Quantitative Analysis of Variability and Uncertainty in Emission Estimation: An Illustration of Methods Using Mixture Distributions

Air pollutant emission inventories are a vital component of environmental decision-making. Errors in emission factor estimation can lead to errors in emission inventory estimation. Potential sources of error include unaccounted for variability and uncertainty. Variability refers to diversity over time or space. Uncertainty is a lack of knowledge about the true value of a quantity. Probability distribution models can be used to describe variability in a data set and as a starting point for characterizing uncertainty, such as for mean values. Mixture distributions have the potential to be useful in the quantification of variability and uncertainty because they can improve the goodness of fit to a dataset compared to the use of a single parametric distribution. In this paper, parameter estimation of mixture distributions is discussed. An approach for quantifying the variability and uncertainty based on mixture distributions by using Bootstrap simulation is developed. An emission factor case study based upon NOx emissions from coalfired tangential boilers with low NOx burners and overfire air is used to illustrate the method. Results from the use of single parametric distributions are compared with results from the use of a mixture distribution. The case study results indicate that a mixture lognormal distribution is a better fit to the selected case compared to single distributions. Furthermore, the estimate of the range of uncertainty in the mean is narrower with the mixture distribution than with the single component distribution, indicating that the mixture distribution has the potential to yield more "efficient" statistical estimates. This project is one component of a larger effort aimed at developing improved methods for characterizing uncertainty in emission inventories.

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