Evaluation of Machine Learning Models for Daily Reference Evapotranspiration Modeling Using Limited Meteorological Data in Eastern Inner Mongolia, North China
Authors: Zhang Hao , Meng Fansheng , Xu Jia , Liu Zhandong , Meng Jun 
Published: September 2022

Background: Water shortages limit agricultural production in arid and semiarid regions around the world. The accurate estimation of reference evapotranspiration (ET0) is of the utmost importance for computing crop water requirements, agricultural water management, and irrigation scheduling design. However, due to the combination of insufficient meteorological data and uncertain inputs, the accuracy and stability of the ET0 prediction model were different to varying degrees. Methods: Six machine learning models were proposed in the current study for daily ET0 estimation. Information on the weather, such as the maximum and minimum air temperatures, solar radiation, relative humidity, and wind speed, during the period 1960~2019 was obtained from eighteen stations in the northeast of Inner Mongolia, China. Three input combinations were utilized to train and test the proposed models and compared with the corresponding empirical equations, including two temperature-based, three radiation-based, and two humidity-based empirical equations. To evaluate the ET0 estimation models, two strategies were used: (1) in each weather station, we trained and tested the proposed machine learning model, and then compared it with the empirical equations, and (2) using the K-means algorithm, all weather stations were sorted into three groups based on their average climatic features. Then, each station tested the machine learning model trained using the other stations within the group. Three statistical indicators, namely, determination coefficient (R2), root mean square error (RMSE), and mean absolute error (MAE), were used to evaluate the performance of the models. Results: The results showed the following: (1) The temperature-based temporal convolutional neural network (TCN) model outperformed the empirical equations in the first strategy, as shown by the TCN’s R2 values being 0.091, 0.050, and 0.061 higher than those of empirical equations; the RMSE of the TCN being significantly lower than that of empirical equations by 0.224, 0.135, and 0.159 mm/d; and the MAE of the TCN being significantly lower than that of empirical equations by 0.208, 0.151, and 0.097 mm/d, and compared with the temperature-based empirical equations, the TCN model markedly reduced RMSE and MAE while increasing R2 in the second strategy. (2) In comparison to the radiation-based empirical equations, all machine learning models reduced RMSE and MAE, while significantly increasing R2 in both strategies, particularly the TCN model. (3) In addition, in both strategies, all machine learning models, particularly the TCN model, enhanced R2 and reduced RMSE and MAE significantly when compared to humidity-based empirical equations. Conclusions: When the radiation or humidity characteristics were added to the given temperature characteristics, all the proposed machine learning models could estimate ET0, and its accuracy was higher than the calibrated empirical equations external to the training study area, which makes it possible to develop an ET0 estimation model for cross-station data with similar meteorological characteristics to obtain a satisfactory ET0 estimation for the target station.