## 1 Introduction  
Vegetation gross primary production (GPP) is the largest CO\({}_{2}\) flux of the carbon cycle in terrestrial ecosystems and impacts all of the carbon cycle variables [1]. Recent studies report the strong regulation of GPP on the atmospheric CO\({}_{2}\) concentration variation and, potentially, climate change [2, 3]. Terrestrial GPP also provides important societal services through the provision of food, fiber, and energy. Therefore, accurate simulation of terrestrial GPP is very important for better understanding of the state and controlling mechanisms of the current ecosystem production. Numerous models have been developed to estimate terrestrial ecosystem production [4, 5, 6]. However, model estimates differ substantially in magnitude, spatial and temporal variability. For example, global net primary production (NPP) simulations differ substantially among 17 models, with a more than 20 Pg C\(\cdot\)yr\({}^{-1}\) difference over the global scale [7]. GPP estimates by three terrestrial biosphere models over Europe show large differences in magnitude, spatial pattern, and interannual variation [8]. In Asia, the GPP estimates of eight models exhibit large discrepancies over various ecosystems in terms of spatial pattern and magnitude [9]. Satellite-based light use efficiency (LUE) models are important tools in simulating GPP at the continental to global scale due to practicability [10, 11, 12, 13]. Among all of the model methods, LUE models are driven by satellite data, which may have the most potential to adequately address the spatial and temporal dynamics of vegetation production [14]. Independently or as a part of the integrated ecosystem models, the LUE approach has been used to estimate GPP or NPP at various spatial and temporal scales [15, 16, 17]. During the past three decades, many LUE models have been developed with various algorithm combinations [18, 19, 20, 21, 22]. Most LUE models are developed based on eddy covariance measurements and have been calibrated and evaluated for various ecosystem types and geographical regions [23, 24, 25]. A recent comparison of seven satellite-based LUE models using CO\({}_{2}\) flux measurements from 157 globally-distributed eddy covariance towers shows the large differences among models [26]. However, to our knowledge, no study has been conducted to compare the model differences over the global scale. GPP estimates by the LUE models depend on some key environmental variables, including solar radiation, air temperature, water availability, and vegetation conditions. The understanding of how these factors influence GPP remains unclear due to the complex interactions of these factors and the vegetation [27]. Therefore, the performance of LUE models depends on how a model integrates environmental variables to describe the mechanisms that drive the ecosystem processes [28, 29]. Model inter-comparison can provide insights to help resolve model discrepancies in GPP estimates and improve our understanding of the terrestrial production. It should be noted that the inter-comparison of models can also provide other insights on model differences, which are useful for model development and global estimates. In a previous study, we examined the performance of seven LUE models using eddy covariance measurements of 157 global sites [26]. All models are calibrated and evaluated at sites, and their performances are comparable at the site scale [26]. However, the simulations of models over large scale show substantial differences [17, 30, 31]. The model inter-comparison can provide the direct results on the differences of large-scale GPP estimates and interannual variability [32, 33]. These results are important for understanding the differences of GPP estimates among models [7]. Moreover, the inter-comparison of models can identify the simulation differences induced by different environmental variables integrated into the models.