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 coefficients (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 meteorological 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, HS 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 meteorological data on the Loess Plateau, which is very helpful for farmers or irrigation system operators to improve their irrigation scheduling.