## 3 Results
### LUE at the Monthly Time Scale and Influencing Factors  
Seasonal variations in the monthly biophysical factors and LUE from 2006 to 2019 are shown in Figure 8. The monthly PAR exhibited a general trend similar to the monthly Ta; the former peaked in May, and the latter peaked in July (Figure 8a,b). The monthly VPD generally increased during January-June and sharply decreased in July, indicating the beginning of summer monsoon influence (Figure 8c). The monthly P was relatively greater in June-September because of the summer monsoon (Figure 8d). The monthly EF was lower in the non-growing season, generally increased during April-August, and then declined (Figure 8e). The monthly CI had no major seasonal variations and was relatively lower during June-September (Figure 8f). The monthly NDVI sharply increased in April, remained relatively stable from May to September, and decreased from October (Figure 8g). The monthly GPP exhibited general trends similar to the monthly NDVI, but it increased from March and decreased from September (Figure 8h). The monthly LUE generally first increased and then decreased in the growing season, and the mean monthly LUE was lower than 0.1 g C mol photon\({}^{-1}\) in the non-growing season (Figure 8i).  
The results of the correlation analysis among the monthly biophysical factors and LUE is shown in Figure 9, where only the CI had a negative effect on LUE, with an \(r\) value of \(-0.52\) at a significance level of \(p<0.001\). The PAR (\(r=0.28\)) and VPD (\(r=0.18\)) influenced the LUE at significance levels of \(p<0.01\) and \(p<0.05\), respectively. The remaining factors (T\({}_{\alpha}\), P, EF, NDVI, and GPP) were positively correlated with LUE, with \(r\) values ranging from 0.53 to 0.83 at a significance level of \(p<0.001\).  
As shown in Figure 10a, the values of the variance inflation factors for PAR, T\({}_{\alpha}\), EF, and NDVI were greater than five, indicating that multicollinearity existed in the monthly biophysical factors, and the path analysis was unsuitable for assessing the independent effect of each biophysical factor on the LUE. A partial correlation analysis between the biophysical factors and the LUE showed that the monthly PAR, CI, and GPP influenced the LUE at a significance level of \(p<0.001\), with partial correlation values of \(-0.61\), \(-0.33\), and \(0.90\), respectively. The partial correlation coefficient values between the monthly T\({}_{\alpha}\), VPD,  
Figure 7: Relationship between the CI and (**a**) GPP; (**b**) the ratio of diffuse PAR (PAR\({}_{\rm{f}}\)) to PAR (TD\({}_{\rm{f}}\)), (**c**) direct PAR (PAR\({}_{\rm{r}}\)), and PAR\({}_{\rm{f}}\) (**d**); and the effects of PAR\({}_{\rm{r}}\) (**e**) and PAR\({}_{\rm{f}}\) (**f**) on GPP during May–September in 2018 and 2019 in the Chinese cork oak plantation. Daily GPP (**a**), TD\({}_{\rm{f}}\) (**b**), PAR\({}_{\rm{r}}\) (**c**), and PAR\({}_{\rm{f}}\) (**d**) were bin-averaged into 0.05 CI increments. Daily GPP was bin-averaged into 2.50 PAR\({}_{\rm{r}}\) (**e**) and 2.50 PAR\({}_{\rm{f}}\) (**f**).  
P, EF, and NDVI and the LUE were approximately zero at a significance level of \(p>0.05\) (Figure 10b). Figure 10c shows the performance of the stepwise regression model, where the monthly estimated LUE (LUE\({}_{\text{e}}\)) was close to the measured LUE (LUE\({}_{\text{m}}\)), with an R\({}^{2}\) value of 0.93 at a significance level of \(p<0.001\).  
Figure 8: Seasonal variations in monthly PAR (**a**), T\({}_{\text{a}}\) (**b**), (**c**) vapor pressure deficit (VPD), P (**d**), (**e**) evaporative fraction (EF), CI (**f**), NDVI (**g**), GPP (**h**), and LUE (**i**) in 2006–2019 in the Chinese cork oak plantation.  
Figure 9: Correlation analysis among monthly biophysical factors and LUE in 2006–2019 in the Chinese cork oak plantation. * Significant at \(p<0.05\); ** significant at \(p<0.01\); *** significant at \(p<0.001\).