## 1 Introduction  
To keep human-induced global warming below 2 \({}^{\circ}\)C, it is essential to rapidly decrease CO\({}_{2}\) emissions and implement measures to increase the accumulation and sequestration of CO\({}_{2}\)[1; 2]. Thus, improving the terrestrial ecosystem carbon sink is a significant approach to decelerate the ongoing rise in atmospheric CO\({}_{2}\) concentrations and to achieve the carbon neutrality target [2; 3]. Terrestrial gross primary productivity (GPP) is defined as the quantity of CO\({}_{2}\) that land plants 'fix' into organic material via photosynthesis. It stands as the primary carbon input to the terrestrial ecosystem [4; 5; 6]. GPP holds significance for human welfare as it forms the foundation to produce food, fiber, and wood [7]. The variations of GPP can be attributed to climate changes and anthropogenic activities. It should be noted that studying the influences of climate changes on GPP is a crucial first step [8]. First, climate variables like temperature, precipitation, and solar radiation directly influence GPP [9]. Moreover, those effects may be more profound and potentially alter the structure of terrestrial ecosystems as well as the physiology of vegetation [10; 11]. Understanding the climate sensitives of GPP helps predict how ecosystems might respond to future climate changes, whether they are natural or anthropogenically amplified. It plays an important role for us in formulating measures to address climate changes. Second, investigating the influences of climate changes on GPP is the basis of partitioning the influences of anthropogenic and naturally induced changes in GPP. Based on the understanding of the contributions of climate changes on GPP, the additional or synergistic impacts of anthropogenic factors, such as land-use change, pollution, or direct human interference can be easily measured [12; 13]. Thus, in this study, we mainly focused on the GPP variations and its responses to climate factors. Even though there were many studies investigating GPP [14], it remains challenging to monitor GPP across different scales [15]. Over the past decades, eddy covariance (EC) technologies have become crucial tools for deriving GPP through direct observations of CO\({}_{2}\) exchange at the canopy-atmosphere interface [16]. However, the EC data is limited from 100 m to 2000 m surrounding the flux site [17] and is thus usually constrained by scale and expenses, which is not suitable for spatial analysis [18]. Another commonly used method for estimating GPP involves the integration of satellite-based estimates and ecosystem models [19; 20]. Satellite remote sensing technologies enable the rapid and cost-effective acquisition of extensive land surface data that reflects vegetation-related and environmental variables [21]. Over the past few decades, multiple GPP models using remote sensing data have been developed to model GPP on a regional and global scale [4; 22; 23; 24; 25]. Nevertheless, different products based on different models may have uncertainties. There exists 4 advanced global GPP products with exceptional spatial and temporal resolutions, which are the Moderate Resolution Imaging Spectroradiometer Photosynthesis (MOD17) [26], the Vegetation Photosynthesis Model (VPM) [27], the Breathing Earth System Simulator (BESS) [28], and the Penman-Monteith-Lening (PML) models [29]. MOD17 and VPM GPP data were generated based on light use efficiency (LUE) models [30]. BESS and PML are process-based models. MOD17 and PML employed vapor pressure deficit (VPD) as an indicator of moisture stress [31; 29; 32; 33], and BESS applied relative humidity (RH) via the Ball-Berry model [34; 35] to consider the water stress conditions. Both VPD and RH are parameters associated with atmosphere moisture [36]. VPM applied a satellite-based land surface water index (LSWI) to consider water stress conditions, which is closely associated with the moisture status of plants [27; 37; 38]. [PERSON] et al.