The Sensitivity of Probabilistic Risk Assessment ...

Journal of the Air & Waste Management Association

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The Sensitivity of Probabilistic Risk Assessment Results to Alternative Model Structures: A Case Study of Municipal Waste Incineration Alison C. Cullen To cite this article: Alison C. Cullen (1995) The Sensitivity of Probabilistic Risk Assessment Results to Alternative Model Structures: A Case Study of Municipal Waste Incineration, Journal of the Air & Waste Management Association, 45:7, 538-546, DOI: 10.1080/10473289.1995.10467385 To link to this article: http://dx.doi.org/10.1080/10473289.1995.10467385

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TECHNICAL PAPER

ISSN 1047-3289 /. Air & Waste Manage. Assoc. 4 5 : 538-546 Copyright 1995 Air & Waste Management Association

The Sensitivity of Probabilistic Risk Assessment Results to Alternative Model Structures: A Case Study of Municipal Waste Incineration Alison C. Cullen Harvard School of Public Health, Department of Environmental Health, and Harvard Center for Risk Analysis, Boston, Massachusetts ABSTRACT In this analysis, human health risk due to exposure to municipal waste incinerator emissions is assessed as an example of the application of probabilistic techniques (e.g., Monte Carlo or Latin Hypercube simulations). Incinerator risk assessments are characterized by the dominance of indirect exposure, thus this analysis focuses on exposure via the ingestion of locally grown foods. In addition, since exposure to 2,3,7,8-TCDD drives most incinerator risk assessments, this compound is the subject of the illustrative calculations. An important part of probabilistic risk assessment is determining the relative influence of the input parameters on the magnitude of the variance in the output distribution. This constitutes an important step toward prioritizing data needs for additional research. However, under various possible model forms reflecting incompletely understood aspects of contaminant transport, differences may be observed in estimates of risk, variance in risk, and the relative contributions of individual uncertain and variable inputs to the variance. In this analysis, a sequential structural decomposition of the relationships between the input variables is used to partition the variance in the output (i.e., risk) to identify the most influential contributors to overall vari-

IMPLICATIONS Risk assessments performed to inform incinerator siting decisions generally find that indirect exposures, such as the consumption of locally derived foods, dominate human exposure to incinerator emissions. Estimates of exposure via indirect pathways are a function of the rate of deposition of airborne contaminants. Deposition rate in turn depends on assumptions made regarding the character of airborne contaminants as well as about their partitioning between the gas and particle phases. This is especially true of semi-volatile compounds, e.g., dioxins and furans, which tend to drive risk estimates. This analysis shows that results of probabilistic risk assessments are sensitive to selection of models representing the fate and transport of these contaminants, especially assumptions about gas/particle partitioning. Estimates of exposure and risk, and also the magnitude of uncertainty and variability in these estimates, are found to be sensitive to such assumptions.

538


ance among them. For comparison, the partitioning of variance is repeated, using techniques of multivariate regression. In summary, this study considers the degree to which results of a probabilistic assessment are contingent on critical model assumptions about the representation of deposition velocity. Specifically, this analysis assesses the impact on the results of uncertainty about the best model of the vapor/particle partitioning behavior of semivolatile airborne pollutants. INTRODUCTION Probabilistic approaches increasingly are used to estimate distributions of individual risk reflecting uncertainty and variability in human health risk for a range of proposed facilities and activities. Risk assessments performed during the siting of municipal solid waste combustors (MSWCs) have been the subject of several of these analyses. The distributions produced represent an improvement over deterministic point estimates; however, they are sometimes difficult to interpret. This analysis explores available techniques which assist in the interpretation of the results of probabilistic analyses. The focus is a narrowly defined example, i.e., ingestion exposure to 2,3,7,8-TCDD (referred to hereafter as "dioxin") through consumption of locally grown produce in the vicinity of an MSWC, a pathway contributing a significant portion of the risk attributable to many such facilities.1 Further, this pathway is represented by a number of complex fate, transport, and exposure models that provide a revealing look at the sensitivity of probabilistic results to model assumptions. Several researchers have specifically examined contributors to uncertainty in human exposure to emissions from MSW incinerators.2-6 These analyses report that variance in risk from ingestion of contaminated crops may span three to four orders of magnitude. Particle deposition velocity and ambient concentration of air contaminants are identified as major contributors to variance. However, although basic research indicates that deposition velocity is strongly dependent on particle diameter, its variability and uncertainty are combined in the probabilistic descriptions developed. In short, often a single distribution is assigned to represent particle deposition velocity, in spite of the dependence of deposition velocity on particle size.7 Volume 45 July 1995

Cullen Admittedly, a lack of knowledge about the vapor/particle partitioning of dioxin emitted from MSW incinerators further complicates the correct treatment of the relationship between particle diameter and deposition velocity.810 The magnitude of indirect human exposure (e.g., via ingestion) is proportional to deposition velocity, which in turn depends on partitioning status and, where relevant, particle diameter. There are two plausible but incompatible views about dioxin's partitioning. It is possible that a large fraction of airborne dioxin emanating from incinerators exists as a vapor, according to predictions of its state under thermodynamic stability dictated by its subcooled liquid vapor pressure.9-11-12 In the present context, this view incorporates a non-equilibrium assumption holding that the kinetic processes necessary to bring about binding to particulate matter lag behind the dilution of the plume. 13 This assumption is used in the base case analysis in this work. The opposing view, that dioxin is largely sorbed to particulate matter, is supported by the belief that the vapor pressure over the solid describes its partitioning in the ambient environment, and is the alternative case. Among physical chemists, the former view is increasingly favored. In summary, this analysis investigates the importance of alternative models in a probabilistic risk assessment simulation. To this end, cases are considered which adopt opposing assumptions about the phase behavior of airborne dioxin—i.e., vapor phase versus particle bound. A comparison of risk distributions generated under the two model assumptions is presented. Also, major contributors to uncertainty and variability are identified, and the relative significance of uncertainty and variability in risk is gauged. In addition this analysis assesses the effectiveness of an explicit treatment of the relationship between particle size and several inputs (e.g., deposition velocity) in resolving a significant amount of the variance in the output distribution of risk. METHODS The measure of human risk estimated in this analysis is the lifetime risk of developing cancer, for an individual living and working in the "sector" of the maximum incremental concentration of contaminants in air due to the presence of an MSWC as established by a plume dispersion model.14 Any specific individual's risk is a function of the location of that person's residence and workplace, the efficiency of transport of contaminants emitted from the facility, and the form and manner in which the contaminants are released. In addition, risk depends on an individual's rate of intake of contaminated media (in this analysis, air and food), body weight, and susceptibility to cancer. Incremental cancer risk to an individual in the zth sector is computed according to the following model (sectors are identified by subscript i). Volume 45 July19iS

Figure 1 . Dispersion factors between 400 and 30,000 meters from the source (dispersion factors in |xg/m3/mg/s; distances are on a log scale). R

Bw

(1)

R, =

incremental risk of cancer to an individual, living in sector i (lifetime incremental increase in probability of developing cancer) P = cancer potency factor for dioxin (mg/kg/day) 1 Bw = body weight of an individual, lifetime weighted average (kg) Ih, = average daily intake due to inhalation, for an individual in sector i (mg/d) Ig, = average daily intake due to ingestion of crops grown in sector / (mg/d) In the example calculations, the Industrial Source Complex Long Term model (ISCLT), a sector-averaged Gaussian model,15 is run with five years of climatic data (1970-1974) from Bridgeport, CT, to estimate the annual average concentration of airborne dioxin at ground level within annular sectors located 400, 600, 800,1,000,1,500, 2,500,4,000, 7,000,10,000, 20,000, and 30,000 meters from a proposed facility (Figure 1). As stated above, the focus of the example is uncertainty in the risk estimate for a receptor living and working in the sector where the maximum concentration of dioxin in ambient air is expected, i.e., about a kilometer from the source; however, the spatial variability in exposure evident in Figure 1 is also discussed. Depletion of airborne dioxin between the source and the previously indicated receptor locations was calculated based on the output from ISCLT. Characteristics of the incinerator and emissions are drawn from EPA's Municipal Waste Combustion Survey with modifications to reflect periods of less Journal of the Air & Waste Management Association

539

Cullen

1

2

3

4

5

6

7

8

9

10

Figure 2. Loguniform distributions for deposition velocity by particle diameter.

than optimal performance.16 Distributions of other input parameters and the structure of the risk submodels are drawn from the primary literature (Tables 1-3 and Figure 2). All distributions are designed to reflect long term averaging suitable for cancer risk assessment and are discussed in detail elsewhere.18 Latin Hypercube simulations of 1,000 realizations each (Crystal Ball™) are used to analyze the propagation of error.

Input distributions are truncated at three standard deviations above and below the median to avoid the assignment of physically meaningless values. The analysis was also repeated without truncation of input distributions, and no significant difference in results was observed. Two cases are considered in this analysis. Under "base case" assumptions: (1) two-thirds of the airborne dioxin mass is assumed to occur as a vapor, and (2) the sorbed mass of dioxin is distributed on particulate matter in proportion to particle mass. The dominant sources contributing to overall variance in the risk estimate are identified. Also a sensitivity analysis is performed in which the vapor/particle partitioning model is altered and the airborne dioxin is assumed to be entirely sorbed to particulate matter. Two approaches are used to assess the relative importance of the variance in individual input parameters to the overall variance in risk, multivariate regression, and structural decomposition. Since functional relationships between risk and some of the basic variables are nonlinear, only a portion of the variance in risk can be explained by the linear regression model. In any case, the relative importance of each input parameter in predicting the variance in risk is equivalent whether the ranking is established via the standardized regression coefficient, the t-statistic, or the partial correlation coefficient.45 In the decomposition analysis, information on the structural relationships between the variables was used to partition the

Table 1 . Inputs to risk calculations. Input

Definition

Distribution

Form and Parameters

References

P

cancer potency factor for dioxin (1/(mg/kg-d)) decay rate constant of contaminant in soil (1/day) body weight (kg) depth of mixed layer of soil (m) the dispersion factor calculated for the /th sector, using the ISCLT model, ((mg/m3)/(mg/s)) deposition fraction in the lung for particle or vapor class j a , assuming all deposited material is bioavailable (fraction) interception fraction for depositing particles and vapor by crop k b(fraction) inhalation rate of an individual, weighted lifetime average (m3/day) daily consumption of locally grown crop k, lifetime average (g/day)

Lognormal Uniform Lognormal Uniform

med=40000, gsd=2.0 0.0001 -0.0002 med=65, gsd=1.2 0.15-0.25

3,17,18 19,20 21,22 23 24,25

Lognormal

med=0.00017, gsd=1.4

Uniform

by diameter, see Table 3

Uniform

rootylne, tree: 0.05-0.25 leafy: 0.16-0.4

5,28

Lognormal Lognormal

med=0.00017, gsd=1.4 root,leaf:med=12.5,gsd=1.8 vine: med=35.0, gsd=1.8 tree: med=20.0, gsd=1.8 1.5x10-6-5x10-6

21,22 29,30

med=1.4, gsd=1.15 vine: 90-110 tree: 120-150 leafy: 40- 60 root: 0.25 -1.0 vine, leafy: 0.05-0.15

37

b Bw D Df. Dr J

Ir

K

26,27

Loguniform

P

contaminant mass emitted by incinerator, annual average, (mg/s); see Table 3 bulk density of soil (g/m3)

%

duration of growing season for crop /((day)

Uniform

root uptake factor, for translocation of contaminant into crop type /((fraction), i.e., the ratio of the concentration in plant tissues to the concentration in soil deposition velocity of particle or vapor class y, (m/day) weathering rate constant of particulate adhering to crop (1/day) yield of crop k (g/m2)

Uniform

Q

u

*

Vd. W

Lognormal

16,31-36

38 39-41

Loguniform

med by diameter, var=.8 log units

7,42,43

Loguniform

0.01-0.1

37

Uniform

vine, tree: 5-15 leafy; 6-10

44

a To account for size dependencies of several key parameters, subgroups were established by particle diameter, each with size-specific properties, identified by subscript y, as shown in Table 3 and Figure 2. b The incremental intake due to ingestion is the sum over all crops of the dose due to ingesting each crop. Individual crops are subscripted k, i.e., root, vine, leafy, or tree. Not all inputs with subscript kare listed for all four crop types since 1) accumulation of dioxin in root crops is modeled through the equation for root uptake only (i.e., Cpr^, Table 2), and 2) accumulation of dioxin by tree crops is modeled through the equation for foliar uptake only (i.e., Cpa/k, Table 2).18 Accumulation of dioxin in vine and leafy crops is modeled as the sum of Cpa,A and Cpr/7(; thus all crop specific inputs are listed for these two crop types.

5 4 0 Journal of the Air & Waste Management Association

Volume 45 July 1995

Cullen Table 2. Submodels of the risk calculation.

Intermediate Result

Mathematical Expression

Definition

Ih,.

XlrDr, Ca,y

(in text) (in text) annual average concentration in air, particle or vapor class / at ground level in sector / (mg/m3)

Ca,,

contaminant concentration in plant tissue, crop k from sector / (mg/g)

Cp Cpa

c)

7

Cpr,

contribution to concentration in crop k incorporated via foliar uptake (mg/g)

(W)

contribution to concentration in crop k from root uptake (mg/g)

Cs,.

Cs,.

long term average concentration of contaminant in surface soil in sector / (mg/g).

1 1

\/

7 bDp

Table 3. Distributions for particle diameter specific input parameters.*

Deposition in Respiratory Tract

Deposition Velocity (m/d)

Categories (diameters in mm)

(%) Dr uniform

log(Vd) median

Fraction of Source(%Q) Distribution by Particle Mass 2/3 Vapor All Sorbed 1/3 Sorbed

gas

85-100%

3

67.0%

8.1

85-100%

3

4.0%

18.0%

RESULTS Estimation of Risk and Variance in Risk

'References appear in Table 1.

Table 4. Latin Hypercube results—base case partitioning of dioxin. Risk Incremental Percentile Lifetime Increase

Ingestion Dose mg/kg/d

Inhalation Concentration Dose in Vine Crops mg/kg/d mg/g

5%

7.2 E-06

2.1 E-10

4.3E-11

1.3 E-10

25%

3.3 E-05

7.8E-10

7.5E-11

4.0 E-10

50%

8.1 E-05

2.0 E-09

1.0 E-10

9.0 E-10

75%

2.1 E-04

5.0 E-09

1.6 E-10

2.4 E-09

95%

9.1 E-04

1.9 E-08

2.7 E-10

7.6 E-09

126

90

6

58

Ratio of 95%/5%

Volume 45 July 1995

variance in the risk estimate. The fraction of the overall variance in risk attributed to a given input can be calculated by multiplying the fraction of variance associated with each input by the regression R2, which is the fraction of the overall variance in risk explained collectively by the input variables. Where variance is partitioned among correlated inputs, the portion attributable to covariance is also calculated and represented in a tree format.

The base case results suggest that the median increment in individual lifetime cancer risk in the sectors with maximal predicted air concentrations is about 8 x 1O5 (Table 4, Figure 3).46 Two orders of magnitude lie between the ninetyfifth percentile and fifth percentile of the risk distribution, an indication of its overall spread. The median ingestion dose is twentyfold greater than the median inhalation dose. The ninety-fifth percentiles of the ingestion and inhalation doses differ by two orders of magnitude, with ingestion surpassing inhalation in importance. These results can be compared to those generated in previous analyses. Although several sources of variance not considered in other analyses were included in this analysis,24 (e.g., model uncerConcentration tainty associated with the Gaussian disin Soil persion approach and uncertainty mg/g about the impact of upset periods on emissions), the estimate of uncertainty in dose via the crop ingestion route is 1.8 E-09 similar or smaller in magnitude than 4.2 E-09 previous estimates. The use of a par9.8 E-09 ticle size distribution for incinerator 2.6 E-08 emissions and a linked set of distri8.4 E-08 butions for deposition velocity with particle size in predicting deposition 47 flux to soil and plant surfaces in the Journal of the Air & Waste Management Association

§41

Cullen particle deposition velocity, and the importance of deposition in determining the concentration of dioxin in soil and crops. In contrast, uncertainty about the inhalation dose is independent of the assumption made about the vapor/solid partitioning of dioxin, since the deposition of airborne dioxin between the source and the receptor location of interest is negligible; i.e., only about 1% of the mass is deposited within 1500 meters of the source.

Base Case S

Risk

10-3 •

lO"4-

^F \^r

All Sorbed Case

Apportionment of Overall Variance Among Key Contributors

10-5-

IO"6-

/

o -7 _ 10 T ' .01 .1

1

i i i 99 99.999.99

i 1 I 1 ! 5 10 2030 50 7080 9095 Cumulative Density

Figure 3. A comparison of Latin Hypercube simulated distributions of risk under two models of gas/particle partitioning.46

present analysis may explain the difference. The finding that ingestion exposure is significantly greater than inhalation exposure is consistent with many earlier analyses.24-47

Sensitivity of the Results to Uncertainty about Dioxin Partitioning Behavior To assess the sensitivity of the results to assumptions about the vapor/particle partitioning behavior of dioxin, an alternative assumption was adopted, i.e., that airborne dioxin is sorbed to particles. In the "all sorbed case" the medians of the concentration, exposure, and risk distributions are smaller in magnitude than under the base case (Figure 3, Table 5). There is also less spread in these distributions. This result is a consequence of the greater degree of uncertainty associated with vapor deposition velocity, relative to Table 5. Latin Hypercube results—dioxin all sorbed case.

Risk Incremental Lifetime Increase

Ingestion Dose mg/kg/d

Inhalation Concentration Dose in Vine Crops mg/kg/d mg/g

5.1 E-06

1.7 E-10

3.0E-11

25%

1.7E-05

4.6 E-10

5.3E-11

2.3 E-10

50%

3.4 E-05

7.9 E-10

8.0E-11

4.3 E-10

75%

7.5 E-05

1.5 E-09

1.2 E-10

7.6 E-10

95%

2.1 E-04

3.5 E-09

2.1 E-10

1.5 E-09

41

21

7

15

Percentile

5%

1.0 E-10

The results of the structural decomposition analysis are displayed in Figures 4 and 5. For the base case the fraction of the variance in risk attributable to uncertainty about cancer potency is about 12%, i.e., 25% if considered as a fraction of the explained variance (R2 = 0.46), which is consistent with the answer provided by the standardized regression coefficient (Figure 6).48 The results from the two approaches for partitioning of variance agree closely across all the inputs. The assumption made about the partitioning of dioxin between vapor and solid influences the relative dominance of inputs (Figures 4 and 5). A smaller fraction of the variance in risk is attributable to dose (61%) and a greater share to potency (39%) when all the dioxin is assumed to sorb to particulate matter, than under the base case. Uncertainty about the deposition of vapor, previously a major contributor to overall variance, is not an input in the dose calculation under this model and uncertainty about cancer potency assumes more importance.

Uncertainty and Variability in Risk Although the terms uncertainty and variability are sometimes used interchangeably, they are distinct. Uncertainty generally is considered to arise from errors of omission, specification, measurement, or extrapolation, while variability refers to spatial, temporal, physiological, and behavioral differences between individuals or elements in a population or larger group.49 Results of probabilistic analyses increasingly are reported in a form in which inter-individual variability is partitioned from uncertainty to facilitate consideration of their different sources and implications in a decision-making context. In truth Concentration most inputs are neither solely uncerin Soil tain, nor solely variable, but may be mg/g roughly categorized. For example, in this analysis the model inputs repre1.3 E-09 senting body weight, inhalation rate, 2.5 E-09 and rate of consumption of locally 4.5 E-09 grown crops may be classified as vary7.5 E-08 ing inter-individually, whereas the re1.5E-08 mainder of the inputs is uncertain.

Ratio of 95%/5%


12

To partition the variance in individual risk into uncertainty and Volume 45 July 1995

Cullen Vapor Deposition Vet,

Cnsmptn Rate 58% Crop Factors 42% Cnsmptn Rate 65% Crop Factors 35% Cnsmptn Rate

69% Crop Factors 31% Ri.sk

Figure 4. Structural decomposition of the variance in risk under the base case partitioning assumption.

Root 72%

Vine Consumption 39%

15%

Ingestion >99%

Cnsmptn Rat a 58% Crop Faetori 42% Cnsmptn Rate 85% Crop Factors 35% Cnsmptn rate 69% Crop Factors 31%

Intake Dose Risk

94%

11%

61%

i Inhalation

iDiaprsn Fastr 13% {Emissions 15% [Depoatn-prtcl 33% Dlsprsn Factr 37% Emissions 40% Inhalatn Rate l 11 % L R&splf. Dspo8. 12%

[Body Weight 6% Cineer Ptney 39%

Figure S. Structural decomposition of the variance in risk under the assumption that all dioxin is sorbed to particulate matter. Volume 45 July 1995


543

Cullen

All Sorbed Case

Base Case Olhci 15%

L-or Potency Factor 25%

Ciiikcr Potency Faclor

Consumption Ratc-Rool 6%

Dispersion Factor

Consumption Rate-Root

Deposition Velocity-Vapor 48%

Dispersion !• Deposition Velocity-Particles 17%

Figure 6. Portion of overall variance in risk attributable to individual inputs.

variability, the simulation was repeated. First the uncertain inputs were fixed at their median values and the variable inputs were allowed to vary, and then the variable inputs were fixed at their median values and the uncertain inputs were allowed to vary. In this case, 88% of the total variance in individual risk in the base case was contributed by uncertain inputs and 12% was contributed by inter-individually varying inputs. On closer inspection it is clear that a more general result could have been obtained quite simply. Specifically, since a limited number of inputs dominates the variance so completely, this complex model can be written as a simple product of four uncertain terms, one variable term, and one constant, which capture about 90% of the explained variance of the full model:

- Reduced Risk Model - Eq. (2)

io-3-

Uncertain Onlj

o io-4-

Variable Only

io-5-

10*-

.01 .1

1

5 10 2030 50 7080 9095

99

99.999.99

Cumulative Density

Figure 7. A comparison of three cases of Latin Hypercube generated distributions of risk (reduced risk model, uncertain only, variable only). 544


= (3DfQVdMrK

(2)

In this model, K is a constant replacing all of the less influential terms. All terms contributing to K are of sufficiently small variance that representing each with a constant value selected from any fractile of its given distribution does not appreciably alter the base case results. The variance in this product is readily partitioned among the uncertain and variable terms,46-50 approximating the result described above (Figure 7). Finally, to explore the representativeness of risk in the sector of maximum ambient air concentration, the magnitude of the spatial variability in dispersion was considered (Figure 1), as well as the magnitude of air concentrations and ultimately exposure, which would form the basis of a population risk estimate. Spatial variability in dispersion within a 30 km radius is similar in magnitude to the total variance in individual risk estimated in this analysis. Both the spatial variability in concentration and the variance in the estimate of individual risk have 95% bounds which span approximately two or three orders of magnitude. Thus, for the case and location considered, the estimates of risk for individuals residing in the sector of maximum air concentration are within two or three orders of magnitude of risk estimates that could be generated for individuals in less contaminated sectors within a 35 km radius of the facility. DISCUSSION In summary, it is evident that probabilistic assessment results are sensitive to model assumptions and model uncertainties. This sensitivity is sufficient to alter conclusions about the magnitude of estimates of exposure and risk, the uncertainty and variability associated with these estimates, and the specific inputs contributing most significantly to uncertainty in a decision variable. In this analysis, uncertainty about cancer potency, deposition velocity, the rate of consumption of specific foods, the rate of emissions from a facility and the dispersion behavior of the plume are the most important contributors to overall variance in risk. Volume 45 July 1995

Cullen Due to the overwhelming dominance of a handful of multiplicatively combined inputs over the total variance in risk, this complex model red&es to a simple product in which uncertainty and inter-individual variability are easily separated. In this example, inputs defined as uncertain contribute much of the spread in the overall risk distribution. Of course, cancer potency could be reclassified as a variable input, since it is without question a quantity that varies among individuals, and efforts could be made to quantify that variability, potentially reversing this finding. Still, extrapolations between species, and between experimental doses and environmental exposures, introduce a very high degree of uncertainty into the cancer potency factor for dioxins, and thus the current classification seems warranted. As discussed above, in many crop ingestion exposure assessments, deposition velocity is found to be the dominant source of uncertainty. The present analysis represented deposition velocity by ten individual distributions linked with features of partitioning and particle diameter, resulting in a reduction in absolute variance in exposure and risk.2-6 However, despite this detailed treatment, uncertainty about the deposition velocity of either particles or vapor remains an important contributor to overall uncertainty in exposure and risk relative to other inputs. ACKNOWLEDGMENTS

The author wishes to thank John Evans and Alan Eschenroeder for helpful comments during the preparation of this manuscript. Support from the Switzer Foundation, Lawrence Livermore National Laboratory, the Silverman Fund, and the Harvard Center for Risk Analysis is gratefully acknowledged. REFERENCES Levin, A.; Fratt, D.B.; Leonard, A.; Bruins, R.J.F.; Fradkin, L."Comparative analysis of health risk assessments for municipal waste combustors," /. Air & Waste Manage. Assoc. 1991, 41, 20-31. McKone, T.E.; Ryan, P.B. "Human exposures to chemicals through food chains: An uncertainty analysis," ES&T 1989, 23, 1154-1163. Fries, G.F.; Paustenbach, D.J. "Evaluation of potential transmission of 2,3,7,8-tetrachlorodibenzo-p-dioxin contaminated incinerator emissions to humans via foods," /. ofTox. and Env. Health 1990, 29, 1-43. Belcher, G.D.; Travis, C.C'An uncertainty analysis of food chain exposure to pollutants emitted from municipal waste combustors," Ch. 11 in Health Effects of Municipal Waste Incineration; HattemerFrey, Holly; Travis, Curtis, Eds.; CRC Press, 1991. Breshears, D.D.; Kirchner, T.B.; Otis, M.D.; Whicker, F.W. "Uncertainty in predictions of fallout radionuclides in foods and of subsequent ingestion,"Health Physics 1989, 57, 943-953. Crick, M.J.; Hofer, E.; Jones, J.A.; Haywood, S.M. "Uncertainty analysis of the food chain and atmospheric dispersion modules of MARC"; National Radiological Protection Board: Chilton, Oxfordshire, England, 1988 (NRPB-R184). Sehmel, G.A. "Particle and gas dry deposition: a review," Atm. Env. 1980, 14, 983-1011. Eitzer, B.D.; Hites, R.A. "Concentrations of dioxins and dibenzofurans in the atmosphere," Int. J. Environ. Anal. Chem. 1986, 27, 215-230. Bidleman, T.F. "Atmospheric processes," ES&T 1988, 22, 361-367. 9. 10. Pankow, J.F.; Bidleman, T.F. "Interdependence of the slopes and intercepts from log-log correlations of measured gas-particle partitioning and vapor pressure -1. Theory and analysis of available data," Atm. Env. 1992, 26A, 1071-1080. 1.

Volume 45 July 1995

11. Eitzer, B.D.; Hites, R.A. "Polychlorinated dibenzo-p-dioxins and dibenzofurans in the ambient atmosphere of Bloomington, Indiana," ES&T 1989, 23, 1389-1396 . 12. Rounds, S.A.; Tiffany, B.A.; Pankow, J.F. "Description of gas/particle sorption kinetics with an intraparticle diffusion model: desorption experiments," ES&T 1993, 27, 366-377. 13. Eschenroeder, A.Q.; von Stackelberg, K.; Taylor, A.C. "Gas/particle partitioning influences exposures to heavy organic carcinogens," presented at the 1992 Annual Meeting of the Society for Risk Analysis. 14. A sector in this analysis is defined as one sixteenth of an annular ring, an area bounded by two specified distances from the incinerator stack or source radially, and representing one of the 16 compass points. 15. Bowers, J.F.; Bjorkland, J.R.; Cheney, C.S. Industrial Source Complex (ISC) Dispersion Model User's Guide, Vol. I & I I ; U.S. Environmental

Protection Agency: Research Triangle Park, North Carolina, 1979 (EPA-450/4-79-030 and -031). 16. U.S. Environmental Protection Agency. Municipal Waste Combustor Study; Office of Solid Waste and Emergency Response, Office of Air and Radiation, Office of Research and Development, 1987 (EPA/ 530-SW-87-021). 17. Keenan, R.E.; Wenning, R.J.; Parsons, A.H.; Paustenbach, D.J. "A reevaluation of the tumor histopathology of Kociba et al. (1978) using 1990 criteria: implications for the risk assessment of 2,3,7,8-TCDD using the linearized multistage model," Dioxin '90 EPRI Seminar Toxicology-Environment, Food, Exposure-Risk; Hutzinger,

O.; Fiedler, H., Eds.; Ecoinforma Press: Bayreuth, Germany, 1990. 18. Taylor, A.C. "Addressing the uncertainty in the estimation of environmental exposure and cancer potency," Sc.D. Thesis, Harvard School of Public Health, 1992. 19. Young, A.L. "Long term studies on the persistence and movement of TCDD in a natural ecosystem," In Human and Environmental Risks of Chlorinated Dioxins and Related Compounds; Tucker, R.E.; Young, A.L.; Gray, A.P., Eds.; Plenum Press: New York, 1983, 173-190. 20. Kimbrough, R.; Falk, H.; Stehr, P.; Fries, G. "Health implications of 2,3,7,8-tetrachlorinated dibenzo-p-dioxin contamination of residential soil," J of Tox. and Env. Health, 1984, 14, 47-93. 21. U.S. Environmental Protection Agency. "Methodology for characterization of uncertainty in exposure assessments," Office of Health and Environmental Assessment, Exposure Assessment Group: Washington, D.C., 1985 (EPA/600/8-85-009, NTIS PB85-240455, 1985a). 22. U.S. Environmental Protection Agency. "Health assessment document for polychlorinated dibenzo-p-dioxins," Office of Environmental Assessment: Cincinnati, OH, 1985 (EPA-500-8-84-014f, 1985b). 23. Cleverly, D.; Fradkin, L; Bruins, R.; McGinnis, P.; Dawson, G.; Bond, R. "Methodology for the assessment of health risk associated with municipal waste combustor emissions"; U.S. Environmental Protection Agency, Office of Health and Environmental Assessment: Cincinnati, OH, 1986 (EPA-530-SW-87-021g). 24. Freeman, D.L.; Egami, R.T.; Robinson, N.F.; Watson, J.G. "A method for propagating measurement uncertainties through dispersion models," JAPCA 1986, 36, 246-253. 25. Simpson, R.W.; Hanna, S.R. "A review of deterministic urban air quality models for inert gases"; National Oceanic and Atmospheric Administration: Silver Spring, MD, 1981 (NOAA-TM-ERL-ARL-106). 26. Brain, J.D.; Valberg, P.A. "Deposition of aerosol in the respiratory tract," American Review of Respiratory Disease 1979,120, 1325-1373. 27. Lippmann, M. "Regional deposition of particles in the human respiratory tract," in Handbook of Physiology, Reaction to Environmental Agents, Lee, D.H.K; Falk, H.L.; Murphy, S.O.; Geiger, S.R., Eds.; American Physiological Society: Bethesda, MD, 1977. 28. Miller, C.W.; Hoffman, F.O. "An examination of the environmental half-life for radionuclides deposited on vegetation," Health Physics 1983, 45, 731. 29. U.S. Environmental Protection Agency. "Exposure Factors Handbook"; Office of Health and Environmental Assessment: Washington, D.C., 1989 (EPA 600/8-89/043). 30. U.S. Deparment of Agriculture. "Food Consumption: Households in the United States, Seasons and Year, 1977-8," 1983. 31. Goldfarb, T.A. Prefiled testimony before New York Department of Environmental Conservation Office of Administrative Law, in the matter of the application of Signal Environmental Systems for permits to construct and operate the proposed Brooklyn Navy Yard Resource Recovery Facility, DEC Project no. 20-85-0306, New York, 1988. 32. Denison, R.A.; Silbergeld, E.K. "Risks of municipal solid waste incineration: an environmental perspective," Risk Analysis 1988, 8, 343-355. Journal of the Air & Waste Management Association

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46.

Figures 3 and 7 contain distributions of risk generated by Latin Hypercube simulation under various sets of assumptions. The individual risk estimates from each iteration of the simulation are ordered and then plotted on probability paper with a logscaled vertical axis. As the plotted points arise from an underlying distribution that is primarily a product of many distributions, they approximate a lognormal distribution and the plot approximates a line. Further, the parameters of that lognormal distribution may be read from the plotted line; i.e., the slope corresponds to the geometric standard deviation and the intercept corresponds to the median. Thus, a steeper slope indicates greater variance in risk and an upward shift of the 50th percentile indicates a greater median estimate of risk. 47. Nessel, C.S.; Butler, J.P.; Post, G.B.; Held, J.E.; Gochfeld, M.; Gallo, M.A. "Evaluation of the relative contribution of exposure routes in a health risk assessment of dioxin emissions from a municipal waste incinerator,"/- ofExp. An. andEnv. Epi. 1991, 1, 283-307. 48. For exposure model inputs appearing on the tree structure, the overall portion of variance attributable is calculated as the product of all the probabilities along the path from the left-most node to that input. If the input appears on multiple paths in the tree, the sum of the product probability for each path is calculated. 49. Bogen, K.T. Uncertainty in Environmental Health Risk Assessment. Garland Publishing: New York, NY, 1990. 50. Partitioning of the variance in the Reduced Risk Model (Figure 7) into uncertainty and inter-individual variability follows from the rules governing the addition in quadrature of the standard deviations of factors in a product. The parameters of the lognormal distributions depicted in Figure 7 are used in this calculation under the approach described above (see Reference 46).

About the Author Alison C. Cullen is an assistant professor at the Harvard School of Public Health, jointly appointed by the Harvard Center for Risk Analysis and the Department of Environmental Health. This work was completed at the Harvard Center for Risk Analysis, 718 Huntington Avenue, Boston, MA 02115.

Volume 45 July 1995