MULTI-MODEL ANALYSIS FOR GROUNDWATER MODELING USING AICC AND KIC - A MORE REALISTIC ASSESSMENT OF UNCERTAINTY IN PREDICTIONS

Groundwater models are commonly calibrated with sparse observation data relative to the scale of the groundwater system being modeled. This allows for multiple interpretations with regard to model structure because more than one conceptual model may explain the data. Multi-model analysis (MMA) is a method which uses information criteria equations to identify those models, within a defined set of models, most likely to represent a true but unknown system. MMA accounts for the uncertainty of using different model structures for the same set of observation data and provides a more realistic assessment of uncertainty of predictions. Akaike (AICc) and Kashyup (KIC) are two information criteria used for MMA. An example problem illustrates how AICc results in high probability for simple models if the number of observations is low relative to the number of estimated parameters. As the number of observations is increased, using AICc can result in complex models being assigned high model probabilities. KIC results in high probability for more complex models because of the Fisher Information term in the KIC equation. More complex models may be deficient and parameters may not be well estimated resulting in unreliable predictions. We propose the following criteria to identify and remove deficient models prior to performing MMA; 1) unreasonable parameter values, 2) unreasonable confidence intervals on parameters estimates, 3) correlations between parameters, 4) low value of the determinant of the correlation matrix, 5) high value of the condition number, and 6) unreasonable confidence intervals for predictions. We demonstrate that AICc and KIC can result in a broader distribution of the uncertainty and therefore a more realistic assessment of uncertainty if more than one model in the set has a significant AICc or KIC model probability.