Challenges Applying Calibration-Constrained Subspace Monte Carlo Methodology to Uncertainty Assessments

Louis-Charles Boutin

In the proceedings of: GeoMontréal 2013: 66th Canadian Geotechnical Conference; 11th joint with IAH-CNC

Session: General Hydrogeology I

ABSTRACT: As with any effort of predicting future outcomes, there is a degree of uncertainty in the predictions associated with a numerical model of groundwater flow. Sources of groundwater flow model prediction uncertainty include the model parameter values. Quantifying prediction uncertainty is a perennial challenge. In recent years, calibration constrained sub-space Monte Carlo analysis has been used for quantifying prediction uncertainty due to calibrated parameter in environmental impact assessments of groundwater withdrawal in Alberta. This presentation summarizes the calibration constraint sub-space Monte Carlo methodology (Tonkin and Doherty 2009), which consist in generating random sets of parameters from the prior information. In order to assess the prediction uncertainty associated with parameter sets which honor the calibration data, the random sets of parameters generated are subtracted from the calibrated solution and the differences are projected onto the calibration null space, given the dimensionality of the solution space (defined by significantly non-zero singular values of calibrated solution™s Jacobian matrix). This presentation also discusses challenges related to the selection of eigenvalue threshold defined as the threshold between the solution space and null space (Yoon and al. 2013), an appropriate degree of model parameterization, random parameter selection and the number of Monte Carlo realizations required to quantify prediction uncertainty. REFERENCES Tonkin, M., and J. Doherty 2009. Calibration-constrained Monte Carlo analysis of highly parameterized models using subspace techniques, Water Resour. Res., 45, W00B10, doi: 10.1029/2005WR004723. Yoon, H., D. B. Hart, and S. A. McKenna 2013. Parameter estimation and predictive uncertainty in stochastic inverse modeling of groundwater flow: Comparing null-space Monte Carlo and multiple starting point methods, Water Resour. Res., 49, doi: 10.1002/wrcr.20064.

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