# Underestimates of Grassland Gross Primary Production in MODIS Standard Products
## 4 Discussion
### Attributing Underestimation in Grassland GPP and Its Implications  
In this study, GPPMOD explained GPPEC by 72% (68%-75%) at temperate grassland sites, 64% (59%-68%) at alpine grassland sites, and 40% (27%-52%) at tropical grassland sites (Figure 5). Potential \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Grass Type** & **Slope** & \(R^{2}\) & **RMSE** \\ \hline Tropical grassland & 1.02 (0.83, 1.21) & 0.40 (0.27, 0.52) & 2.45 (2.13, 2.76) \\ Temperate grassland & 1.25 (1.19, 1.30) & 0.72 (0.68, 0.75) & 2.40 (2.25, 2.54) \\ Alpine grassland & 1.24 (1.17, 1.32) & 0.64 (0.59, 0.68) & 2.55 (2.30, 2.79) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Statistics regarding the comparison between GPPEC and GPPMOD for temperate, tropical, and alpine grassland biomes using a linear regression model. The 95% confidence interval derived by the bootstrapping method is in parenthesis. Figure 5: The relationships between GPPEC and GPPMOD for the temperate, tropical, and alpine grassland biomes. The short-dashed line is a 1:1 line. The unit of RMSE was g C m\({}^{-2}\) day\({}^{-1}\). reasons for the uncertainty in MODIS GPP products could be due to different factors such as maximum LUE, meteorological data, FPAR, and land cover/vegetation types [50]. These varied performances may be related to the maximum light use efficiency (\(\varepsilon_{max}\)) [51]. For the MODIS GPP algorithm, \(\varepsilon_{max}\) was determined by using the Biome Properties Look-Up (BPLUT) for given biome types, which was for 0.86 g C MJ\({}^{-1}\) grass [38]. The underestimated \(\varepsilon_{max}\) values could be the major reason for underestimates of GPP in the grasslands [51]. Based on the nonlinear model (Equation (6)), we estimated the \(\varepsilon_{max}\) for each grassland site in this study (Table 4). In most sites (except for AU-Stp, US-SRG, and US-Var), the estimated values of \(\varepsilon_{max}\) were larger than that used in the MOD17 GPP algorithm, which can partly explain the underestimation of the MODIS GPP in these grassland sites. Moreover, when the \(\varepsilon_{max}\) used in the MOD17 GPP algorithm (\(\varepsilon_{max}\)-BPLUT) were simply replaced with the estimated \(\varepsilon_{max}\) (\(\varepsilon_{max}\)-EST), the RMSEs were smaller than before (except for the site of CZ-Bk2) (Figure 6). This demonstrated that the \(\varepsilon_{max}\) have an important influence on the result of the GPP estimation based on the MOD17 GPP algorithm. Previous studies have also suggested different \(\varepsilon_{max}\) for different grassland biomes. For example, 1.31 g C MJ\({}^{-1}\) for alpine grassland and 1.21 g C MJ\({}^{-1}\) for tropical grassland [52; 53]. [PERSON] et al. [27] increased \(\varepsilon_{max}\) for grasslands from 0.86 g C MJ\({}^{-1}\) to 2.01 g C MJ\({}^{-1}\), which improved the ability for GPP\({}_{\text{MOD}}\) to explain the variance of GPP\({}_{\text{EC}}\) from 25% to 74%. There are also potential uncertainties from FPAR, which could affect the accuracy of GPP\({}_{\text{MOD}}\). The GPP\({}_{\text{MOD}}\) algorithm directly used the MODIS FPAR products (MOD15A2H), which was derived from a radiative transfer model. The MODIS FPAR usually overestimated the \"green\" FPAR with a positive offset for barren land and was saturated at high GPP values. This behavior further affected \(\varepsilon\) and GPP estimation [54]. In this study, GPP\({}_{\text{MOD}}\) underestimated GPP\({}_{\text{EC}}\) for grassland ecosystems, which may be caused by the uncertainty of FPAR and the methods used to simulate FPAR. For example, [PERSON] et al. [55] used a three-dimensional formulation of the radiative transfer process in the canopy and assessed FPAR\({}_{\text{canopy}}\) performances of scaled EVI (FPAR\({}_{\text{chl1}}\)), NDVI, scaled NDVI (FPAR\({}_{\text{chl2}}\)), and EVL The results showed that the FPAR\({}_{\text{canopy}}\) of scaled EVI (FPAR\({}_{\text{chl}}\)) improved the accuracy of GPP\({}_{\text{MOD}}\) for grasslands.