## 1 Introduction  
Estimations of global vegetation productivity are essential for improving the understanding of the interaction between the terrestrial biosphere and the atmosphere in the context of global changes and the further formulation of climate policy decisions [1; 2]. GPP, a key variable in the global carbon cycle, is influenced by various factors such as temperature [3], soil moisture [4], vegetation types and even tree species [5], crop types [6], tree ages [7] and radiation [8]. To date, many models, including process models and LUE-based models, have been established to estimate global GPP; however, they vary greatly in terms of produced values [9; 10; 11; 12; 13; 14; 15; 16; 17; 18]. Currently, some GPP models try to build the relationships between GPP and climate factors, FPAR and the vegetation indices with which global GPP is produced [19; 20; 21]. However, those models don't care about the intermediate variable LUE and its impact on GPP. LUE is of great significance in GPP estimation, and it can help us to deeply understand and clarify the key processes of the vegetation carbon sequestration. This paper focuses on the estimation of LUE based on remote sensing data, and then explores its impact on GPP estimation. The LUE-based model was originally described by [PERSON] [22; 23]. It has a simple formula and can present consistent ecosystem processes across various vegetation types [24; 25], which makes it the most promising method for adequately addressing the spatial and temporal dynamics of GPP. The input data, such as the fraction of absorbed photosynthetically active radiation (FPAR), could be produced by remote sensing techniques. Therefore, it has been widely used to estimate GPP at local, regional and global scales [3; 26; 27; 28; 29]. LUE is defined as the ratio of carbon uptake to absorbed photosynthetically active radiation (APAR) for a plant canopy [30]. The dominant methods used to determine LUE are based on environmental stress factors and vegetation spectral indexes. The photochemical reflectance index (PRI), as one popular vegetation spectral index, is a good estimator of LUE, especially in the short-term [31; 32] and at the leaf/canopy scale [33; 34]. However, confounding factors appear at larger temporal and spatial scales. The correlations of PRI with LUE varied dramatically throughout the growing season [35] and were decoupled in severe circumstances, consequently leading to an overestimation of LUE [36]. Some studies process temperature and water stress factors based on the parameterization approach [37] and machine learning methods [38], and have obtained high-quality LUE values. The LUE-based GPP model is built upon two fundamental assumptions: (1) GPP equals the product of APAR and LUE; (2) actual LUE may be reduced below its potential value by environmental stresses such as low temperatures or water shortages. Consequently, the accuracy of the LUE greatly influences the quality of the GPP. However, it is quite difficult to accurately calculate global LUE because it cannot be directly measured and is sensitive to various factors. In different models, parameters such as temperatures or water stress factors are described in different ways, which leads to significant variations in the estimation results. The evaporative fraction (EF) is widely used as a water stress factor in LUE and GPP models [39]. [PERSON] et al. (2015) [40] showed that LUE was more responsive to plant moisture indicators, such as plant EF, than to atmospheric indicators, such as the vapor pressure deficit (VPD). Previous studies suggest that the efficiency of carbon uptake is usually higher under diffuse light (cloudy or hazy skies) than under direct light (clear sky) [41; 42]. The underlying mechanism for this growth is the increased penetration of light into deeper layers of the canopy under diffuse light [8]. In contrast, clouds may reduce the total radiation, which would lead to the reduction of PAR and GPP [43]. Therefore, the effect of radiation mode on LUE and GPP is complicated.