Complexity vs. simplicity: groundwater model ranking using information criteria

A groundwater model characterized by a lack of field data about hydraulic model parameters and boundary conditions combined with many observation data sets for calibration purpose was investigated concerning model uncertainty. Seven different conceptual models with a stepwise increase from 0 to 30 adjustable parameters were calibrated using PEST. Residuals, sensitivities, the Akaike information criterion (AIC and AICc), Bayesian information criterion (BIC), and Kashyap's information criterion (KIC) were calculated for a set of seven inverse calibrated models with increasing complexity. Finally, the likelihood of each model was computed. Comparing only residuals of the different conceptual models leads to an overparameterization and certainty loss in the conceptual model approach. The model employing only uncalibrated hydraulic parameters, estimated from sedimentological information, obtained the worst AIC, BIC, and KIC values. Using only sedimentological data to derive hydraulic parameters introduces a systematic error into the simulation results and cannot be recommended for generating a valuable model. For numerical investigations with high numbers of calibration data the BIC and KIC select as optimal a simpler model than the AIC. The model with 15 adjusted parameters was evaluated by AIC as the best option and obtained a likelihood of 98%. The AIC disregards the potential model structure error and the selection of the KIC is, therefore, more appropriate. Sensitivities to piezometric heads were highest for the model with only five adjustable parameters and sensitivity coefficients were directly influenced by the changes in extracted groundwater volumes.