Maximum likelihood Bayesian model averaging and its predictive analysis for groundwater reactive transport models
Abstract
While Bayesian model averaging (BMA) has been widely used in groundwater modeling, it is infrequently applied to groundwater reactive transport modeling because of multiple sources of uncertainty in the coupled hydrogeochemical processes and because of the long execution time of each model run. To resolve these problems, this study analyzed different levels of uncertainty in a hierarchical way, and used the maximum likelihood version of BMA, i.e., MLBMA, to improve the computational efficiency. Our study demonstrates the applicability of MLBMA to groundwater reactive transport modeling in a synthetic case in which twenty-seven reactive transport models were designed to predict the reactive transport of hexavalent uranium (U(VI)) based on observations at a former uranium mill site near Naturita, CO. Moreover, these reactive transport models contain three uncertain model components, i.e., parameterization of hydraulic conductivity, configuration of model boundary, and surface complexation reactions that simulate U(VI) adsorption. These uncertain model components were aggregated into the alternative models by integrating a hierarchical structure into MLBMA. The modeling results of the individual models and MLBMA were analyzed to investigate their predictive performance. The predictive logscore results show that MLBMA generally outperforms the best model, suggesting that using MLBMA is a sound strategy to achievemore »
- Authors:
-
- Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
- Florida State Univ., Tallahassee, FL (United States)
- U.S. Geological Survey, Menlo Park, CA (United States)
- Publication Date:
- Research Org.:
- Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
- Sponsoring Org.:
- USDOE
- OSTI Identifier:
- 1265806
- Alternate Identifier(s):
- OSTI ID: 1248433
- Grant/Contract Number:
- AC05-00OR22725; SC0002687; SC0000801; SC0008272; 0911074; 51328902; SC0003681
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Journal of Hydrology
- Additional Journal Information:
- Journal Volume: 529; Journal Issue: P3; Journal ID: ISSN 0022-1694
- Publisher:
- Elsevier
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 58 GEOSCIENCES; Uncertainty analysis; Reactive transport; Maximum likelihood Bayesian model averaging
Citation Formats
Lu, Dan, Ye, Ming, and Curtis, Gary P. Maximum likelihood Bayesian model averaging and its predictive analysis for groundwater reactive transport models. United States: N. p., 2015.
Web. doi:10.1016/j.jhydrol.2015.07.029.
Lu, Dan, Ye, Ming, & Curtis, Gary P. Maximum likelihood Bayesian model averaging and its predictive analysis for groundwater reactive transport models. United States. https://doi.org/10.1016/j.jhydrol.2015.07.029
Lu, Dan, Ye, Ming, and Curtis, Gary P. Sat .
"Maximum likelihood Bayesian model averaging and its predictive analysis for groundwater reactive transport models". United States. https://doi.org/10.1016/j.jhydrol.2015.07.029. https://www.osti.gov/servlets/purl/1265806.
@article{osti_1265806,
title = {Maximum likelihood Bayesian model averaging and its predictive analysis for groundwater reactive transport models},
author = {Lu, Dan and Ye, Ming and Curtis, Gary P.},
abstractNote = {While Bayesian model averaging (BMA) has been widely used in groundwater modeling, it is infrequently applied to groundwater reactive transport modeling because of multiple sources of uncertainty in the coupled hydrogeochemical processes and because of the long execution time of each model run. To resolve these problems, this study analyzed different levels of uncertainty in a hierarchical way, and used the maximum likelihood version of BMA, i.e., MLBMA, to improve the computational efficiency. Our study demonstrates the applicability of MLBMA to groundwater reactive transport modeling in a synthetic case in which twenty-seven reactive transport models were designed to predict the reactive transport of hexavalent uranium (U(VI)) based on observations at a former uranium mill site near Naturita, CO. Moreover, these reactive transport models contain three uncertain model components, i.e., parameterization of hydraulic conductivity, configuration of model boundary, and surface complexation reactions that simulate U(VI) adsorption. These uncertain model components were aggregated into the alternative models by integrating a hierarchical structure into MLBMA. The modeling results of the individual models and MLBMA were analyzed to investigate their predictive performance. The predictive logscore results show that MLBMA generally outperforms the best model, suggesting that using MLBMA is a sound strategy to achieve more robust model predictions relative to a single model. MLBMA works best when the alternative models are structurally distinct and have diverse model predictions. When correlation in model structure exists, two strategies were used to improve predictive performance by retaining structurally distinct models or assigning smaller prior model probabilities to correlated models. Since the synthetic models were designed using data from the Naturita site, the results of this study are expected to provide guidance for real-world modeling. Finally, limitations of applying MLBMA to the synthetic study and future real-world modeling are discussed.},
doi = {10.1016/j.jhydrol.2015.07.029},
journal = {Journal of Hydrology},
number = P3,
volume = 529,
place = {United States},
year = {Sat Aug 01 00:00:00 EDT 2015},
month = {Sat Aug 01 00:00:00 EDT 2015}
}
Web of Science
Works referenced in this record:
Climate model dependence and the replicate Earth paradigm
journal, December 2012
- Bishop, Craig H.; Abramowitz, Gab
- Climate Dynamics, Vol. 41, Issue 3-4
The Combination of Simulated Discharges of Hydrological Models
journal, February 1986
- Cavadias, G.; Morin, G.
- Hydrology Research, Vol. 17, Issue 1
Comparison of in situ uranium KD values with a laboratory determined surface complexation model
journal, October 2004
- Curtis, Gary P.; Fox, Patricia; Kohler, Matthias
- Applied Geochemistry, Vol. 19, Issue 10
Simulation of reactive transport of uranium(VI) in groundwater with variable chemical conditions: SIMULATION OF REACTIVE TRANSPORT OF URANIUM(VI)
journal, April 2006
- Curtis, Gary P.; Davis, James A.; Naftz, David L.
- Water Resources Research, Vol. 42, Issue 4
Comparing Approaches for Simulating the Reactive Transport of U(VI) in Ground Water
journal, February 2009
- Curtis, Gary P.; Kohler, Matthias; Davis, James A.
- Mine Water and the Environment, Vol. 28, Issue 2
Approaches to surface complexation modeling of Uranium(VI) adsorption on aquifer sediments
journal, September 2004
- Davis, James A.; Meece, David E.; Kohler, Matthias
- Geochimica et Cosmochimica Acta, Vol. 68, Issue 18
Uncertainty Analysis of Multiple Hydrologic Models Using the Bayesian Model Averaging Method
journal, January 2013
- Dong, Leihua; Xiong, Lihua; Yu, Kun-xia
- Journal of Applied Mathematics, Vol. 2013
Multi-model ensemble hydrologic prediction using Bayesian model averaging
journal, May 2007
- Duan, Qingyun; Ajami, Newsha K.; Gao, Xiaogang
- Advances in Water Resources, Vol. 30, Issue 5
Constructive epistemic modeling of groundwater flow with geological structure and boundary condition uncertainty under the Bayesian paradigm
journal, September 2014
- Elshall, Ahmed S.; Tsai, Frank T. -C.
- Journal of Hydrology, Vol. 517
Testing Alternative Ground Water Models Using Cross-Validation and Other Methods
journal, September 2007
- Foglia, L.; Mehl, S. W.; Hill, M. C.
- Ground Water, Vol. 45, Issue 5
Evaluating model structure adequacy: The case of the Maggia Valley groundwater system, southern Switzerland: Evaluating Model Structure Adequacy
journal, January 2013
- Foglia, L.; Mehl, S. W.; Hill, M. C.
- Water Resources Research, Vol. 49, Issue 1
Surface Complexation Modeling of U(VI) Adsorption by Aquifer Sediments from a Former Mill Tailings Site at Rifle, Colorado
journal, December 2009
- Hyun, Sung Pil; Fox, Patricia M.; Davis, James A.
- Environmental Science & Technology, Vol. 43, Issue 24
Optimal Choice of AR and MA Parts in Autoregressive Moving Average Models
journal, March 1982
- Kashyap, Rangasami L.
- IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. PAMI-4, Issue 2
Bayes Factors
journal, June 1995
- Kass, Robert E.; Raftery, Adrian E.
- Journal of the American Statistical Association, Vol. 90, Issue 430
Maximum likelihood parameter estimation of hydrologic spatial processes by the Gauss-Newton method
journal, July 1985
- Kitanidis, Peter K.; Lane, Robert W.
- Journal of Hydrology, Vol. 79, Issue 1-2
Methods for Estimating Adsorbed Uranium(VI) and Distribution Coefficients of Contaminated Sediments
journal, January 2004
- Kohler, Matthias; Curtis, Gary P.; Meece, David E.
- Environmental Science & Technology, Vol. 38, Issue 1
Dependence of Bayesian Model Selection Criteria and Fisher Information Matrix on Sample Size
journal, October 2011
- Lu, Dan; Ye, Ming; Neuman, Shlomo P.
- Mathematical Geosciences, Vol. 43, Issue 8
Multimodel Bayesian analysis of data-worth applied to unsaturated fractured tuffs
journal, January 2012
- Lu, Dan; Ye, Ming; Neuman, Shlomo P.
- Advances in Water Resources, Vol. 35
Effects of error covariance structure on estimation of model averaging weights and predictive performance: EFFECTS OF ERROR COVARIANCE STRUCTURE ON MODEL AVERAGING
journal, September 2013
- Lu, Dan; Ye, Ming; Meyer, Philip D.
- Water Resources Research, Vol. 49, Issue 9
Maximum likelihood Bayesian averaging of uncertain model predictions
journal, November 2003
- Neuman, S. P.
- Stochastic Environmental Research and Risk Assessment (SERRA), Vol. 17, Issue 5
Bayesian analysis of data-worth considering model and parameter uncertainties
journal, February 2012
- Neuman, Shlomo P.; Xue, Liang; Ye, Ming
- Advances in Water Resources, Vol. 36
Multimodel Ranking and Inference in Ground Water Modeling
journal, July 2005
- Poeter, Eileen; Anderson, David
- Ground Water, Vol. 43, Issue 4
Role of model selection criteria in geostatistical inverse estimation of statistical data- and model-parameters: INVERSE ESTIMATION OF STATISTICAL DATA AND MODEL PARAMETERS
journal, July 2011
- Riva, Monica; Panzeri, Marco; Guadagnini, Alberto
- Water Resources Research, Vol. 47, Issue 7
Conceptual model uncertainty in groundwater modeling: Combining generalized likelihood uncertainty estimation and Bayesian model averaging: EVALUATING CONCEPTUAL MODEL
journal, December 2008
- Rojas, Rodrigo; Feyen, Luc; Dassargues, Alain
- Water Resources Research, Vol. 44, Issue 12
Sensitivity analysis of prior model probabilities and the value of prior knowledge in the assessment of conceptual model uncertainty in groundwater modelling
journal, April 2009
- Rojas, Rodrigo; Feyen, Luc; Dassargues, Alain
- Hydrological Processes, Vol. 23, Issue 8
Combining climate model output via model correlations
journal, April 2010
- Sain, Stephan R.; Furrer, Reinhard
- Stochastic Environmental Research and Risk Assessment, Vol. 24, Issue 6
Reactive facies: An approach for parameterizing field-scale reactive transport models using geophysical methods: GEOPHYSICS FOR DISTRIBUTING REACTIVE FACIES
journal, October 2012
- Sassen, Douglas S.; Hubbard, Susan S.; Bea, Sergio A.
- Water Resources Research, Vol. 48, Issue 10
Model Averaging Techniques for Quantifying Conceptual Model Uncertainty
journal, August 2010
- Singh, Abhishek; Mishra, Srikanta; Ruskauff, Greg
- Ground Water, Vol. 48, Issue 5
Incorporating subjective and stochastic uncertainty in an interactive multi-objective groundwater calibration framework
journal, May 2010
- Singh, Abhishek; Walker, Douglas D.; Minsker, Barbara S.
- Stochastic Environmental Research and Risk Assessment, Vol. 24, Issue 6
Reactive transport modeling: An essential tool and a new research approach for the Earth sciences
journal, December 2005
- Steefel, C.; Depaolo, D.; Lichtner, P.
- Earth and Planetary Science Letters, Vol. 240, Issue 3-4
The importance of alternative conceptual models for simulation of concentrations in a multi-aquifer system
journal, May 2007
- Troldborg, Lars; Refsgaard, Jens Christian; Jensen, Karsten Høgh
- Hydrogeology Journal, Vol. 15, Issue 5
Hierarchical Bayesian model averaging for hydrostratigraphic modeling: Uncertainty segregation and comparative evaluation: HIERARCHICAL BAYESIAN MODEL AVERAGING
journal, September 2013
- Tsai, Frank T. -C.; Elshall, Ahmed S.
- Water Resources Research, Vol. 49, Issue 9
Bayesian Model Averaging in Proportional Hazard Models: Assessing the Risk of a Stroke
journal, January 1997
- Volinsky, Chris T.; Madigan, David; Raftery, Adrian E.
- Journal of the Royal Statistical Society: Series C (Applied Statistics), Vol. 46, Issue 4
Treatment of uncertainty using ensemble methods: Comparison of sequential data assimilation and Bayesian model averaging: SEQUENTIAL DATA ASSIMILATION
journal, January 2007
- Vrugt, Jasper A.; Robinson, Bruce A.
- Water Resources Research, Vol. 43, Issue 1
Forecasting skill of model averages
journal, October 2009
- Winter, C. L.; Nychka, Doug
- Stochastic Environmental Research and Risk Assessment, Vol. 24, Issue 5
Combining multiobjective optimization and Bayesian model averaging to calibrate forecast ensembles of soil hydraulic models: BAYESIAN MODEL AVERAGING OF SOIL HYDRAULIC MODELS
journal, December 2008
- Wöhling, Thomas; Vrugt, Jasper A.
- Water Resources Research, Vol. 44, Issue 12
Maximum likelihood Bayesian averaging of spatial variability models in unsaturated fractured tuff: MAXIMUM LIKELIHOOD BAYESIAN MODEL AVERAGING
journal, May 2004
- Ye, Ming; Neuman, Shlomo P.; Meyer, Philip D.
- Water Resources Research, Vol. 40, Issue 5
Sensitivity analysis and assessment of prior model probabilities in MLBMA with application to unsaturated fractured tuff: SENSITIVITY AND ASSESSMENT OF PRIOR PROBABILITIES
journal, December 2005
- Ye, Ming; Neuman, Shlomo P.; Meyer, Philip D.
- Water Resources Research, Vol. 41, Issue 12
On model selection criteria in multimodel analysis: ON MODEL SELECTION CRITERIA IN MULTIMODEL ANALYSIS
journal, March 2008
- Ye, Ming; Meyer, Philip D.; Neuman, Shlomo P.
- Water Resources Research, Vol. 44, Issue 3
Expert elicitation of recharge model probabilities for the Death Valley regional flow system
journal, June 2008
- Ye, Ming; Pohlmann, Karl F.; Chapman, Jenny B.
- Journal of Hydrology, Vol. 354, Issue 1-4
Quantification of model uncertainty in environmental modeling
journal, April 2010
- Ye, Ming; Meyer, Philip D.; Lin, Yu-Feng
- Stochastic Environmental Research and Risk Assessment, Vol. 24, Issue 6
A Model-Averaging Method for Assessing Groundwater Conceptual Model Uncertainty
journal, August 2010
- Ye, Ming; Pohlmann, Karl F.; Chapman, Jenny B.
- Ground Water, Vol. 48, Issue 5
Comment on “Inverse groundwater modeling for hydraulic conductivity estimation using Bayesian model averaging and variance window” by Frank T.-C. Tsai and Xiaobao Li: COMMENTARY
journal, February 2010
- Ye, Ming; Lu, Dan; Neuman, Shlomo P.
- Water Resources Research, Vol. 46, Issue 2
Works referencing / citing this record:
Assessing titanium dioxide nanoparticles transport models by Bayesian uncertainty analysis
journal, October 2018
- Liu, Jin; Zeng, Xiankui; Wu, Jichun
- Stochastic Environmental Research and Risk Assessment, Vol. 32, Issue 12
Relative model score: a scoring rule for evaluating ensemble simulations with application to microbial soil respiration modeling
journal, August 2018
- Elshall, Ahmed S.; Ye, Ming; Pei, Yongzhen
- Stochastic Environmental Research and Risk Assessment, Vol. 32, Issue 10