## 4 Discussion
### Feasibility of PRI to Indicate LUE
The relationship between PRI and LUE differed in different months and under different combinations of bioclimatic factors (Table 1), implying the necessity to estimate LUE based on PRI using different empirical equations in different months and under different weather conditions. It is still a challenge to derive a generalized relationship between LUE and PRI. Tower-based LUE was estimated according to GPP derived from NEP measurements and empirically estimated APAR. The latter would definitely affect the relationship between PRI and LUE. When APAR was calculated using the two-leaf LUE approach, which differentiates the different interactions of direct and diffuse radiation within the canopy and the different responses of photosynthesis rates of sunlit and shaded leaves to incoming PAR, the ability of PRI to approximate LUE was improved (Appendix C). For thoroughly investigating the ability of PRI to indicate LUE, accurate estimates or measurements of APAR were required. The effect of sun-view geometry on PRI has been discussed in many ways [3, 27, 40, 69, 73], and with no doubt that multi-angle measurements are the best way to tackle this issue (Figure 1). The fraction of sunlit leaves of the whole canopy is the biggest at noon. However, the sensor is possibly unable to observe all sunlit leaves at this moment, which might lead to a smaller diurnal variation of observed PRI than the reality. Similarly, [PERSON] and [PERSON] [27] also reported that the relationship between PRI and PAR was influenced by the ratio of observed sunlit leaves to shaded ones. At the beginning and the end of the growing season, the values of PRI were relatively low. This phenomenon might be caused by more measurements of sunlit leaves with low PRI, which was induced by larger solar zenith angles. Therefore, it is needed for an effective way to reduce the impact of sun-view geometry and varied shadow and sunlit fractions on PRI. A semi-empirical kernel-driven bidirectional reflectance distribution function (BRDF) model was first applied to standardize the directional reflectance to one direction that significantly enhanced the correlation between canopy PRI and LUE [3]. However, based on _in situ_ observations and model simulations, [PERSON] [72] mentioned that, as directional PRI responses associated with sunlit/shaded foliage, various sunlit/shaded canopy ratios affected the utilization of canopy PRI over different stages of corn during a growing season. Additionally, the best sunlit/shaded canopy ratio for retrieving \"true\" canopy PRI might change with canopy types. Thus, a best direction with a proper sunlit/shaded foliage ratio, a structure-based parameter, needs to be considered when using the BRDF model to interpret canopy PRI. Furthermore, the contribution of the background to the reflectance of the forest canopy varyieswith the changing view angle [31,74], and it is hard to eliminate the influence of the background signal using the semi-empirical kernel-driven model. Additionally, the changing diffuse fraction of the incident radiation amplified the effect of sun-view geometry. It is necessary to consider the impact of diffuse irradiance that may cause variations of structurally and physiologically absorbed PAR, which induces carbon uptake [75,76], and further influences the relationship between PRI and LUE (Appendix C) under changing sky conditions. As both PRI and LUE are very sensitive to the shadow fraction in the canopy [39,42], separating the canopy to sunlit and shaded parts and then calculating the true (two-leaf) PRI and LUE of the whole canopy might be a robust and widely applicable approach to overcome this issue, based on the multi-angle observation. Further consideration of this approach could help interpret PRI information to identify underlying leaf physiological mechanisms, and to reduce uncertainties in LUE estimates using remote-sensing observations.