## 3 Results
### Modeling of Daily Ecosystem Respiration  
The estimated precision of the used models for predicting daily \(R\) in the testing period in the three sites are provided in Table 7. As shown from the table, the models with full input variables (\(T_{a}\), \(R_{n}\), \(R_{h}\), \(T_{s}\)) perform the best for each method and site. The machine learning models with these variables consistently outperform the corresponding MLR models at both CA-Obs and CA-Oas sites, but at CA-Gro site, all the five models provide similar estimates. Specifically at CA-Obs site, the ANN model performs the best among the four machine learning models in the testing period, with respect to \(R^{2}\), NSE and RMSE. The predictive precision of the ANFIS is similar to that of the SVM. These two models give the inferior performance. As a whole, the GRNN model provides the lowest precision in  
Figure 2: Eddy covariance measured and model simulated daily gross primary productivity (GPP) in the whole period in the three boreal forest stands. (**a**) For CA-Obs stand using ANN model; (**b**) for CA-Oas stand using ANFIS model; and (**c**) for CA-Gro stand using ANN model. the prediction of daily \(R\). At CA-Oas site, the GRNN model is also inferior to the other three models (ANN, ANFIS and SVM) in terms of \(R^{2}\), NSE and RMSE. Besides, the ANFIS model performs the best among the five models. In conclusion, the overall model rankings of the applied models over the testing period can be ranked as follows: ANFIS, ANN, SVM, GRNN and MLR. In contrast to CA-Obs and CA-Oas sites as mentioned before, the GRNN model yields the best performance among the five models at CA-Gro site according to the four performance indices. In addition, the ANFIS performs the second best. The ANN and SVM models give similar accuracy. On the other hand, it is clearly seen from Table 5 that the GRNN model in the three stands for forecasting daily \(R\) gives the best accuracy in the testing period, in terms of NSE, Bias and RMSE. However, the MLR model gives the worst accuracy. The ANN, ANFIS and SVM models achieve similar performance, according to the four indices. As shown in Table 6, no apparent performance indicator is found among the three stands in the prediction of daily \(R\) using the five data-driven models. Nevertheless, it should be noted that at CA-Gro site, the models give the best accuracy in terms of \(R^{2}\) and NSE indices. Figure 3 presents the comparisons of daily \(R\) between observed and predicted using the five models at the three sites in the form of scatter plot. As shown in Figure 3, although the regression fit lines between measured and estimated \(R\) by the ANN, GRNN, ANFIS and SVM models at CA-Oas stand are closer to the 1:1 lines, higher mean values of \(R^{2}\) = 0.937 and NSE = 0.925 are obtained by the  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Model**} & \multicolumn{4}{c}{**CA-Obs**} & \multicolumn{4}{c}{**CA-Oas**} & \multicolumn{4}{c}{**CA-Gro**} \\ \cline{2-13}  & \(R^{2}\) & **NSE** & **Bias** & **RMSE** & \(R^{2}\) & **NSE** & **Bias** & **RMSE** & \(R^{2}\) & **NSE** & **Bias** & **RMSE** \\ \hline ANN1 & 0.829 & 0.821 & \(-\)0.032 & 0.776 & 0.837 & 0.830 & \(-\)0.116 & 0.892 & 0.847 &  
models at CA-Obs site (Table 6). Besides, these models at CA-Obs site display less scattered estimates than those at CA-Oas and CA-Gro sites. It is evident from Figure 4 that the distribution of predicted values versus observed values for daily \(R\) in the testing period varies among different sites. Similar to the time series comparison of daily GPP in Figure 2, the under- and over-estimation of the best model (especially in the peaks) in forecasting daily \(R\) in the testing period are clearly seen at CA-Obs and CA-Gro sites, respectively, as shown in Figure 4. This is consistent with the scatter plots in Figure 3 as mentioned before. Figure 3: Comparisons of measured and simulated daily ecosystem respiration (\(R\)) in the testing period in the three boreal forest stands.