Interactive multi-objective inverse groundwater modelling - Incorporating subjective knowledge and conceptual uncertainty

This paper addresses the important question of uncertainty assessment for predictions obtained from an interactive multi-objective groundwater inverse framework (proposed by the authors). This framework is based on an interactive multi-objective genetic algorithm (IMOGA) and considers subjective user preferences in addition to quantitative calibration measures such as calibration errors and regularization to solve the groundwater inverse problem. Given these criteria the IMOGA converges to a set of Pareto optimal parameter fields (transmissivity, in this case) that represent the best trade-off among all (qualitative as well as quantitative) objectives. Predictive uncertainty analysis for the IMOGA consists of assessing the uncertainty in the transmissivity fields found by the IMOGA, and the impact this uncertainty has on model predictions. To do this, we propose a multi-level sampling approach, incorporating uncertainty in both large-scale trends and the small-scale stochastic variability in the transmissivity fields found by the IMOGA. The multiple solutions found by the IMOGA are considered alternative models of the large-scale structure of the transmissivity field. Small-scale uncertainty is considered to be conditioned on the large-scale trend and correlated with a specified covariance structure. The prediction model is run using all simulated fields 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). The methodology has been applied to a field-scale case study based on the Waste Isolation Pilot Plant (WIPP) situated in Carlsbad, New Mexico. Results, with and without expert interaction, are analyzed and the impact expert judgment has on predictive uncertainty at the WIPP site are also 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.