i ABSTRACT ZHENG, JUNYU. Quantification of Variability and Uncertainty in Emission Estimation

323 Pages·2002·2.76 MB·English

ABSTRACT

ZHENG, JUNYU. Quantification of Variability and Uncertainty in Emission Estimation:
General Methodology and Software Implementation.(Under the supervision of Dr. H.
Christopher Frey).
The use of probabilistic analysis methods for dealing with variability and
uncertainty is being more widely recognized and recommended in the development of
emission factor and emission inventory. Probabilistic analysis provides decision-makers
with quantitative information about the confidence with which an emission factor may be
used. Variability refers to the heterogeneity of a quantity with respect to time, space, or
different members of a population. Uncertainty refers to the lack of knowledge regarding
the true value of an empirical quantity. Ignorance of the distinction between variability
and uncertainty may lead to erroneous conclusions regarding emission factor and
emission inventory. This dissertation extensively and systematically discusses
methodologies associated with quantification of variability and uncertainty in the
development of emission factors and emission inventory, including the method based
upon use of mixture distribution and the method for accounting for the effect of
measurement error on variability and uncertainty analysis. A general approach for
developing a probabilistic emission inventory is presented. A few example case studies
were conducted to demonstrate the methodologies. The case studies range from utility
power plant emission source to highway vehicle emission sources. A prototype software
tool, AUVEE, was developed to demonstrate the general approach in developing a
probabilistic emission inventory based upon an example utility power plant emission
source. A general software tool, AuvTool, was developed to implement all
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methodologies and algorithms presented in this dissertation for variability and uncertainty
analysis. The tool can be used in any quantitative analysis fields where variability and
uncertainty analysis are needed in model inputs.

KEY WORDS: Variability, Uncertainty, Emission Factor, Emission Inventory, Software
Implementation, Bootstrap Simulation, Monte Carlo Simulation, Two-Dimensional
Simulation

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To my beloved parents, Yongnian Zheng and Guifang Zhang for their constant
understanding and support
To my wonderful wife, Yan Ouyang, for her love, concerns and encouragements
To my upcoming son, Alexander Zheng, for his inciting my responsibility and hope
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BIOGRAPHY
Junyu Zheng received his Bachelor of Engineering degree in Water Supply and Drainage
from Wuhan Urban Construction Institute, Wuhan, China, in 1991. During the period of
August of 1991 through August of 1993, he worked as a water supply process manager in
Power Plant, Beijing Yanshan Petrol & Chemical Corporation (BYPCC), where he was
responsible for process management of industrial and civil water supply of BYPCC.
Junyu Zheng was admitted to the Department of Environmental Engineering of
Tsinghua University, China, in September of 1993 for his pursuit of master degree, where
he worked as research assistant at the Environmental System Lab and his research focused
on the probabilistic analysis of water quality model. He earned his Master of Science
degree in Environmental Engineering from Tsinghua University in 1996. After he received
his M.S degree, he accepted a position of real-estate appraiser from Jingdu Certified Public
Accountant (one member of Horwath International), Beijing, and part-time worked as an
assistant general manager and software developer at Beijing Kelier Information Inc. to
engage in the software development and network installation of Automatic Check
Telephone Query System.
Junyu Zheng came to North Carolina State University, Raleigh, North Carolina,
USA, in August 1998 for his Ph.D. in Environmental Engineering program. During his
Ph.D study, he worked as a research assistant at the Computational Laboratory for
Energy, Air and Risk (CLEAR).
Junyu Zheng’s research interests include application of statistics and computer
techniques to the quantification of variability and uncertainty in environmental data,
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probabilistic risk or exposure assessment, and uncertainty analysis in air or water quality
modeling.

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ACKNOWLEDGEMENTS

This research was supported by U.S. EPA STAR Grants Nos. R826766 and
R826790. The ORD of U.S. EPA funded the development of AuvTool via contract ID-
S794-NTEX.
The author wishes to express his appreciation to Dr. H. Christopher Frey for his
constant inspiration and guidance throughout the course of this research. Appreciation is
also extended to Drs. L.A. Stefanski, E.D. Brill, J. W. Baugh, D. Vandervaart and A.
Anton for their valuable suggestions. The author appreciates the guidance and
encouragement of Dr. Jianping Xue and Dr. Haluk Ozkaynak of U.S. EPA during the
development of the AuvTool.
The author thanks Alper Unal for his help in both research and life and his
friendship. Thanks also go to all other members in the group of Computational
Laboratory for Energy, Air and Risk.

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Table of Contents

LIST OF TABLES............................................................................................................xii
LIST OF FIGURES.........................................................................................................xiv

PART I INTRODUCTION.......................................................................................1
1.0 Introduction.................................................................................................3
1.1 Variability...................................................................................................5
1.2 Uncertainty..................................................................................................6
1.3 Distinctions Between Variability and Uncertainty.....................................8
1.4 Examples of Probabilistic Analysis..........................................................10
1.5 Limitations of Current Studies in Variability and Uncertainty Analysis..11
1.6 Available Software Tools in Probabilistic Analysis.................................14
1.7 Objectives.................................................................................................15
1.8 Overview of Research...............................................................................16
1.9 Organization..............................................................................................18
1.10 References.................................................................................................20

PART II GENERAL METHODLOGY OF QUANTIFICATION OF
VARIABILITY AND UNCERTAINTY IN EMISSION
ESTIMATION..........................................................................................25
2.0 General Methodology...............................................................................27
2.1 General Approach for Developing a Probabilistic Emission Inventory...28
2.2 Data Preparation........................................................................................29
2.3 Emission Inventory Models......................................................................30
2.4 Numerical sampling techniques................................................................32
2.4.1 Monte Carlo Sampling..................................................................32
2.4.3 Latin Hypercube Sampling...........................................................34
2.5 Visualization of Datasets Using Empirical Distributions.........................35
2.6 Definitions of Probability Distribution Models........................................38
2.6.1 Definition of Parametric Probability Distributions.......................39
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2.6.2 Empirical Distribution..................................................................39
2.7 Parameter Estimation of Parameter Distributions.....................................40
2.7.1 Method of Matching Moments.....................................................43
2.7.2 Maximum Likelihood Estimation (MLE).....................................43
2.8 Evaluation of Goodness-of-Fit of a Probability Distribution Model........47
2.8.1 Graphical Comparison of CDF of Fitted Distribution to
the Data.........................................................................................50
2.8.2 Kolmogorov-Smirnov Test...........................................................51
2.8.3 Anderson-Darling Test..................................................................54
2.8.4 Graphical Comparison of Confidence Intervals for CDF of
Fitted Distribution to the Data......................................................56
2.8.5 Summary of Methods for Evaluating Goodness-of-Fit................57
2.9 Algorithms for Generating Random Samples from Probability
Distributions..............................................................................................58
2.9.1 Pseudo Random Number Generator.............................................59
2.9.2 Empirical Distribution..................................................................60
2.10 Characterization of Uncertainty in the Distribution for Variability..........61
2.10.1 Bootstrap Method..........................................................................63
2.10.2 Methods of Generating Bootstrap Samples..................................64
2.10.3 Methods of Forming Bootstrap Confidence Intervals..................65
2.10.4 Two-Dimensional Simulation of Variability and Uncertainty......69
2.11 Probabilistic Approaches for Simulating Variability and Uncertainty
in the Emission Inventories.......................................................................72
2.12 Identification of Key Sources of Variability and Uncertainty..................73
2.13 Summary...................................................................................................76
2.14 References.................................................................................................78

PART III SOFTWARE IMPLEMENTATION........................................................81
3.0 Software Implementation..........................................................................83
3.1 Software Implementation of AuvTool......................................................83
3.1.1 AuvTool Software Design Considerations...................................84
3.1.2 Development Environment and Tools..........................................84
3.1.3 Structure Design of the AuvTool System.....................................85
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3.1.4 AuvTool Main Modules................................................................85
3.2 Software Implementation of AUVEE.......................................................98
3.2.1 General Structure of the AUVEE Prototype Software.................98
3.2.2 Databases in the AUVEE Prototype Software..............................98
3.2.3 Modules in the AUVEE Prototype Software..............................100
3.2.4 Software Development Tools.....................................................102
3.3 References...............................................................................................104

PART IV QUANTIFICATION OF VARIABILITY AND UNCERTAINTY
USING MIXTURE DISTRIBUTION: EVALUATION OF SAMPLE
SIZE, MIXING WEIGHTS AND SEPARATION BETWEEN
COMPONENTS.....................................................................................105
Abstract...............................................................................................................107
1.0 Introduction.............................................................................................108
2.0 Methodology...........................................................................................113
2.1 Mixture Distribution.......................................................................113
2.2 Parameter Estimation of Mixture Distributions.............................115
2.3 Quantification of Variability and Uncertainty Using Mixture
Distribution.....................................................................................118
3.0 Introduction to Study Design.................................................................122
4.0 Results and Discussion..........................................................................123
4.1 Properties of Confidence Intervals of Cumulative Distributions....123
4.2 Comparisons between Single Distribution and Mixture
Distributions....................................................................................125
4.3 Dependencies among Sampling Distributions of Parameters of
Mixture Distributions......................................................................127
5.0 An Illustrative Case Study: NO Emission Factor for a Coal-Fired of
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Power Plant.............................................................................................128
5.1 Parameter Estimation for the Fitted Distribution............................129
5.2 Variability and Uncertainty in the NO Emission Factor...............129
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5.3 Uncertainty in the Mean NO Emission Factor..............................130
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6.0 Conclusion..............................................................................................131
References...........................................................................................................133

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