## 3 Results and Discussion
### Test of Three Methods for Estimating the Fraction of Sunlit Leaves
[62] demonstrated that APAR was directly linked with dissipation of a part of energy as heat, which was related to PRI [29; 33; 36; 85], while LUE was dominated by further processes linked with energy distribution. This indicated the stronger mechanistic linkage between PRI and APAR than LUE. PRI\({}_{\rm t}\) could better capture variations of half-hourly APAR (Figure 7) than those of daily APAR, indicating that the two-leaf PRI was efficient to track short-term (sub-day or even instantaneous) variations of APAR. The penumbra region probably contributed a large amount of absorbed radiation almost like or even more than that absorbed by sunlit leaves in this conifer forest, demonstrating that treating penumbra region as sunlit leaves was suitable for understanding the link between fast-change APAR and canopy PRI (PRI\({}_{\rm t}\)). Mechanistically, PRI mainly represented the absorbed energy allocated to photoprotection at short time scale [62; 84; 86; 87; 88; 84], and was consequently effective to indicate APAR under generally steady conditions (when the distribution of absorbed energy does not change dramatically) as PRI was a direct outcome driven by APAR. But more importantly, this result demonstrated that, at short term, PRI was only able to track changes in LUE driven by APAR, which also had been mentioned by [PERSON] et al. [73]. This finding further revealed the limitation of using PRI to track diurnal variation of LUE at some circumstances that LUE was not mainly driven by radiation. Figure 7: Relationships of PRI\({}_{\rm b}\) and PRI\({}_{\rm t}\) with APAR and LUE at half-hourly temporal scales with observations from 7:00 to 17:30 throughout the study period. The two \(R^{2}\) represent the coefficients of determination of linear (red) and exponential (green) regressions, respectively. Above all, the two-leaf approach, which used the canopy reflectance ratio to leaf reflectance to represent the fraction of sunlit leaves, was simple and very effective, verifying the work presented by [PERSON] et al. (2017). During the process of two-leaf PRI calculation, it was proved that the penumbra region should be mostly treated as sunlit leaves only on concept. If intending to quantify the penumbra effect, light detection and ranging (LiDAR) could be a useful technology to simulate the radiation distribution within the canopy, and then identify the sunlit, penumbra and shaded elements, even could map the 3D distribution of LUE within the canopy ([PERSON] et al., 2018). PRI could be used to indicate both of the two key parameters (i.e., LUE and APAR) of LUE model, while two-leaf PRI was a better proxy for APAR at a shorter time scale. It was promising to estimate APAR from hyperspectral data through PRI\({}_{t}\) with high spatial and temporal resolution, while to estimate LUE was limited under the circumstance that LUE was mainly driven by radiation. However, to generalize the utilization of PRI, further works are needed for clarifying the benefits and limitations of PRI in indicating photosynthetic parameters. To promote using PRI as a proxy for LUE, their relationships at different temporal scales and under different weather conditions should be investigated in different ecosystems.