Evaluation of stacking and blending ensemble learning methods for estimating daily reference evapotranspiration

Precise reference evapotranspiration (ETo) estimation and prediction are the first steps to realize efficient agricultural water resources management. As machine learning methods are widely applied in ETo estimation, we assess whether a high accuracy can be attained by stacking or integrating more models. Can the accuracy be increased indefinitely and at what cost? To this end, this study reports the first evaluation of stacking and blending ensemble models for daily ETo estimation. The stacking and blending models adopted a 2-layer structure: level-0 basic models included random forest (RF), support vector regression (SVR), multilayer perceptron neural network (MLP) and K-Nearest Neighbor regression (KNN); level-1 outputted the final result via linear regression (LR). The accuracy and computational costs of stacking and blending models were compared with those of the 4 basic models and 3 empirical models under 5 complete and limited input conditions. A station-cross validation on models with solar radiation input was further performed to study the portability of the tested models. The results indicated that both stacking and blending models performed better than the basic and empirical models regardless of input combination, and the former (R2 ranged from 0.6602 to 0.9977, with an average AIC of -7785.68) achieved a slightly higher accuracy than the latter models (R2: 0.6562?0.9974; average AIC: -7689.68). Meanwhile, the stacking and blending models were more portable (RMSE ranged from 0.5445 to 0.8799 and 0.5511?0.8767 mm day- 1, respectively) than basic models across stations in different climate zones. In terms of computational cost, both stacking and blending models were able to achieve significantly better accuracy than basic models in reasonable time with smaller training data size, while the blending models could obtain similar high accuracy to stacking models in less time after increasing the size of the training data. Therefore, the stacking and blending ensemble models can be highly recommend for ETo estimation, especially when the available training data set or meteorological variables are limited.