## 1 Introduction  
Remote sensing data have been widely used to calculate gross primary productivity (GPP) in combination with light use efficiency (LUE) models, which commonly express GPP as the product of the amount of absorbed photosynthetically active radiation (APAR) and a LUE term (GPP = LUE \(\times\) APAR) [1,2]. LUE models are applied to estimation of GPP at the regional or global scale. However, the estimations of the two key input parameters of LUE models, i.e., LUE and APAR, remain challenging [3, 4, 5]. Proper determination of LUE and APAR are critical for calculating GPP using remote sensing data and LUE models. In LUE models, stress-based approaches considering a maximum LUE downregulated by environmental factors, such as soil water, vapor pressure deficit (VPD), minimum and maximum air temperature [3, 6, 7, 8, 9, 10, 11, 12]. However, such an assumption probably induces considerable uncertainties in determining GPP [13, 14, 15, 16, 17]. As canopy LUE is hard to be directly measured, flux-tower-based canopy LUE is treated as almost the'real' LUE and is often used for evaluating or validating LUE models at stand and landscape scales [8, 18, 19, 20, 21, 22]. It is estimated as GPP derived from net ecosystem CO\({}_{2}\) exchange (NEE) measurements from eddy covariance technique divided by empirically estimated or observed APAR. Previous studies indicated that the fractions of diffuse and direct radiation absorbed by leaves were different [23, 24, 25], and that LUE was affected by both the quantity and composition of the incoming solar radiation [14, 16, 26]. With a given value of total incoming radiation, the canopy-level LUE generally increases with increasing fraction of diffuse radiation due to an increase in the canopy fraction that is receiving illumination without photo-saturation [15, 17, 26, 27, 28]. The calculation of APAR is suitable for clear sky conditions due to its theoretic basis on direct radiative transfer regime, but may overestimate APAR of sunlit leaves and underestimate that of shaded leaves when the fraction of diffuse radiation is high. A promising method used for accurately estimating LUE is the photochemical reflectance index (PRI = (R\({}_{531}\) - R\({}_{570}\))/(R\({}_{531}\) + R\({}_{570}\)), where R\({}_{531}\) and R\({}_{570}\) are canopy reflectance at wavelengths 531 and 570 nm, respectively) [29]. The xanthophyll cycle, which is part of the leaf photoprotective mechanisms and functionally related to photosynthetic rates, is closely correlated with the rate of dissipation of excess absorbed energy as heat [30]. During this cycle, the xanthophyll pigment diepoxide violaxanthin is converted rapidly via the intermediate monoepoxide antheraanthin into the epoxide-free form zeaxanthin by the enzyme violaxanthin de-epoxidase, known as a de-epoxidation sequence [30, 31, 32, 33, 34]. As the reflectance change at 531 nm is caused by the appearance of zeaxanthin, PRI is currently considered as the most representative index of the xanthophyll cycle [29, 35, 36]. As we know, energy absorbed by plants (i.e., APAR) is distributed to three parts (i.e., photochemistry, fluorescence and photoproduction dissipating as heat), and these three portions are competitive. PRI being the proxy for the portion of photoprotection shows the potential to indicate LUE which is an outcome of the competition, as well as APAR which is an input of the competition [22]. Strong correlations were observed between PRI and LUE for individual species, and significant but much weaker correlations were observed for several species as a group [37, 38, 39, 40, 41, 42, 43, 44]. However, the relationship between PRI and LUE remains elusive because of the complex influence of canopy architecture [38, 42, 45, 46, 47, 48]. Even worse, PRI may be decoupled with LUE when different inherent mechanisms driving PRI and LUE variations under some circumstances [49, 50, 51].