## 3 Results
### The Key Drought Synergistic Effect Factor for the GPP-SIF Relationship  
The results of the random forest model indicated that meteorological factors generally had greater explanatory power for the GPP-SIF relationship than canopy structural factors (Figure 7). The low correlations between PWSI and NIRv, REDv, and \(f_{\rm PAR}\) on the observation days suggest the minimal interference of drought stress in the canopy structure, and, owing to the minimal contribution of the canopy structure to SIF and GPP (Figure 6), the effects of the canopy structure could be neglected. A path analysis-based structural equation model (SEM) was constructed to further examine the synergistic effects of meteorological factors on the GPP-SIF relationship under drought conditions. The results are shown in Figure 8. The GPP-SIF relationship was mainly influenced by VPD: in comparison to PAR and SWC, VPD had greater direct and total effects on R\({}^{2}\) and K. The direct effect of PAR on R\({}^{2}\) and K was greater than its total effect, but the total effect of PAR on GPP and SIF was greater than that of VPD, demonstrating the main driving role of PAR on GPP and SIF. SWC had a positive but low total effect on R\({}^{2}\) and K. The effect of SWC on GPP and SIF was also weaker than that of VPD. Therefore, VPD was the key meteorological factor with a drought synergistic effect on the relationship between GPP and SIF. Figure 6: The relative importance metrics of the natural-log-transformed PAR, \(\Phi\)F\({}_{760}\), NIRv, \(\Phi\)F\({}_{687}\), REDv, LUE, and \(f_{\rm PAR}\) as drivers of (**a**) transformed SIF\({}_{760}\), (**b**) transformed SIF\({}_{687}\), and (**c**) transformed GPP at different PWSI\({}_{\rm bin}\) levels. Figure 8: Results of path analysis. Subfigures (**a**,**b**) are path diagrams where the path coefficients show the direct effects between variables. Subfigure (**c**) describes the total effects of variables on (**c1**,**c5**) GPP, (**c2**,**c6**) SIF\({}_{760}\) and SIF\({}_{687}\), (**c3**,**c7**) K of GPP-SIF\({}_{760}\) and GPP-SIF\({}_{687}\), and (**c4**,**c8**) R\({}^{2}\) of GPP-SIF\({}_{760}\) and GPP-SIF\({}_{687}\). The path coefficients with \(p<0.05\) are shown in the figure. Figure 7: Random forest analysis indicating the influence of major meteorological factors and canopy structural factors, highlighting the synergistic effects of drought on (**a**,**b**) R\({}^{2}\) (R\({}^{2}\) = 0.53) and K (R\({}^{2}\) = 0.44) of GPP-SIF\({}_{760}\), (**c**,**d**) R\({}^{2}\) (R\({}^{2}\) = 0.45) and K (R\({}^{2}\) = 0.41) of GPP-SIF\({}_{687}\). “**” indicates significance at the 0.05 level. The Response of the GPP-SIF Relationship to Drought by Considering the Key Drought Synergistic Effect Factor  
We attempted to incorporate VPD into the diurnal GPP-SIF relationship to mitigate the decoupling effect of drought stress. The R\({}^{2}\) of GPP-SIF with the VPD effect was significantly improved (Figure 9a,b), and the R\({}^{2}\) of GPP-SIF\({}_{760}\) and GPP-SIF\({}_{687}\) increased by 29% and 24%, respectively, on all observation days. Moreover, the higher the level of PWSI\({}_{\text{bin}}\), the more pronounced the improvement in R\({}^{2}\). The RMSE of GPP-SIF with the VPD effect was decreased (Figure 9c,d). The results of independent sample verification showed that SIF, when considering the synergistic effect of VPD, could capture more than 89% of GPP (Figure 10). The accuracy of GPP estimation (R\({}^{2}\)) based on SIF with VPD improved by 20% (SIF\({}_{760}\)) and 16% (SIF\({}_{687}\)), respectively, on all observation days (Figure 11a,b), and the RMSE decreased by 19% and 18%, respectively (Figure 11c,d). The R\({}^{2}\) improved by 55% and 48%, respectively, under severe drought stress (PWSI\({}_{\text{bin}}\) was 0.8-0.9), and the RMSE decreased by 23% and 24%, respectively. Figure 10: The relationship between the observed GPP in the validation set and the predicted GPP based on (**a**) SIF\({}_{760}\) and (**b**) SIF\({}_{687}\) with the VPD effect.