40301156)
9. Chatwin, P., D. Lewis, and, P. J. Sullivan, (1995), Turbulent dispersion and the beta distribution, Environmetrics, 6 (4), 395-402. (Pubitemid 26435752)
10. Cirpka, O., R. Schwede, J. Luo, and, M. Dentz, (2008), Concentration statistics for mixing-controlled reactive transport in random heterogeneous media, J. Contam. Hydrol., 98 (1-2), 61-74.
11. Cirpka, O., F. P. J. de Barros, G. Chiogna, and, W. Nowak, (2011), Probability density function of steady state concentration in two-dimensional heterogeneous porous media, Water Resour. Res., 47, W11523, doi: 10.1029/2011WR010750.
12. Cvetkovic, V., and, G. Dagan, (1994), Transport of kinetically sorbing solute by steady random velocity in heterogeneous porous formations, J. Fluid Mech., 265, 189-216.
13. Dagan, G., (1982), Stochastic modeling of groundwater flow by unconditional and conditional probabilities. 2: The solute transport, Water Resour. Res., 18 (4), 835-848.
14. Dagan, G., (1987), Theory of solute transport by groundwater, Annu. Rev. Fluid Mech., 19, 183-215.
15. Dagan, G., (1989), Flow and Transport in Porous Formations, Springer, Berlin.
16. Dagan, G., and, S. P. E. Neuman, (1997), Subsurface Flow and Transport: A Stochastic Approach, 1st ed., Cambridge University Press, N. Y.
17. de Barros, F. P. J., and, Y. Rubin, (2008), A risk-driven approach for subsurface site characterization, Water Resour. Res., 44, W01414, doi: 10.1029/2007WR006081.
18. de Barros, F. P. J., Y. Rubin, and, R. M. Maxwell, (2009), The concept of comparative information yield curves and its application to risk-based site characterization, Water Resour. Res., 45, W06401, doi: 10.1029/2008WR007324.
19. de Barros, F. P. J., A. Fiori, and, A. Bellin, (2011), A simple closed-form solution for assessing concentration uncertainty, Water Resour. Res., 47, W12603, doi: 10.1029/2011WR011107.
20. de Barros, F. P. J., S. Ezzedine, and, Y. Rubin, (2012), Impact of hydrogeological data on measures of uncertainty, site characterization and environmental performance metrics, Adv. Water Resour., 36, 51-63.
21. Dentz, M., (2012), Concentration statistics for transport in heterogeneous media due to stochastic fluctuations of the center of mass velocity, Adv. Water Resour., 36, 11-22.
22. Dentz, M., and, D. M. Tartakovsky, (2010), Probability density functions for passive scalars dispersed in random velocity fields, Geophys. Res. Lett., 37, L24406, doi: 10.1029/2010GL045748.
23. Destouni, G., and, W. Graham, (1997), The influence of observation method on local concentration statistics in the subsurface, Water Resour. Res., 33 (4), 663-676.
24. Ezzedine, S., and, Y. Rubin, (1997), Analysis of the Cape Cod tracer data, Water Resour. Res., 33 (1), 1-11.
25. Fiori, A., (2001), The Lagrangian concentration approach for determining dilution in aquifer transport: Theoretical analysis and comparison with field experiments, Water Resour. Res., 37 (12), 3105-3114. (Pubitemid 34108266)
26. Fiori, A., and, G. Dagan, (2000), Concentration fluctuations in aquifer transport: A rigorous first-order solution and applications, J. Contam. Hydrol., 45 (1-2), 139-163.
27. Fiori, A., S. Berglund, V. Cvetkovic, and, G. Dagan, (2002), A first-order analysis of solute flux statistics in aquifers: The combined effect of pore-scale dispersion, sampling, and linear sorption kinetics, Water Resour. Res., 38 (8), 1137, doi: 10.1029/2001WR000678.
28. Fiorotto, V., and, E. Caroni, (2002), Solute concentration statistics in heterogeneous aquifers for finite Peclet values, Transp. Porous Media, 48 (3), 331-351. (Pubitemid 34735973)
29. Gelhar, L., (1992), Stochastic Subsurface Hydrology, Prentice Hall, Englewood Cliffs, N. J.
30. Gelhar, L., and, C. Axness, (1983), Three-dimensional stochastic analysis of macrodispersion in aquifers, Water Resour. Res., 19 (1), 161-180.
31. Girimaji, S., (1991), Assumed β-pdf model for turbulent mixing: Validation and extension to multiple scalar mixing, Combust. Sci. Technol., 78 (4-6), 177-196.
32. Kabala, Z., and, G. Sposito, (1994), Statistical moments of reactive solute concentration in a heterogeneous aquifer, Water Resour. Res., 30 (3), 759-768. (Pubitemid 24405814)
33. Kapoor, V., and, L. W. Gelhar, (1994), Transport in three-dimensionally heterogeneous aquifers. 1: dynamics of concentration fluctuations, Water Resour. Res., 30 (6), 1775-1788. (Pubitemid 285247)
34. Kapoor, V., and, P. Kitanidis, (1998), Concentration fluctuations and dilution in aquifers, Water Resour. Res., 34 (5), 1181-1193. (Pubitemid 28219546)
35. Kitanidis, P., (1986), Parameter uncertainty in estimation of spatial functions: Bayesian analysis, Water Resour. Res., 22 (4), 499-507.
36. Kitanidis, P. K., (1994), The concept of the dilution index, Water Resour. Res., 30 (7), 2011-2026. (Pubitemid 286134)
37. Maxwell, R. M., and, W. E. Kastenberg, (1999), Stochastic environmental risk analysis: An integrated methodology for predicting cancer risk from contaminated groundwater, Stochastic Environ. Res. Risk Assess., 13 (1), 27-47. (Pubitemid 129514558)
38. Maxwell, R. M., W. E. Kastenberg, and, Y. Rubin, (1999), A methodology to integrate site characterization information into groundwater-driven health risk assessment, Water Resour. Res., 35 (9), 2841-2885.
39. Meyer, D. W., P. Jenny, and, H. A. Tchelepi, (2010), A joint velocity-concentration PDF method for tracer flow in heterogeneous porous media, Water Resour. Res., 46, W12522, doi: 10.1029/2010WR009450.
40. Mood, A. M., F. Graybill, and, D. Boes, (1974), Introduction to the Theory of Statistics, 3rd ed. McGraw-Hill International Editions, Singapore.
41. Pannone, M., and, P. Kitanidis, (1999), Large-time behavior of concentration variance and dilution in heterogeneous formations, Water Resour. Res., 35 (3), 623-634. (Pubitemid 29111794)
42. Pope, S., (1985), PDF methods for turbulent reactive flows, Prog. Energy Combust. Sci., 11 (2), 119-192. (Pubitemid 15541710)
43. Rubin, Y., (1991), Transport in heterogeneous porous media: Prediction and uncertainty, Water Resour. Res., 27 (7), 1723-1738.
44. Rubin, Y., (2003), Applied Stochastic Hydrogeology, Oxford Univ. Press, Oxford.
45. Rubin, Y., and, G. Dagan, (1992), Conditional estimation of solute travel time in heterogeneous formations: Impact of transmissivity measurements, Water Resour. Res., 28 (4), 1033-1040.
46. Rubin, Y., M. Cushey, and, A. Bellin, (1994), Modeling of transport in groundwater for environmental risk assessment, Stochastic Hydrol. Hydraul., 8 (1), 57-77.
47. Sanchez-Vila, X., A. Guadagnini, and, D. Fernandez-Garcia, (2009), Conditional probability density functions of concentrations for mixing-controlled reactive transport in heterogeneous aquifers, Math. Geosci., 41 (3), 323-351.
48. Schwede, R., O. Cirpka, W. Nowak, and, I. Neuweiler, (2008), Impact of sampling volume on the probability density function of steady state concentration, Water Resour. Res., 44, W12433, doi: 10.1029/2007WR006668.
49. Shvidler, M., and, K. Karasaki, (2003), Probability density functions for solute transport in random field, Transp. Porous Media, 50 (3), 243-266. (Pubitemid 36225638)
50. Siirila, E. R., and, R. M. Maxwell, (2012), Evaluating effective reaction rates of kinetically driven solutes in large-scale, statistically anisotropic media: Human health risk implications, Water Resour. Res., 48, W04527, doi: 10.1029/2011WR011516.
51. Srzic, V., V. Cvetkovic, R. Andricevic, and, H. Gotovac, (2013), Impact of aquifer heterogeneity structure and local-scale dispersion on solute concentration uncertainty, Water Resour. Res., 46, 3712-3728, doi: 10.1002/wrcr.20314.
52. Tartakovsky, D. M., (2013), Assessment and management of risk in subsurface hydrology: A review and perspective, Adv. Water Resour., 51, 247-260, doi: 10.1016/j.advwatres.2012.04.007.
53. Tartakovsky, D. M., and, S. Broyda, (2011), PDF equations for advective-reactive transport in heterogeneous porous media with uncertain properties, J. Contam. Hydrol., 120, 129-140.
54. Tartakovsky, D. M., M. Dentz, and, P. Lichtner, (2009), Probability density functions for advective-reactive transport with uncertain reaction rates, Water Resour. Res., 45 (7), W07414, doi: 10.1029/2008WR007383.
55. Tonina, D., and, A. Bellin, (2008), Effects of pore-scale dispersion, degree of heterogeneity, sampling size, and source volume on the concentration moments of conservative solutes in heterogeneous formations, Adv. Water Resour., 31 (2), 339-354. (Pubitemid 350246407)
56. USEPA (2001), Risk assessment guidance for Superfund: Volume III-Part A: Process for conducting probabilistic risk assessment, Tech. Rep. EPA 540/R-02/002, Office of Emergency and Remedial Response, US Environmental Protection Agency, Washington, D. C.
57. Vanderborght, J., (2001), Concentration variance and spatial covariance in second-order stationary heterogeneous conductivity fields, Water Resour. Res., 37 (7), 1893-1912. (Pubitemid 32632477)
58. Zarlenga, A., and, A. Fiori, (2013), Steady plumes in heterogeneous porous formations: A stochastic Lagrangian approach, Water Resour. Res., 49, 864-873, doi: 10.1002/wrcr.20106.
59. Zarlenga, A., I. Jankovic̈, and, A. Fiori, (2013), Advective transport in heterogeneous formations: The impact of spatial anisotropy on the breakthrough curve, Transp. Porous Media, 96 (2), 295-304.
60. Zhang, D., and, S. P. Neuman, (1996), Effect of local dispersion on solute transport in randomly heterogeneous media, Water Resour. Res., 32 (9), 2715-2723.
61. Zhang, D., L. Shi, H. Chang, and, J. Yang, (2010), A comparative study of numerical approaches to risk assessment of contaminant transport, Stochastic Environ. Res. Risk Assess., 24 (7), 971-984.