Water Resour Manage (2010) 24:3349–3369 DOI 10.1007/s11269-010-9610-3

An Integrated Simulation-Assessment Approach for Evaluating Health Risks of Groundwater Contamination Under Multiple Uncertainties A. L. Yang · G. H. Huang · X. S. Qin

Received: 9 August 2009 / Accepted: 3 February 2010 / Published online: 18 February 2010 © Springer Science+Business Media B.V. 2010

Abstract An integrated simulation-assessment approach (ISAA) was developed in this study to systematically tackle multiple uncertainties associated with hydrocarbon contaminant transport in subsurface and assessment of carcinogenic health risk. The fuzzy vertex analysis technique and the Latin hypercube sampling (LHS) based stochastic simulation approach were combined into a fuzzy-Latin hypercube sampling (FLHS) simulation model and was used for predicting contaminant transport in subsurface under coupled fuzzy and stochastic uncertainties. The fuzzy-rule-based risk assessment (FRRA) was used for interpreting the general risk level through fuzzy inference to deal with the possibilistic uncertainties associated with both FLHS simulations and health-risk criteria. A study case involving health risk assessment for a benzene-contaminated site was examined. The study results demonstrated the proposed ISAA was useful for evaluating risks within a system containing complicated uncertainties and interactions and providing supports for identifying cost-effective site management strategies. Keywords Carcinogenic risk · Fuzzy risk assessment · Fuzzy vertex · Latin hypercube sampling · Monte Carlo simulation

A. L. Yang · G. H. Huang Sino-Canada Center of Energy and Environmental Research, North China Electric Power University, Beijing, 102206, China G. H. Huang Faculty of Engineering, University of Regina, Regina, Saskatchewan, S4S 0A2, Canada X. S. Qin School of Civil and Environmental Engineering, Nanyang Technological University, 50 Nanyang Avenue, Singapore 639798, Singapore G. H. Huang (B) Centre for Studies in Energy and Environment, University of Regina, Regina, Saskatchewan, S4S 0A2, Canada e-mail: [email protected]

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1 Introduction Leakage and spill of petroleum hydrocarbons from a variety of facilities associated with petroleum activities have contaminated groundwater resources and posed significant threats to public health of the neighboring communities (Qin et al. 2006, 2007, 2008a, 2009). Risk assessment is an important task for evaluating such threats and providing supports for site management (Huang et al. 1999; Al-Sefry and Sen ¸ 2006). The general formulation of risk assessment includes identification of sources of risk agents and their fate and transport through porous media, estimation of human exposure doses, and conversion of such exposures into risk levels (Liu et al. 2004). However, the insight about risk is limited by the randomness inherent in nature and the lack of sufficient information related to the chances of risk occurrence and the potential consequences of such occurrence (Li et al. 2007; Xu et al. 2009a; Qin et al. 2010). As a result, risk assessment is inherently linked with uncertainty and negligence of such uncertainty in the assessment procedures would bring biased or even false information to the related site managers and eventually harm the appropriateness of the final remediation decisions. It is thus desired that effective approaches be developed for supporting risk assessment under uncertainties. Uncertainties can be classified into two broad categories: probabilistic and possibilistic (Blair et al. 2001; Baudrit et al. 2007; Qin and Huang 2008; Xu et al. 2009b, c, d). Stochastic techniques could deal with the probabilistic type of uncertainties, where probability distributions were used to describe random variability in parameters (Seuntjens 2002). Monte Carlo sampling algorithm was one of the examples widely used to propagate these distributions to the output variables. Fuzzy techniques could be used to express the possibilistic uncertainties, where membership functions were used to characterize vagueness. Previously, stochastic and fuzzy methodologies were developed for supporting management of petroleumcontaminated sites (Hamed and Bedient 1999; Mylopoulos et al. 1999; Chen 2000; Maxwell et al. 1998; Maqsood et al. 2003; Kentel and Aral 2004; Li et al. 2007; Qin et al. 2008b; Chu and Chang 2009). However the rationales behind these two uncertainty manipulation approaches are different. Definition of probability distribution might suffer from lack of data, which would significantly limit the practical applicability of the stochastic techniques; fuzzy techniques might lead to loss of information when some parameters have sufficient data and would better be represented as stochastic variables (Chen 2000). This implies that, when model inputs are at different information-quality levels, any single approach may result in considerable under- or over-estimation of risk levels (Li et al. 2007; Qin and Huang 2008). To mitigate such a problem, integrated stochastic and fuzzy approaches are desired to be advanced. A number of attempts were made over the past years. Guyonnet et al. (2003) proposed a hybrid fuzzy-stochastic risk assessment approach through integrating Monte Carlo simulation and alpha-cut based fuzzy interval analysis. Baudrit et al. (2007) advanced a joint-propagation method (JPM) to evaluate the risk under various uncertainties. More related studies can be found in Chen et al. (2003), Liu et al. (2004), Kentel and Aral (2004), and Li et al. (2006). Nevertheless, the previous approaches of coupling stochastic and fuzzy techniques into a general risk-assessment framework still have a number of concerns. Firstly, integration of two uncertainty-analysis methods suffers from the difficulties of linking different algorithms and interpreting the relevant results. Most of the previous studies used separate treatment for dual uncertainties (Liu et al. 2004; Li et al. 2006;

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Qin and Huang 2008). Secondly, the conventional fuzzy risk assessment efforts were based on outputs of stochastic transport modeling which has strict data requirement in order to obtain the probability density functions (PDFs) of input parameters. Thirdly, the previous coupled methods could hardly deal with multiple uncertainties which may be associated with both transport modeling and risk assessment. It is therefore a more advanced method be developed. Thus, as an extension to the previous studies, an integrated simulation-assessment approach (ISAA) is to be developed for evaluating health risks of groundwater contamination. Techniques of fuzzy Latin hypercube sampling (FLHS) and fuzzyrule-based risk assessment (FRRA) will be integrated within a general risk assessment framework; this makes ISAA possible to deal with multiple uncertainties associated with contaminant transport modeling, health-risk quantification, and risk evaluation. The objective entails: (1) development of a fuzzy-stochastic simulation system for modeling contaminant transport and quantifying the health risk under coupled uncertainties; (2) advancement of a fuzzy risk assessment method for supporting interpretation of health risks; (3) application of the proposed method to a hypothetical groundwater contamination case.

2 Health Risk Assessment Under Uncertainty Health risk assessment normally involves processes of identifying sources of risk agents, predicting pollutant fate and transport, estimating human exposure rate, and translating such information into risk levels (Liu et al. 2004). All these processes were more or less influenced by uncertainties which may be related to aquifer characteristics, physical, chemical and biological properties of the pollutants, and human judgment (Huang et al. 1999). For example, the porosity associated with a contaminated site may be generally difficult to acquire with accurate and deterministic value due to aquifer complexity (Chen et al. 2003; Liu et al. 2004; Li et al. 2007); the first-order decay rate of a contaminant may show high uncertainties due to variations of subsurface temperature and pressure (Liu et al. 2004; Baudrit et al. 2007); determination of a “general” risk level from multiple influencing factors may not be known with certainty due to subjectivity of human judgment (Li et al. 2007; Qin et al. 2008b). Another issue is how to effectively address these uncertainties in a risk assessment process. Although many techniques, either stochastic or fuzzy, are applicable for such a purpose, there are certain limitations. If uncertainties, which can be more adequately described through probabilistic distributions, are represented through fuzzy membership functions, there might be a chance of losing critical information. On the other hand, if the probabilistic distributions are used to represent uncertainties that can only be described by linguistic variables, the over-manipulation of input information may lead to significant errors at the very beginning of modeling efforts (Li et al. 2003). A mixed approach would be more desirable for quantitatively analyzing coupled types of uncertainties. In addition, identification of risk levels usually needs to be based on experts’ knowledge, and is associated with subjective features. Presenting “Risk” as possibility (i.e. fuzzy sets) might better reflect such information and help mitigate influences of decision-makers’ biased or even false decisions (Liu et al. 2004). Thus, the health risk assessment process may involve

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uncertain inputs that are expressed in multiple formats and should be systematically handled by an integrated risk assessment framework (Liu et al. 2004; Brainard and Burmaster 1992).

3 Methodology 3.1 General Framework of ISAA The ISAA includes two major components: (1) fuzzy-stochastic simulation and (2) fuzzy-rule-based risk assessment. The general framework is shown in Fig. 1. The hybrid FLHS-based simulation process facilitates prediction of contaminant concentration under specified temporal and spatial variations. The obtained groundwater concentrations, presented as probability density functions (PDFs) under various membership grades, will serve as inputs for health risk evaluation which is based on the excess life time cancer risk (ELCR; USEPA 1992). Finally, a fuzzy-rule-based risk assessment will be applied to quantify the risk levels based on the predefined membership functions and fuzzy rule base. The detailed procedures are described in the following sections.

Fig. 1 General framework of ISAA

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3.2 Simulation under Uncertainty 3.2.1 Fuzzy-Stochastic Simulation The fuzzy Latin hypercube sampling (FLHS) is used to characterize uncertainties in input parameters of subsurface models. FLHS is developed based on fuzzy vertex analysis and LHS-based Monte Carlo simulation. Fuzzy sets are used for addressing uncertainties derived from fuzziness or vagueness, whose data can be generally received in terms of linguistic judgments (Qin and Huang 2008). Fuzzy vertex method, as one of the fuzzy arithmetic techniques, was firstly proposed by Hanss (2002) for dealing with uncertainties associated with simulation models. Previously, many applications of fuzzy vertex method were reported (Qin et al. 2008b; Kumar et al. 2009). The Latin hypercube sampling (LHS) technique proposed by McKay et al. (1979) is a stratified Monte Carlo sampling method which is effective in dealing with uncertainties that can be described by probability distribution functions (PDFs) if the available information is sufficient. Generally, FLHS could deal with uncertain inputs that are expressed in both stochastic and fuzzy formats. (1) Fuzzy vertex analysis: Given an arithmetic function f that depends on m fuzzy parameters represented as fuzzy numbers X1 , . . . , Xi , . . . , Xm . The basic idea of fuzzy vertex method is to divide the input membership domain into a series ( j) of equally spaced α-cuts: Xi , where j is the index of α-cut level and i is the number of fuzzy parameters. The lower and upper bounds of a fuzzy variable  ( j) ( j)  ( j) ( j) ( j) are obtained at each α-cut as Xi = ai , b i , where ai ≤ b i . As proposed by Hanss (2002), a fuzzy transformation technique could be used to transfer fuzzy parameters into various arrays; these arrays will be used as inputs for simulation models and help generate a series of results which form the lower and upper limits of different α-cut levels of the final simulation outputs. (Kumar et al. 2009).  ( j) is given in the following form (Hanss 2002): The transformed array X i

 ( j) X i

⎛ ⎞ 2i−1th pair 1    



⎜ ( j) ( j) ( j) ( j) ( j) ( j) ( j) ( j) ⎟ ⎟ =⎜ ⎝ ai , ...ai , b i , ...b i , ..., ai , ...ai , b i , ...b i ⎠





 



2m−i elements

2m−i elements



2m−i elements

2m−i elements

(1)



2i−1 pairs

 ( j) and generate 2m arrays (denoted as h(j) , where h(j) is the kth Combine various X i k k combinatorial array generated from fuzzy transformation at α-cut level of j, k = 1, 2,  ( j) . . . , 2m , j = 0, 1, . . . , n). For example, let X1(0) = X2(0) = X3(0) = [0.2, 4.8]. Then X i could be given in the following form (Hanss 2002): ⎧ 0  = (0.2, 0.2, 0.2, 0.2, 4.8, 4.8, 4.8, 4.8) , ⎨ X 1  (0) = (0.2, 0.2, 4.8, 4.8, 0.2, 0.2, 4.8, 4.8) , X 2 ⎩  (0) X = (0.2, 4.8, 0.2, 4.8, 0.2, 4.8, 0.2, 4.8) . 3

(2)

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Through combination, the generated arrays are: ⎧ (0) h = (0.2, 0.2, 0.2) , ⎪ ⎪ ⎪ 1(0) ⎪ h2 = (0.2, 0.2, 4.8), ⎪ ⎪ ⎪ (0) ⎪ ⎪ h ⎪ 3 = (0.2, 4.8, 0.2) , ⎪ ⎨ (0) h4 = (0.2, 4.8, 4.8) , ⎪ h(0) ⎪ 5 = (4.8, 0.2, 0.2) , ⎪ ⎪ (0) ⎪ h = (4.8, 0.2, 4.8) , ⎪ 6 ⎪ ⎪ (0) ⎪ ⎪ h ⎪ 7 = (4.8, 4.8, 0.2) , ⎩ h(0) 8 = (4.8, 4.8, 4.8) .

(3)

Detailed description of fuzzy transformation can be referred to Hanss (2002). More introduction of fuzzy vertex method can be found in Li et al. (2003). (2) Latin hypercube sampling: LHS improves upon the conventional Monte Carlo sampling method by using larger sample space with less computational effort. In LHS, the probability distribution functions (PDFs) of stochastic variables will be divided into N discrete equiprobable intervals, where at least one sample will be selected randomly from each interval. Note that the accuracy for the LHS technique is roughly dependent on the ratio of samples to variables (Huntington and Lyrintzis 1998); therefore, enough samples are taken to ensure accuracy in the variance for each variable. When the stratification of the group number is not fixed, according to Kumar et al. (2009), the variable space would have relatively few samples and the number recommended in the literature would span from 4n/3 (Iman and Helton 1985) to 2n (n is the number of the stochastic variables; McKay 1992) or a much larger value (Pebesma and Heuvelink 1999). The detailed procedures are described as follows (Iman et al. 1981): (1) Divide the cumulative distribution of each variable into N equiprobable intervals; (2) Select a value randomly from each interval; for the ith interval, the sampled cumulative probability can be written as (Wyss and Jorgensen 1998): Prob i =

rl (i − 1) + N N

(4)

where rl is a uniformly distributed random number ranging from 0 to 1, i = 1, 2,. . . , N; (3) Transform the probability values sampled into the value xi using the inverse of the distribution function F −1 (Iman et al. 1981): xi = F −1 (Prob )

(5)

(4) Pair the N values obtained for each variable xi randomly (i.e. the N values obtained for each variable are equally combined with the sampled values of the other variables). We will then propose the procedures of FLHS-based simulation. Consider a model for predicting an unknown value notated by W: W = g (P1 , . . . , Pn , f1 , . . . fm )

(6)

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where Pi (i = 1, 2, . . . , n) are stochastic parameters; n is the total number of stochastic parameters; fl (l = 1, 2, . . . , m) are model parameters represented by fuzzy sets; m is the number of fuzzy parameters. Note that the model can also deal with deterministic parameters. In order to emphasize the uncertain features of the model, we omit the expressions of deterministic parameters. The operational steps of FLHS-based simulation are: Step 1: Generate n random variables (as stochastic parameters for the simulation model) using Latin hypercube sampling based on their PDFs information; Step 2: Select an α-cut level for fuzzy parameters of the simulation model and generate 2m combinatorial arrays through fuzzy vertex analysis; ( j) ( j) Step 3: Calculate the values of Wk = f P1 , P2 , . . . , Pn , hk , (k = 1, 2, . . . , 2m ); ( j)

Step 4: Assign the smallest and largest values of Wk to the lower and upper limits of W ( j) ; Step 5: Return to step 2 and repeat steps 3 and 4 for other α-cut levels. The fuzzy set of the predicted contaminant concentration are approximated based on the obtained lower and upper boundaries of W under various α-cut levels; Step 6: Return to step 1 to generate a new set of realizations of random variables. The final results will be expressed as PDFs under various membership grades. 3.2.2 Application of FLHS in Transport Modeling Mathematical modeling in subsurface is a critical step to investigate the fate and transport of contaminants in subsurface (Theodossiou 2004). As the main purpose of this study is to demonstrate the ISAA, the groundwater transport processes will be simulated through an analytical model developed by Galya (1987). The model is based on a three dimensional solute advection-dispersion equation with degradation and retardation effects being considered. The model assumes that the aquifer is homogeneous and isotropic across the flow domain and in all directions. The governing equation and analytical solution are (Galya 1987): Dy ∂ 2 C ∂C Dz ∂ 2 C m u ∂C Dx ∂ 2 C + + − λC + + = 2 2 ∂t R ∂x R ∂x R ∂y R ∂z2 φ

1 C (x, y, z, t) = φR

(7a)

t mX0 (x, t) Y0 (y, t) Z 0 (z, t) exp (−λt) dt

(7b)

0

where: C(x, y, z, t) (mg/l) is contaminant concentration at point x, y, z and at time t; φ is aquifer porosity (unitless); R is solute retardation coefficient (unitless); t is time (d); m is mass flux entering the aquifer via the point source (mg/a); X0 , Y0 , Z 0 is Green’s functions for transport in the x, y and z directions (m); λ is first-order decay rate (d−1 ); u is linear groundwater velocity (m/d); Dx is longitudinal aquifer dispersion coefficient (m2 /d); D y is horizontal transverse dispersion coefficient (m2 /d); Dz is vertical transverse dispersion coefficient (m2 /d).

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Let an aquifer be a tree-dimensional domain in the saturated zone, where infinite ranges in both x and y directions and semi-infinite range in the z direction are present. The contaminant concentration at the initial time would be: C (x, y, z, 0) = 0

(8)

The Green’s functions in the z direction are defined by (Carslaw and Jaeger 1959):   1 −zs2  (9a) Z0 =   exp 4 Dz t R 4πD t R z



− (y − ys)2  exp Y0 =   4D y t R 4π D y t R 1



− (x − xs)2  exp X0 =   4Dx t R 4π Dx t R 1

 (9b)

 (9c)

where (xs, ys, zs) is the coordinates of the point of the polluted source; (x, y, z) is the coordinates of the point of the water supply well. As mentioned above, the models may involve some parameters which are justifiably represented by PDFs, while others are represented by fuzzy sets. Figure 2 illustrates the process of the FLHS-based simulation: (a) generate n random variables (P1 , . . . , Pn ) using Latin hypercube sampling from n PDFs; (b) apply method of fuzzy vertex analysis: calculate the smallest and largest values of C on the α cuts ( j) and build fuzzy number of C = g P1 , . . . , Pn, hk , reported in (c); (c) repeat step

( j) (b) T times: obtain T fuzzy results of C = g P1 , . . . , Pn, hk ; (d) repeat steps (a) through (c): obtain PDFs of C under a variety of α-cut levels. 3.2.3 Application of FLHS in Health Risk Quantif ication The related risk characterization associated with a contaminated site can usually be conducted through health risk assessment (HRA; Carrington and Bolger 1998). The health risk (HR) is considered as the risk of health impacts due to chronic intake of the contaminant. To quantify human health risks, the excess life time cancer risk (ELCR) model was used to assess carcinogenic risk (USEPA 1992):  CDI = (C × I R × EF × ED) (AT × BW)

(10a)

ELC R = CDI × SF

(10b)

where: CDI is the chronic daily intake (mg/kg·d); C is pollutant concentration in groundwater (mg/l); IR is human ingestion rate (l/d); EF is exposure frequency (d/y);

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Fig. 2 Schematic illustration of the FLHS simulation

ED is exposure duration (year); BW is average body weight (kg); and AT is averaged exposure time (year); SF is a carcinogen slope factor (kg·d/mg). To calculate the ELCR, the obtained groundwater concentration presented as PDF under each membership grade will serve as inputs for health risk model. The parameters of the risk model (i.e. presented as PDFs) were based on many epidemiological and animal studies. Using FLHS simulation, the ELCR will also be presented as PDFs under various membership grades.

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3.3 Fuzzy-Rule-Based Risk Assessment Fuzzy-rule-based risk assessment is used to quantify the potential health impacts from groundwater contamination and provide support for identifying suitable remediation actions (Liu et al. 2004; Li et al. 2007; Qin et al. 2008b). In this study, the approach involves generation of a membership function of excess life time cancer risk, identification of the risk level for the contamination, and quantification of the general risk levels through fuzzy-rule-based approach for decision analysis of site management. The USEPA defines acceptable risk for carcinogens within the range of 10−4 to10−6 (USEPA 2002). The health risk in this study will be categorized into five levels, namely “Clean”, “Practically Not Risky”, “Slightly Risky”, “Risky”, and “Highly Risky”, by associating them with the degree of ELCR exceeding the USEPA standard level of 10−4 (as shown in Fig. 3). After the fuzzy membership functions of ELCR under different risk categories are defined, the risk values would be presented as PDFs of the upper and lower limits under different membership grades. Following Zadeh’s definition, the “OR” operator, the union of both the fuzzy sets defined as the maximum of both membership functions is used for this study (Nait-Said et al. 2008): μ E (x) = max (μ A (x) , μ B (x))

(11)

The following inference algorithm is used for a fuzzy-rule-based judgement: The degree of ELCR exceeding the USEPA standard level of 10−4 is notated as PF. If PF fully attributes to fuzzy risk set A, the ELCR level would attribute to A; if PF partly attributes to fuzzy risk set A with a higher membership degree (such as 0.8) and partly attributes to fuzzy risk set B with a lower membership degree (such as 0.2), the ELCR level would attribute to A; if PF attributes to A and B with the same membership degree, the ELCR level would attribute to the higher risk level considering “risk priority”. Fuzzy membership functions will be used to classify the risk level of the upper and lower limits under different membership grades. Then, the general risk level (GRL) will be derived from a combinative consideration of the upper and lower levels of

Fig. 3 Membership functions of fuzzy cancer risks associated with probability of exceeding USEPA guidelines

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Table 1 Fuzzy rules for identifying general risk levels Antecedent

Survey results

ELCR level of upper limit (EU )

ELCR level of lower limit (EL )

General risk level (ER )

Clean Practically not risky Slightly risky Risky Highly risky Practically not risky Slightly risky Risky Highly risky Slightly risky Risky Highly risky Risky Highly risky Highly risky

Clean Clean Clean Clean Clean Practically not risky Practically not risky Practically not risky Practically not risky Slightly risky Slightly risky Slightly risky Risky Risky Highly risky

Clean Practically not risky Slightly risky Risky Highly risky Practically not risky Slightly risky Risky Highly risky Slightly risky Risky Highly risky Risky Highly Risky Highly risky

fuzzy membership grades. Such an operation requires fuzzy rules for classification, and is usually based on experts’ knowledge (Mohamed and Cote 1999). A number of fuzzy IF-THEN rules are extracted using the linguistic descriptors. The general form of a derived fuzzy rule is: Ri : IF E L is AiEL and EU is AiEu THEN E R is Bi

(12)

where E L, EU are the inputs of the lower and upper limits of ELCR; AiEL and AiEu are their linguistic values, respectively; E R is the output of the general ELCR level with Bi as its linguistic value. Considering “risk priority”, 15 sets of fuzzy rules are obtained (as shown in Table 1).

4 Case Study 4.1 An Overview of the Study System The application considers the carcinogenic risk of ingesting contaminated groundwater from a petroleum-contaminated site. Figure 4 shows a conceptual graph of the study system. A large volume of benzene has been leaked into a soil system, and the duration of the spillage is very long; therefore a steady-state condition is assumed. There have been no actions undertaken to mitigate the pollution. A water supply well is located about 80 m down gradient of groundwater flow direction. Thus, the contaminated groundwater is posing threats to the surrounding communities. Risk assessment is required to evaluate the impacts of contamination on human health in the near future. The semi-infinite aquifer mainly contains clay and the groundwater table is relatively shallow (about 5 m). The coordinates of the point of water supply well are (80, 0, 5). Since associations between exposure to benzene and cancer-related diseases (such as acute and chronic nonlymphocytic leukemia) of workers in the chemical industries, shoemaking factories, and oil refineries have

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Fig. 4 The study system

been widely reported (Rinsky et al. 1981, 1987), ELCR model was used to evaluate the cancer risks from benzene. However, the major problems associated with risk assessment are how to identify the fate of contaminant in the groundwater and how to define the risks in consideration of many possible uncertainties. The proposed ISAA framework will be used for dealing with such a problem. 4.2 Characterization of Uncertainties Modeling for contaminant transport in the subsurface requires inputs of various soil and hydrological parameters, such as porosity (φ) and aquifer dispersion coefficient (D). Porosity was used to be described by PDF (Chen et al. 2003); however, it is difficult to acquire an accurate PDF of the aquifer dispersion coefficient when the aquifer media is anisotropy. We assume that the hard-to-acquire data associated with longitudinal dispersion coefficient, horizontal transverse dispersion coefficient, vertical transverse dispersion coefficient, and retardation coefficient could be described as triangular fuzzy sets. Each fuzzy set is defined by specifying the most credible values, as well as the lowest and the highest possible values. The fuzzy numbers and random variables are given in Table 2. This study focuses on the carcinogenic aspect of human health impacts that the benzene contaminated site would pose to the local communities when water is used for drinking purpose. Carcinogenic risk is usually evaluated by ELCR. The benzene concentrations acquired by the solute transport modeling are served as bases for ELCR modeling. Other parameters, including human ingestion rate, exposure frequency, average exposure duration, average body weight, and averaging time will be expressed as PDFs, and the detailed data are referred to literatures (see Table 2; Liu et al. 2004; USOHEA 1989; Brainard and Burmaster 1992).

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Table 2 List of uncertain parameters Input parameter

Source of information

Representation

Porosity (unitless) First-order decay rate (d−1 )

Literaturea Literatureb

Mass flux (mg/y)

Measurements

Retardation factor

Expert opinion

Longitudinal dispersion coefficient (m2 /d) Horizontal transverse dispersion coefficient (m2 /d) Vertical transverse dispersion coefficient (m2 /d) Slope factor (unitless) Body Weight (kg) Ingestion rate (l/d) Averaged exposure time (y) Exposure frequency (d/y) Exposure duration (y)

Expert opinion

Probabilistic distribution: Normal (0.30, 0.028) Probabilistic distribution: Lognormal (0.00012, 0.0008) Probabilistic distribution: Normal (2.5 × 106 , 81.9) Possibilistic distribution: Support = [4, 8], core = 6 Possibilistic distribution: Support = [0.5, 0.7], core = 0.6 Possibility distribution: Support = [0.06, 0.08], core = 0.07 Possibility distribution: Support = [0.01, 0.03], core = 0.02 0.055 Probability distribution: Lognormal (70.1, 14.7) Probability distribution: Lognormal (0.5, 0.25) Probability distribution: Normal (30, 6) Probability distribution: Uniform (200, 350) Probability distribution: Triangular (18, 38, 69)

Expert opinion Expert opinion Deterministic Literatureb Literature b Literatureb Literatureb Measurements

a Were

referred to Chen et al. (2003)

b Were

referred to Liu et al. (2004)

5 Result Analysis and Discussions 5.1 Results from FLHS-Based Simulation Simulations for the transport model are conducted through FLHS modeling. The PDFs and fuzzy sets of input parameters for the analytical solute transport model are presented in the Table 2. Based on FLHS, the probability distributions of benzene concentrations under membership grades of 0, 0.6, and 1 can be obtained. Figure 5 shows the distributions at the location of the drinking well. It is indicated that the results are presented in Gamma distributions and the input uncertainties associated with n, m, R, Dx , D y , Dz , and λ have significant impacts on the predicted modeling outputs. For example, under a membership grade of 0.6, the benzene concentrations are obtained as probability distributions under a lower alpha-cut level limit (defined as α-cut level = 0.6 [low]) and an upper alpha-cut level limit (defined as α-cut level = 0.6 [up]), with the mean values ranging from 9.33 × 10−5 mg/l to 1.67 × 10−3 mg/l. From Table 3, the mean values of the lower limit of benzene concentration would increase as alpha-cut levels increase (the mean values range from 7.07 × 10−6 mg/l at α-cut level = 0 [low] to 9.33 × 10−5 mg/l at α-cut level = 0.6 [low]), while the mean values of upper limit would decrease as alpha-cut levels increase (the mean values range from 1.27 × 10−2 mg/l at α-cut level = 0 [up] to 1.67 × 10−3 mg/l at α-cut level = 0.6 [up] In addition, the degree of uncertainty varies with the changes of sampling and alpha-cut levels. At a lower alpha-cut level, the intervals of the mean values of outputs are wider, demonstrating a higher vagueness in representing benzene

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Fig. 5 Distributions of Benzene concentrations in the water supply well under five α-cut scenarios

concentrations; when the alpha-cut level increases, the results would become more deterministic. Particularly, under membership grade of 1, the benzene concentration was produced as only a probabilistic distribution with the mean value of 4.13 × 10−4 mg/l.

Table 3 The mean values of probability distribution functions of benzene concentrations under various membership grades

α cut levels

Mean values of the upper limit

Mean values of the lower limit

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

1.27 × 10−2 9.08 × 10−3 6.47 × 10−3 4.64 × 10−3 3.22 × 10−3 2.35 × 10−3 1.67 × 10−3 1.18 × 10−3 8.04 × 10−4 5.91 × 10−4 4.13 × 10−4

7.07 × 10−4 1.14 × 10−4 1.79 × 10−4 2.78 × 10−4 4.60 × 10−4 6.32 × 10−4 9.33 × 10−4 1.37 × 10−4 2.00 × 10−4 2.89 × 10−4 4.13 × 10−4

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Fig. 6 Cumulative probability distributions of ELCR under five α-cut scenarios

5.2 Results from FLHS-Based Simulation of Cancer Risk Assessment Model The CDFs (Cumulative Density Functions) of parameters in the ELCR model are summarized in Table 2. The LHPS simulation technique is also applied to this model for generating probability distributions for the contaminant concentrations of concern. The probability distributions of ELCR of ingestion exposure to benzene under each membership grade are presented in Fig. 6. The result demonstrates that: (1) under different membership grades, the probability distributions subject to different distributions (the benzene concentration is subjected to Gamma distribution, while the ELCR will be subjected to Lognormal distribution); (2) the mean values of the lower limit would increase as the alpha-cut levels increase, while the mean values of upper limit decrease as alpha-cut levels increase; (3) the degree of uncertainty would vary with the changes of sampling and alpha-cut levels. From Fig. 6, it is also indicated that the uncertainties associated with C, IR, EF, AT, and BW significantly affect the predicted modeling outputs. For example, under a membership grade of 0.6, the mean values of ELCR would range from 1.52 × 10−5 to 2.73 × 10−4 ; such a large difference may lead to biased or even false conclusions in judging the cancer risk level. The ELCR of benzene in the ingested water from the polluted water supply well is used for further fuzzy risk assessment. 5.3 Results from Fuzzy Risk Assessment Carcinogenic health risks at multiple alpha-cut levels introduced by benzene were then investigated. The general risk level was obtained through fuzzy inference operations. It is indicated from Fig. 6 that Eu of benzene at α-cut 0 is P (ELCR < 10−4 ) = 0.0; thus the probability of guideline violation is PF = 1.0. As a result, the Eu is “Highly Risky” with a membership grade of 1.0 according to Fig. 4. The associated EL is “Clean” with a membership grade of 1.0. Therefore, the general cancer risk (ER ) at membership grade of 0 is “Highly Risky” according to the rule base as shown in Table 1. However, when it comes to this scenario, the corresponding risk (i.e., Eu ) would be partly “Slightly Risky” with a membership grade of 0.57 and partly “Risky” with a membership grade of 0.43. The fuzzy “OR” operation would  be applied to the  two fuzzy risks to determine its consequences (e.g. μ Risk = Max μ Slightly Risky , μ Risky .

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Table 4 General risk levels obtained by fuzzy risk assessment α-cut levels

ELCR level of the upper limit (EU )

ELCR level of the lower limit (EL )

General risk level (ER )

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Highly risky Highly risky Highly risky Highly risky Highly risky Highly risky Highly risky Risky Slightly risky Practically not risky Clean

Clean Clean Clean Clean Clean Clean Clean Clean Clean Clean Clean

Highly risky Highly risky Highly risky Highly risky Highly risky Highly risky Highly risky Risky Slightly risky Practically not risky Clean

Then the Eu is “Risky”. Another scenario may be that the Eu would be partly “Practically Not Risky” and partly “Clean” with the same membership grade of 0.5. Considering “risk priority”, the combinational risk (ER ) is “Practically Not Risky”. The different general cancer risk levels at multiple α-cut levels for ingesting the benzene-contaminated water in the supply well are given in Table 4. Then, a full spectrum of risk information under uncertainty could be produced, implying that risk events may occur in many possible ways. For example, the risk output could be “Highly Risky” under the condition that the membership grade is 0; the output could also be “Risky” under the condition that the membership grade is 0.8. This implies that risk assessment outputs would be considerably influenced by system uncertainties. Therefore, presenting “Risk” as both possibility and probability might better help decision-makers manage contamination issues (Liu et al. 2004). A tradeoff among the acceptable level of “possibility” of reference membership grade needs to be analyzed, which is critical for guiding identification of potential responsive actions for site management. Generally, the above results demonstrate that the uncertainties of inputs have significant impacts on predictions of the health risks; FLHS could be used to calculate the contaminant transport and evaluate health risk with uncertain inputs being expressed in both stochastic and fuzzy formats; fuzzy risk assessment with fuzzy-rulebased operations could be used to tackle risk information which was characterized by fuzzy-stochastic features. Thus, ISAA was capable of helping decision-makers in identifying desired contaminated-site management strategies under complex uncertainties. 5.4 Discussions The key point in this study was that some of the parameters could be imprecisely known, and this imprecision was handled by means of either fuzzy sets and/or stochastic theory. However, applications of these theories were significantly restricted by difficulties in linking stochastic and fuzzy algorithms and elucidating implications from the generated fuzzy stochastic risk outputs (Qin et al. 2008b). The ISAA was the first attempt to quantify health risk that attribute to benzene-polluted groundwater by fuzzy vertex analysis, Latin hypercube sampling simulation and fuzzy inference

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technique. The study results demonstrated that the proposed ISAA can efficiently analyze the impact of different uncertainty sources on the prediction of the health risks. In ISAA, hybrid uncertainties can be directly communicated into the risk assessment processes when they are represented as both fuzzy sets and random variables. Fuzzy vertex analysis converts each fuzzy set into a group of intervals associated with multiple alpha-cut levels. The intervals under the same alpha-cut level from all fuzzy sets can be processed by interval analysis. This leads to an interval output under the same alpha-cut level (Li et al. 2009). The solutions under a set of alpha-cut levels can then be generated by solving a series of deterministic models. In this study, taking the end points of these intervals by fuzzy vertex analysis, 24 combinations for fuzzy parameters x1, x2,. . . , x4 could be generated. Evaluation of the model for each of the 24 combinations would obtain 16 values of concentration outputs. The desired lower and upper limits of contaminant concentration may be the smallest and largest values of the system outputs. In addition, the time required for conducting stochastic simulation was dependent with the number of runs of Latin hypercube sampling, and the processing of fuzzy manipulation relied on the numbers of alpha-cut levels and fuzzy sets. Note that large samples are normally needed to make the simulated variance accurate. In this study, 1,000 iterations of Latin hypercube sampling and 10 alpha-cuts have been used. Normally, a large sampling process may result in a heavy computational burden (Huntington and Lyrintzis 1998). In order to obtain cost-effective results, we can increase the number of iterations gradually through test runs. If the results start to vary insignificantly, then the number is acceptable. Otherwise, further tests are needed.. To better reflect the advantages of ISAA, individual Monte Carlo simulation and fuzzy modeling for the study case are also investigated. When Monte Carlo simulation is applied, the fuzzy numbers in Table 2 were converted to probability distribution functions. The cumulative distribution function of the pure Monte Carlo simulation (with 1,000 iterations) is shown in Fig. 7. It appears that the probability that the calculated ELCR will exceed 10−4 lies around 15%; consequently, the calculated ELCR would be considered as “Clean”, which means the water supply

Fig. 7 Cumulative density function of ELCR obtained from Monte Carlo simulation

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well would be considered suitable for drinking. This implies that, if all parameters are assumed to be PDFs, the range of results could be narrowed, and may bring potential risks to decision-making processes. When only fuzzy simulation is used, all parameters would be presented by fuzzy sets and the range of results would be too conservative. Generally, the results from ISAA are more reasonable, and could provide strong supports for health risk assessment and remediation design for under multiple uncertainties. Despite the potential advantages of the proposed approach, there are also a number of limitations regarding its application. Firstly, it may deliver poorly informative results in some situations, which will highlight the need for collecting new information by conducting more extensive data investigations. Secondly, the fuzzy rule base selected a “risk priority”, which might be considered appropriate for an application with conservative management policies; however, it may lead to lower economic benefit. Thirdly, only a combinatory impact of uncertainties on system outputs could be accounted for by ISAA; the degree of influence of an individual uncertainty was unknown. Finally, it was unclear how to use ISAA-based risk information to guide identification of proper responsive actions for site remediation. Further investigations are desired to tackle these issues. The application of ISAA was demonstrated in a hypothetical case. In real-world applications, some modifications may need to be considered: (1) soil heterogeneity may result in further uncertainties, the modeling parameters such as porosity and permeability could vary significantly from one site, exhibiting spatial variability; (2) the contaminant transport process may be more complicated and its prediction requires sophisticated numerical models; this leads to difficulties in ISAA coding or programming; (3) the varied ways of risk exposure and difference of exposure groups may bring additional uncertainties to risk outputs; risk levels of acquiring cancer among different exposure ways such as ingestion, inhalation among different age groups for their owning different ingestion rate, body weight and exposure time may be quite different.

6 Conclusions An integrated simulation-assessment approach (ISAA) for analyzing the health risks of groundwater contamination was proposed in this study. ISAA integrated FLHSbased simulation (including contaminant transport and health-risk quantification) and fuzzy rule-based risk assessment (FRRA) into a general framework and could handle uncertainties expressed in multiple formats. ISAA was successfully applied to a hypothetical case where assessment of cancer risks derived from an underground benzene leakage was investigated. Compared with other risk assessment techniques, ISAA has the following advantages: (1) it can address uncertainties associated with hydrogeological and health risk quantification parameters as not only PDFs but also fuzzy membership functions; (2) it may mitigate subjectivity of human judgment through application of fuzzy rule-based inference operation; (3) it can reasonably generate a full spectrum of risk information under multiple uncertainties, and lead to better results than those generated by pure Monte Carlo simulation or fuzzy modeling techniques; (4) it can

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help determine potential responsive actions for site management under complex uncertainties; (5) it is also applicable for other environmental systems. Acknowledgements This research was supported by the Major State Basic Research Development Program of MOST (2005CB724200 and 2006CB403307), the Special Research Grant for University Doctoral Programs (20070027029), the Canadian Water Network under the Networks of Centers of Excellence (NCE) and the Natural Science and Engineering Research Council of Canada.

References Al-Sefry SA, Sen ¸ Z (2006) Groundwater rise problem and risk evaluation in major cities of arid lands—Jedddah case in Kingdom of Saudi Arabia. Water Resour Manage 20(1):91–108 Baudrit C, Guyonnet D, Dubois D (2007) Joint propagation of variability and imprecision in assessing the risk of groundwater contamination. J Contam Hydrol 93(1–4):72–84 Blair AN, Ayyub BM, Bender WJ (2001) Fuzzy stochastic risk-based decision analysis with the mobile offshore base as a case study. Mar Struct 14(1):69–88 Brainard J, Burmaster DE (1992) Bivariate distributions for height and weight of men and women in the United States. Risk Anal 12(2):267–274 Carrington CD, Bolger PM (1998) Uncertainty and risk assessment. Hum Ecol Risk Assess 4(2): 253–257 Carslaw HS, Jaeger JC (1959) Conduction of heat in solids. Oxford University Press, New York Chen SQ (2000) Comparing probabilistic and fuzzy set approaches for design in the presence of uncertainty. PhD Dissertation, Virginia Polytechnic Institute and State University Chen Z, Huang GH, Chakma A (2003) Hybrid fuzzy-stochastic modeling approach for assessing environmental risks at contaminated groundwater systems. J Environ Eng 129(1):79–88 Chu HJ, Chang LC (2009) Application of optimal control and fuzzy theory for dynamic groundwater remediation design. Water Resour Manage 23(4):647–660 Galya DP (1987) A horizontal plane source model for groundwater transport. Ground Water 25(6):733–739 Guyonnet D, Bourgine B, Dubois D, Fargier H et al (2003) Hybrid approach for addressing uncertainty in risk assessments. J Environ Eng 129:68–78 Hamed M, Bedient P (1999) Reliability-based uncertainty analysis of groundwater contaminant transport and remediation. USEPA Report EPA/600/R-99/028 Hanss W (2002) The transformation method for the simulation and analysis of systems with uncertain parameters. Fuzzy Sets Syst 130:277–289 Huang GH, Chen Z, Tontiwachwuthicul P et al (1999) Environmental risk assessment for underground storage tanks through an interval parameter fuzzy relation analysis approach. Energ Sourc 21(1–2):75–96 Huntington DE, Lyrintzis CS (1998) Improvements to and limitations of Latin hypercube sampling. Probabilist Eng Mech 13(4):245–253 Iman RL, Helton JC (1985) A comparison of uncertainty and sensitivity analysis techniques for computer models. Technical Report SAND84-1461. Sandia National Laboratories, Albuquerque Iman RL, Helton JC, Campbell JE (1981) An approach to sensitivity analysis of computer models, Part 1. Introduction, input variable selection and preliminary variable assessment. J Qual Technol 13(3):174–183 Kentel E, Aral MM (2004) Probabilistic-fuzzy health risk modeling. Stoch Environ Res Risk Assess 18(5):324–338 Kumar V, Mari M, Schuhmacher M et al (2009) Partitioning total variance in risk assessment: application to a municipal solid waste incinerator. Environ Model Softw 24:247–261 Li JB, Huang GH, Chakma A, Zeng GM (2003) Integrated fuzzy-stochastic modeling of petroleum contamination in subsurface. Energy Sources 25(6):547–564 Li JB, Liu L, Huang GH, Zeng GM (2006) A fuzzy-set approach for addressing uncertainties in risk assessment of hydrocarbon-contaminated site. Water Air Soil Pollut 171(1–4):5–18 Li JB, Huang GH, Zeng GM, Maqsood I, Huang YF (2007) An integrated fuzzy-stochastic modeling approach for risk assessment of groundwater contamination. J Environ Manag 82(2): 173–188

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A.L. Yang et al.

Li YP, Huang GH, Huang YF, Zhou HD (2009) A multistage fuzzy-stochastic programming model for supporting sustainable water-resources allocation and management. Environ Model Softw 24:786–797 Liu L, Cheng SY, Guo HC (2004) A simulation-assessment modeling approach for analyzing environmental risks of groundwater contamination at waste landfill sites. Hum Ecol Risk Assess 10(2):373–388 Maqsood I, Li JB, Huang GH (2003) Inexact multiphase modeling system for the management of uncertainty in subsurface contamination. Pract Period Hazard Toxic Radioact Waste Manag 7(2):86–94 Maxwell RM, Pelmulder SD, Tompson AFB, Kastenberg WE (1998) On the development of a new methodology for groundwater-driven health risk assessment. Water Resour Res 34(4): 833–848 McKay MD (1992) Latin hypercube sampling as a tool in uncertainty analysis of computer models. In: Proceedings of the 24th conference on winter simulation. Association for Computing Machinery, Arlington McKay MD, Beckman RJ, Conover WJ (1979) A comparison of three methods for selecting values of input variables in the analysis of output from a computer code. Technometrics 21(2):239–245 Mohamed AMO, Cote K (1999) Decision analysis of polluted sites—a fuzzy set approach. J Waste Manag 19:519–533 Mylopoulos YA, Theodosiou N, Mylopoulos NA (1999) A stochastic optimization approach in the design of an aquifer remediation under hydrogeologic uncertainty. Water Resour Manage 13(5):335–351 Nait-Said R, Zidani F, Ouzraoui N (2008) Fuzzy risk graph model for determining safety integrity level. International Journal of Quality, Statistics, and Reliability 2008:1–12 Pebesma EJ, Heuvelink GBM (1999) Latin hypercube sampling of Gaussian random fields. Technometrics 41:303–312 Qin XS, Huang GH (2008) Characterizing uncertainties associated with contaminant transport modeling through a coupled fuzzy-stochastic approach. Water Air Soil Pollut 197(1–4): 331–348 Qin XS, Huang GH, Huang YF, Zeng GM, Chakma A (2006) NRSRM: a decision support system and visualization software for the management of petroleum-contaminated sites. Energy Sources, Part A 28(1–3):199–220 Qin XS, Huang GH, Chakma A (2007) A stepwise-inference-based optimization system for supporting remediation of petroleum-contaminated sites. Water Air Soil Pollut 185(1–4):349–368 Qin XS, Huang GH, Zeng GM, Chakma A (2008a) Optimization of dual-phase vacuum extraction to remove nonaqueous phase liquids in subsurface. Water Resour Res 44:W04422 Qin XS, Huang GH, Li YP (2008b) Risk management of BTEX contamination in ground water—an integrated fuzzy approach. Ground Water 46(5):755–767 Qin XS, Huang GH, Yu H (2009) Enhancing remediation of LNAPL recovery through a response-surface-based optimization approach. Journal of Environmental Engineering (ASCE) 135(10):999–1008 Qin XS, Huang GH, Liu L (2010) A genetic-algorithm-aided chance-constrained programming model for regional air quality management under uncertainty. J Air Waste Manage Assoc 60(1):63–71 Rinsky RA, Young RJ, Smith AB (1981) Leukemia in benzene workers. Am J Ind Med 2:217–45 Rinsky RA, Smith AB, Horning R (1987) Benzene and leukemia: an epidemiologic risk assessment. N Engl J Med 316:1044–1050 Seuntjens P (2002) Field-scale cadmium transport in a heterogeneous layered soil. Water, Air, & Soil Pollution 140(1–4):401–423 Theodossiou NP (2004) Application of non-linear simulation and optimization models in groundwater aquifer management. Water Resour Manage 18(2):125–141 USEPA (U S Environmental Protection Agency) (1992) Guidelines for exposure assessment. EPA 600Z-92-001. U.S. Environmental Protection Agency, Washington USEPA (U S Environmental Protection Agency) (2002) Toxicological review of xylenes (CAS No. 1330-20-7). National Center for Environmental Assessment, Washington USOHEA (US Office of Health and Environmental Assessment) (1989) Exposure factors handbook. Report No. EPA /600/8-89/043. US Office of Health and Environmental Assessment, Washington Wyss GD, Jorgensen KH (1998) A user’s guide to LHS: Sandia’s Latin hypercube sampling software. Technical Report SAND98-0210. Sandia National Laboratories, Albuquerque

An Integrated Simulation-Assessment Approach for Evaluating Health Risks

3369

Xu Y, Huang GH, Qin XS, Cao MF (2009a) SRCCP: a stochastic robust chance-constrained programming model for municipal solid waste management under uncertainty. Resour Conserv Recycl 53(6):352–363 Xu Y, Huang GH, Qin XS (2009b) An inexact two-stage stochastic robust optimization model for water resources management under uncertainty. Environ Eng Sci 26(12):1765–1767 Xu Y, Huang GH, Qin XS, Cao MF, Sun Y (2009c) An interval-parameter robust optimization model for supporting municipal solid waste management under uncertainty. Waste Manage 30(2): 316–327 Xu Y, Huang GH, Qin XS, Huang Y (2009d) SRFILP: a stochastic robust fuzzy interval linear programming model for municipal solid waste management under uncertainty. J Environ Inform 14(2):1–9