## 1 Introduction  
As the main component of the terrestrial ecosystem, vegetation is an important link in the exchange of energy, water, and carbon between land surface and atmosphere [1, 2]. Gross primary productivity (GPP), the total amount of carbon absorbed by vegetation at ecosystem scale [3], directly reflects the productivity of vegetation under specific environmental conditions, indicating the growth characteristics and health status of terrestrial ecosystems [4]. Moreover, GPP is the main component of terrestrial carbon sequestration and plays a key role in the global carbon balance, providing the terrestrial ecosystem with the ability to partially offset anthropogenic CO\({}_{2}\) emissions [5]. Accurate estimation and attribution of GPP is of great significance for facilitating a deeper understanding of the global and regional terrestrial carbon cycle and assessing ecosystem health [6]. In addition, future climate changes will inevitably affect the global vegetation dynamics, so it is extremely important to project the possible changes in vegetation productivity under future climate changes [7]. So far, there is still no technology available to measure GPP directly, because of the lack of measuring at scales greater than the leaf level [8]. At ecosystem scale, the eddy covariance (EC) technique, which quantifies the continuous net ecosystem exchange (NEE) of CO\({}_{2}\), can be used to infer GPP by separating ecosystem respiration and GPP from NEE [9]. However, this method limits the estimate of GPP from tens of meters to several kilometers, making it difficult to calculate at a large scale [10; 11]. In order to estimate and project GPP at regional and global scales, ecosystem models have been developed and applied as scientific tools to obtain GPP [12]. This mainly includes process-based models and LUE models [13; 14]. The process-based models consider the growth processes of vegetation, such as photosynthesis, respiration, and evapotranspiration. Although this provides a solid physiological and ecological mechanism for the models, it also leads to a complex simulation process, which is easily limited by a large number of model inputs and physical parameters. Moreover, the parameters vary greatly between different regions and vegetation, thereby increasing the difficulties of obtaining appropriate parameters, subsequently leading to more difficulties in GPP estimation. The LUE models are generally based on the theory of light use efficiency, stating a relatively constant relationship exists between photosynthetic carbon uptake and absorbed photosynthetically active radiation at the canopy level [15; 16]. [PERSON] et al. [17] developed the first CASA model for estimating global vegetation productivity, and then a series of LUE models have been developed, including the GLO-PEM model [18], MOD17 GPP model [19], Vegetation Photosynthesis Model [20], Eddy Covariance Light Use Efficiency Model [21], etc. In contrast to the process-based models which are limited by a large number of model inputs and physical parameters, LUE models have less model inputs and could simulate GPP at high spatial-temporal resolution by means of high-resolution remote sensing products [22; 23]. As a consequence, LUE models are widely used in current research. In addition, LUE models directly use a wide range of satellite remote sensing data; they have great potential to fully solve the dynamic changes of GPP in time and space. At present, a lot of researchers have also proven that the LUE models are effective tools for large-scale research of GPP [24; 25; 26]. Moreover, the LUE model has been improved in different degrees during its development, treating the fraction of photosynthetic active radiation in disparate ways or using more reasonable means to represent temperature stress (TS) and water stress (WS) [27].