Shannon entropy of performance metrics to choose the best novel hybrid algorithm to predict groundwater level (case study: Tabriz plain, Iran)

Predicting groundwater level (GWL) fluctuations, which act as a reserve water reservoir, particularly in arid and semi-arid climates, is vital in water resources management and planning. Within the scope of current research, a novel hybrid algorithm is proposed for estimating GWL values in the Tabriz plain of Iran by combining the artificial neural network (ANN) algorithm with newly developed nature-inspired Coot and Honey Badger metaheuristic optimization algorithms. Various combinations of meteorological data such as temperature, evaporation, and precipitation, previous GWL values, and the month and year values of the data were used to evaluate the algorithm’s success. Furthermore, the Shannon entropy of model performance was assessed according to 44 different statistical indicators, classified into two classes: accuracy and error. Hence, based on the high value of Shannon entropy, the best statistical indicator was selected. The results of the best model and the best scenario were analyzed. Results indicated that value of Shannon entropy is higher for the accuracy class than error class. Also, for accuracy and error class, respectively, Akaike information criterion (AIC) and residual sum of squares (RSS) indexes with the highest entropy value which is equal to 12.72 and 7.3 are the best indicators of both classes, and Legate-McCabe efficiency (LME) and normalized root mean square error-mean (NRMSE-Mean) indexes with the lowest entropy value which is equal to 3.7 and − 8.3 are the worst indicators of both classes. According to the evaluation best indicator results in the testing phase, the AIC indicator value for HBA-ANN, COOT-ANN, and the standalone ANN models is equal to − 344, − 332.8, and − 175.8, respectively. Furthermore, it was revealed that the proposed metaheuristic algorithms significantly improve the performance of the standalone ANN model and offer satisfactory GWL prediction results. Finally, it was concluded that the Honey Badger optimization algorithm showed superior results than the Coot optimization algorithm in GWL prediction. Graphical Abstract