## 2 Materials and Methods
### Methods  
#### 2.3.1 MODIS GPP Algorithm  
Firstly, we used the MODIS GPP algorithm to estimate GPP. The MODIS GPP algorithm is applied based on the LUE model, which mainly uses the relationship between LUE and environmental factors (temperature, water vapor, and light) [28; 72]. The algorithm can be expressed as follows:  
\[\text{GPP}=\ \varepsilon*\text{FAPAR}*\text{IPAR} \tag{1a}\] \[\varepsilon=\ \varepsilon_{\text{max}}*\text{TMIN}_{\text{scalar}}*\text{VPD} _{\text{scalar}} \tag{1b}\]  
\begin{table}
\begin{tabular}{l c c c c c c c} \hline \hline
**Site ID** & **Lat (\({}^{\circ}\)N)** & **Lon (\({}^{\circ}\)E)** &
\begin{tabular}{c} **Biome** \\ **Type** \\ \end{tabular} & **Location** & **Height** & **Period Used** & **Reference** \\ \hline US-GLE & 41.37 & \(-\)106.24 & ENF & Wyoming & 22.65 m & 2017.01–2018.03 & [65] \\ US-WCr & 45.81 & \(-\)90.08 & DBF & Wisconsin & 29.60 m & 2017.01–2018.12 & [66] \\ US-PFa & 45.94 & \(-\)90.24 & MF & Wisconsin & – & 2017.01–2018.12 & [67] \\ US-RIs & 43.14 & \(-\)116.74 & CSH & Idaho & 2.09 m & 2017.01–2018.09 & [68] \\ US-Rws & 43.17 & \(-\)116.71 & OSH & Idaho & 2.05 m & 2017.01–2018.09 & [68] \\ US-Ton & 38.43 & \(-\)120.97 & WSA & California & 23.50 m & 2017.01–2018.12 & [69] \\ US-Var & 38.41 & \(-\)120.95 & GRA & California & 2.00 m & 2017.01–2018.12 & [70] \\ US-Bi2 & 38.11 & \(-\)121.54 & CRO & California & 5.11 m & 2017.04–2018.12 & [71] \\ \hline \hline \end{tabular} ENF: evergreen needleleaf forests; DBF: deciduous broadleaf forests; MF: mixed forests; CSH: closed shrublands; OSH: open shrublands; WSA: woody savannas; GRA: grasslands; and CRO: croplands.  
\end{table}
Table 1: List of AmeriFlux eddy covariance tower sites adopted within the research.  
\[\text{TMIN\_scalar}\;=\;\begin{cases}0&\text{T}_{\text{min}}<\text{TMIN}_{\text{ min}}\\ \frac{\text{T}_{\text{min}}-\text{TMIN}_{\text{min}}}{\text{TMIN}_{\text{max}}- \text{TMIN}_{\text{min}}}&\text{TMIN}_{\text{min}}<\text{T}_{\text{min}}<\text{ TMIN}_{\text{max}}\\ 1&\text{T}_{\text{min}}>\text{TMIN}_{\text{max}}\end{cases} \tag{1c}\] \[\text{VPD\_scalar}=\begin{cases}0&\text{VPD}>\text{VPD}_{\text{max}}\\ \frac{\text{VPD}_{\text{max}}-\text{VPD}}{\text{VPD}_{\text{max}}-\text{VPD}_{ \text{min}}}&\text{VPD}_{\text{min}}<\text{VPD}<\text{VPD}_{\text{max}}\\ 1&\text{VPD}<\text{VPD}_{\text{min}}\end{cases} \tag{1d}\]  
where \(\varepsilon_{\text{max}}\), \(\text{TMIN}_{\text{max}}\), \(\text{TMIN}_{\text{min}}\), \(\text{VPD}_{\text{max}}\), and \(\text{VPD}_{\text{min}}\) are shown in Table 2. The biome-specific physiological parameters for each biome type are determined according to the MOD12Q1 UMD classification scheme and BPLUT (Table 3) [59]. TMIN and VPD scalars are simple linear ramp saturated at the maximum and minimum, respectively, and the range is from 0 to 1 [73]. FAPAR was obtained from the OLCI FAPAR product (OGVI). IPAR is equal to SWRad times 0.45 (Equation (1e)):  
\[\text{IPAR}=\text{SWRad}\text{+}0.45 \tag{1e}\]  
where SWRad, \(\text{T}_{\text{min}}\) and VPD are obtained from MERRA2 meteorology reanalysis data. VPD is calculated with T2 MMEAN and RH (Equation (1f)) [73]:  
\[\text{VPD}=610.78\text{+}\epsilon^{\frac{(1.2/204+T2 MMEAN)}{12 MMEAN+283}} \left(1-\frac{\text{RH}}{100}\right) \tag{1f}\]