# An Open Data Approach for Estimating Vegetation Gross Primary Production at Fine Spatial Resolution
## 2 Materials and Data
### Statistical Analysis  
We compared the GPP in each product with the FLUXNET 16-day mean GPP at 193 sites of nine major vegetation types and derived the comparative results of GPP products at three spatial resolutions (i.e., 30-m, 500-m, 8-km). We used the determination coefficient (R\({}^{2}\)), root mean square error (RMSE), mean bias (bias), and relative predict error (RPE) to quantify the GPP estimation accuracy.  
\[\mathbb{R}^{2}=1-\frac{\sum\Bigl{(}\mathrm{GPP}_{f}-\mathrm{GPP}_{i}\Bigr{)} ^{2}}{\sum\Bigl{(}\mathrm{GPP}_{f}-\mathrm{GPP}_{f,m}\Bigr{)}^{2}} \tag{7}\]  
\[\mathrm{RMSE}=\sqrt{\frac{\sum\Bigl{(}\mathrm{GPP}_{f}-\mathrm{GPP}_{i} \Bigr{)}^{2}}{n}} \tag{8}\]  
\[\mathrm{bias}=\frac{\sum\Bigl{(}\mathrm{GPP}_{i}-\mathrm{GPP}_{f}\Bigr{)} }{n} \tag{9}\]  
\[\mathrm{RPE}\;(\%)=\frac{\mathrm{GPP}_{i,m}-\mathrm{GPP}_{f,m}}{\mathrm{GPP }_{f,m}}\times 100\% \tag{10}\]  
The \(\mathrm{GPP}_{i}\), \(\mathrm{GPP}_{f}\), \(\mathrm{GPP}_{f,m}\), and \(\mathrm{GPP}_{i,m}\), n in Equations (7)-(10) represent the modeled GPP, GPP from flux towers, mean GPP data from flux towers, mean modeled GPP, and number of samples, respectively.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Vegetation Type** & \(\boldsymbol{\varepsilon_{\max}}\) **(g C m\({}^{-2}\) MJ\({}^{-1}\))** & \(\boldsymbol{\phi}\) & **VPD0 (kPa)** \\ \hline DBF & 3.26 & 71.09 & 1.16 \\ EBF & 2.50 & 49.42 & 0.94 \\ ENF & 2.89 & 45.69 & 0.81 \\ MF & 2.93 & 66.87 & 0.86 \\ GRA & 3.37 & 70.11 & 1.05 \\ SAV & 2.33 & 53.24 & 1.89 \\ SHR & 1.23 & 37.21 & 1.30 \\ WET & 2.94 & 76.79 & 1.28 \\ CRO & 4.50 & 64.00 & 1.50 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Model coefficients of the fine-spatial-resolution GPP from the GEE APP. Model coefficients are linked to Equations (1), (4) and (5).  
Subsequently, we chose some typical sites and compared their seasonal change in GPP with the GPP\({}_{\text{FLUX}}\). Next, we selected some typical regions to quantify the spatial heterogeneity of GPP\({}_{\text{L}}\), GPP\({}_{\text{M}}\), and GPP\({}_{\text{A}}\). We used all the pixels in the selected regions and calculated the standard deviation (STD, Equation (11)) to quantify the spatial heterogeneity. The coefficient of variation (CV, Equation (12)) of GPP during all the selected 16-day intervals, was used to characterize the temporal change in GPP at each pixel. The standard deviation and CV were calculated as:  
\[\text{STD}=\sqrt{\frac{\Sigma\Big{(}\text{GPP}_{i}-\text{GPP}_{f,m}\Big{)}^{ 2}}{n}} \tag{11}\]  
\[\text{CV}=\text{STD}/\text{GPP}_{f,m} \tag{12}\]  
Finally, to quantify the influence of missing Landsat data on fine-resolution GPP estimation, we classified the GPP into three groups of GPP\({}_{\text{L}}\) driven by observed short-term gap-filled, and long-term gap-filled reconstructed NDVI: GPP\({}_{\text{L0}}\), GPP\({}_{\text{L1}}\), and GPP\({}_{\text{L2}}\), respectively. Next, we used the R\({}^{2}\), RMSE, and RPE of each group in nine vegetation types to evaluate the effect of missing remote sensing data on fine-resolution GPP modeling.