## 3 Results
### \(q_{L}\) Estimation Results  
The modeled \(q_{\rm L}\) (\(q_{\rm L\_MOD}\)), using the method proposed by [PERSON] et al. [22], is presented in Figure 5. Similarly to \(q_{\rm L\_PAM}\), \(q_{\rm L\_MOD}\) exhibits a strong response to variations in light intensity, decreasing sharply under low light conditions and stabilizing as light intensity increases (Figure 5a). A modest underestimation of \(q_{\rm L\_MOD}\) was observed under low light conditions, possibly due to the absence of low-light measurements in the dataset used to fit the empirical parameters. Despite this underestimation, \(q_{\rm L\_MOD}\) accounted for 90% of the variation in \(q_{\rm L\_PAM}\), with an RMSE and rRMSE of 0.09 and 10.01%, respectively (Figure 5b). These results suggest that the fitted empirical parameters (Table S1) provide a robust framework for modeling \(q_{\rm L}\) across a wide range of environmental conditions.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline  & **ENF** & **EBF** & **DNF** & **DBF** & **SHR** & **GRA** & **CRO** \\ \hline \(f_{\rm{PSII\_760}}\) & 0.45 \(\pm\) 0.15 & 0.71 \(\pm\) 0.16 & 0.27 \(\pm\) 0.18 & 0.52 \(\pm\) 0.15 & 0.53 \(\pm\) 0.15 & 0.64 \(\pm\) 0.11 & 0.67 \(\pm\) 0.14 \\ \(R^{2}\) & 0.85 & 0.79 & 0.99 & 0.84 & 0.86 & 0.92 & 0.95 \\ RMSE & 2.73 & 4.66 & 0.58 & 4.49 & 2.55 & 2.99 & 2.33 \\ rRMSE & 11.64 & 18.96 & 2.03 & 18.39 & 12.28 & 12.64 & 16.51 \\ \hline \end{tabular}
\end{table}
Table 1: \(f_{\rm{PSII\_760}}\) values for different plant functional types (PFTs) and comparisons of \(\rm{ChlF_{PSII\_IFPSII}}\) and \(\rm{ChlF_{PSII\_PAM}}\) for each PFT. \(R^{2}\), RMSE, and rRMSE are the coefficient of determination, root-mean-square error (μmol m\({}^{-2}\) s\({}^{-1}\)), and relative root-mean-square error (%), respectively. ENF: evergreen needleleaf forest; EBF: evergreen broadleaf forest; DNF: deciduous needleleaf forest; SHR: shrubland; GRA: grass; CRO: cropland.  
Figure 5: **(a)** Light response curve of the modeled \(q_{\rm L}\) (\(q_{\rm L\_MOD}\)). **(b)** Comparison of the modeled \(q_{\rm L}\) (\(q_{\rm L\_MOD}\)) with that derived from PAM measurements (\(q_{\rm L\_PAM}\)). The red circles and error bars in panel **(a)** denote the means and standard deviations for 52 species, respectively, while the gray dots show the results for each species. In panel **(b)**, the black dashed line and red solid line indicate the 1:1 line and the linear regression result, respectively. The color scheme indicates photosynthetically active radiation (PAR, μmol m\({}^{-2}\) s\({}^{-1}\)). The coefficient of determination (\(R^{2}\)), root-mean-square error (RMSE), and relative root-mean-square error (rRMSE, %) are reported. The regression slope and intercept are also included.  
The proposed model demonstrated a strong performance in estimating \(q_{\rm L}\) across all seven PFTs. \(q_{\rm L\_MOD}\) closely aligns with \(q_{\rm L\_PAM}\) for all PFTs, with \(R^{2}\) values exceeding 0.85 and rRMSE values below 12.66% (Table 2). Notably, the model performed best in cropland (CRO) (\(R^{2}\) = 0.96, RMSE = 0.1, and rRMSE = 11.24%, Table 2). While the weakest correlation was observed in shrubland (SHR), \(q_{\rm L\_MOD}\) still explained 85% of the variation in \(q_{\rm L\_PAM}\), with RMSE and rRMSE values of 0.11 and 12.66%, respectively (Table 2).