Uncertainty reduction and characterization for complex environmental fate and transport models: An empirical Bayesian framework incorporating the stochastic response surface method

Abstract

In this work, a computationally efficient Bayesian framework for the reduction and characterization of parametric uncertainty in computationally demanding environmental 3‐D numerical models has been developed. The framework is based on the combined application of the Stochastic Response Surface Method (SRSM, which generates accurate and computationally efficient statistically equivalent reduced models) and the Markov chain Monte Carlo method. The application selected to demonstrate this framework involves steady state groundwater flow at the U.S. Department of Energy Savannah River Site General Separations Area, modeled using the Subsurface Flow And Contaminant Transport (FACT) code. Input parameter uncertainty, based initially on expert opinion, was found to decrease in all variables of the posterior distribution. The joint posterior distribution obtained was then further used for the final uncertainty analysis of the stream base flows and well location hydraulic head values.

Direct Computation of Statistical Variations in Electromagnetic Problems

“…Fig. 9-10A shows the comparison between the MC and UT approximations for the average S 21 coupling over a range of frequencies. The results show good agreement between the two methods.…”

“…The results show good agreement between the two methods. The UT approximation of the standard deviation of S 21 coupling is calculated using (8.7a). The results for this compared with the MC method and presented in Fig.…”

A Gibbs sampler for inequality‐constrained geostatistical interpolation and inverse modeling

“…A few other applications, such as parameter optimization for groundwater contaminant fate and transport models [e.g. Balakrishnan et al, 2003] and zonation estimation [Chen et al, 2006], have also been developed.…”

Computationally efficient Bayesian inference for inverse problems.

“…The choice of inputs to these simulations-in particular, how closely the inputs must resemble the inverse solution-can be important [98]. Balakrishnan et al [8] introduce a PC representation of the forward model in a groundwater transport parameter identification problem, but obtain the PC coefficients by collocation; again, this process depends on a series of "snapshots" obtained from repeated forward simulations.…”

“…where there is a one-to-one correspondence between the coefficients and functionals in (8) and in (9) [40]. For the standard normal random variables ξ i chosen above, orthogonality of successive Γ p requires that the Γ p be multivariate Hermite polynomials; both these and the corresponding Ψ k may be generated from univariate Hermite polynomials by taking tensor products.…”