Uncertainty Analysis of Transport-Transformation Models

by

Sastry S. Isukapalli

A dissertation submitted to the Graduate School--New Brunswick
Rutgers, The State University of New Jersey

in partial fulfillment of the requirements for the degree of
Doctor of Philosophy
Graduate Program in Chemical and Biochemical Engineering

Written under the direction of
Dr. Panos G. Georgopoulos

and approved by
Dr. Daewon W. Byun
Dr. Alkis Constantinides
Dr. Henrik Pedersen, and
Dr. David S.Kosson

New Brunswick, New Jersey
January, 1999

Abstract

Characterization of uncertainty associated with transport-transformation models is often of critical importance, as for example in cases where environmental and biological models are employed in risk assessment. However, uncertainty analysis using conventional methods such as standard Monte Carlo or Latin Hypercube Sampling may not be efficient, or even feasible, for complex, computationally demanding models.

This work introduces a computationally efficient alternative method for uncertainty propagation, the Stochastic Response Surface Method (SRSM). The SRSM approximates uncertainties in model outputs through a series expansion in normal random variables (polynomial chaos expansion). The unknown coefficients in series expansions are calculated using a limited number of model simulations. This method is analogous to approximation of a deterministic system by an algebraic response surface.

Further improvements in the computational efficiency of the SRSM are accomplished by coupling the SRSM with ADIFOR, which facilitates automatic calculation of partial derivatives in numerical models coded in Fortran. The coupled method, SRSM-ADIFOR, uses the model outputs and their derivatives to calculate the unknown coefficients.

The SRSM and the SRSM-ADIFOR are general methods, and are applicable to any model with random inputs. The SRSM has also been implemented as a black-box, web-based tool for facilitating its easy use.

The SRSM and the SRSM-ADIFOR have been applied to a set of environmental and biological models. In all the case studies, the SRSM required an order of magnitude fewer simulations compared to conventional methods, and the SRSM-ADIFOR required even fewer simulations. In addition to their computational efficiency, these methods directly provide sensitivity information and individual contributions of input uncertainties to output uncertainties; conventional methods require substantially larger numbers of simulations to provide such information. Thus, the SRSM and the SRSM-ADIFOR provide computationally efficient means for uncertainty and sensitivity analysis.

Finally, this research addresses uncertainties associated with model structure and resolution with application to photochemical air quality modeling. A three dimensional version of the regulatory Reactive Plume Model (RPM), RPM-3D, has been developed and applied to understand model uncertainty.

Acknowledgements

I would like to express my sincere thanks and appreciation to my advisor, Panos G. Georgopoulos, for guidance, and for providing me with excellent facilities to pursue my work, and for ensuring financial support throughout my studies.

I am also grateful to the members of my committee for taking the time to guide me through my dissertation. I would like express my appreciation to Professor Alkis Constantinides for his insightful remarks, and to Professor Henrik Pedersen, and Professor David Kosson for their valuable comments and ideas. I am also grateful to Dr. Daewon Byun for his continued encouragement and support. I also thank Dr. Yee Chiew for introducing me to the concepts of Monte Carlo simulations, and for his insightful remarks on this thesis. I am also grateful to Dr. Amit Roy for his continued support, valuable guidance, and frank, critical comments throughout my research.

This work has benefited from various researchers. Special mention goes to Dr. Menner Tatang, whose work served as the starting point for this thesis. I would also like to acknowledge the following researchers and organizations who have provided models and input files for the evaluation of the methods developed here: Dr. Amit Roy for the PERC PBPK model and input data for the RPM model, the ozone modeling group (Dr. Shengwei Wang and Dr. Saravanan Arunachalam) for the input data for the UAM model, and Hydrogeologic Inc. for the input data for the EPACMTP model. I am also thankful to Dr. Ashwin Walia and Dr. Shengwei Wang for sharing their documentation on the UAM-IV and CB-IV (adapted here as Appendix C).

I am grateful to my colleagues at the CCL for their valuable discussions and suggestions. I am also thankful to Ms. Arlene Bicknell, Ms. Roberta Salinger, and Ms. Julie Greenman for their continued help. I thank the countless authors of all the free software that I have used during my research work - their selfless efforts have significantly aided my work.

I would also like to acknowledge financial support provided by the U.S. EPA, NERL (National Exposure Research Laboratories), and U.S. DOE through CRESP (Consortium for Risk Evaluation with Stakeholder Participation).

Special thanks go to my friends, Ravi Bhupathiraju, Padma Isukapalli, and Ramana Isukapalli, for providing a constant source of encouragement and support, and for being there for me at all times.

This thesis would not have materialized but for the help of Amit Roy. As a friend, as a colleague, and as a mentor, he has helped me continuously, and has contributed tremendously to this thesis. I consider it as my fortune to be his friend, and to have worked with him.

Dedication

to my parents

and to Amit Roy