Formulation of Shannon entropy model averaging for groundwater level prediction using artificial intelligence models

A two-level modeling strategy is formulated to predict groundwater levels (GWL) within a portion of Lake Urmia's aquifer in NW Iran during 14 years (2001-2015), which both aquifer and lake suffer significant water decline. At Level 1, three artificial intelligence (AI) models were trained and tested, which comprise artificial neural network (ANN), Sugeno fuzzy logic (SFL), and neuro-fuzzy (NF). At Level 2, a novel formulation was employed, referred to as the Shannon entropy model averaging (EMA). This formulation combines the results at Level 1 by calculating the weights of Level 1 models based on an innovative approach, which incorporates performance, stability, and parsimony criteria. The results indicate that the models at Level 1 are fit-for-purpose and can capture the water table decline in GWL, but EMA improves RMSE by 5% in the testing phase. Although EMA does not significantly increase the performance of the models, the results of the homoscedastic test in models' residuals indicate that EMA increases the reliability of prediction owing to the homoscedastic residuals with the highest p value compared to Level 1 models. The p values as per Breusch-Pagan and White tests are 0.88 and 1, respectively, which indicates further information does not remain in the EMA residual. The EMA formulation can be applied to other water resource management problems.