Hybrid Approach for Addressing Uncertainty in Risk Assessments
Publication: Journal of Environmental Engineering
Volume 129, Issue 1
Abstract
Parameter uncertainty is a major aspect of the model-based estimation of the risk of human exposure to pollutants. The Monte Carlo method, which applies probability theory to address model parameter uncertainty, relies on a statistical representation of available information. In recent years, other uncertainty theories have been proposed as alternative approaches to address model parameter uncertainty in situations where available information is insufficient to identify statistically representative probability distributions, due in particular to data scarcity. The simplest such theory is possibility theory, which uses so-called fuzzy numbers to represent model parameter uncertainty. In practice, it may occur that certain model parameters can be reasonably represented by probability distributions, because there are sufficient data available to substantiate such distributions by statistical analysis, while others are better represented by fuzzy numbers (due to data scarcity). The question then arises as to how these two modes of representation of model parameter uncertainty can be combined for the purpose of estimating the risk of exposure. This paper proposes an approach (termed a hybrid approach) which combines Monte Carlo random sampling of probability distribution functions with fuzzy calculus. The approach is applied to a real case of estimation of human exposure, via vegetable consumption, to cadmium present in the surficial soils of an industrial site located in the north of France. The application illustrates the potential of the proposed approach, which allows the uncertainty affecting model parameters to be represented in a way that is consistent with the information at hand. Also, because the hybrid approach takes advantage of the “rich” information provided by probability distributions, while retaining the conservative character of fuzzy calculus, it is believed to hold value in terms of a “reasonable” application of the precautionary principle.
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References
Bardossy, A., Bronstert, A., and Merz, B.(1995). “1-, 2- and 3-dimensional modeling of groundwater movement in the unsaturated soil matrix using a fuzzy approach.” Adv. Water Resour., 18(4), 237–251.
Bonano, E., Hora, S., Keeney, R., and von Winterfeldt, D. (1990). “Elicitation and use of expert judgement in performance assessments for high-level radioactive waste repositories.” Rep. No. SAND89-1821, Sandia, Albuquerque, National Laboratories, N.M.
Cazemier, D. (1999). “Utilisation de l’information incertaine dérivée d’une base de données sols. (Use of uncertain information derived from a soil data-base).” PhD thesis, National School of Agronomy, Montpellier, France.
Chaney, R., Ryan, J., Li, Y.-M., and Brown, S. (1999). “Soil cadmium as a threat to human health.” Cadmium in soils and plants, M. McLaughlin and B. Singh, eds., Kluwer Academic, Dordrecht, The Netherlands, 219–256.
Chang, A., Page, A., and Warneke, J.(1987). “Long-term sludge application on cadmium and zinc accumulation in Swiss chard and radish.” J. Environ. Qual., 16, 217–221.
Chilès, J.-P., and Delfiner, P. (1999). Geostatistics: Modeling spatial uncertainty, Wiley, New York.
Cooke, R. (1991). Experts in uncertainty, Oxford University Press, New York.
Cullen, A. C., and Frey, H. C. (1999). Probabilistic techniques in exposure assessment: A handbook for dealing with variability and uncertainty in models and inputs, Plenum, New York.
de Cooman, G., and Aeyels, D.(1999). “Supremum-preserving upper probabilities.” Inf. Sci. (N.Y.), 118, 173–212.
Dijkshoorn, W., Lampe, J., and Van Broekhovern, L.(1983). “The effect of soil pH and chemical form of nitrogen fertilizer on heavy metal contents in ryegrass.” Fertilizer Res., 4, 63–74.
Dou, C., Woldt, W., Bogardi, I., and Dahab, M.(1995). “Steady-state groundwater flow simulation with imprecise parameters.” Water Resour. Res., 31(11), 2709–2719.
Dubois, D., Kerre E., Mesiar R., and Prade, H. (2000). “Fuzzy interval analysis.” Fundamentals of fuzzy sets, D. Dubois and H. Prade, eds., The Handbooks of Fuzzy Sets Series, Kluwer, Boston, 483–581.
Dubois, D., and Prade, H. (1988). Possibility theory, Plenum, New York.
Dubois, D., and Prade, H.(1991). “Random sets and fuzzy interval analysis.” Fuzzy Sets Syst., 42, 87–101.
Dubois, D., and Prade, H.(1992a). “On the relevance of non-standard theories of uncertainty in modeling and pooling expert opinions.” Reliability Eng. Sys. Safety, 36, 95–107.
Dubois, D., and Prade, H.(1992b). “When upper probabilities are possibility measures.” Fuzzy Sets Syst., 49, 65–74.
Dubois, D., Prade, H., and Sandri, S. (1993). “On possibility/probability transformations.” Fuzzy logic: State of the art, R. Lowen and M. Roubens, eds., Kluwer Academic, Dordrecht, The Netherlands, 103–112.
Freissinet, C., Erlich, M., and Vauclin, M.(1998). “A fuzzy logic-based approach to assess imprecision of soil water contamination modelling.” Soil Tillage Res., 47, 1–17.
Gil, M. A., ed. (2001). “Special issue on fuzzy random variables.” Inf. Sci., 133(1-2).
Guyonnet, D., Co⁁me, B., Perrochet, P., and Parriaux, A.(1999). “Comparing two methods for addressing uncertainty in risk assessments.” J. Environ. Eng., 125(7), 660–666.
INERIS (1999). “Méthode de calcul des valeurs de constat d’impact dans les sols (Method for calculating risk-based concentration limits in soils).” Unpublished Rep., April 1999, Verneuil-en Halatte, France.
Jopony, M., and Young, S.(1993). “Assessment of lead availability in soils contaminated by mine spoil.” Plant Soil, 151, 273–278.
Labieniec, P., Dzombak, D., and Siegrist, R.(1997). “Qualitative evaluation of uncertainty in a site-specific risk assessment.” J. Environ. Eng., 123(3), 234–243.
Lorenz, S., Hamon, R., Holm, P., Domingues, H., Sequeira, E., Christensen, T., and McGrath, S.(1997). “Cadmium and zinc in plants and soil solutions from contaminated soils.” Plant Soil, 189, 21–31.
Luttringer, M., and de Cormis, L. (1979). “La pollution par les métaux lourds à Noyelles-Godault et ses environs, Pas de Calais (Pollution by heavy metals at Noyelles-Godault and surrounding area, Pas de Calais).” Unpublished Rep., National Institute for Agronomic Research (INRA), Montfavet, France.
Moore R. (1966). Interval analysis, Prentice-Hall, Englewood Cliffs, N.J.
Oreskes, N., Shrader-Frechette, K., and Belitz, K.(1994). “Verification, validation, and confirmation of numerical models in earth sciences.” Science, 263, 641–646.
Poels, C., Gruntz, U., Isnard, P., Riley, D., Spiteller, M., ten Berge, W., Veerkamp, W, and Bonyinck, W. (1990). “Hazard assessment of chemical contaminants in soil.” Rep. No. 40, ISSN-0773-8072-40, European Chemical Industry Ecology and Toxicology Center (ECETOC), Brussels, Belgium.
Prado, P., Draper, D., Saltelli, S., Pereira, A., Mendes, B., Eguilior, S., Cheal, R., and Tarantola, S. (1999). “Gesamac: Conceptual and computational tools to tackle the long-term risk from nuclear waste disposal in the geosphere.” European Commission Rep. No. EUR 19113 EN, Office for Official Publications of the European Communities, Luxembourg.
Shackle, G. (1961). Decision order and time in human affairs, Cambridge University Press, Cambridge, England.
Shafer, G. (1976). A mathematical theory of evidence, Princeton University Press, Princeton, N.J.
Singh, B., Narwal, R., Jeng, A., and Almas, A.(1995). “Crop uptake and extractability of cadmium in soils naturally high in metals at different pH levels.” Commun. Soil Sci. Plant Anal., 26(13&14), 2123–2142.
Smets, P., and Kennes, R.(1994). “The transferable belief model.” Artif. Inte., 66, 191–234.
Smilde, K., Van Luit, B., and Van Driel, W.(1992). “The extraction by soil and absorption by plants of applied zinc and cadmium.” Plant Soil, 143, 233–238.
Tessier, A. P., Campbell, G. C., and Bisson, M.(1979). “Sequential extraction procedure for speciation of particulate trace metals.” Anal. Chem., 51, 844–850.
Vose, D. (1996). Quantitative risk analysis—A guide to Monte Carlo simulation modeling, Wiley, New York.
Walley, P. (1991). Statistical reasoning with imprecise probabilities, Chapman and Hall, London.
World Health Organization (WHO). (1994). Quality directives for drinking water. Vol. 1: Recommendations, 2nd Ed., World Health Organisation, Geneva, Switzerland.
Wonneberger, S., Kistinger, S., and Deckert, A. (1995). “Unbiased guess, a concept to cope with fuzzy and random parameters?” European Commission Rep. No. EUR 16199 EN, Office for Official Publications of the European Communities, Luxembourg.
Zadeh, L.(1965). “Fuzzy sets.” Inf. Control., 8, 338–353.
Zadeh, L.(1978). “Fuzzy sets as a basis for a theory of possibility.” Fuzzy Sets Syst., 1, 3–28.
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Copyright © 2003 American Society of Civil Engineers.
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Received: Sep 11, 2001
Accepted: Apr 12, 2002
Published online: Dec 13, 2002
Published in print: Jan 2003
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