## 4 Results
### Comparison with the GPP Obtained by BESS  
To evaluate the role of the Two-stage linear model in improving GPP simulation, we compared the GPP simulation results using BESS, BESS_P and our Two-stage linear model for calculating V\({}_{\rm m25}\), and validated them with flux site GPP data (Figure 6, Table 3). The results indicate that the original BESS model consistently underestimates GPP across all five sites. On average, GPP is underestimated by 12.60%, with the most significant underestimation observed at US-Ne2 (16.29%). Similarly, BESS_P generally overestimates GPP, averaging 20.73% across all sites, with the most significant overestimation recorded at US-Ne1 (24.05%). In contrast, the GPP simulated by BESS incorporating our Two-stage linear model exhibits a strong correlation with the flux site's observed GPP data, with RMSE ranging from 2.03 to 2.32 gC m\({}^{-2}\)d\({}^{-1}\) and R\({}^{2}\) ranging from 0.82 to 0.90. On average, GPP is only underestimated by 0.85% across all sites. The most substantial underestimation occurs at Daman (16.38%), while the most significant overestimation is at Fenzidi (4.60%). The simulation result of BESS_TL significantly outperform the BESS and BESS_P in GPP estimation. Figure 6: The GPP calculated by BESS (blue dots and trend lines), BESS_P (green dots and trend lines), and BESS_TL (red dots and trend lines) vs. flux site observed GPP (GPP_EC) at (**a**) US-Ne1, (**b**) US-Ne2, (**c**) US-Ne3, (**d**) Daman, (**e**) Fenzidi. To better reveal the role of the Two-stage linear model in improving GPP simulation, the discrepancy of the annual GPP estimation by BESS, BESS_P and BESS_TL were compared (Figures 7 and 8). The mean GPP estimation discrepancy by BESS, BESS_P and BESS_TL are \(-\)1.56, 2.39 and 0.12 gC m\({}^{-2}\)d\({}^{-1}\) in US-Ne1, respectively, with the corresponding standard deviations of 3.35, 3.30 and 2.29 gC m\({}^{-2}\)d\({}^{-1}\) (Table 4). Except for the Daman site, the means and standard deviations of GPP discrepancy of BESS_TL estimation are closer to 0 for most years compared to the BESS and BESS_P estimation (Table 4). At the Daman site, although the absolute value of the mean GPP estimation discrepancy of BESS_TL is greater than that of BESS, the standard deviation of BESS_TL GPP estimation discrepancy remains the smallest. Thus, it can be concluded that BESS_TL effectively enhances the simulation accuracy of GPP. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Site**} & \multicolumn{2}{c}{**BESS**} & \multicolumn{2}{c}{**BESS\_P**} & \multicolumn{2}{c}{**BESS\_TL**} \\ \cline{2-7}  & **RMSE** & **R\({}^{2}\)** & **RMSE** & **R\({}^{2}\)** & **RMSE** & **R\({}^{2}\)** \\ \hline US-Ne1 & 3.69 & 0.66 & 4.07 & 0.70 & 2.29 & 0.86 \\ US-Ne2 & 3.48 & 0.80 & 3.53 & 0.83 & 2.03 & 0.90 \\ US-Ne3 & 2.99 & 0.83 & 3.32 & 0.85 & 2.04 & 0.89 \\ Daman & 2.96 & 0.53 & 3.02 & 0.53 & 2.32 & 0.82 \\ Fenzidi & 3.35 & 0.63 & 3.64 & 0.63 & 2.06 & 0.87 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The performance of the original BESS, BESS_P and BESS_TL in estimating observed GPP at the five flux sites. Figure 7: The annual GPP estimation discrepancy of the BESS (blue lines), BESS_P (green lines) and BESS_TL (red lines) at (**a**) US-Ne1, (**b**) US-Ne2, (**c**) US-Ne3. To provide a clearer view of the simulation results of the three methods, the seasonal variation in the GPP difference between the simulated GPP and EC observations is represented in Figures 9 and 10. Figure 9 displays the annual simulation results for each site, while Figure 10 presents the multi-year average simulation outcomes across all sites. Significant seasonal differences are evident in the simulation outputs of all three methods. The original BESS model tends to slightly overestimate GPP towards the end of the growth period and underestimates during other times, particularly in the mid-growth period, where the underestimation is pronounced.