## 2 Materials and Methods
### Machine Learning Methods
#### 2.3.2 Extreme Learning Machine  
ELM as a comparatively new machine learning approach was proposed by [PERSON] et al. [54]. In the last few years, this state of the art approach has been extensively applied in solving different nonlinear problems in other research fields [55; 56]. These applications have demonstrated that the ELM method with a single hidden-layer feedforward neural network architecture has many remarkable strengths against the conventional machine learning techniques. A noteworthy strength of the ELM method is that the number of hidden nodes as well as their related parameters (weights and biases), which can be randomly generated, are commonly independent of the training dataset and thus do not need to be tuned. In contrast, for a traditional ANN model, these parameters and other additional ones, such as the number of hidden layers, the learning epochs, and the learning rate, should be delicately set or updated by a commonly used, time-consuming trial and error algorithm. Moreover, another \begin{table}
\begin{tabular}{l l l l l l l l l l l} \hline \hline
**Stand** & **Variable** & \(\mathbf{X_{mean}}\) & \(\mathbf{X_{max}}\) & \(\mathbf{X_{min}}\) & \(\mathbf{X_{sd}}\) & \(\mathbf{X_{ku}}\) & \(\mathbf{X_{sk}}\) & \(\mathbf{CC_{GFP}}\) & \(\mathbf{CC_{R}}\) & \(\mathbf{CC_{NEE}}\) \\ \hline \multirow{4}{*}{AT-Neu} & \(T_{a}\) & 6.68 & 22.96 & \(-\)17.63 & 8.19 & 2.24 & \(-\)0.29 & 0.80 & 0.88 & \(-\)0.23 \\  & \(R_{a}\) & 4.24 & 16.51 & \(-\)6.44 & 5.33 & 1.97 & 0.16 & 0.81 & 0.77 & \(-\)0.43 \\  & \(R_{h}\) & 79.80 & 99.98 & 44.36 & 10.98 & 2.52 & \(-\)0.46 & \(-\)0.39 & \(-\)0.35 & 0.24 \\  & \(T_{s}\) & 8.71 & 21.28 & \(-\)2.56 & 6.86 & 1.50 & 0.01 & 0.81 & 0.88 & \(-\)0.24 \\  & \(T_{a}\) & 2.90 & 28.40 & \(-\)26.79 & 9.43 & 2.90 & \(-\)0.08 & 0.77 & 0.74 & \(-\)0.54 \\  & \(R_{a}\) & 2.43 & 14.72 & \(-\)12.74 & 4.33 & 2.41 & 0.54 & 0.67 & 0.50 & \(-\)0.62 \\  & \(R_{h}\) & 81.04 & 100.00 & 37.50 & 13.10 & 2.56 & \(-\)0.62 & \(-\)0.45 & \(-\)0.28 & 0.48 \\  & \(T_{s}\) & 4.98 & 16.75 & \(-\)0.31 & 4.99 & 1.89 & 0.61 & 0.79 & 0.73 & \(-\)0.59 \\  & \(T_{a}\) & 11.52 & 29.21 & \(-\)20.46 & 10.31 & 2.09 & \(-\)0.33 & 0.52 & 0.72 & \(-\)0.28 \\  & \(R_{a}\) & 6.37 & 23.14 & \(-\)4.31 & 6.12 & 2.13 & 0.58 & 0.38 & 0.48 & \(-\)0.24 \\  & \(R_{h}\) & 74.80 & 100.00 & 17.98 & 17.46 & 3.60 & \(-\)0.97 & \(-\)0.01 & \(-\)0.02 & 0.01 \\  & \(T_{s}\) & 12.30 & 30.63 & \(-\)5.35 & 9.29 & 1.65 & 0.03 & 0.58 & 0.76 & \(-\)0.36 \\  & \(T_{a}\) & 1.82 & 26.46 & \(-\)35.04 & 13.02 & 2.22 & \(-\)0.40 & 0.70 & 0.82 & \(-\)0.50 \\  & \(R_{a}\) & 5.19 & 18.94 & \(-\)4.67 & 5.66 & 2.02 & 0.45 & 0.69 & 0.68 & \(-\)0.60 \\  & \(R_{h}\) & 69.88 & 98.78 & 21.83 & 16.15 & 2.62 & \(-\)0.52 & \(-\)0.18 & \(-\)0.21 & 0.13 \\  & \(T_{s}\) & 4.73 & 17.31 & \(-\)5.81 & 5.81 & 1.69 & 0.30 & 0.83 & 0.93 & \(-\)0.64 \\  & \(T_{a}\) & 1.00 & 26.37 & \(-\)35.31 & 13.15 & 2.15 & \(-\)0.34 & 0.83 & 0.81 & \(-\)0.58 \\  & \(R_{a}\) & 6.71 & 21.90 & \(-\)4.28 & 6.17 & 2.05 & 0.48 & 0.72 & 0.56 & \(-\)0.71 \\  & \(R_{h}\) & 72.35 & 100.00 & 24.56 & 16.69 & 2.46 & \(-\)0.43 & \(-\)0.31 & \(-\)0.16 & 0.42 \\  & \(T_{s}\) & 3.19 & 15.41 & \(-\)9.18 & 4.99 & 1.99 & 0.58 & 0.87 & 0.94 & \(-\)0.48 \\ \hline \hline \end{tabular} Note: \(\mathbf{X_{mean}}\), \(\mathbf{X_{max}}\), \(\mathbf{X_{min}}\), \(\mathbf{X_{sd}}\), \(\mathbf{X_{ku}}\), and \(\mathbf{X_{sk}}\) refer to the mean, maximum, minimum, standard deviation, kurtosis, and skewness of each variable, respectively; \(\mathbf{CC_{GFP}}\), \(\mathbf{CC_{R}}\), and \(\mathbf{CC_{NEE}}\) refer to the correlation coefficient between each variable and GFP, \(R\), and NEE, respectively.  
\end{table} 
Table 2: Daily statistical parameters of eddy covariance tower measured environmental variables including air temperature (\(T_{a}\), \({}^{\circ}\)C), net radiation (\(R_{n}\), mol m\({}^{-2}\)), relative humidity (\(R_{h}\), %), and soil temperature (\(T_{s}\), \({}^{\circ}\)C) in the whole period in all five stands.