## 1 Introduction  
Remote-sensing satellites provide continuous spatio-temporal land surface data, which can be used to monitor vegetation-growing conditions. Gross primary productivity (GPP) is one of the most important components of carbon flux in terrestrial ecosystems [1]. In recent years, many remote-sensingGPP products were developed based on moderate-resolution imaging spectroradiometer (MODIS) data at spatial resolutions of 500 to 1000 m, such as MODIS GPP (MOD17 [2; 3]), the breathing earth system simulator (BESS [4]), the vegetation photosynthesis model (VPM [5; 6]), and the eddy covariance light-use efficiency (EC-LUE [7]) model, which explained up to 70% of the eight-day average GPP variance when correlated with FLUXNET 2015 carbon flux datasets at the site level [8]. The GPP products were successfully applied to environmental monitoring such as assessing drought limitation for regional photosynthesis [9; 10; 11]. However, an uncertainty of approximately 30% results from two major aspects: light intercepted by canopies, and carbon transfer rates from energy to productivity [12]. The amount of canopy-absorbed photosynthetic active radiation is influenced by solar radiation [13] and canopy structure [14], while the carbon transfer rate is constrained by environmental limitations [15] such as weather conditions [3] and nutrient availability [16]. Many remote-sensing-based GPP estimation methods utilize vegetation indices (VIs) as important input variables [5; 17; 18], because the VIs integrate nutrient and absorption characteristics. In addition, some indices based on satellite reflectance are strongly correlated with CO\({}_{2}\) uptake by the vegetation canopy [19]. [PERSON] et al. [20] utilized a satellite-derived normalized difference vegetation index (NDVI) to estimate vegetation photosynthesis. Later, a robust relationship between the enhanced vegetation index (EVI) and GPP was found at the site level or regional scale [21; 22; 23]. Meanwhile, VIs were used as input parameters to estimate the fraction of absorbed photosynthetic active radiation (FPAR), which improved the estimation of intercepted canopy light during the GPP estimation process [24; 25]. The photochemical reflectance index (PRI), which provides information on non-photochemical quenching (NPQ) during the photosynthesis process, showed potential in light-use efficiency (LUE) estimations from remote-sensing data [26; 27; 28]. However, the mechanistic link between the PRI and LUE appears to be highly dependent on the spatial scale from leaf to canopy [29]. The vegetation red-edge (680-780 nm) reflectance provides an integrated response of vegetation function [30; 31]. The vegetation red edge contains information on the absorption of chlorophyll at 680 nm and higher absorption at 780 nm; thus, the VI derived from the red-edge region is sensitive to chlorophyll absorption at moderate-to-high values [32]. This information was shown to be optimal for the non-destructive estimation of vegetation chlorophyll content [33; 34; 35]. Unlike the rapid changes in diurnal photosynthetic capacity, vegetation chlorophyll contents play an important role in GPP estimation [36; 37] at half-monthly (mid-term) or seasonal (long-term) scales [38]. Because red-edge reflectance strongly corresponds to vegetation chlorophyll content, researchers used it to construct VIs to estimate canopy chlorophyll contents and improve GPP estimations [39; 40]. Previous studies used vegetation red-edge reflectance VIs based on remote sensing as proxy information to improve GPP estimation. Researchers used spectra from ground-based measurements to construct red-edge VIs and then connected these to chlorophyll contents [41; 42]. For instance, some authors built the red-edge chlorophyll index (CI red edge, Clr) and green chlorophyll index (CI green, Clg) [39; 43], and correlated these indices with canopy chlorophyll content and linked them to GPP at cropland sites. They then applied the red-edge VI to model GPP directly [44; 45] or indirectly [40; 46].