Assessment of Parametric Uncertainty using Markov Chain Monte Carlo Methods for Surface Complexation Models in Groundwater Reactive Transport Modeling
Abstract
Parametric uncertainty in groundwater modeling is commonly assessed using the first-order-second-moment method, which yields the linear confidence/prediction intervals. More advanced techniques are able to produce the nonlinear confidence/prediction intervals that are more accurate than the linear intervals for nonlinear models. However, both the methods are restricted to certain assumptions such as normality in model parameters. We developed a Markov Chain Monte Carlo (MCMC) method to directly investigate the parametric distributions and confidence/prediction intervals. The MCMC results are used to evaluate accuracy of the linear and nonlinear confidence/prediction intervals. The MCMC method is applied to nonlinear surface complexation models developed by Kohler et al. (1996) to simulate reactive transport of uranium (VI). The breakthrough data of Kohler et al. (1996) obtained from a series of column experiments are used as the basis of the investigation. The calibrated parameters of the models are the equilibrium constants of the surface complexation reactions and fractions of functional groups. The Morris method sensitivity analysis shows that all of the parameters exhibit highly nonlinear effects on the simulation. The MCMC method is combined with traditional optimization method to improve computational efficiency. The parameters of the surface complexation models are first calibrated using a global optimization technique, multi-start quasi-Newton BFGS, which employs an approximation to the Hessian. The parameter correlation is measured by the covariance matrix computed via the Fisher information matrix. Parameter ranges are necessary to improve convergence of the MCMC simulation, even when the adaptive Metropolis method is used. The MCMC results indicate that the parameters do not necessarily follow a normal distribution and that the nonlinear intervals are more accurate than the linear intervals for the nonlinear surface complexation models. In comparison with the linear and nonlinear prediction intervals, the prediction intervals of MCMC are more robust to simulate the breakthrough curves that are not used for the parameter calibration and estimation of parameter distributions.
- Publication:
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AGU Fall Meeting Abstracts
- Pub Date:
- December 2010
- Bibcode:
- 2010AGUFM.H42D..03M
- Keywords:
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- 1832 HYDROLOGY / Groundwater transport;
- 1847 HYDROLOGY / Modeling;
- 1873 HYDROLOGY / Uncertainty assessment