Estimating reference crop evapotranspiration using improved convolutional bidirectional long short-term memory network by multi-head attention mechanism in the four climatic zones of China

Accurate reference crop evapotranspiration (ET0) estimation is essential for agricultural water management, crop productivity, and irrigation systems. As the standard ET0 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 ET0 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 ET0 based on radiation-based (Rn-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, Rn-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 ET0 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.