## 2 Materials and Methods
### Methods
#### 2.2.1 LUE Estimation
\(\bullet\) **Parameterization approach with CI (approach V2)**  
In the second parameterization approach (approach V2), we considered the effect of the CI, and LUE was estimated by Formula (7):  
\[\text{LUE}=\left[\text{LUE}_{max}^{su}\times\text{CI}+\text{LUE}_{max}^{sl} \times(1-\text{CI})\right]\times\text{f}(\text{W})\times\text{f}(\text{T}) \tag{7}\]  
\[\text{CI}=\frac{SW_{surfac}}{SW_{top}} \tag{8}\]  
\[SW_{top}=\frac{T}{\pi}S_{0}(\omega_{0}sino\sin\delta+cosqcos\delta sin\omega_{ 0}) \tag{9}\]  
\[S_{0}=\overline{S_{0}}\times\left(1+0.033\times cos\left(2\pi\times\frac{day}{ 365}\right)\right)^{2} \tag{10}\]  
where \(\text{LUE}_{max}^{su}\) and \(\text{LUE}_{max}^{sl}\) are the coefficients of CI and 1-CI, respectively. \(\text{LUE}_{max}^{su}\) equals the LUE in completely direct light. \(\text{LUE}_{max}^{sl}\) is positively related to LUE in diffuse light. CI represents the fraction of solar incident radiation on the surface of the earth (\(SW_{surface}\)) to the extraterrestrial radiation at the top of the atmosphere (\(SW_{top}\)). T denotes the time period corresponding to SW; thus, \(\text{T}=60\times 60\times 24=86\),\(400\) s in this study. \(\overline{S_{0}}\) represents the solar radiation constant, which is equal to \(1367\) W/m\({}^{2}\). \(\omega_{0}\) is the solar horizon at sunrise. \(\varphi\) is the latitude. \(\delta\) is the solar declination. In order to optimize \(\text{LUE}_{max}^{su}\) and \(\text{LUE}_{max}^{sl}\), we firstly set reasonable ranges for them based on the value of \(\text{LUE}_{max}\) for each vegetation type; and then different values are randomly selected from the specific ranges, in addition, the corresponding LUE is calculated which would be compared with FLUNNET LUE. Finally, we built the cost function (RMSE) and minimized it to simultaneously optimize \(\text{LUE}_{max}^{su}\) and \(\text{LUE}_{max}^{sl}\) using the SCE-UA optimization algorithm. \(\bullet\) **Cubist regression tree approach (approach V3)**  
The Cubist regression tree approach (approach V3) was finally established to estimate LUE. Cubist is a tool to generate rule-based predictive approaches from data. This approach partitions data into smaller groups that are more homogenous. To achieve outcome homogeneity, regression trees determine: (1) the predictor to split on and the value of the split; (2) the depth or complexity of the tree; and (3) the prediction formula at the terminal nodes. Cubist is one of the most utilized regression tree approaches. Some specific features of Cubist are (1) the specific techniques used for linear smoothing, creating rules, and pruning; (2) an optional boosting; and (3) the predictions generated by the rules can be adjusted using nearby points from the training set data [78]. For the Cubist regression tree approach, an assumption that LUE is determined by vegetation growth, water stress, temperature stress, radiation condition and vegetation type was made. Therefore, we selected 4 continuous parameters, LAI, EF, Tmean and CI and one discrete variable, vegetation type, which respectively represent the 5 factors in order, as input. The maximum number of regression trees was set to 10. The established linear formulas are listed in Table 2.