## 3 Results and Discussion
### Test of Three Methods for Estimating the Fraction of Sunlit Leaves
The two-leaf treatment obviously improved the ability of PRI to track diurnal variations of LUE in comparison to the big-leaf PRI. The correlation between \(\mathrm{PRI_{t}}\) and APAR (Figure 6b) was highly enhanced as among 173 days, with more than 80% days that \(\mathrm{PRI_{t}}\) was highly significantly correlated to APAR (\(p<0.001\)) while more than 60% days that \(\mathrm{PRI_{b}}\) was weakly related to APAR (\(p>0.05\)). These results suggested that two-leaf PRI was a better proxy for APAR at a short temporal scale than LUE. Figure 7 illustrated the relationships of \(\mathrm{PRI_{b}}\) and \(\mathrm{PRI_{t}}\) to APAR and LUE, respectively, at half-hourly temporal scales with observations from 7:00 to 17:30 throughout the study period in all weather conditions. \(\mathrm{PRI_{b}}\) was less correlated with either APAR or LUE than \(\mathrm{PRI_{t}}\). The relationship between \(\mathrm{PRI_{t}}\) and APAR was much stronger than that between \(\mathrm{PRI_{b}}\) and APAR with significantly increased \(R^{2}\) value (increased \(\sim\)71%; Figure 7a,c). Generally, these results again proved the feasibility of the two-leaf approach tested in this study and presented by [PERSON] et al. (2017). In addition, both \(\mathrm{PRI_{b}}\) and \(\mathrm{PRI_{t}}\) showed higher correlation with APAR than LUE, which indicated that PRI was probably a better proxy for APAR than for LUE. Even though previous studies were focused on using PRI to indicate LUE, stronger correlation between PRI and APAR than that between PRI and LUE at short-term across a growing season have been reported for different forests by [PERSON] et al. (2018). Decrease of PRI with increased APAR is linked with an increase in light absorption associated with the conversion of violaxanthin into antheraxanthin and zeaxanthin pigments, which can be detected by the decrease in reflectance at 531 nm ([PERSON] et al., 2017). PRI is more sensitive to absorbed energy, exhibiting closely increasing with APAR even when net photosynthesis rate and LUE are still low (often occur with low stomatal conductance in the afternoon) ([PERSON] et al., 2017). The relationships of daily mean \(\mathrm{PRI_{b}}\) and \(\mathrm{PRI_{t}}\) to APAR and LUE averaged from observations between 10:00 and 15:30 throughout the study period were shown in Figure 8. Significant linear correlations were also found for all relationships, while the relationshipships of \(\mathrm{PRI_{b}}\) and \(\mathrm{PRI_{t}}\) with LUE were more non-linear (exponential). The correlation between \(\mathrm{PRI_{t}}\) and LUE was about 35% stronger than that between \(\mathrm{PRI_{b}}\) and LUE, although some low \(\mathrm{PRI_{t}}\) values corresponding to high LUE (Figure 8b,d). The relationship between daily \(\mathrm{PRI_{t}}\) and APAR was also stronger than that between daily \(\mathrm{PRI_{b}}\) and APAR (Figure 8a,c), but was weaker than the relationship at half-hourly scale (Figure 7c). Figure 6: Number of days on which the correlation coefficients (\(R\)) of \(\mathrm{PRI_{b}}\) and \(\mathrm{PRI_{t}}\) with (**a**) LUE and (**b**) APAR are significant at different levels (\(p\)). The value of \(R\) between half-hourly \(\mathrm{PRI_{b}}\)/\(\mathrm{PRI_{t}}\) and LUE and APAR was calculated per day with more than five good-quality observations from 7:00 to 17:30. Even though the ability of PRI to indicate LUE had been discussed in previous works [4; 22; 44; 47; 82; 83; 4], PRI was still difficult to be use to estimate LUE over different tempo-spatial scales as their relationship was influenced by many factors, such as pigment concentration, sun-target-view geometry, background reflectance, diffuse sky radiation, canopy structure. This limited the effectiveness of PRI to be involved in LUE models for GPP estimations [2; 41; 43; 46; 65; 78; 83; 84]. Generally, either PRI\({}_{\rm b}\) or PRI\({}_{\rm t}\) was more linked to APAR than LUE at different temporal scales (Figures 7 and 8). [PERSON] et al.