## 2 Materials and Methods
### Model Implement and Evaluation  
In this study, four different machine learning methods, ANN, GRNN, ANFIS and SVM, were investigated and compared to estimate daily carbon fluxes in three forest ecosystems. In addition, the MLR model was also used in this investigation with the intention of examining the strength of machine learning approaches against traditional regression technique. The correlation coefficient values between environmental variables and each carbon flux in all the ecosystems have been given in Table 2. The results showed that all the carbon fluxes were highly correlated with \(T_{a}\), \(T_{s}\) and \(R_{n}\), implying that these variables were the most effective parameter influencing carbon fluxes. To obtain an accurate and reasonable comparison of modeling performance among different carbon fluxes, the applied methods with different variable combinations for inputs were tried in this study. For the sake of convenience, these abbreviated models are summarized in Table 3. We used all the models for each flux in order to make the comparison of various carbon fluxes as fair as possible.  
Complete 6-year environmental and carbon flux data were used at all the sites. These data were divided into three datasets. The first 4-year dataset was used for training, the fifth year dataset was used for validation for the purpose of avoiding over-fitting and assuring the ability of model generalization, and the last 1-year dataset was for testing. It is noteworthy that all the applied models were separately trained and extrapolated for validation and prediction, owing to the differences in age among the three sites. Before the training of the applied models was started, all input and output  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & \multicolumn{3}{c}{**Models**} & \multicolumn{2}{c}{**Input**} \\ \hline
**ANN** & **GRNN** & **ANFIS** & **SVM** & **MLR** & **Combinations** \\ \hline ANN1 & GRNN1 & ANFIS1 & SVM1 & MLR1 & \(T_{a}\) \\ ANN2 & GRNN2 & ANFIS2 & SVM2 & MLR2 & \(R_{n}\) \\ ANN3 & GRNN3 & ANFIS3 & SVM3 & MLR3 & \(R_{h}\) \\ ANN4 & GRNN4 & ANFIS4 & SVM4 & MLR4 & \(T_{s}\) \\ ANN5 & GRNN5 & ANFIS5 & SVM5 & MLR5 & \(T_{a_{s}}R_{n}\) \\ ANN6 & GRNN6 & ANFIS6 & SVM6 & MLR6 & \(T_{a_{s}}R_{n}\), \(R_{h}\) \\ ANN7 & GRNN7 & ANFIS7 & SVM7 & MLR7 & \(T_{a_{s}}R_{n_{s}}R_{n_{s}}\), \(T_{s}\) \\ \hline \hline \end{tabular}
\end{table}
Table 3: The input combinations for different methods with environmental variables including air temperature (\(T_{a_{s}}\), \({}^{\circ}\)C), net radiation (\(R_{n}\), mol m\({}^{-2}\)), relative humidity (\(R_{h}\), %), soil temperature (\(T_{s}\), \({}^{\circ}\)C).  
variables were normalized between 0 and 1, respectively. The computer programs of all the machine learning models and statistical analysis of estimated results were undertaken in MATLAB (version 8.2, The Mathworks, Inc., Natick, MA, USA). Coefficient of determination (\(R^{2}\)), Nash-Sutcliffe efficiency (NSE), bias error (Bias) and root mean square error (RMSE) were considered for the performance evaluation of the used models. These performances indices are defined as below:  
\[R^{2}=\left[\begin{array}{c}\sum\limits_{i=1}^{N}{(Y_{o,j}-\overline{Y_{o}}) (Y_{m,j}-\overline{Y_{m}})}\\ \sqrt{\sum\limits_{i=1}^{N}{(Y_{o,j}-\overline{Y_{o}})^{2}\sum\limits_{i=1}^{N }{(Y_{m,i}-\overline{Y_{m}})^{2}}}}\\ \end{array}\right]^{2} \tag{1}\]  
\[\text{NSE}=1-\frac{\sum\limits_{i=1}^{N}{(Y_{o,i}-Y_{m,i})^{2}}}{\sum\limits_ {i=1}^{N}{(Y_{o,j}-\overline{Y_{o}})^{2}}} \tag{2}\]  
\[\text{Bias}=\frac{1}{N}\sum\limits_{i=1}^{N}{(Y_{m,i}-Y_{o,i})} \tag{3}\]  
\[\text{RMSE}=\sqrt{\frac{1}{N}\sum\limits_{i=1}^{N}{(Y_{o,i}-Y_{m,i})^{2}}} \tag{4}\]  
where \(Y_{o}\) and \(Y_{m}\) denote the observed and modeled values of daily carbon fluxes, respectively; \(\overline{Y_{o}}\) and \(\overline{Y_{m}}\) are the means of observed and modeled values, respectively; \(N\) is the number of observed values.