## 1 Introduction
Under severe stress conditions, some other photoprotection mechanism like photorespiration is also involved in as a sink of excess energy as heat dissipation is not enough for stress protection [52, 53]. Decoupling between PRI and photoprotection might occur in response to different sources of stress, mostly reported as severe drought stress and high light intense [49, 51], that further make the relationship between PRI and LUE break down [50], limiting the ability of PRI to indicate LUE. Estimation of APAR of a vegetation canopy is also challenging. Considerable research has been conducted using vegetation indices to calculate the fraction of photosynthetically active radiation absorbed by a canopy (FPAR) and then APAR with photosynthetically active radiation (PAR) mostly from reanalysis remote sensing data [7, 54, 55]. With products from a moderate resolution imagingspectroradiometer (MODIS), [PERSON] et al. [56; 57; 58] presented a method to retrieve the fraction of PAR absorbed by chlorophyll contained throughout the canopy (fPAR\({}_{\text{chl}}\)) with the advanced radiative transfer model PROSAIL2 and a type of Markov Chain Monte Carlo (MCMC) estimation procedure, which opens a new perspective for accurate estimation of APAR used for photosynthesis. However, estimation of FPAR was sensitive to two structural parameter (i.e., leaf area index (LAI) and the average leaf inclination angle (ALA)) and illumination conditions [59], and estimation of PAR was also of uncertainty [60; 61], both of which introduced errors in estimation of APAR. To our limited knowledge, no works have been conducted to estimate APAR directly using remote sensing data. As variation of PRI is directly driven by absorbed energy while LUE changes from more processes [62; 63], to some extent PRI is assumed to be a better proxy for APAR than for LUE if the effects of non-physiological factors on PRI are reduced. To reduce the effects of non-physiological factors on PRI, such as sun-target-view geometry, background reflectance, diffuse sky radiation, and canopy structure, many works have been done in last several years. [PERSON] et al. [64; 65] demonstrated that directional changes in observed canopy PRI at a given time interval can be attributed almost entirely to shadow fraction (\(\alpha_{\text{s}}\)) variations. The partial derivative of PRI with respect to \(\alpha_{\text{s}}\) (\(\partial\)PRI/\(\partial\alpha_{\text{s}}\)) was used to indicate the relative light use efficiency \(\Delta\varepsilon\) (relative to unstressed, where the unstressed value \(\Delta\varepsilon=1.0\), so that \(\Delta\varepsilon\) ranges from 0 to 1) [64; 65]. However, this assessment of \(\alpha_{\text{s}}\) could only be used under clear sky conditions, since the model does not account for diffuse radiation. [66]. The ratio of direct to total irradiance should certainly be considered [26], and simpler and more universal methods by separating the canopy into sunlit and shaded parts under various weather conditions should be developed for LUE models. Separating sunlit and shaded leaves is vital to accurately predict canopy photosynthesis due to their different light responses [67; 68]. Sunlit leaves are illuminated by both the direct and diffuse radiation while shaded leaves are illuminated by only diffuse radiation [69], however, quantifying the fractions of these two parts is hard to achieve. Previous studies could only estimate sunlit and shaded leaf areas of the whole canopy using [PERSON]'s method based on solar zenith angle and measurements of leaf area index [23]. Geometric-optical models can be used to simulate the fractions of sunlit and shaded leaves [70; 71; 72] but need many accurate input parameters and some assumptions. [PERSON] et al. [73] developed a simple two-leaf approach to separate a canopy-level PRI observation into sunlit and shaded PRI values using a ratio of observed canopy reflectance to leaf reflectance.