Effect of Temporal Residual Correlation on Estimation of Model Averaging Weights

When conducting model averaging for assessing groundwater conceptual model uncertainty, the averaging weights are always calculated using model selection criteria such as AIC, AICc, BIC, and KIC. However, this method sometimes leads to an unrealistic situation in which one model receives overwhelmingly high averaging weight (even 100%), which cannot be justified by available data and knowledge. It is found in this study that the unrealistic situation is due partly, if not solely, to ignorance of residual correlation when estimating the negative log-likelihood function common to all the model selection criteria. In the context of maximum-likelihood or least-square inverse modeling, the residual correlation is accounted for in the full covariance matrix; when the full covariance matrix is replaced by its diagonal counterpart, it assumes data independence and ignores the correlation. As a result, treating the correlated residuals as independent distorts the distance between observations and simulations of alternative models. As a result, it may lead to incorrect estimation of model selection criteria and model averaging weights. This is illustrated for a set of surface complexation models developed to simulate uranium transport based on a series of column experiments. The residuals are correlated in time, and the time correlation is addressed using a second-order autoregressive model. The modeling results reveal importance of considering residual correlation in the estimation of model averaging weights.