Multi-step ahead forecasting of daily reference evapotranspiration using deep learning

Daily reference evapotranspiration (ETo) forecasts can help farmers in irrigation planning. Therefore, this study assesses the potential of deep learning (long short-term memory (LSTM), one-dimensional convolutional neural network (1D CNN) and a combination of the two previous models (CNN-LSTM)) and traditional machine learning models (artificial neural network (ANN) and random forest (RF)), in regional and local scenarios, to forecast multi-step ahead daily ETo (seven days) using iterated, direct and multiple input multiple output (MIMO) forecasting strategies. Three input data combinations were assessed: (1) only lagged ETo; (2) lagged ETo + day of the year of each step of the time lag considered; and (3) the same of input combination 2 + lagged meteorological variables. Data from 53 weather stations located in Minas Gerais, Brazil, were used. Four stations were used as test stations. Two baselines were also employed: (B1), all the forecasting horizon is considered equal to the mean ETo measured during the last seven days; and (B2), ahead ETo values are considered equal to their respective historical monthly means. In general, MIMO was the best forecasting strategy, offering good performance and lower computational cost. The deep learning models performed slightly better than the machine learning models, and both were better than the best baseline (B2), mainly on the first and second forecasting days. Among the deep learning models, CNN-LSTM2 (i.e., CNN-LSTM with input combination 2) performed the best in local scenario (mean RMSE over the prediction horizon and stations equal to 0.87), and CNNLSTM3 performed the best in regional scenario (mean RMSE equal to 0.88). The regional models are recommended instead of the local models since they exhibited similar performances and have higher generalization capacity. Finally, although the models developed have not exhibited high accuracies, they can be useful tools in places where historical monthly mean ETo is used to forecast ETo.