Forecast of short-term daily reference evapotranspiration under limited meteorological variables using a hybrid bi-directional long short-term memory model (Bi-LSTM)

Abstract As the standard method to compute reference evapotranspiration (ET0), Penman-Monteith (PM) method requires complete eight meteorological variables, which makes it difficult to apply in most of the data scarce regions. To overcome this problem, the hybrid bi-directional long short-term memory (Bi-LSTM) model was developed to forecast short-term (1–7-day lead time) daily ET0. The model was trained, validated and tested using the meteorological variables for the period of 2006–2018 at the three meteorological stations located in the semi-arid region of central Ningxia, China. The performance of the hybrid Bi-LSTM model to forecast short-term daily ET0 was evaluated against the daily ET0 calculated by the Penman-Monteith method using the statistical indicators namely, mean absolute error (MAE), root mean square error (RMSE), Pearson correlation coefficient (R) and Nash-Sutcliffe efficiency (NSE). The results revealed that the hybrid Bi-LSTM model with a combination of three meteorological inputs (maximum temperature, minimum temperature and sunshine duration) provides the best forecast performance for short-term daily ET0 at all the meteorological stations. When averaged across stations, the statistical indicators for different forecast lead time were observed as follows; 1-day lead time: MAE = 0.159 mm day−1, RMSE = 0.039 mm day−1, R = 0.992, NSE = 0.988; 4-day lead time: MAE = 0.247 mm day−1, RMSE = 0.075 mm day−1, R = 0.972, NSE = 0.985 and 7-day lead time: MAE = 0.323 mm day−1, RMSE = 0.089 mm day−1, R = 0.943, NS = 0.982. Moreover, the hybrid Bi-LSTM model substantially improved the forecast performance of short-term daily ET0 compared to the adjusted Hargreaves-Samani (HS) method and the general Bi-LSTM model. The hybrid Bi-LSTM model developed in this study is currently integrated into the modern intelligent irrigation system of 30 ha of Lycium barbarum plantation in central Ningxia in China, a region with the limitation of meteorological data. To confirm the broad applicability of this model to forecast short-term daily ET0, it should be evaluated across a wide range of climatic conditions in different regions of the world.