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Incorporating subjective and stochastic uncertainty in an interactive multi-objective groundwater calibration framework

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Abstract

The interactive multi-objective genetic algorithm (IMOGA) combines traditional optimization with an interactive framework that considers the subjective knowledge of hydro-geological experts in addition to quantitative calibration measures such as calibration errors and regularization to solve the groundwater inverse problem. The IMOGA is inherently a deterministic framework and identifies multiple large-scale parameter fields (typically head and transmissivity data are used to identify transmissivity fields). These large-scale parameter fields represent the optimal trade-offs between the different criteria (quantitative and qualitative) used in the IMOGA. This paper further extends the IMOGA to incorporate uncertainty both in the large-scale trends as well as the small-scale variability (which can not be resolved using the field data) in the parameter fields. The different parameter fields identified by the IMOGA represent the uncertainty in large-scale trends, and this uncertainty is modeled using a Bayesian approach where calibration error, regularization, and the expert’s subjective preference are combined to compute a likelihood metric for each parameter field. Small-scale (stochastic) variability is modeled using a geostatistical approach and added onto the large-scale trends identified by the IMOGA. This approach is applied to the Waste Isolation Pilot Plant (WIPP) case-study. Results, with and without expert interaction, are analyzed and the impact that expert judgment has on predictive uncertainty at the WIPP site is discussed. It is shown that for this case, expert interaction leads to more conservative solutions as the expert compensates for some of the lack of data and modeling approximations introduced in the formulation of the problem.

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Acknowledgements

This research was funded by the Department of Energy—Grant No.: DE-FG07-02ER635302. We thank Dr. Sean McKenna, Dr. David Hart, and Dr. Richard Beauheim from the Sandia National Laboratory for providing us with the WIPP dataset and giving us input on the IMOGA’s application to this case study. We also wish to thank Dr. Timothy Ellsworth (Department of Natural Resources and Environmental Sciences, University of Illinois, Urbana-Champaign) for his insights on the geostatistical aspects of this work.

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Authors and Affiliations

  1. INTERA, Inc., 1812 Centre Creek Dr., Austin, TX, 78727, USA

    Abhishek Singh

  2. Illinois State Water Survey, 2204 Griffith Drive, Champaign, IL, 61820, USA

    Douglas D. Walker

  3. Department of Civil and Environmental Engineering, University of Illinois at Urbana-Champaign, Urbana, IL, 61801, USA

    Barbara S. Minsker & Albert J. Valocchi

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  1. Abhishek Singh
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Correspondence to Abhishek Singh.

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Singh, A., Walker, D.D., Minsker, B.S. et al. Incorporating subjective and stochastic uncertainty in an interactive multi-objective groundwater calibration framework. Stoch Environ Res Risk Assess 24, 881–898 (2010). https://doi.org/10.1007/s00477-010-0384-1

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