## 3 Results  
### Evaluation of Model Performance for the GPP Flux in Different Ecosystems  
In order to assess the influences of intrinsic parameters on the machine learning models (ANN, ELM, ANFIS, and SVM) in the prediction of carbon fluxes (GPP, \(R\), and NEE), a total of 130 models for each flux were developed, trained, validated, and tested in the present study according to the application of the 26 models (10 ANN, 3 ELM, 10 ANFIS, and 3 SVM models) to the five sites. The accuracy of these applied models was evaluated by using the performance indices, \(R^{2}\), IA, RMSE, and MAE. Specifically, \(R^{2}\) and IA with larger values and RMSE and MAE with smaller values imply a higher model performance. Based on this criterion, each performance index of the applied models was ranked. Overall performance rankings for the employed models were obtained by summing the rankings of the four performance indices and by then sorting the added ranking values. Two types of statistics for overall performance rankings for GPP prediction in the testing period are illustrated in Figure 1. The numbers shown in the figure reveal the overall rankings of model efficiency that were calculated based on the aforementioned approach. A smaller number indicates higher model efficiency. Figure 1a shows the overall model performance rankings of GPP estimation for five different sites and four different machine learning methods with their respective internal functions (130 models). It can be clearly seen in the figure that the performance of all models depends on the intrinsic parameters and sites. The ANN1, ANN2, ANN5, ANFIS9, and SVM1 models at the CA-Obs site provide better model performance, while the ANFIS8 and SVM3 models at AT-Neu, as well as the ANFIS2, ANFIS7, and SVM3 models at US-Bo1, produce worse model performance. Moreover, except for the SVM2 and SVM3 models, other models generally yield the highest model efficiency at CA-Obs among the five sites, and all models achieve the second highest efficiency at SE-Deg but generate the lowest efficiency at US-Bo1. The performance rankings of the GPP prediction for four different machine learning methods with their respective internal functions (26 models) at each site are displayed in Figure 1b. The numbers represent the rankings of model efficiency at each stand. It is clear from the figure that, among the 26 models, ANN1, ANN2, ANFIS10, and SVM1 perform better than the others at the AT-Neu site. Similarly, the first four best models at other stands can be concluded as follows: ANN3, ANN5, ANN6, and ELM2 at SE-Deg; ANN1, ANN3, ANN4, and ANN9 at US-Bo1; ANN1, ANFIS9, ANFIS10, and SVM1 at CA-Oas; ANN1, ANN2, ANN5, and ANFIS9 at CA-Obs. In addition, it should be pointed out that the ANN1 model gives the best model performance at both AT-Neu and CA-Obs, and the second and fourth best at US-Bo1 and CA-Oas, respectively. However, the ANN6 model yields the highest model efficiency at SE-Deg. On the other hand, it can be seen in Figure 1b that the performance of all methods appreciably depends on their internal parameters, when they were used for the GPP prediction in different stands. The optimal models for each approach are briefly summarized as follows: for the ANN, the ANN1 model generates the highest model efficiency at AT-Neu, CA-Oas, and CA-Obs, and the second highest at US-Bo1; for the ELM, the ELM1 and ELM2 models achieve similar model efficiency and are both substantially superior to the ELM3 model at all stands; for the ANFIS, ANFIS9 obtains the best model performance at CA-Obs, and the second best at US-Bo1, while ANFIS10 attains the best performance at AT-Neu, SE-Deg, and CA-Oas; for the SVM, SVM1 performs considerably superior to the SVM2 and SVM3 models at all stands.