Geology topics

Xiaoqing Shi

Publications and source records attributed to Xiaoqing Shi.

2 recordsLinked to original sources

USGS2014

Assessment of parametric uncertainty for groundwater reactive transport modeling,

The validity of using Gaussian assumptions for model residuals in uncertainty quantification of a groundwater reactive transport model was evaluated in this study. Least squares regression methods explicitly assume Gaussian residuals, and the assumption leads to Gaussian likelihood functions, model parameters, and model predictions. While the Bayesian methods do not explicitly require the Gaussian assumption, Gaussian residuals are widely used. This paper shows that the residuals of the reactive transport model are non-Gaussian, heteroscedastic, and correlated in time; characterizing them requires using a generalized likelihood function such as the formal generalized likelihood function developed by Schoups and Vrugt (2010). For the surface complexation model considered in this study for simulating uranium reactive transport in groundwater, parametric uncertainty is quantified using the least squares regression methods and Bayesian methods with both Gaussian and formal generalized likelihood functions. While the least squares methods and Bayesian methods with Gaussian likelihood function produce similar Gaussian parameter distributions, the parameter distributions of Bayesian uncertainty quantification using the formal generalized likelihood function are non-Gaussian. In addition, predictive performance of formal generalized likelihood function is superior to that of least squares regression and Bayesian methods with Gaussian likelihood function. The Bayesian uncertainty quantification is conducted using the differential evolution adaptive metropolis (DREAM (zs) ) algorithm; as a Markov chain Monte Carlo (MCMC) method, it is a robust tool for quantifying uncertainty in groundwater reactive transport models. For the surface complexation model, the regression-based local sensitivity analysis and Morris- and DREAM (ZS) -based global sensitivity analysis yield almost identical ranking of parameter importance. The uncertainty analysis may help select appropriate likelihood functions, improve model calibration, and reduce predictive uncertainty in other groundwater reactive transport and environmental modeling.

Water Resources Research↗

USGS2013

Effects of error covariance structure on estimation of model averaging weights and predictive performance

When conducting model averaging for assessing groundwater conceptual model uncertainty, the averaging weights are often evaluated using model selection criteria such as AIC, AICc, BIC, and KIC (Akaike Information Criterion, Corrected Akaike Information Criterion, Bayesian Information Criterion, and Kashyap Information Criterion, respectively). However, this method often leads to an unrealistic situation in which the best model receives overwhelmingly large averaging weight (close to 100%), which cannot be justified by available data and knowledge. It was found in this study that this problem was caused by using the covariance matrix, C E , of measurement errors for estimating the negative log likelihood function common to all the model selection criteria. This problem can be resolved by using the covariance matrix, C ek , of total errors (including model errors and measurement errors) to account for the correlation between the total errors. An iterative two-stage method was developed in the context of maximum likelihood inverse modeling to iteratively infer the unknown C ek from the residuals during model calibration. The inferred C ek was then used in the evaluation of model selection criteria and model averaging weights. While this method was limited to serial data using time series techniques in this study, it can be extended to spatial data using geostatistical techniques. The method was first evaluated in a synthetic study and then applied to an experimental study, in which alternative surface complexation models were developed to simulate column experiments of uranium reactive transport. It was found that the total errors of the alternative models were temporally correlated due to the model errors. The iterative two-stage method using C ek resolved the problem that the best model receives 100% model averaging weight, and the resulting model averaging weights were supported by the calibration results and physical understanding of the alternative models. Using C ek obtained from the iterative two-stage method also improved predictive performance of the individual models and model averaging in both synthetic and experimental studies.

Water Resources Research↗