# Modeling and Predicting Carbon and Water Fluxes Using Data-Driven Techniques in a Forest Ecosystem
## 3 Results  
### GPP Modeling Using the Machine Learning Methods  
The performance indices, including \(R^{2}\), NSE, RMSE and MAE, are used in order to evaluate the efficiency of applied models in predicting the daily GPP, \(R\), NEE and ET. \(R^{2}\) and NSE with larger values and RMSE and MAE with smaller values indicate higher model efficiency. The estimated results in predicting the daily GPP by the six data-driven methods (ANN, GRNN, ELM, ANFIS, SVM and GMDH) for the training, validation and testing periods are summarized in Table 2. It is shown in the table that the ANN model performs superior to the other models in the estimation of daily GPP in the testing period, with the highest values of \(R^{2}\) and NSE and the lowest values of RMSE and MAE. The SVM model performs slightly inferior to the ANN model and gives the second-best efficiency among all the models. However, the GMDH model yields the worst precision with respect to NSE, RMSE and MAE metrics. According to the aforementioned four evaluation indices, the overall performance rankings of the applied models for carbon and water fluxes for the testing period are given in Table 3. It can be seen from the table that the model performance rankings for GPP prediction can be ranked as follows: ANN, SVM, ANFIS, GRNN, ELM and GMDH. The comparisons of daily GPP between measured and predicted using the data-driven models over the testing period in the form of scatter plot are illustrated in Figure 2. As shown in Figure 2, the fit lines of ANN and SVM models (slope = 0.86) are closer to the ideal fit lines (1:1 lines), whereas for the GMDH model, the fit line (slope = 0.76) is more inconsistent with the ideal fit line than those for the other models. Furthermore, the estimates from both the ELM and GMDH models fail to match the corresponding observed values around their minimum values. Although obvious performance differences for GPP prediction exist among the applied models (Table 2), these models provide similar scattered estimates as a whole (Figure 2). Accordingly, we describe only the seasonal and annual variation in carbon and water fluxes estimated by the ANN model. Figure 3 compares the measured and predicted values for daily GPP, \(R\), NEE and ET using 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}{**Training**} & \multicolumn{4}{c}{**Validation**} & \multicolumn{4}{c}{**Testing**} \\ \cline{2-13}  & \(R^{2}\) & NSE & RMSE & MAE & \(R^{2}\) & NSE & RMSE & MAE & \(R^{2}\) & NSE & RMSE & MAE \\ \hline ANN & 0.9491 & 0.9491 & 0.5500 & 0.3633 & 0.9565 & 0.9248 & 0.7722 & 0.5063 & 0.9622 & 0.9427 & 0.6548 & 0.4220 \\ GRNN & 0.9705 & 0.9703 & 0.4199 & 0.2461 & 0.9507 & 0.9186 & 0.8034 & 0.4880 & 0.9443 & 0.9254 & 0.7473 & 0.4364 \\ ELM & 0.9119 & 0.9119 & 0.7234 & 0.5254 & 0.9289 & 0.8897 & 0.9350 & 0.6667 & 0.9312 & 0.9098 & 0.8218 & 0.5800 \\ ANFIS & 0.9460 & 0.9460 & 0.5661 & 0.3588 & 0.9521 & 0.9224 & 0.7845 & 0.4878 & 0.9570 & 0.9341 & 0.7024 & 0.4394 \\ SVM & 0.9553 & 0.9552 & 0.5156 & 0.3091 & 0.9556 & 0.9242 & 0.7750 & 0.4936 & 0.9574 & 0.9361 & 0.6915 & 0.4290 \\ GMDH & 0.9041 & 0.9040 & 0.7549 & 0.5962 & 0.9157 & 0.8809 & 0.9715 & 0.7308 & 0.9323 & 0.8894 & 0.9100 & 0.6691 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Comparisons of data-driven models for gross primary productivity (GPP, g\(\cdot\)C\(\cdot\)m\({}^{-2}\cdot\)Day\({}^{-1}\)) for the training, validation and testing periods. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Model** & **GPP** & **R** & **NEE** & **ET** \\ \hline ANN & 1 & 4 & 1 & 4 \\ GRNN & 4 & 5 & 3 & 5 \\ ELM & 5 & 3 & 5 & 3 \\ ANFIS & 3 & 1 & 4 & 2 \\ SVM & 2 & 2 & 2 & 1 \\ GMDH & 6 & 6 & 6 & 6 \\ \hline \hline \end{tabular} Note: Model performance rankings were determined according to the \(R^{2}\), NSE, RMSE and MAE indices. For example, for GPP, the ANN performs the best (No. 1), while the GMDH gives the worst accuracy (No. 6).  
\end{table}