Estimating daily reference evapotranspiration using a novel hybrid deep learning model

Reference evapotranspiration (ET0) is usually employed for estimating actual crop ET together with crop co-efficients (Kc). However, it is necessary to explore an alternative model to estimate ET0 concisely because of numerous limitations in the Penman-Monteith method. To improve the ET0 estimation accuracy using limited meteorological data, this study developed a novel hybrid deep learning model (D-LSTM) based on the meteo-rological data during 1961-2020 observed at fifty stations on the Loess Plateau, which used the Deep Belief Network (DBN) module to extract features from meteorological data and the Long Short-Term Memory (LSTM) module to expand time features and process data information with sequential features, respectively. Based on the comparative evaluation of ET0 estimation accuracy between the D-LSTM, DBN, LSTM, and nine empirical models, the results drawn from this study demonstrated that the D-LSTM model manifested the best performance as RH-based, Rn-based, and T-based ET0 estimating models. For local strategy, the value of R2, NSE, RMSE, MAPE, and GPI ranging 0.941 +/- 0.020, 0.940 +/- 0.032, 0.436 +/- 0.457 mm d-1, 0.150 +/- 0.016, and 1.611 +/- 0.180 for D-LSTM1 (RH-based), 0.944 +/- 0.030, 0.943 +/- 0.037, 0.423 +/- 0.313 mm d-1, 0.119 +/- 0.013, and 1.917 +/- 0.155 for D-LSTM2 (Rn-based), and 0.902 +/- 0.091, 0.891 +/- 0.094, 0.558 +/- 0.319 mm d-1, 0.181 +/- 0.058, and 1.440 +/- 0.550 for D-LSTM3 (T-based). For external strategy, the average value of R2, NSE, RMSE, MAPE, and GPI were 0.874, 0.872, 0.651 mm d-1, 0.159, and 1.837 for D-LSTM1, 0.894, 0.892, 0.591 mm d-1, 0.138, and 2.000 for D-LSTM2, and 0.839, 0.827, 0.768 mm d-1, 0.212, and 1.482 for D-LSTM3. Following, the LSTM performed better than DBN for local strategy, but vice versa for external strategy. Despite DL models outperforming RH-based and Rn-based empirical models, H-S outperformed the DBN3 for local strategy, and was superior to LSTM3 for external strategy. Under limited meteorological data, the Rn-based ET0 estimating models are superior to RH-based and T-based models, and RH-based achieved better accuracy than T-based for DL models, but vice versa for empirical models. There is significant spatial variability in the accuracy of daily ET0 models, but the high precision of the D-LSTM was stable on the Loess Plateau. Overall, the D-LSTM model, which combines the advantages of DBN and LSTM, is the most recommended ET0 model using incomplete meteoro-logical data on the Loess Plateau, which is very helpful for farmers or irrigation system operators to improve their irrigation scheduling.