## 3 Data
### Meteorological and Remote Sensing Forcing Data  
Meteorological and remote sensing input data are showed in Table 3. The meteorological forcing data used in this study, including air temperature, dew point temperature, and downward short-wave radiation flux, were derived from ERA5 (fifth generation ECMWF atmospheric reanalysis) dataset [60] ([[https://www.ecmwf.int/en/forecasts/datasets/reanalysis-datasets/era5](https://www.ecmwf.int/en/forecasts/datasets/reanalysis-datasets/era5)]([https://www.ecmwf.int/en/forecasts/datasets/reanalysis-datasets/era5](https://www.ecmwf.int/en/forecasts/datasets/reanalysis-datasets/era5)), accessed on 25 January 2022). The ERA5 meteorological forcing data with temporal/spatial resolution of 1-h/0.25\({}^{\circ}\) were averaged to daily and downscaled to 1 km resolution using statistical downscaling approaches [61]. Additionally, atmospheric vapor pressure deficit (\(VPD\)) was calculated from air temperature (\(T_{a}\), \({}^{\circ}\)C) and dew point temperature (\(T_{d}\), \({}^{\circ}\)C) by:  
\[VPD=SVP\times(1-RH) \tag{12}\]  
\[SVP=0.6112\times e^{\frac{17.625\,T_{d}}{14.243.5}} \tag{13}\]  
\[RH=e^{\frac{17.625\,T_{d}}{14.243.61}-\frac{17.625\,T_{d}}{14.243.61}} \tag{14}\]  
where \(SVP\) represents the saturated vapor pressure (kPa), and \(RH\) represents the relative humidity (%).  
The global-scale remote sensing datasets used as inputs in this study included FAPAR, evapotranspiration (ET) and land cover (LC).  
Figure 1: The cropland flux tower sites on a map of Köppen climate zones used in the present study. Codes of climate zones in the color legend are adopted from [56] and given in Table 1 of Appendix A. Numbers with star symbol denote the cropland flux tower sites, ground data from which were used in this study.  
Global annual land cover maps at 300 m spatial resolution from the European Space Agency Climate Change Initiative Land Cover (ESA CCI-LC) project [62] were used and aggregated to 1 km spatial resolution ([[http://maps.elie.ucl.ac.be/CCI/viewer/download.php](http://maps.elie.ucl.ac.be/CCI/viewer/download.php)]([http://maps.elie.ucl.ac.be/CCI/viewer/download.php](http://maps.elie.ucl.ac.be/CCI/viewer/download.php)), accessed on 23 January 2022). A 1 km pixel was classified as cropland if 50% of the 300 m pixels in the 1 km pixel were cropland.  
FAPAR quantifies the fraction of the solar radiation absorbed by vegetation canopy during photosynthesis (Table 3). The 1 km resolution and 10-day global FAPAR product provided by the Copernicus Global Land Service System (CGLS) [63] was used in this study ([[https://land.copernicus.eu/global/products/fapar](https://land.copernicus.eu/global/products/fapar)]([https://land.copernicus.eu/global/products/fapar](https://land.copernicus.eu/global/products/fapar)), accessed on 23 January 2022).  
The global ET data with 1 km spatial resolution and 1-day temporal step were produced (in our parallel study) by the ETMonitor model by using multiple remote sensing data and validated using ground flux measurements at flux tower sites. The detailed description of the ETMonitor model and its applications in regional scales can be found in [64, 65, 32, 66, 33, 67], and a brief introduction to ETMonitor is given in Appendix B. Pixel-wise net radiation and surface soil heat flux were estimated in the same way as used in ETMonitor.