In this paper, we employ bootstrap simulation methods to quantify both variability and uncertainty in air pollutant emissions. We illustrate the methods using examples of hazardous air pollutant (HAP) emissions from coal-fired power plants. 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. Methods for quantifying variability and uncertainty in model inputs, simulating variability and uncertainty in a model, and analyzing the results are presented. Gamma distributions are fitted to data for bituminous coal trace species concentrations of 11 HAPs. Partitioning factor data for major devices of a power plant, including the furnace and particulate matter control device, were used to estimate the parameters of Beta distributions. Bootstrap simulation was used to estimate the uncertainty in the parameters of the distributions and as the basis for a two-dimensional simulation of both variability in the measurements and uncertainty in the distributions used to represent variability. Uncertainty and variability in coal concentrations and partitioning factors were propagated through a model of power plant air toxic emissions to predict the uncertainty and variability in short term (three-day average) air toxic mass flow rates from the stack. In addition, the uncertainty in annual average emissions was simulated. These case studies illustrate how quantitative methods for analysis of variability and uncertainty may be used to develop insights regarding the state of knowledge regarding emissions estimates, development of and compliance with air pollutant regulations, and recommendations regarding additional data collection and research to improve predictions
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