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Title: Quantifying model structural error: Efficient Bayesian calibration of a regional groundwater flow model using surrogates and a data-driven error model

Abstract

Groundwater model structural error is ubiquitous, due to simplification and/or misrepresentation of real aquifer systems. During model calibration, the basic hydrogeological parameters may be adjusted to compensate for structural error. This may result in biased predictions when such calibrated models are used to forecast aquifer responses to new forcing. Here, we investigate the impact of model structural error on calibration and prediction of a real-world groundwater flow model, using a Bayesian method with a data-driven error model to explicitly account for model structural error. The error-explicit Bayesian method jointly infers model parameters and structural error and thereby reduces parameter compensation. In this study, Bayesian inference is facilitated using high performance computing and fast surrogate models (based on machine learning techniques) as a substitute for the computationally expensive groundwater model. We demonstrate that with explicit treatment of model structural error, the Bayesian method yields parameter posterior distributions that are substantially different from those derived using classical Bayesian calibration that does not account for model structural error. We also found that the error-explicit Bayesian method gives signficantly more accurate prediction along with reasonable credible intervals. Finally, through variance decomposition, we provide a comprehensive assessment of prediction uncertainty contributed from parameter, model structure,more » and measurement uncertainty. The results suggest that the error-explicit Bayesian approach provides a solution to real-world modeling applications for which data support the presence of model structural error, yet model deficiency cannot be specifically identified or corrected.« less

Authors:
ORCiD logo [1]; ORCiD logo [2]; ORCiD logo [3];  [4]
+ Show Author Affiliations
  1. Univ. of Illinois at Urbana-Champaign, Urbana, IL (United States). Dept. of Civil and Environmental Engineering; Michigan State Univ., East Lansing, MI (United States). Dept. of Earth and Environmental Sciences
  2. Univ. of Illinois at Urbana-Champaign, Urbana, IL (United States). Dept. of Civil and Environmental Engineering
  3. Florida State Univ., Tallahassee, FL (United States). Dept. of Scientific Computing
  4. Univ. of Illinois at Urbana-Champaign, Urbana, IL (United States). Dept. of Statistics
Publication Date:
Research Org.:
Florida State Univ., Tallahassee, FL (United States)
Sponsoring Org.:
USDOE Office of Science (SC)
OSTI Identifier:
1532997
Grant/Contract Number:  
SC0008272
Resource Type:
Accepted Manuscript
Journal Name:
Water Resources Research
Additional Journal Information:
Journal Volume: 53; Journal Issue: 5; Journal ID: ISSN 0043-1397
Publisher:
American Geophysical Union (AGU)
Country of Publication:
United States
Language:
English
Subject:
54 ENVIRONMENTAL SCIENCES; environmental sciences & ecology; marine & freshwater biology; water resources; Bayesian calibration; uncertainty decomposition; model structural error; surrogate modeling; groundwater

Citation Formats

Xu, Tianfang, Valocchi, Albert J., Ye, Ming, and Liang, Feng. Quantifying model structural error: Efficient Bayesian calibration of a regional groundwater flow model using surrogates and a data-driven error model. United States: N. p., 2017. Web. doi:10.1002/2016wr019831.
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Xu, Tianfang, Valocchi, Albert J., Ye, Ming, & Liang, Feng. Quantifying model structural error: Efficient Bayesian calibration of a regional groundwater flow model using surrogates and a data-driven error model. United States. https://doi.org/10.1002/2016wr019831
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Xu, Tianfang, Valocchi, Albert J., Ye, Ming, and Liang, Feng. Mon . "Quantifying model structural error: Efficient Bayesian calibration of a regional groundwater flow model using surrogates and a data-driven error model". United States. https://doi.org/10.1002/2016wr019831. https://www.osti.gov/servlets/purl/1532997.
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@article{osti_1532997,
title = {Quantifying model structural error: Efficient Bayesian calibration of a regional groundwater flow model using surrogates and a data-driven error model},
author = {Xu, Tianfang and Valocchi, Albert J. and Ye, Ming and Liang, Feng},
abstractNote = {Groundwater model structural error is ubiquitous, due to simplification and/or misrepresentation of real aquifer systems. During model calibration, the basic hydrogeological parameters may be adjusted to compensate for structural error. This may result in biased predictions when such calibrated models are used to forecast aquifer responses to new forcing. Here, we investigate the impact of model structural error on calibration and prediction of a real-world groundwater flow model, using a Bayesian method with a data-driven error model to explicitly account for model structural error. The error-explicit Bayesian method jointly infers model parameters and structural error and thereby reduces parameter compensation. In this study, Bayesian inference is facilitated using high performance computing and fast surrogate models (based on machine learning techniques) as a substitute for the computationally expensive groundwater model. We demonstrate that with explicit treatment of model structural error, the Bayesian method yields parameter posterior distributions that are substantially different from those derived using classical Bayesian calibration that does not account for model structural error. We also found that the error-explicit Bayesian method gives signficantly more accurate prediction along with reasonable credible intervals. Finally, through variance decomposition, we provide a comprehensive assessment of prediction uncertainty contributed from parameter, model structure, and measurement uncertainty. The results suggest that the error-explicit Bayesian approach provides a solution to real-world modeling applications for which data support the presence of model structural error, yet model deficiency cannot be specifically identified or corrected.},
doi = {10.1002/2016wr019831},
journal = {Water Resources Research},
number = 5,
volume = 53,
place = {United States},
year = {Mon May 08 00:00:00 EDT 2017},
month = {Mon May 08 00:00:00 EDT 2017}
}
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https://doi.org/10.1002/2016wr019831
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