Partitioning total variance in risk assessment: Application to a municipal solid waste incinerator

Abstract

Comprehensive health risk assessment based on aggregate exposure and cumulative risk calculations requires a better understanding of exposure variables and uncertainty associated with them. Although there are many sources of uncertainty in system models, two basic kinds of parametric uncertainty are fundamentally different from each other: natural/stochastic and epistemic uncertainties. However, conventional methods such as standard Monte Carlo Sampling (MCS), which assumes vagueness as random property, may not be suitable for this type of uncertainty analysis. An improved systematic uncertainty and variability analysis can provide insight into the level of confidence in model estimates, and it can aid in assessing how various possible model estimates should be weighed. The main goal of the present study was to introduce Fuzzy Latin Hypercube Sampling (FLHS), a hybrid approach for incorporating epistemic and stochastic uncertainties separately. An important property of this technique is its ability to merge inexact generated data of the LHS approach to increase the quality of information. The FLHS technique ensures that the entire range of each variable is sampled with proper incorporation of uncertainty and variability. A fuzzified statistical summary of the model results produces a detailed sensitivity analysis, which relates the effects of variability and uncertainty of input variables to model predictions. The feasibility of the method has been tested with a case study, analyzing total variance in the calculation of incremental lifetime risks due to polychlorinated dibenzo-p-dioxins and dibenzofurans (PCDD/Fs) for the residents living in the surroundings of a municipal solid waste incinerator (MSWI) in the Basque Country, Spain.

Introduction

Recent health risk assessment studies often consider aggregate exposure and cumulative risk calculation. Accumulated uncertainty in the final result can produce a misleading assessment if it is not incorporated adequately. Studies in risk analysis have shown that consideration of different sources of uncertainty may be crucial for reliable results. Uncertainty and ignorance associated with assessments and predictions on which to base policies make the communication even more difficult (van der Sluijs, 2007). The characterization and quantification of uncertainty and variability in health risk assessment are important to prevent erroneous inferences in multimedia modeling and exposure assessment, which may lead to major environmental policy implications (Frey and Zhao, 2004).

Several different classifications of uncertainty have been suggested (Alefeld and Herzberger, 1983, Haimes, 1998, van Asselt and Rotmans, 2002, Walker et al., 2003). However, for the objectives of the current study, only parametric uncertainty has been considered. The parametric uncertainty has been classified on the basis of its source and nature. Sources of parameter uncertainty are measurement errors, sampling errors, variability, and the use of surrogate data (Moschandreas and Karuchit, 2005). Measurement errors refer to random (imprecision) or systematic errors (bias), while sampling errors are errors from small sample size and/or misrepresentative samples. Heterogeneity in environmental and exposure-related data includes seasonal variation, spatial variation, and variation of human activity patterns by age, gender, and geographic location, leading to variability errors. Surrogate data refer to errors from the use of substitute data. van Asselt and Rotmans (2002) and Walker et al. (2003) classified uncertainty based on its nature. They called it epistemic uncertainty/imprecision, and stochastic uncertainty/natural variability. Epistemic uncertainty which results from incomplete knowledge about the system under study is reducible by additional studies (e.g. further research and data collection). Stochastic uncertainty which stems from variability of the underlying stochastic process is non-reducible for a given system and under specific management scenario. Natural variability has also been termed (basic) variability, randomly uncertainty, objective uncertainty, inherent variability, (basic) randomness, and type-I uncertainty. Terms for epistemic uncertainty are systematic uncertainty, subjective uncertainty, lack of knowledge or limited-knowledge uncertainty, ignorance, specification error, prediction error, and type-II uncertainty (Haimes, 1998, Rotmans and van Asselt, 2001, van Asselt and Rotmans, 2002, Merz and Thieken, 2005, Moschandreas and Karuchit, 2005, Refsgaard et al., 2007). In this paper, the term uncertainty is used to denote epistemic, variability to denote stochastic uncertainty, and total variance or simply variance to denote total uncertainty and variability in the outcome.

In spite of this obvious distinction, uncertainty and variability have been used as synonym. Some of the reasons are the blurred knowledge about uncertainty and variability and the lack of commonly agreed guidelines on uncertainty characterization and appropriate methodology. Consequently, in uncertainty estimation both types of uncertainty are clubbed together and treated as random variables, though epistemic uncertainty is not random in nature. The purpose of uncertainty analysis is to provide decision makers with a complete spectrum of information concerning the assessment and its quality. It also gives some scope to improve predictive results (Rotmans and van Asselt, 2001). When the uncertainty in the risk estimate is unacceptable for decision-making, additional data are acquired for the major uncertainty contributing model components. This process is repeated until the level of residual uncertainty is acceptable. For this we need to identify uncertainty components which are reducible. Further, separate measurements can provide us relevant information to the risk management decision (Spencer et al., 2001).

From a practical viewpoint, it is rare to encounter only one type of uncertainty. Pure variability would mean that all relations and their parameters which describe the random process are exactly known. Pure epistemic uncertainty would mean that a deterministic process is considered, but the relevant information cannot be obtained (e.g. due to the inability to measure the relevant parameters) (Merz and Thieken, 2005). For example, given a parameter X with total variance V_x, it can sometimes be straightforward to partition the variance into uncertainty and variability components, where α is the uncertainty component and (1 − α) attributable to variability (Fig. 1). Notwithstanding, there also can be an intermediate vague region in which uncertainty and variability commingle. So sometimes it is difficult to separate them and in that case it needs special handling to measure both uncertainty and variability together.

Several approaches to uncertainty analysis in environmental risk analysis have been developed (Isukapalli, 1999, Schulz and Huwe, 1999). Among them, probabilistic approaches (e.g. Monte Carlo Simulation) are quite common and have been commonly used in the treatment and processing of uncertainty for solution of system modeling (Schuhmacher et al., 2001). Another prominent approach based on fuzzy set theory (e.g. fuzzy α-cut analysis) has been recently applied in various fields including environmental modeling for uncertainty quantification (Isukapalli, 1999, Mauris et al., 2001, Cho et al., 2002, Hanss, 2002, Kentel and Aral, 2004, Kumar and Schuhmacher, 2005). However, this model has been branded as too conservative and basically applied in pure epistemic condition (Mauris et al., 2001). All these methods have been developed to handle either variability or uncertainty of the process parameters or they club them together without valid distinction in analysis. Few recent efforts have been made to treat them separately. One common approach used in this field is 2D Monte Carlo Analysis, which classifies epistemic uncertainty as second order uncertainty (Simon, 1999). This technique requires knowledge of parameter values and their statistical distribution from which a formal mathematical description of uncertainty must be developed. However, site investigation is generally not detailed enough to determine values for some of the parameters and their distribution pattern, and sufficient data may not be collected for calibrating a model (Kentel and Aral, 2005). These approaches suffer from an obvious lack of precision and specific site-characterization, making difficult to determine how much error is introduced into the result due to assumptions and prediction. Recently, a number of authors have suggested adopting other approaches in the data limited situation. Refsgaard et al. (2007) reported: ‘The test theory of classical statistics permits the testing of a sample for randomness. If the sample does not exhibit the property of randomness, other uncertainty models such as, e.g. fuzzy randomness must be adopted’. Previously, Möller et al. (2002) presented the idea of fuzzy randomness and formalized the concept of random variable and uncertain variable. Kentel and Aral (2005) introduced 2D Fuzzy Monte Carlo and applied it in the area of health risk assessment. 2D Fuzzy Monte Carlo and fuzzy randomness have been classified as hybrid approach mixing the concept of probability and fuzzy set theory. The present study aims to continue this area of research and introduces a new hybrid approach, Fuzzy Latin Hypercube Sampling (FLHS), for uncertainty and variability analysis. It needs lesser computational effort and allows incorporating parameters correlation. Further we present a way to apply sensitivity analysis in fuzzy–stochastic modeling paradigm. The feasibility of the method has been validated analyzing total variance in the calculation of incremental lifetime risks due to polychlorinated dibenzo-p-dioxins and dibenzofurans (PCDD/Fs) for the residents living in the surroundings of a municipal solid waste incinerator (MSWI) in the Basque Country, Spain.