The multiple solutions found by the IMOGA are considered alternative models of the large-scale structure of the transmissivity field. The large-scale uncertainty is modeled using a statistical approach where calibration error, regularization, and the expert’s subjective preferences for different parameter fields are incorporated in the likelihood of a given transmissivity field. Small-scale uncertainty is considered to be conditioned on the large-scale trend and correlated with a specified covariance structure. A state-of-the-art stochastic simulation algorithm called ‘direct sequential simulation’ is used to ensure that the local mean structure of the large-scale trend is preserved, thus maintaining the solutions’ calibration errors within bounds. The prediction model is run for the resulting realizations to obtain the distribution of predictions, which are then combined using model averaging approaches such as GLUE (generalized likelihood uncertainty estimation) and MLBMA (maximum likelihood Bayesian model averaging).

This methodology has been applied to a field-scale case study based on the Waste Isolation Pilot Plant (WIPP) situated in Carlsbad, NM. Results indicate that taking expert judgment into consideration leads to more conservative solutions and allows the expert to compensate for some of the lack of data and model simplifications introduced in the formulation of the problem.