Quantitative Analysis of Variability and Uncertainty in Emission Estimation: An Illustration of Methods Using Mixture Distribution. J. Zheng and H. C. Frey, N.C. State University
Emission inventory is a vital component of environmental decision-making. Errors in the emission factor can lead to errors in emission inventory estimation. Variability refers to the diversity over time or space, Uncertainty is a lack of knowledge about the true value of a quantity. Single distributions sometimes are not good fits to an emission factor dataset; however, in such situations, a mixture distribution might be a good fit. To improve the quantitative analysis of variability and uncertainty, this paper discuses parameter estimation of mixture distribution; evaluates the behavior of confidence interval on the cumulative distribution function of mixture distributions using synthetic datasets generated from the assumed population mixture distributions; develops an approach for quantifying variability and uncertainty using mixture distribution; illustrates the use of methods and compares results from the single distribution-based estimates and the mixture distribution-based estimates by using an empirical dataset of NOx emission factors in power plants from USEPA database. The results from synthetic datasets indicate that confidence interval tend to be wider in the central portion of the distribution compared to a single component model, the mixture distributions are better able to represent variability in a dataset but with a trade-off of wider confidence interval in the central portion of the distribution. The results from the empirical dataset indicate that a mixture Lognormal distribution is a better fit to describe the variability in the NOx emission factor for the selected case. Compared to single distributions, there are narrower uncertainty range and smaller random error when using a mixture Lognormal distribution.
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