## 1 Introduction  
Carbon sequestration by terrestrial ecosystems is a key factor underpinning a comprehensive understanding of the carbon budget at a global scale. Terrestrial plants fix carbon through photosynthesis, known as gross primary production (GPP) at the ecosystem scale--the largest carbon exchange between the biosphere and the atmosphere [1]. Accurate measurements and estimates of GPP will allow us to achieve improved carbon monitoring and to quantitatively assess impacts from climate changes and human activities [2; 3]. Remote sensing observations provide a unique opportunity to track photosynthetic activities at various spatial and temporal scales, and much effort has been put towards this goal over the past decades. Many remote-sensing-based indices and algorithms were developed and utilized to track leaf biochemical properties (e.g., chlorophyll, water content) and canopy biophysical properties (e.g., leaf area index, LAI; absorbed photosynthetically active radiation, APAR; fraction of APAR, fAPAR) have been applied to the estimation of GPP in various ecosystems, with variable success [2; 4; 5; 6; 7; 8; 9; 10; 11; 12; 13; 14]. For instance, some studies reported good performances for GPP estimation (r\({}^{2}\) = 0.67 to 0.95) for agricultural sites [6; 14] and grasslands [13] while less than satisfactory results (r\({}^{2}\) \(<\) 0.48) have been found for hardwood forests [13]. The light use efficiency (LUE) model [15; 16] has been widely utilized and coupled with remote sensing data to estimate GPP at various spatial scales [17; 18; 19; 20; 21; 22], including the Moderate Resolution Imaging Spectroradiometer (MODIS) Terra/Aqua satellite GPP Products [5; 23; 24]. The LUE concept measures the ability of vegetation to utilize atmospheric carbon dioxide (CO\({}_{2}\)) and solar energy to produce biomass, and is usually defined as the ratio of GPP to APAR over a given period of time:  
\[LUE=\frac{GPP}{PAR\times fAPAR} \tag{1}\]  
Whether based on biomass accumulation over full growing seasons as originally formulated or as instantaneous flux measurements, LUE is highly variable among different species and over phenological and environmental conditions. Instantaneous estimates of LUE are especially vulnerable to large uncertainties when used in GPP modeling [3,18,21,22,25,26]. For simplicity, the maximum expected LUE (LUE\({}_{\textrm{max}}\)) has often been used to model GPP (e.g., MODIS GPP Product), but this approach requires considerable environmental information to down-scale from assumed optimal values to predict actual ones [23,24] and to describe GPP under non-optimal, unfavorable environmental conditions. LUE has been shown to be closely correlated to biochemical responses related to photoproduction of plant tissues, when more solar radiation is absorbed than can be utilized for photosynthesis [27]. One such process is non-photochemical quenching (NPQ), regulated by the xanthophyll cycle, in which the pigment violaxanthin is reversibly de-epoxidized to zeaxanthin via anthraxanthin [18,27,28,29,30,31,32,33]. The xanthophyll cycle can be monitored with the Photochemical Reflectance Index (PRI), a normalized difference band ratio based on the narrow spectral bands centered at a physiologically active 531 nm response and a reference band insensitive to the xanthophyll signal (e.g., 570 nm), as proposed by [PERSON] and colleagues [32,34]. The capability of the PRI to track photosynthetic activities, including LUE, has been investigated across plant functional types at leaf, canopy, and landscape levels using various instruments [19,20,29,32,34,35,36,37,38,39,40,41]. Moreover, many recent studies have investigated various factors that influence the PRI:LUE relationship at canopy or ecosystem scales including viewing geometry, canopy structure, leaf area index (LAI), soil background, pigment content (e.g., carotenoids/chlorophyll ratio), and shadow fraction [17,18,21,22,42,43,44,45,46,47,48,49,50,51].