Characterizing, simulating, and analyzing variability and uncertainty: An illustration of methods using an air toxics emissions example

Variability is the heterogeneity of values with respect to time, space, or a population. Variability may be quantified using frequency distributions. Uncertainty arises due to lack of knowledge regarding the true value of a quantity. Uncertainty may be quantified using probability distributions. These two concepts are distinct and, therefore, should be treated separately in an analysis. In this paper, methods for quantifying variability and uncertainty in model inputs, simulating variability and uncertainty in a model, and analyzing the results are presented. The method is demonstrated via an illustrative case study involving emissions characterization. The analysis of input data illustrates methods for characterizing variability and uncertainty when uncertainties arise due to sampling error (i.e., small sample sizes) or measurement error, as well as for dealing with differences in averaging times among multiple datasets. Correlation structures between sampling distributions representing uncertainty in frequency distributions were evaluated using bootstrap simulation. The frequency distributions for variability and the probability distributions for uncertainty were entered into a two-dimensional simulation framework in which the distinction between variability and uncertainty is maintained. The model output is a two-dimensional array of values which are analyzed to characterize the variability and uncertainty in the plant emission rate. The results are analyzed to identify the key sources of uncertainty and variability and to evaluate the likelihood that emissions will exceed limits from possible future regulations. The results are compared to one-dimensional probabilistic simulations. The benefits and limitations of two-dimensional simulation are evaluated. The applicability of the approach to other aspects of risk assessment is discussed.