## 2 Materials and Methods
### Machine Learning Methods  
SVMs and RFs were employed in this study to fuse single LUE models and global Koppen-Geiger climate types at 45 forest FLUXNET2015 sites.  
An SVM is a widely used classification method and processes multi-dimensional data according to structural risk minimization criteria and VC dimension theory. An SVM can be employed to solve nonlinear problems in a new feature space [PERSON] et al. (2005); [PERSON] et al. (2005). Considering a labeled training set \((x_{i},y_{i}),i=1,2,3,\cdots h\), where \(x_{i}\) denotes a vector (\(x_{i}\in R^{n}\), and \(y_{i}\in[-1,+1]\)), to acquire the functional dependency \(f(x)=(w\cdot x)+b\), the SVM requires the following expression to be minimized:  
\[minimize\left(\frac{w^{T}w}{2}+C{\sum_{i=1}^{h}\xi_{i}}\right) \tag{4}\]  
subject to \(y_{i}\left(w^{T}\phi(x)+b\right)\geq 1-\xi_{i},\xi_{i}>0\). In Equation (4), \(w\) represents a weight vector; \(b\) denotes the bias; \(C\) represents a cost parameter; \(\phi(x)\) converts \(x_{i}\) into a higher-dimensional space; and \(\xi_{i}\) represents the error. In addition, \(K\left(x_{i},x_{j}\right)=\phi(x_{i})^{T}\phi(x_{j})\) is the kernel function. As a popular kernel in previous studies, the RBF (radial basis function) was chosen [PERSON] et al. (2005); [PERSON] et al. (2005). More SVM algorithm details can be found in the literature [PERSON] et al. (2005); [PERSON] et al. (2005).  
The RF classifier was developed by [PERSON], (2001) and has been a widely used method in geographical fields for its robustness, easier implementation, and small number  
\begin{table}
\begin{tabular}{c c c c c} \hline
**PFT** & \(\mathbf{\epsilon_{0}}\) **(gC/m2/d/MJ)** & **Tmin (\({}^{\circ}\)C)** & **Tmax (\({}^{\circ}\)C)** & **Topt (\({}^{\circ}\)C)** \\ \hline DBF & \(-1\) & 40 & 20 \\ EBF & 2.14 for EC-LUE & \(-2\) & 48 & 28 \\ ENF & 1.93 for other LUE Models & \(-1\) & 40 & 20 \\ MF & & \(-1\) & 48 & 19 \\ \hline \end{tabular}
\end{table}
Table 2: Look-up table of maximum LUE, optimal, minimum, and maximum temperature parameters for each forest type.  
of hyperparameters [10; 50; 51; 52]. An RF is famous as a classifier which includes many decision tree classifiers \(\{h(x,\Theta_{k}),k=1,2,3\cdots\}\) where the item \(h(x,\Theta_{k})\) denotes a specific classifier; \(\Theta_{k}\) is the random vector that is distributed in the \(k\)th place; and \(x\) is an input vector [50]. An RF is a robust machine learning method which includes many small decision trees and can be used as an ensemble method for different tasks including classification and regression.  
For each forest type (i.e., DBF, EBF, ENF, and MF), the grid-search method was employed to identify the optimum parameters for the RF and SVM. We tried many trees (ntree, from 100 to 1000) and variables sampled as candidates at each split (mtry, from 1 to 5) separately for the RF across each forest type. Similarly, for the SVM, different values of the kernel parameter (gamma, from 0.1 to 10) and the cost of violating constraints (cost, from 0.1 to 10) were tried. The optimum parameters (see Table S4 in the Supporting Information File) were applied to the process of fusing CASA, GLO-PEM, C-Fix, VPM and EC-LUE models together with Koppen-Geiger climate zones. The workflow is shown in Figure 2.