## 4 Results  
### Comparison of Different \(\mathcal{E}_{\mathrm{max}}\)  
Different PAR-\(\mathcal{E}_{\mathrm{max}}\) calculated usingthe different GPP\({}_{\mathrm{max}}\) sample percentiles have similar performances in GPP estimation (Table 1). With the decrease in the GPP\({}_{\mathrm{max}}\) sample percentile, the R\({}^{2}\) between the PAR-LUE-estimated GPP and observed GPP slightly increased, while the RMSE obviously increased (hereafter, _PAR-\(\mathcal{E}_{\mathrm{max}}\)_ was calculated according to GPP\({}_{\mathrm{max}}\)). At all selected flux sites, the spatiotemporal dynamic ranges of daily _PAR-\(\mathcal{E}_{\mathrm{max}}\)_ and _RS-\(\mathcal{E}_{\mathrm{max}}\)_ were 1.86-3.85 g C m\({}^{-2}\) MJ\({}^{-1}\) and 0.73-4.39 g C m\({}^{-2}\) MJ\({}^{-1}\), respectively (Figure 3). Obviously, the variation range of RS-\(\mathcal{E}_{\mathrm{max}}\) was larger than that of _PAR-\(\mathcal{E}_{\mathrm{max}}\)_, and both dynamic \(\mathcal{E}_{\mathrm{max}}\) contained a constant value of 2.14 g C m\({}^{-2}\) MJ\({}^{-1}\).  
_PAR-\(\mathcal{E}_{\mathrm{max}}\)_ showed significant seasonal dynamics, which presented as a \"U\" shaped variation in a natural year (Figure 4). The seasonal trends of _PAR-\(\mathcal{E}_{\mathrm{max}}\)_ were relatively similar at the 10 typical vegetation sites, and their annual minimal _PAR-\(\mathcal{E}_{\mathrm{max}}\)_ values were close to 2.14 g C m\({}^{-2}\) MJ\({}^{-1}\). However, although _RS-\(\mathcal{E}_{\mathrm{max}}\)_ showed spatial and interannual variations, there was no seasonal dynamic.  
Figure 2: Schematic of _PAR-\(\mathcal{E}_{\mathrm{max}}\)_ based on the relationship between daily observed GPP and PAR. (The color from purple to yellow indicates that the point density increases gradually. The orange fit curve indicates the vegetation GPPmax at different PAR levels, and the dashed curves from top to bottom are fitted curves at the 99 th, 98 th, 95 th, and 90 th percentiles of GPP\({}_{\mathrm{max}}\). The fitted curve indicates the unconstrained ideal GPP, while the points below the curve indicate the true GPP constrained by vegetation physiology and environmental factors.)  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Percentile** & **a** & **b** & **c** & **R2** & **RMSE** \\ \hline
100 th & 0.00030 & \(-\)0.12376 & 3.84951 & 0.61202 & 2.8979 \\
99 th & \(-\)0.00039 & \(-\)0.06768 & 2.59194 & 0.61019 & 2.9812 \\
98 th & 0.00052 & \(-\)0.09087 & 2.52062 & 0.61343 & 3.1780 \\
95 th & 0.00073 & \(-\)0.09035 & 2.24867 & 0.61492 & 3.4993 \\
90 th & 0.00033 & \(-\)0.07156 & 1.91375 & 0.61463 & 3.7946 \\ \hline \hline \end{tabular}
\end{table}
Table 1: \(\mathcal{P}\)AR-\(\mathcal{E}_{\max}\) estimation coefficients and GPP estimation accuracy under different sampling percentiles.  
Figure 4: Seasonal dynamics comparison of three \(\mathcal{E}_{max}\) at typical sites. Ten sites from different vegetation types were selected and shown in two adjacent years (2011-2012) to exhibit the differences in seasonal variation among the three \(\mathcal{E}_{max}\).  
Figure 3: Variation range comparison of three daily \(\mathcal{E}\)max at all selected flux sites. (The top and bottom edges of the box are the 75% and 25% quartiles, respectively; the short horizontal line and the small square in the middle of the box are the median and mean, respectively; the shape of the violin displays frequencies of values.)