Estimating daily reference evapotranspiration based on limited meteorological data using deep learning and classical machine learning methods

To evaluate the performance of deep learning methods (DL) for reference evapotranspiration estimation and to assess the applicability of the developed DL models beyond the study areas where they were trained, three popular DL models named deep neural network (DNN), temporal convolution neural network (TCN), and long short-term memory neural network (LSTM) were developed to estimate daily reference evapotranspiration (ETo) using incomplete meteorological data in the Northeast plain, China. The performances of the three DL models were compared to two classical machine learning models (CML)-support vector machine (SVM) and random forest (RF)-and empirical equations, including two temperature-based (Hargreaves (H) and modified Hargreaves (MH)), three radiation-based (Ritchie (R), Priestley-Talor (P), and Makkink (M)), and two humiditybased (Romanenko (ROM) and Schendel (S)) empirical models, in two strategies: (1) all proposed models were trained, tested, and compared in each single weather station, and (2) all-weather stations were split into several groups using the K-means method with their mean climatic characteristics. Then, in each group, stations took turns testing the proposed models which were trained by rest of the stations. The results showed that (1) the coefficient of determination (R-2) values of the TCN and RF were 0.048 and 0.035 significantly higher than that of MH, respectively, and the relative root mean error (RMSE) values of TCN and RF were substantially 0.096, and 0.074 mm/d lower than that of MH, indicating that TCN and RF performed better than empirical models in the first strategy, and TCN and LSTM exhibited an RMSE that was significantly decreased by 0.069 and 0.079 mm/d, showing that TCN and LSTM outperformed empirical models in the second strategy, compared with the MH method; (2) in both strategies, compared with the Ritchie (R) model, TCN, LSTM, DNN, RF, and SVM increased R-2 and decreased RMSE significantly, especially the TCN model; (3) similarly, TCN, LSTM, DNN, RF, and SVM models all augmented R-2 and reduced RMSE substantially in comparison to humidity-based empirical models in both strategies, especially the TCN model. Overall, when temperature-based features were available, the TCN and LSTM models performed markedly better than temperature-based empirical models beyond the study areas, and when radiation-based or humidity-based features were available, all of the proposed DL and CML models outperformed radiation-based or humidity-based empirical equations beyond the study areas in which they were trained.