## 3 Results
### Evaluation of Model Performance for the \(R\) Flux in Different Ecosystems  
The overall model performance rankings for the \(R\) prediction for five different sites and four different machine learning methods with their respective internal functions in the testing period are  
Figure 3: Daily GPP observed via the eddy covariance method and modeled by the optimal machine learning models for the five sites in the whole period including training (the first four years), validation (the fifth year), and testing (the final year) periods. (**a**) ANN1 at AT-Neu; (**b**) ANN6 at SE-Deg; (**c**) ANN9 at US-Bo1; (**d**) ANFIS10 at CA-Oas; (**e**) ANN1 at CA-Obs. displayed in Figure 4a. As shown from the figure, the ANN1, ANN4, ANN6, ANFIS8, and ANN10 models at the CA-Obs site gain higher model efficiency, while the SVM3 models at AT-Neu, and the ANFIS2, ANFIS6, ANFIS7 and SVM3 models at US-Bo1 obtain lower model efficiency. In addition, except for the SVM2 and SVM3 models, the models generally achieve the best model performance at CA-Obs among the five sites, and all models achieve the second best efficiency at CA-Oas but provide the worst performance at Us-Bo1. Figure 4b presents the overall model performance rankings of \(R\) prediction for four different machine learning methods with their respective internal functions at each site. As shown from the figure, among the 26 models at AT-Neu, the ANN1, ANN2, ANFIS9 and ANFIS10 models are superior. Similarly, at the other four sites, the first four best models can be summarized as follows: ANN8, ANN9, ANN10, and ELM1 at SE-Deg; ANN2, ANN5, ANN9, and ELM1 at US-Bo1; ANN1, ANN3, ANN4, and ANN5 at CA-Oas; ANN1, ANN4, ANN6, and ANN10 at CA-Obs. Moreover, it should be noted that the ANN4 model gains the highest model efficiency at CA-Obs and the second highest at US-Bo1 and CA-Oas. However, the ANN2 and ANN8 obtain the highest model efficiency at AT-Neu and SE-Deg, respectively. Figure 4: Model performance rankings of ecosystem respiration (\(R\)) estimation in the testing period: (**a**) for five different sites and four different machine learning methods with their respective internal functions (130 models); (**b**) for four different machine learning methods with their respective internal functions (26 models) at each site. Furthermore, as illustrated in Figure 4b, the selection of the internal parameters has significant effects on the performance of the corresponding method in the prediction of \(R\) among the five stands. The optimal models for each machine learning method are briefly overviewed as follows: for the ANN, the ANN4 model achieves the best model performance at US-Bo1 and CA-Obs and achieves the second best at CA-Oas, while the ANN2 and ANN8 models obtain the best model efficiency at AT-Neu and SE-Deg, respectively; for the ELM, ELM1 generally performs the best at all sites, and the ELM2 model achieves an inferior performance; for the ANFIS, the ANFIS9 and ANFIS10 models achieve similar model performance and both surpass the other ANFIS models in all stands; for the SVM, SVM1 substantially outperforms the SVM2 and SVM3 models at all sites. The estimated accuracies of the applied methods with the optimal internal functions in the forecasting of daily \(R\) among the training, validation, and testing periods in the five stands are displayed in Table 4. As shown in the table, during the testing period, the ANN2 model with higher \(R^{2}\) and IA values and lower RMSE and MAE values performs better than the other optimal models at AT-Neu, which is similar to the ANN8, ELM1, ANN5 and ANN4 models at SE-Deg, US-Bo1, CA-Oas, and CA-Obs, respectively. This is confirmed by Figure 4b. In addition, as presented in Table 4, similar to GPP forecasting among the five stands, the models at CA-Obs generally achieve higher prediction precision in terms of \(R^{2}\), IA, RMSE, and MAE metrics than those of the optimal models at the other four sites.