## 2 Materials and Methods
### Statistical Analysis  
All daily and annual-scale GPP estimations derived from diverse methods, GPP_EC, GPP_MOD, GPP_MODR1, GPP_MODR2, GPP_MODR3, and GPP_MODR4, passed the normality (Shapiro-Wilk test) and homogeneity of variance test (Bartlett test) (\(p>0.05\)). Thus, we employed the one-way analysis of variance (ANOVA) and Tukey's honest significant difference (HSD) to investigate GPP estimations differences among those different methods and among temporal series at \(\alpha=0.05\). In this study, we employed the linear regression analysis and the following two indices, RMSE and RPE (Equations (12) and (13)), to adequately compare the performance of MODIS-based GPP with GPP_EC.  
\[RMSE=\sqrt{\frac{\sum\limits_{i=1}^{n}{(x_{i}-y_{i})}^{2}}{n}} \tag{12}\]  
\[RPE=(\frac{\overline{y}-\overline{x}}{\overline{x}})\times 100\% \tag{13}\]  
where the \(x_{i}\) are the GPP_EC data, the \(y_{i}\) are the MODIS-based GPP estimations depending on different parameterization schemes (Table 1), and \(\overline{x}\) and \(\overline{y}\) are the averages of corresponding data, respectively. The \(n\) is the number of samples. The root mean square error (RMSE) is used to measure the bias from the simulated data compared to tower measurements. The relative predictive error (RPE) is used to quantify the percentage of mean difference between MODIS-based GPP estimations and GPP_EC, which provides the direct effectiveness (underestimation as negative, or overestimation as positive)  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
\begin{tabular}{c} 1.61 \\ (1.33–1.80) \({}^{\ddagger}\) \\ \end{tabular} & 12.02 & \(-8.00\) & 3.50 & 0.65 & \(\text{FPAR}_{\text{M}}\) & Ground measurements \\ \hline \hline \end{tabular}  
* GPP list represents the diverse GPP values from different models based on the MOD17A2 algorithm according to data source showed in this table;
* Tmin_max, Tmin_min, VPDmax, and VPDmin are the upper limit, the lower of daily minimum temperature, the upper, and the lower of daily minimum vapor pressure difference, respectively. All of them are extracted from the Biome Properties Look-Up Table (BPLUT) in grassland biome,
* FPAR is the fraction of absorbed PAR by vegetation canopy from the MOD15A2 product (\(\text{FPAR}_{\text{M}}\)) and estimation based on ground measurements (\(\text{FPAR}_{\text{G}}\)); \({}^{\ddagger}\) The \(\epsilon_{\text{max}}\) is the maximum light use efficiency. The default of the collection 5.1 MOD17A2 algorithm for grassland is 0.68 g C M]\({}^{-1}\). Based on ground measurements, the mean \(\epsilon_{\text{max}}\) value for this alpine wetland we calculated using two methods is 1.61, which ranges from 1.33 to 1.80 due to the vegetation condition in different observational years;
* DAO is the NASA Data Assimilation Office, which provided the meteorology data for the MODIS data product.  
\end{table}
Table 1: Parameterization schemes for estimating gross primary production (GPP) in this alpine wetland based on the MOD17A2 algorithm.  
in predicted values compared to measured values [27]. All statistical and modeling procedures were performed in the R statistical computing package (Version 3.2.0).