Quantification of model uncertainty in environmental modeling

Abstract

The last few decades have seen considerable progress in the quantification of environmental model uncertainty. Initially the emphasis has been on uncertainty in model parameters. A more recent trend has been to consider uncertainties in both model structure and parameters, most commonly by analyzing jointly predictions generated by several alternative models of the environment. This has been motivated by a growing recognition that the open and complex nature of environmental systems renders them suitable to multiple conceptualizations and mathematical descriptions. Predictions generated by a single model are prone to statistical bias (by reliance on an invalid model) and underestimation of uncertainty (by under-sampling the relevant model space) (Neuman 2003; Neuman and Wierenga 2003). Some multimodel approaches blend or average statistical results generated by a set of alternative models. A common approach to model averaging is to (1) postulate several alternative models for a site, (a) associate each model with a weight or probability, and (c) generate weighted average predictions and statistics of all the models. Ways to accomplish this have varied; some are included in a public-domain code (Multimodel Analysis or MMA by Poeter and Hill 2007) recently reviewed by Ye (2010). This special issue of SERRA focuses on such and other emerging methods of model and parameter uncertainty quantification. The special issue contains seven papers devoted to model averaging. Diks and Vrugt compare model averaging methods that weigh models in different ways, without always requiring that the weights sum up to unity. The methods are applied to two sites and compared in term of their predictive performance measured by out-of-sample root mean squared prediction error. Sain and Furrer estimate weights based on variation and correlation of alternative hierarchical models. They use a Bayesian hierarchical model to estimate correlation between models and the impact of parameter estimation uncertainty on the weights. Ajami and Gu use the Bayesian Model Averaging (BMA) approach of Raftery et al. (2005) to assess uncertainty in a suite of biogeochemical models having various levels of complexity to simulate the fate and transport of nitrate at a field site in California. Their results demonstrate that whereas single models, regardless of their complexity levels, are incapable of representing all active processes at the site, the 95% uncertainty bounds of BMA bracket 90% to 100% of the observations. Tsai use a variance-window (Tsai and Li 2008) version of Maximum Likelihood (ML) BMA (MLBMA; Neuman 2003; Ye et al. 2004) to quantify model uncertainty in managing groundwater within a thick sandy aquifer in Louisiana where saltwater intrusion is of concern. Alternative models are postulated to reflect uncertainty in conceptualizing hydraulic head boundaries and geostatistical parameterization through variogram models. The results M. Ye (&) Department of Scientific Computing, Florida State University, Tallahassee, FL 32306, USA e-mail: mye@fsu.edu