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Accurate reference crop evapotranspiration (ET 0) estimation is essential for agricultural water management, crop productivity, and irrigation systems. As the standard ET 0 estimation method, the Penman-Monteith equation has been widely recommended worldwide. However, its application is still restricted to comprehensive meteorological data deficiency, making the exploration of alternative simpler models for acceptable ET 0 estimation highly meaningful. Concerning the aforementioned requirement, this study developed the novel deep learning model (MA-CNN-BiLSTM), which incorporates Multi-Head Attention mechanism (MA), Convolutional Neural Network (CNN), and Bidirectional Long Short-Term Memory network (BiLSTM) as intricate relationship processor, feature extractor, and regression component, to estimate ET 0 based on radiation-based (R n -based), humidity-based (RH-based), and temperature-based (T-based) input combinations at 600 stations during 1961–2020 throughout China under internal and external cross-validation strategies. Besides, through a comparative evaluation among MA-CNN-BiLSTM, CNN-BiLSTM, BiLSTM, LSTM, Multivariate Adaptive Regression Splines (MARS), and empirical models, the result indicated that MA-CNN-BiLSTM achieved superior precision, with values of Determination Coefficient (R2), Nash–Sutcliffe efficiency coefficient (NSE), Relative Root Mean Square Error (RRMSE), Root Mean Square Error (RMSE), and Mean Absolute Error (MAE) ranging 0.877–0.972, 0.844–0.962, 0.129–0.292, 0.294–0.644 mm d−1, 0.244–0.566 mm d−1 for internal strategy and 0.797–0.927, 0.786–0.920, 0.162–0.335, 0.409–0.969 mm d−1, 0.294–0.699 mm d−1 for external strategy. Specifically, R n -based MA-CNN-BiLSTM excelled in the temperate continental zone (TCZ) and mountain plateau zone (MPZ), while RH-based MA-CNN-BiLSTM yielded best precision in others. Furthermore, the internal strategy was superior to external strategy by 2.74–106.04% for R2, 1.11–120.49% for NSE, 1.41–40.27% for RRMSE, 1.68–45.53% for RMSE, and 1.21–38.87% for MAE, respectively. In summary, the main contribution of the present study is the proposal of a novel LSTM-type ET 0 model (MA-CNN-BiLSTM) to cope with various data-missing scenarios throughout China, which can provide effective support for decision-making in regional agriculture water management. • MA-CNN-BiLSTM model provides the highest accuracy for reference crop evapotranspiration estimation across China. • Machine learning and empirical models performed better with internal strategy than external strategy. • Radiation-based models excelled in temperate continental and mountain plateau zone, while humidity-based excelled in others. • Multi-head attention improved Long Short-Term Memory network type model as intricate relationship processor. [ABSTRACT FROM AUTHOR]

• Hybrid deep learning model achieved the best performance for estimating daily ET 0. • Rn– were superior to RH– and T–based ET 0 models on the Loess Plateau. • RH– were superior to T–based deep learning model, but vice versa for empirical model. • Significant spatial accuracy discrepancies exist in ET 0 models on the Loess Plateau. Reference evapotranspiration (ET 0) is usually employed for estimating actual crop ET together with crop coefficients (K c). However, it is necessary to explore an alternative model to estimate ET 0 concisely because of numerous limitations in the Penman–Monteith method. To improve the ET 0 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 ET 0 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 ET 0 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 ET 0 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 ET 0 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 ET 0 model using incomplete meteorological data on the Loess Plateau, which is very helpful for farmers or irrigation system operators to improve their irrigation scheduling. [ABSTRACT FROM AUTHOR]

• Hybrid deep learning model achieved the best performance for estimating daily ET 0. • Rn– were superior to RH– and T–based ET 0 models on the Loess Plateau. • RH– were superior to T–based deep learning model, but vice versa for empirical model. • Significant spatial accuracy discrepancies exist in ET 0 models on the Loess Plateau. Reference evapotranspiration (ET 0) is usually employed for estimating actual crop ET together with crop coefficients (K c). However, it is necessary to explore an alternative model to estimate ET 0 concisely because of numerous limitations in the Penman–Monteith method. To improve the ET 0 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 ET 0 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 ET 0 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 ET 0 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 ET 0 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 ET 0 model using incomplete meteorological data on the Loess Plateau, which is very helpful for farmers or irrigation system operators to improve their irrigation scheduling. [ABSTRACT FROM AUTHOR]

Quantitatively characterizing and accurately predicting plant transpiration are of great significance, but directly measuring transpiration is impractical, time-consuming, and labor-intensive. This study compared the transpiration estimation performance of multiple linear regression (MLR), modified Jarvis–Stewart (MJS), and Shuttleworth–Wallace (S-W) with deep belief network (DBN), long short-term memory recurrent neural network (LSTM-RNN), and LSTM-RNN improved with multiple restricted Boltzmann machines (R- L -RNN) using 31 input combinations comprising complete subsets of Vapor pressure deficit (VPD), Net solar radiation (R n), Average air temperature (T a), Soil water content (SWC), and Leaf area index (LAI) observations collected at Wuwei, Changwu and Taigu stations on the Loess Plateau in China. The results showed that R- L -RNN obtained the most accurate estimations in the partial canopy stage, dense canopy stage, and whole growth stage, compared to MLR, MJS, S-W, DBN, and LSTM-RNN. The accuracy of the deep learning models (DNN) increased exponentially as the number of input variables increased, and the importance of the input variables followed the orders of: LAI > VPD > R n > T a > SWC in the partial and whole canopy stage, and VPD > R n > T a > LAI > SWC in the dense canopy stage. The apple tree transpiration models were more accurate in the partial and dense canopy stages than the whole growth stage. The coefficient of determination and Nash-Sutcliffe efficiency coefficient for the R- L -RNN model increased by 8.1–13.1% and 11.2–25.4% in the partial canopy stage, respectively, and by 2.6–6.9% and 14.7–20.1% in the dense canopy stage, whereas the relative root mean square error decreased by 8.7–28.6% and 17.3–38.2%. Overall, R- L -RNN is the most recommended model for estimating the apple tree transpiration, because it is such a simple method that agricultural water managers can easily determine the water consumption of apple trees using limited accessible observational data. • A hybrid deep learning model provided most accurate apple tree transpiration model. • Importance of different inputs to deep learning models differed with growth stages. • Accuracy of deep learning models improved exponentially with more inputs. • The transpiration models were more accurate in the partial and dense canopy stages. [ABSTRACT FROM AUTHOR]