# Modeling and Predicting Carbon and Water Fluxes Using Data-Driven Techniques in a Forest Ecosystem
## 4 Discussion  
The present study, for the first time to our best knowledge, investigated the adaptability and validity of a variety of machine learning techniques, including GRNN, ELM, ANFIS and GMDH, for modeling and predicting the terrestrial carbon and water fluxes for a forest ecosystem based on the data measured with the eddy covariance technique. In addition, to assess the generalization ability of all the approaches in our research, two conventional data-driven modeling techniques, namely ANN and SVM, were also employed as benchmarks. Furthermore, several performance indices involving \(R^{2}\), NSE, RMSE and MAE were adopted for the model evaluation in order to adequately manifest the efficiency of the applied models. In the following subsections, we concentrate mainly on discussing the predictive capability of various data-driven models and the discrepancy of different carbon and water fluxes in modeling ability, and providing the limitations of the current study and its potential improvements for future research. \begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Model**} & \multicolumn{3}{c}{**Training**} & \multicolumn{3}{c}{**Validation**} & \multicolumn{3}{c}{**Testing**} \\ \cline{2-13}  & \(R^{2}\) & NSE & RMSE & MAE & \(R^{2}\) & NSE & RMSE & MAE & \(R^{2}\) & NSE & RMSE & MAE \\ \hline ANN & 0.9172 & 0.9171 & 0.2387 & 0.1659 & 0.9206 & 0.8743 & 0.3378 & 0.2160 & 0.9105 & 0.8759 & 0.3210 & 0.2169 \\ GRNN & 0.9188 & 0.9180 & 0.2375 & 0.1667 & 0.9139 & 0.8746 & 0.3374 & 0.2171 & 0.9065 & 0.8739 & 0.3236 & 0.2193 \\ ELM & 0.9095 & 0.9095 & 0.2495 & 0.1768 & 0.9186 & 0.8761 & 0.3353 & 0.2233 & 0.9100 & 0.8780 & 0.3183 & 0.2114 \\ ANFIS & 0.9152 & 0.9152 & 0.2416 & 0.1671 & 0.9163 & 0.8768 & 0.3344 & 0.2106 & 0.9109 & 0.8817 & 0.3134 & 0.2129 \\ SVM & 0.9259 & 0.9254 & 0.2265 & 0.1480 & 0.9171 & 0.8766 & 0.3347 & 0.2081 & 0.9120 & 0.8775 & 0.3190 & 0.2129 \\ GMDH & 0.8920 & 0.8920 & 0.2726 & 0.1950 & 0.9032 & 0.8617 & 0.3543 & 0.2579 & 0.8950 & 0.8480 & 0.3553 & 0.2551 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Comparisons of data-driven models for evapotranspiration (ET, mm\(\cdot\)Day\({}^{-1}\)) for the training, validation and testing periods. Figure 7: Comparisons of daily ET measured by eddy covariance technique and predicted by data-driven models for the testing period. (**a**) ANN model; (**b**) GRNN model; (**c**) ELM model; (**d**) ANFIS model; (**e**) SVM model; and (**f**) GMDH model. Our predictive results in the testing periods from Table 2 and Tables 4-6, demonstrated that a large amount of diurnal variance in each carbon and water flux was accounted for by our used models, with average 95%, 94%, 77% and 91% for GPP, \(R\), NEE and ET, respectively. Therefore, these machine learning techniques have adequate capability to describe the complex interactions between the carbon and water fluxes and environmental factors. Moreover, previous studies have also proved the effectiveness of data-driven models, primarily including ANN and SVM methods, for the terrestrial carbon and water flux prediction at ecosystem level [66; 67; 68; 69]. In recent years, another important data-driven technique, namely regression tree method, has been successfully utilized to estimate the carbon fluxes [28; 70]. [PERSON] et al. [28] used model tree ensemble and ANN models to estimate the spatial distributions of global GPP, and found that these two models obtained similar estimates, which are comparable to those of both process-based and atmospheric inversion models. [PERSON] et al. [70] utilized regression tree algorithm to exclusively upscale NEE from flux tower to the continental scale with remotely sensed and AmeriFlux data. They found that the 8-day observed NEE can be reproduced reasonably well by this model at the site level (\(R^{2}\) = 0.73). Additionally, it is interesting to note that, based on the site investigated in this study, [PERSON] et al.