## 4 Discussion  
### Evaluation of Multi-Angle Observed PRI  
This study found that the averages of the multi-angle observed PRI within short time intervals better represented the condition of the entire canopy in estimating LUE than the single angle observed PRI (Figure 3). This relationship indicates that the utilization of multi-angle observations with tens of measurements evenly distributed at different angles could diminish the angular effects to some extent. Crop canopies are non-Lambertian characterized by bidirectional reflection. Their reflectance changes because of the varied fraction of sunlit/shaded elements of the canopy with the changing angles. The reflectance at 531 nm differed significantly over sunlit and shaded elements of the canopy. The canopy elements whose reflectance differed as a function of illumination intensity lead to the variation in the PRI signal viewed at varied angles [25]. The sunlit elements are more likely to be exposed to excess light levels, causing a conversion of violaxanthin to zeaxanthin and resulting in a lowering of PRI. The angular effects of the observed PRI were also reported by [PERSON] et al. [49] and [PERSON] et al. [18], which was consistent with our observations (Figure 2). We used the simple arithmetic averages of the multi-angle observed PRI to represent the whole canopy with assuming the canopy as a big leaf in this study. There are also two-leaf approaches that interpreted the variations of the observed PRI with the sun-view geometry and canopy structure as their sensitivity to the fractions of sunlit/shaded leaves. [PERSON] et al. [58] used a two-leaf model to derive canopy PRI with multi-angle observations and found the two-leaf PRI could effectively improve the ability for indicating LUE over the big-leaf PRI in a subtropical evergreen coniferous forest. However, the canopy of maize was relatively homogeneous compared to the coniferous forest with more species. Different from the previous observation methods, the view zenith angle in this study was assigned to be consistent with the SZA, while the VAAs within half an hour were evenly distributed (Figure 2). Therefore, the arithmetic average was chosen as a more simple approach to reduce the angular effect in this study. Comparison of the PRI-Based and the SIF-Based Models in Estimating Diurnal and Seasonal GPP Variations  
Among different time scales, we found that the PRI-based LUE model exhibited better performance than the SIF-based linear model in estimating the diurnal variations of GPPEC, while the SIF-based linear model performed better at estimating the seasonal variations of GPPEC (Table 1, Figure 4). PRI may be a good indicator of LUE because of the link between PRI and xanthophyll cycle activity. The rapid xanthophyll cycle activity represented physiological regulations of photosynthesis on short-term changes in general environmental conditions and thus PRI was regarded as an optical indicator of LUE at diurnal time scales. Several studies have confirmed that the long-term (seasonal) PRI responses were primarily driven by constitutive changes in pigment pools (i.e., the ratio of carotenoid and chlorophyll) instead of facultative xanthophyll cycle activity [27; 28; 29; 59; 60]. Although the slower or seasonal pigment pool size adjustments of photosynthesis were also shown to correlate with LUE, the mechanistic explanations of the relationships differed [31]. Thus, the PRI-based LUE model showed a high advantage in the estimation of the diurnal photosynthesis variations, but a lower advantage in estimating the seasonal photosynthesis variations. Maize is a C4 plant, which does not have the photosynthetic \"lunch break\" phenomenon under high light at noon. Thus, the distribution of absorbed light energy relies on non-photochemical quenching (NPQ), i.e., heat energy dissipation through the xanthophyll cycle, which may be more conducive to the expression of the diurnal LUE variations by PRI.