Abstract
Precise forecasting of reference evapotranspiration (ET0) is one of the critical initial steps in determining crop water requirements, which contributes to the reliable management and long-term planning of the world's scarce water sources. This study provides daily prediction and multi-step forward forecasting of ET0 utilizing a long short-term memory network (LSTM) and a bi-directional LSTM (Bi-LSTM) model. For daily predictions, the LSTM model's accuracy was compared to that of other artificial intelligence-based models commonly used in ET0 forecasting, including support vector regression (SVR), M5 model tree (M5Tree), multivariate adaptive regression spline (MARS), probabilistic linear regression (PLR), adaptive neuro-fuzzy inference system (ANFIS), and Gaussian process regression (GPR). The LSTM model outperformed the other models in a comparison based on Shannon's entropy-based decision theory, while the M5 tree and PLR models proved to be the lowest performers. Prior to performing a multi-step-ahead forecasting, ANFIS, sequence-to-sequence regression LSTM network (SSR-LSTM), LSTM, and Bi-LSTM approaches were used for one-step-ahead forecasting utilizing the past values of the ET0 time series. The results showed that the Bi-LSTM model outperformed other models and that the sequence of models in ascending order in terms of accuracies was Bi-LSTM > SSR-LSTM > ANFIS > LSTM. The Bi-LSTM model provided multi-step (5 day)-ahead ET0 forecasting in the next step. According to the results, the Bi-LSTM provided reasonably accurate and acceptable forecasting of multi-step-forward ET0 with relatively lower levels of forecasting errors. In the final step, the generalization capability of the proposed best models (LSTM for daily predictions and Bi-LSTM for multi-step-ahead forecasting) was evaluated on new unseen data obtained from a test station, Ishurdi. The model's performance was assessed on three distinct datasets (the entire dataset and the first and the second halves of the entire dataset) derived from the test dataset between 1 January 2015 and 31 December 2020. The results indicated that the deep learning techniques (LSTM and Bi-LSTM) achieved equally good performances as the training station dataset, for which the models were developed. The research outcomes demonstrated the ability of the developed deep learning models to generalize the prediction capabilities outside the training station.