## 3 Results
### Establishing the Model for Estimating \(\text{FCO}_{2}\)
#### 3.3.2 Predicting \(\text{FCO}_{2}\) on the Account of RF Model and Model Accuracy  
Three models, including the optimal RF model with the top 4 selected variables, the RF model with the 10 original variables, and the multivariate linear regression (MLR) model constructed using the same variables as in the optimal RF model, are applied to estimate the \(\text{FCO}_{2}\). We calculated the R\({}^{2}\), MAE, and RMSE between the measured and predicted \(\text{FCO}_{2}\) for the training and testing data to measure the performance of the three models. The two RF models have higher accuracy in predicting \(\text{FCO}_{2}\) (Figure 7a-d), confirming that the machine learning method has better performance in predicting \(\text{FCO}_{2}\) compared with the MLR method (Figure 7e,f). For the optimal RF model, it has the greatest R\({}^{2}\) value but the lowest MAE and RMSE values in predicting \(\text{FCO}_{2}\) when against both the training and testing dataset (Figure 7a,b). For the training dataset, the optimized RF model (Figure 7a) used in this study has a slight improvement in predicating \(\text{FCO}_{2}\) compared with the original RF model (Figure 7c), while the optimized RF model performs better on  
\begin{table}
\begin{tabular}{l l l l l} \hline \hline \multirow{2}{*}{**VIs**} & \multicolumn{2}{c}{**CHD (FCO\({}_{2}\))**} & \multicolumn{2}{c}{**GY (FCO\({}_{2}\))**} \\ \cline{2-5}  & \(\mathbf{R^{2}}\) & \(\boldsymbol{p}\)**-Value** & \(\mathbf{R^{2}}\) & \(\boldsymbol{p}\)**-Value** \\ \hline EVI & 0.71 & \(p\) \textless{} 0.001 & 0.35 & \(p\) \textless{} 0.001 \\ GPP & 0.64 & \(p\) \textless{} 0.001 & 0.49 & \(p\) \textless{} 0.001 \\ LAI & 0.64 & \(p\) \textless{} 0.001 & 0.41 & \(p\) \textless{} 0.001 \\ NDVI & 0.49 & \(p\) \textless{} 0.001 & 0.52 & \(p\) \textless{} 0.001 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Pearson correlation coefficients between the \(\text{FCO}_{2}\) (\(n=35\)) and the different VIs in the CHD and GY area, individually.  
the independent testing dataset (Figure 7b vs. Figure 7d). As a whole, the results indicate that the optimal RF model in combination with the RS indices illustrated a good predictive ability to estimate forest \(\text{FCO}_{2}\) in our study area.  
Figure 5: Influences of Ntree and Mtry values on RF model, and selection of the optimized parameters (Ntree and Mtry) for RF model based on the OOB error.  
Figure 6: Importance ranking of the input variables measured with % IncMSE from 100 repeated runs of the RF model (500 Ntree and 4 Mtry) (**a**). The insert figure (**b**) denotes the selection of the optimal variables by using the backward elimination searching method [75; 77], and the RMSE is calculated based on the 10-folds cross-validation (CV) method.  
Figure 7: Scatter plots showing the relationship between measured and predicated \(\text{FCO}_{2}\) for the training datasets (\(n=49\)) in the left column and the testing datasets (\(n=21\)) in the right column. (**a,b**) The results are computed using the optimal RF model with the 4 selected features. (**c,d**) The results are derived from the RF model developed using the 10 original variables. (**e,f**) The results are calculated based on the MLR model that also constructed using the best 4 selected variables and field-measured \(\text{FCO}_{2}\) as the model input data. The color bar and circle represent the absolute residuals between the measured and predicated \(\text{FCO}_{2}\).