Parameter estimation and predictive uncertainty in stochastic inverse modeling of groundwater flow: Comparing null-space Monte Carlo and multiple starting point methods


Corresponding author: H. Yoon, Geoscience Research and Applications Center, Sandia National Laboratories, P.O. Box 5800, MS 0751, Albuquerque, NM 87185, USA. (


[1] Given a highly parameterized groundwater model in which the conceptual model of the heterogeneity is stochastic, a set of inverse calibrations from multiple starting points (MSPs) provide an ensemble of calibrated parameters and follow-on transport predictions. However, the multiple calibrations are computationally expensive. A recently developed null-space Monte Carlo (NSMC) method combines the calibration solution-space parameters with the ensemble of null-space parameters, creating sets of calibration-constrained parameters for input to follow-on transport predictions. The consistency between probabilistic ensembles of parameter estimates and predictions created using the MSP calibration and the NSMC approaches is examined using a highly parameterized (>1300 parameters) model of the Culebra dolomite previously developed for the Waste Isolation Pilot Plant project in New Mexico as a test case. A total of 100 estimated fields are retained from the MSP approach, and the ensemble of results defining the model fit to the data and prediction of an advective travel time are compared with the same results obtained using NSMC. We demonstrate that the NSMC fields based on a single calibrated model can be significantly constrained by the calibrated solution space, and the resulting distribution of advective travel times is biased toward the travel time from the single calibrated field. To overcome this, newly proposed strategies to employ a multiple calibration-constrained NSMC (M-NSMC) approach are evaluated. Comparison of the M-NSMC and MSP methods demonstrates that M-NSMC can provide a computationally efficient and practical solution for predictive uncertainty analysis in highly nonlinear and complex subsurface flow and transport models.