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

•Deep learning models have excellent performance for estimating ETo beyond study areas.•Temporal convolution neural network outperformed markedly empirical equations.•T-test method was used to test the performance of proposed models.•Temporal convolution neural network outperformed classical machine learning models. 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 humidity-based (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 (R2) 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 R2 and decreased RMSE significantly, especially the TCN model; (3) similarly, TCN, LSTM, DNN, RF, and SVM models all augmented R2 and reduced RMSE substantially in comparison to humidity-based empirical models in both strategies, especially the TCN mo