## 2 Materials and Methods
### Methods
#### 2.2.2 GPP Estimation  
In this part, the main task is to prepare the required spatially continuous parameters listed in Figure 1. With Formula (3), we calculated gridded temperature stress f(T); with Formulas (4) and (6), we obtained gridded EF and water stress f(W), respectively. We already obtained the LUE\({}_{max}\) (Table 1) for each vegetation type during the parameterization process. Having the above data, the global LUE maps in 2014, with a spatial resolution of 5 km and a temporal resolution of 8 days, were produced (V1). The difference between V2 and V1 is the addition of the CI. With Formulas (8)-(10), we obtained the global gridded CI. LUE\({}_{max}^{sul}\) and LUE\({}_{max}^{sfl}\) are listed in Table 1. Then, we obtained the global 8-day LUE in 2014 according to the process described in the blue frame. For the Cubist regression tree approach (V3), we first calculated the gridded parameters (green frame) and then selected the corresponding linear formula (Table 2) for each pixel to calculate global LUE. Having gained LUE maps, the same equation (Equation (11)) was next used to calculate global GPP.  
\[\text{GPP}=0.48\times SW\times FPAR\times\text{LUE} \tag{11}\]  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Rule 1** & **conditions** & vegetation type in [CRO, DNF, WSA, OSH, GRA], LAI \(\leq\) 0.7 and EF \(\leq\) 0.753 \\
**Rule 2** & **linear formula** & LUE = 0.047 + 0.159 LAI + 0.78 EF \(-\) 0.11 CI \\
**Rule 3** & **conditions** & vegetation type in [DBF, SAV] and Tmean \(\leq\) 11.562 \\
**Rule 4** & **linear formula** & LUE = -0.042 + 0.13 LAI + 0.62 EF + 0.0119 Tmean \(-\) 0.07 CI \\
**Rule 5** & **conditions** & vegetation type = WSA \\
**Rule 6** & **linear formula** & LUE = 0.338 + 1 EF - 0.006 Tmean + 0.02 LAI \\
**Rule 7** & **conditions** & vegetation type in [CRO, DNF, OSH, GRA], LAI \(>\) 0.7 and EF \(\leq\) 0.753 \\
**Rule 8** & **linear formula** & LUE = 0.207 + 1.08 EF + 0.091 LAI - 0.006 Tmean \(-\) 0.4 CI \\
**Rule 9** & **conditions** & vegetation type in [MF, ENF, EBF, CSH] and Tmean \(\leq\) 11.562 \\
**Rule 10** & **linear formula** & LUE = 0.784 + 0.029 Tmean + 0.68 EF \(-\) 1.12 CI + 0.062 LAI \\
**Rule 11** & **conditions** & vegetation type in [DBF, SAV, MF, ENF, EBF, CSH], Tmean \(>\) 11.562 and EF \\
**Rule 12** & **conditions** & \(\leq\) 0.753 \\
**Rule 13** & **linear formula** & LUE = 0.682 + 1.17 EF \(-\) 0.57 CI - 0.0066 Tmean + 0.014 LAI \\
**Rule 14** & **nonlinear formula** & LUE = -0.514 + 0.409 LAI + 1.47 EF + 0.025 Tmean \(-\) 1.05 CI \\
**Rule 15** & **conditions** & vegetation type in [DBF, WSA, SAV, MF, GRA, ENF, EBF, CSH], LAI \(>\) 1.8 \\
**Rule 16** & **conditions** & and EF \(>\) 0.7531864 \\
**Rule 17** & **linear formula** & LUE = 0.862 + 1.26 EF \(-\) 1.41 CI + 0.021 LAI \\
**Rule 18** & **conditions** & CI \(<\)= 0.447, LAI \(>\) 1.8 and EF \(>\) 0.753 \\
**Rule 19** & **linear formula** & LUE = 0.439 + 1.71 EF \(-\) 0.93 CI \\
**Rule 10** & **conditions** & vegetation type = CRO, LAI \(>\) 1.8 and EF \(>\) 0.753 \\
**Rule 11** & **linear formula** & LUE = \(-\)0.831 + 3.24 EF + 0.0316 Tmean \(-\) 1.53 CI \\ \hline \hline \end{tabular}
\end{table}
Table 2: Cubist regression tree approach.