Time series-based groundwater level forecasting using gated recurrent unit deep neural networks

In this research, the mean monthly groundwater level with a range of 3.78 m in Qosacay plain, Iran, is forecast. Regarding three different layers of gated recurrent unit (GRU) structures and a hybrid of variational mode decomposition with gated recurrent unit (VMD-GRU), deep learning-based neural network models are developed. As the base model for performance comparison, the general single-long short-term memory-layer network model is developed. In all models, the module of sequence-to-one is used because of the lack of meteorological variables recorded in the study area. For modeling, 216 monthly datasets of the mean monthly water table depth of 33 different monitoring piezometers in the period April 2002-March 2020 are utilized. To boost the performance of the models and reduce the overfitting problem, an algorithm tuning process using different types of hyperparameter accompanied by a trial-and-error procedure is applied. Based on performance evaluation metrics, the total learnable parameters value and especially the model grading process, the new double-GRU model coupled with multiplication layer (x) (GRU2x model) is chosen as the best model. Under the optimal hyperparameters, the GRU2x model results in an R (2) of 0.86, a root mean square error (RMSE) of 0.18 m, a corrected Akaike's information criterion (AICc) of -280.75, a running time for model training of 87 s and a total grade (TG) of 6.21 in the validation stage; and the hybrid VMD-GRU model yields an RMSE of 0.16 m, an R (2) of 0.92, an AICc of -310.52, a running time of 185 s and a TG of 3.34.