This project aims to improve the quantification of uncertainties in the modeling of hydrological systems with uncertain model structure, uncertain parameters, and uncertain input data. To specifically account for uncertainty in model selection, Bayesian Model Averaging (BMA) is used for integral modeling. BMA is a formal statistical approach based on Bayesian probability theory. Weights are assigned to an ensemble of alternative models based on individual calibration performance and the principle of parsimony. These weights enable model ranking, model selection, and model averaging. The conceptual uncertainty within the model ensemble can be quantified as "between-model variance."
A significant obstacle to the widespread application of BMA for integrated modeling and uncertainty estimation is the technical difficulty of determining BMA weights accurately and efficiently. To address this challenge, a comparison of various methods for evaluating BMA equations has been conducted, considering both mathematical approximations and numerical evaluation methods (Schöniger et al., 2014). The results from two synthetic case studies and a hydrological application show that the choice of evaluation method significantly influences the accuracy of the determined weights and, consequently, the resulting model ranking and model-averaged results.
When calculated correctly, BMA weights demonstrate an optimal compromise between model goodness-of-fit and model complexity. To determine the level of complexity justified by the available calibration dataset, we separated the complexity component of the Bayesian compromise from the goodness-of-fit component. This model justification analysis (Schöniger et al., 2015a) was demonstrated through model selection between groundwater models of varying complexity.
Finally, we addressed the question of whether model weights are reliable under uncertain model input or calibration data. The proposed sensitivity analysis aims to assess the permissible confidence in the resulting model ranking correctly (Schöniger et al., 2015b). The impact of noisy calibration data on model ranking is examined using a case study of soil-plant model selection. The results show that model weights can be highly sensitive to random measurement errors, compromising the meaningfulness of the model ranking.
The insights from this research project also have implications for the selection and expansion of the model ensemble, model development, and optimal data collection for a maximally reliable model ranking.
