Long-term forecasting of monthly mean reference evapotranspiration using deep neural network: A comparison of training strategies and approaches.

Prediction of reference evapotranspiration (ET 0) remains a challenge, especially with forward multi-step forecasting. The bottleneck facing current research is the limitation of the span of the forecasting time horizons, which can be rather disappointing, especially when long-term forecasting is desired. In this study, an explainable model structure, represented by a one-dimensional convolutional neural network (CNN-1D) was compared to the long short-term memory network (LSTM) and gated recurrent unit network (GRU), both formulated with black-box model method. The comparison included the application of different forecasting strategies (iterated vs. multiple-input–multiple-output (MIMO)) and approaches (direct vs. indirect). This study was conducted at four stations scattered across the Peninsular Malaysia. From the results of this study, the explainable CNN-1D model generally performed poorer than its black-box counterparts at most of the stations. The type of model and its structure, forecasting strategy and approach formed a complex relationship to indicate that there is no one-for-all solution in the case of the long-term prediction of monthly mean ET 0. Despite that, the GRU-based models stood out as the most well-suited option for the task, with the MIMO forecasting strategy being favoured over the iterated strategy. At the four stations, the average mean absolute error (MAE), root mean square error (RMSE), mean percentage error (MAPE) and the Kling–Gupta efficiency (KGE) of the best GRU models were 0.182 mm/day, 0.260 mm/day, 4.972 % and 0.747, respectively. It was found that the prediction residual of the best GRU models did not possess a clear trend as the forecasting horizon was lengthened. The results implied that theoretically, the forecasting time horizon could be extended over to a longer temporal scale without any deterioration in the model performance. This finding is positive as it brings about the possibility of allocating the water budget with higher confidence. Nevertheless, the LSTM and GRU models developed in this study, were believed to have more tremendous potential if they were to be designed with purpose (such as the integration of optimisation algorithm), instead of being a mere black-box structure. • Current empirical/machine learning models cannot accurately forecast long-term ET 0. • Deep neural networks were trained using iterated and MIMO forecast strategies. • CNN-1D (explainable structure), LSTM, and GRU (black-box structure) were selected. • GRU MIMO,D and GRU MIMO,ID were found to have the best performance among the DNNs. • Prediction residual had a very weak correlation with the forecasting time horizon. [ABSTRACT FROM AUTHOR]