Contents

• Contents
• List of Tables
• List of Figures
• 1. INTRODUCTION
  • 1.1 Uncertainty Analysis
  • 1.2 Transport-Transformation Models
  • 1.3 Limitations in Performing Uncertainty Analysis
  • 1.4 Objective of the Thesis
  • 1.5 Outline of the Thesis
• 2. BACKGROUND
  • 2.1 Types and Origins of Uncertainty in Transport-Transformation Models
    • 2.1.1 Natural Uncertainty and Variability
    • 2.1.2 Model Uncertainty
    • 2.1.3 Parametric/Data Uncertainty
  • 2.2 Reducible and Irreducible Uncertainty
  • 2.3 Approaches for Representation of Uncertainty
    • 2.3.1 Interval Mathematics
    • 2.3.2 Fuzzy Theory
    • 2.3.3 Probabilistic Analysis
  • 2.4 Sensitivity and Sensitivity/Uncertainty Analysis
  • 2.5 Conventional Sensitivity/Uncertainty Analysis Methods
    • 2.5.1 Sensitivity Testing Methods
    • 2.5.2 Analytical Methods
    • 2.5.3 Sampling Based Methods
    • 2.5.4 Computer Algebra Based Methods
  • 2.6 Need for Alternative Sensitivity/Uncertainty Analysis Methods
• 3. THE STOCHASTIC RESPONSE SURFACE METHOD: DEVELOPMENT AND IMPLEMENTATION
  • 3.1 Overview of the Method
  • 3.2 Step I: Representation of Stochastic Inputs
    • 3.2.1 Direct Transformations
    • 3.2.2 Transformation via Series Approximation
    • 3.2.3 Transformation of Empirical Distributions
    • 3.2.4 Transformation of Correlated Inputs
  • 3.3 Step II: Functional Approximation of Outputs
  • 3.4 Step III: Estimation of Parameters in the Functional Approximation
    • 3.4.1 Deterministic Equivalent Modeling Method/Probabilistic Collocation Method (DEMM/PCM)
    • 3.4.2 Efficient Collocation Method (ECM)
    • 3.4.3 Regression Based SRSM
  • 3.5 Step IV: Estimation of the Statistics of the Output Metrics
  • 3.6 Step V: Evaluation of Convergence, Accuracy and Efficiency of Approximation
  • 3.7 An Illustration of the Application of the SRSM
  • 3.8 Computational Implementation
    • 3.8.1 Implementation of the Conventional Uncertainty Propagation Methods
    • 3.8.2 Implementation of the Stochastic Response Surface Method
  • 3.9 Implementation of a Web Interface to the SRSM
• 4. COUPLING OF THE SRSM WITH SENSITIVITY ANALYSIS METHODS: DEVELOPMENT AND IMPLEMENTATION OF SRSM-ADIFOR
  • 4.1 Methods for Estimation of Partial Derivatives
  • 4.2 Automatic Differentiation using ADIFOR
  • 4.3 Coupling of SRSM and ADIFOR
    • 4.3.1 Selection of Sample Points
  • 4.4 An Illustration of the Application of the SRSM-ADIFOR
  • 4.5 Implementation of the SRSM-ADIFOR
• 5. CASE STUDIES FOR THE EVALUATION OF THE SRSM AND THE SRSM-ADIFOR
  • 5.1 Case Study I: A Zero Dimensional Physiological System
    • 5.1.1 Description of the Case Study
    • 5.1.2 Specification of Parameter Uncertainty
    • 5.1.3 Implementation of the PERC PBPK Model
    • 5.1.4 Results for the PBPK case study
  • 5.2 Case Study II: A Two-Dimensional Photochemical Air Quality Model
    • 5.2.1 Description of RPM-IV
    • 5.2.2 Uncertainty Analysis of RPM-IV
    • 5.2.3 Results and Discussion
  • 5.3 Case Study III: A Three-Dimensional Urban/Regional Scale Photochemical Air Quality Model
    • 5.3.1 Uncertainties Associated with Biogenic Emission Estimates
    • 5.3.2 Uncertainty Analysis
    • 5.3.3 Estimation of Uncertainties
    • 5.3.4 Results of the Case Study
  • 5.4 Case Study IV: A Ground Water Model with Discontinuous Probability Distributions
    • 5.4.1 EPACMTP Model
    • 5.4.2 Data Sources for the Application of EPACMTP
    • 5.4.3 Implementation of the Monte Carlo Method in EPACMTP
    • 5.4.4 Uncertainty Analysis
    • 5.4.5 Results and Discussion
• 6. CHARACTERIZATION AND REDUCTION OF MODEL UNCERTAINTY: AN ATMOSPHERIC PLUME MODEL STUDY
  • 6.1 Introduction and Background
  • 6.2 Photochemical Air Pollution Modeling
    • 6.2.1 Mathematical and Numerical Formulation of PAQSMs
  • 6.3 Formulation of The Reactive Plume Model (RPM)
    • 6.3.1 Initial Physical Dimensions of the Plume
    • 6.3.2 RPM-IV Model Equations
    • 6.3.3 Limitations of the RPM-IV
  • 6.4 Formulation of the RPM-3D
  • 6.5 Case Studies
  • 6.6 Discussion
• 7. CONCLUSIONS AND DISCUSSION
  • 7.1 Development and Application of the SRSM
  • 7.2 Development and Application of the SRSM-ADIFOR
  • 7.3 Consideration of Uncertainties Beyond Parametric/Data Uncertainty
  • 7.4 Directions for Future Work
    • 7.4.1 Improvements to the Stochastic Response Surface Method
    • 7.4.2 Further evaluation of the SRSM and the SRSM-ADIFOR
    • 7.4.3 Addressing uncertainty propagation under constraints
    • 7.4.4 Random processes and random fields
    • 7.4.5 Uncertainties Associated with Evaluation Data
• Bibliography
• 8. PROBABILISTIC APPROACH FOR UNCERTAINTY ANALYSIS
  • 8.1 Random Variables
    • 8.1.1 Continuous Random Variables
    • 8.1.2 Moments of a Random Variable
    • 8.1.3 Median, Mode and Percentiles of a distribution
  • 8.2 Jointly Distributed Random Variables
    • 8.2.1 Moments of Jointly Distributed Random Variables
    • 8.2.2 Dependence of Random Variables
• 9. BASIC PBPK MODEL EQUATIONS
• 10. URBAN AIRSHED MODEL (UAM-IV) AND CARBON BOND MECHANISM (CB-IV)^10.2
  • 10.1 The Urban Airshed Model - UAM-IV
    • 10.1.1 Conceptual Overview
    • 10.1.2 Treatment of Physical/Chemical Processes
    • 10.1.3 Applications of the UAM
  • 10.2 Carbon Bond Mechanism (CB-IV)
• 11. THE EPACMTP MODEL
  • 11.1 Introduction
  • 11.2 Description of the FECTUZ Module
    • 11.2.1 Steady State Flow Module Formulation
    • 11.2.2 Solute Transport Module Formulation
  • 11.3 Description of the CANSAZ-3D Module
    • 11.3.1 Formulation of the Groundwater Flow Module
    • 11.3.2 Formulation of the Saturated Zone Contaminant Migration Module
• 12. PROGRAMS INCLUDED IN THE CDROM