## 1 Introduction  
Gross primary productivity (GPP) is an important component of the terrestrial carbon cycle and exhibits significant spatial and temporal variations. Reliable estimation of GPP is a prerequisite for quantifying terrestrial carbon sinks and sources. Remote sensing data have the potential for estimating the regional distributions of GPP, as they can provide the needed spatial and temporal coverages. They have been widely used to calculate 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; 3; 4]. APAR can be computed as the product of photosynthetically active radiation (PAR) incident on the top of vegetation and the fraction of PAR absorbed by the vegetation canopy (FPAR). The incident PAR can normally be obtained from meteorological observation while FPAR can be retrieved from remote sensing data [5; 6; 7; 8]. LUE models take advantage of remotely sensed data and are easy to operate. However, their outputs are very sensitive to LUE [9; 10], which is significantly affected by numerous factors, including vegetation species and types, nutrient supply, temperature, atmospheric water vapor pressure deficit, soil water, and so on [9; 11; 12; 13; 14; 15; 16]. In most LUE models to date, the influences of these factors on LUE are considered through the use of various scalars defined with empirical functions and coefficients [11; 17; 18]. Such simplification for LUE estimation definitely induces considerable uncertainties in calculated GPP [19; 20; 21; 22; 23]. Proper determination of this parameter is a prerequisite and also a challenge for calculating GPP using remote sensing data and LUE models at regional and global scales. A number of studies found that LUE is well related to the photochemical reflectance index (PRI = (R\({}_{531}-R_{570}\))/(R\({}_{531}+R_{570}\)), and R\({}_{531}\) and R\({}_{570}\) are reflectance at wavelengths 531 and 570 nm) [3; 24; 25; 26; 27; 28; 29; 30; 31; 32; 33; 34; 35; 36; 37]. However, there are still some uncertainties regarding to the reliability of this relationship as affected by many factors. [PERSON] and [PERSON] [38] indicated that PRI is strongly influenced by sun-view geometry, and by varying soil background when the leaf area index (LAI) of the canopy is below 3. At large view zenith angles (>30\({}^{\circ}\)), PRI is also sensitive to leaf angle distribution (LAD). Canopy LUE varies with radiation received by the canopy, while PRI also shows a similar property due to its sensitivity to the fraction of shaded or sunlit leaves [26; 39; 40; 41]. Additionally, the dependence of PRI on the shadow fraction is affected by the ratio of diffuse sky radiation [42; 43]. Therefore, the relationship between PRI and LUE is affected by various factors, including the interference to the PRI signal by external factors not related to photosynthetic efficiency, the structural characteristics of canopies, background signals, different reference bands (if the band is not centered at 570 nm), and sun-view geometry [44]. In addition, changes in environmental conditions might induce some pigment activity or photosynthetic physiology variations that confound the PRI signal [27; 45; 46; 47], while they might cause different variation patterns of LUE over a long time span. [PERSON] _et al._[32] reported that correlations between PRI and LUE differ seasonally based on eight years of continuous _in situ_ observations in deciduous and evergreen broadleaf forests. [PERSON] _et al._[30] also showed a limited sensitivity of PRI to LUE across seasons in a tropical rainforest. This highlights that the hypothesis of coordinated regulation between PRI and photosynthetic activity needs to be tested in different seasons and ecosystems [27].