Assessing the impacts of parameter uncertainty for computationally expensive groundwater models

Computational requirements often limit the assessment of uncertainty in complex environmental models. Monte Carlo-based techniques such as generalized likelihood uncertainty estimation (GLUE) and Bayesian uncertainty assessment are limited in applicability because of their heavy computational demands. This paper presents a computationally efficient method that combines automatic calibration using function-approximation-based global optimization with importance weighting for assessing parametric uncertainty in model outputs for computationally expensive models. We call this method automatic calibration and uncertainty assessment using response surfaces (ACUARS). The bias introduced during optimization because of oversampling of high goodness of fit regions of the parameter space is corrected using a multidimensional cell-declustering technique. The proposed method is applied to two hypothetical examples in enhanced bioremediation of chlorinated ethenes in groundwater that differ in computational requirements and the number of parameters that were calibrated. The results from the simpler example in which uncertainty of three model parameters in model outputs was considered showed that for a given acceptability threshold and a given number of permissible model simulations, ACUARS finds many more representative parameter sets than GLUE. GLUE produced only half the number of acceptable parameter sets for uncertainty assessment, even after 10 times as many simulations as ACUARS was performed for GLUE. Further, the median output of ACUARS predicted the true value of the outputs more closely than GLUE. For a more complicated numerical example, where noisy data were used for calibration of seven model parameters, GLUE required 2400 simulations to find 31 acceptable parameter sets, while ACUARS found 46 acceptable parameter sets in only 300 simulations for a moderately stringent threshold. This enabled a more accurate estimate of uncertainty by providing closer estimates of the true outputs.