Interactive Multi-Objective Inverse Groundwater Modelling – Incorporating Subjective Knowledge and Conceptual Uncertainty

摘要

This paper addresses the important question of uncertainty assessment for predictions obtainedfrom an interactive multi-objective groundwater inverse framework (proposed by the authors). Thisframework is based on an interactive multi-objective genetic algorithm (IMOGA) and considerssubjective user preferences in addition to quantitative calibration measures such as calibrationerrors and regularization to solve the groundwater inverse problem. Given these criteria theIMOGA converges to a set of Pareto optimal parameter fields (transmissivity, in this case) thatrepresent the best trade-off among all (qualitative as well as quantitative) objectives. Predictiveuncertainty analysis for the IMOGA consists of assessing the uncertainty in the transmissivityfields 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 trendsand the small-scale stochastic variability in the transmissivity fields found by the IMOGA. Themultiple solutions found by the IMOGA are considered alternative models of the large-scalestructure of the transmissivity field. Small-scale uncertainty is considered to be conditioned on thelarge-scale trend and correlated with a specified covariance structure. The prediction model is runusing all simulated fields to obtain the distribution of predictions, which are then combined usingmodel averaging approaches such as GLUE (generalized likelihood uncertainty estimation) andMLBMA (maximum likelihood Bayesian model averaging). The methodology has been applied toa field-scale case study based on the Waste Isolation Pilot Plant (WIPP) situated in Carlsbad, NewMexico. Results, with and without expert interaction, are analyzed and the impact expert judgmenthas on predictive uncertainty at the WIPP site are also discussed. It is shown that for this caseexpert interaction leads to more conservative solutions as the expert compensates for some of thelack of data and modeling approximations introduced in the formulation of the problem.