Computationally efficient Bayesian uncertainty analysis and reduction of a 3-D finite element groundwater modeling system
Suhrid Balakrishnan (Department of Chemical and Biochemical Engineering,
Rutgers University);
Amit Roy (EOHSI, UMDNJ - R.W. Johnson Medical School and Rutgers University);
Marianthi G. Ierapetritou (Department of Chemical and Biochemical Engineering,
Rutgers University);
Gregory P. Flach (Savannah River Technology Center, Savannah River Site);
Panos G. Georgopoulos (EOHSI, UMDNJ - R.W. Johnson Medical School and Rutgers
University)
Comprehensive uncertainty analyses of complex models of environmental and biological systems are essential but often not feasible due to the computational resources they require. Traditional Monte Carlo methods, e.g. involving standard or Latin Hypercube sampling, for propagating uncertainty and developing probability densities of model outputs, may require performing a large number of model simulations that can be prohibitive in the case of 3D dynamic finite element or finite difference models. An alternative approach is provided by the Stochastic Response Surface Method (SRSM), which is a computationally efficient framework that facilitates uncertainty analysis through the determination of statistically equivalent reduced models; SRSM is applied here to subsurface transport modeling. Past applications of SRSM included the uncertainty analysis of atmospheric chemistry and transport models, groundwater models, and physiologically based pharmacokinetic models [1,2]. The present work further demonstrates how the SRSM framework can be used in a Bayesian manner not only to characterize but also to reduce uncertainties, by incorporating observational information in estimates of model parameters. This is achieved by the combined application of the SRSM and Markov Chain Monte Carlo (MCMC) methods. Current and ongoing work includes the application of this novel framework to the groundwater and unsaturated zone modeling of the General Separations Area (GSA) of the US DOE Savannah River Site. Subsurface processes are simulated with the Subsurface Flow and Contaminant Transport (FACT) code [3]. FACT is transient three-dimensional, finite element code designed to simulate isothermal groundwater flow, moisture movement, and solute transport in variably saturated and fully saturated subsurface porous media. Furthermore, FACT is designed specifically to handle complex multi-layer and/or heterogeneous aquifer systems in an efficient manner while accommodating a wide range of boundary conditions [4]. The present work demonstrates the feasibility of performing systematic uncertainty analysis and parameter optimization with a complex model such as FACT, by employing the combined SRSM/MCMC approach.
ACKNOWLEDGMENTS:
This work has been funded in part by the US Environmental Protection Agency under Cooperative Agreement # EPAR-827033 to the Environmental and Occupational Health Sciences Institute; and by a grant to the Institute for Responsible Management, Consortium for Risk Evaluation with Stakeholder Participation from the U.S. Department of Energy, Instrument DE-FG2600NT 40938.
REFERENCES:
1. Isukapalli, S. S., A. Roy, and P. G. Georgopoulos. 1998. "Stochastic response surface methods (SRSMs) for uncertainty propagation: Application to environmental and biological systems," Risk Analysis, 18 (3): 351-363.
2. Isukapalli, S. S., A. Roy, and P. G. Georgopoulos. 2000. "Efficient sensitivity/uncertainty analysis using the combined Stochastic Response Surface Method and automated differentiation: Application to environmental and biological systems," Risk Analysis, 20 (5): 591-602.
3. Flach, G. and M. Harris. 2000. "Integrated hydrogeological modeling of the General Separations Area," Technical report, Savannah River Technology Center, Aiken, South Carolina, WSRC-TR-96-00399.
4. Hamm, L. and S. Aleman. 2000. "FACT subsurface Flow and Contaminant Transport documentation and user's guide," Technical report, Savannah River Technology Center, Aiken, South Carolina, WSRC-TR-99-00282.