## 2 Materials and Methods
### Data Sources
#### 2.2.2 Spatial Data  
The data used in this study to simulate global gross primary productivity include terrain, environmental attributes, and meteorological data obtained from multiple data platforms. Terrain data consist of the digital elevation model (DEM). Environmental attribute data include soil organic carbon (SOC), land use and land cover (LULC), the standardized precipitation evapotranspiration index (SPEI), soil temperature (ST1) at 0-7 cm, and soil water volumetric content (SW1), as well as soil temperature (ST2) at 8-28 cm and soil water volumetric content (SW2). Meteorological data include mean air temperature (MAT), precipitation (MAP), relative humidity (RH), solar radiation (SRAD), and the fraction of absorbed photosynthetically active radiation (FAPAR). Vegetation attribute data comprise the normalized difference vegetation index (NDVI) and the leaf area index (LAI), among others. Meteorological division data from Beijing college of urban and environmental geography data platform ([[http://geodata.pku.edu.cn](http://geodata.pku.edu.cn)]([http://geodata.pku.edu.cn](http://geodata.pku.edu.cn)) (accessed on 16 March 2024)), the QTP according to the dry humidity is divided into the following: humid zone (denoted by I, precipitation > evaporation, annual precipitation > 800 mm), semi-humid zone (denoted by II, precipitation > evaporation, annual precipitation 400-800 mm), semi-arid zone (denoted by III, precipitation < evaporation, annual precipitation 200-400 mm), arid zone (denoted by IV, precipitation < evaporation, annual precipitation < 200 mm).  
Additionally, the water vapor pressure deficit (VPD), an indicator used in the random forest modeling and simulation of GPP, is calculated using the following formula [52; 53]:  
\[\mathrm{VPD}=\mathrm{P_{s}}-\mathrm{P_{w}} \tag{3}\]  
\[f=1+7\times 10^{-4}+3.46\times 10^{6}\times\mathrm{P_{a}} \tag{4}\]  
\[\mathrm{P_{s}}=6.112\times f\times\mathrm{e}^{\frac{17\delta\mathrm{P_{s}}T_{a }}{\mathrm{a}+28\delta\mathrm{S}}} \tag{5}\]  
\[\mathrm{P_{w}}=\mathrm{P_{s}}\times\mathrm{RH}\times\frac{1}{100\%} \tag{6}\]  
where \(\mathrm{T_{a}}\) represents the air temperature (\({}^{\circ}\)C), \(\mathrm{P_{a}}\) is the atmospheric pressure (data sourced from ERA5) (hpa), relative humidity (RH) denotes the relative humidity (%), \(\mathrm{P_{s}}\) is the saturated vapor pressure, \(\mathrm{P_{w}}\) is the actual vapor pressure, and \(f\) is the atmospheric pressure enhancement factor.  
The data used to simulate ET were sourced from five long-term monthly ET datasets provided by different platforms, covering the QTP and spanning the period from 1982 to 2018. The specific datasets include the GLASS ET Dataset [54], which demonstrates high estimation accuracy and has been extensively applied in global climate change studies; resource assessments; and ecological environment monitoring. PTJPL ET Product integrates the Priestley Taylor Jet Propulsion Laboratory (PTJPL) model with multi-source observational data and uses calibration data from 39 sites and 127 site-years of annual ET observations [55]. PEW ET Dataset, based on the Proportionality Hypothesis-based Surface Energy Water Balance Model (PEW), comprehensively considers the impacts of soil moisture and precipitation on ET, enhancing estimation accuracy [56]. S ET Dataset, calculated using the S-shaped generalized complementary evaporation principle [57; 58]. SiTHv2 ET Dataset and developed using the Simple Terrestrial Hydrosphere Model Version 2 (SiTHv2), incorporates potential eco-hydrological processes [59]. All spatial data were resampled and processed at monthly or annual scales to facilitate subsequent analyses. Detailed information on data sources, temporal coverage, and spatial resolutions is provided in Table 1.