## 2 Materials and Methods
### Data Sources  
Vegetation index production, meteorological data and the grassland conservation and protection policy in IMAR are basic data sets in this research (Table 1). NDVI and NPP were obtained from moderate-resolution imaging spectroradiometer (MODIS). IMAR is covered by seven tiles of global MODIS data. We collected 1392 tiles of MOD13A1 NDVI data in a temporal resolution of 16 days and spatial resolution of 500 m, and 63 annual MOD17A3 HGF NPP data products with 500 m resolution [30] covering the period from 2011 to 2019. MOD13A1 NDVI data provides VIs, including NDVI and EVI. The algorithm for this product chooses the best available pixel value from the 16-day image composites. The criteria are low cloud cover, a low view angle, and the highest NDVI value. Annual NPP (MOD17A3 HGF NPP) is derived from Net Photosynthesis (PSN), which is the difference of the Gross Primary Productivity (GPP) and the Maintenance Respiration (MR).  
We conducted data preprocessing including data format transformation, reprojection, mosaicking and resampling with the MODIS Reprojection Tool (MRT). To further reduce the influence of clouds, atmosphere and solar altitude angle, we transferred the 16-day NDVI composites to yearly composites using Maximum Value Compositions (MVC), extracted by the Inner Mongolia administrative boundary and thus obtained yearly NDVI products of IMAR from 2011 to 2019.  
The Climate Prediction Center (CPC) Global Temperature and Precipitation meteorological dataset from 2011 to 2019 (Table 1), included global daily precipitation and daily maximum and minimum temperatures in a 0.50-degree spatial resolution. We transformed the NetCDF (network Common Data Format) daily value data from 2011 to 2019 into raster sets through raster calculation, projection and resampling. The resulting annual average precipitation and temperature products in a resolution of 500 m were finally used in conjunction with the processed NPP and NDVI data.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Data Indicator** & **Spatial Resolution** & **Temporal Resolution** & **Sources** & **Objective Output** \\ \hline NDVI & 500 m & 16-days & & FVC \\ \hline NPP & 500 m & 1 year & & NPP, HNPP, PNPP \\ \hline Annual mean temperature & 0.5 degree & 1 day & CPC Global Temperature and Precipitation & PNPP \\ \hline Annual mean precipitation & & & dataset provided by the NOAA/OAR/ESRL PSL, & \\ \hline Grassland management & 0.5 degree & 1 day & Boulder, Colorado, USA ([[https://psl.noaa.gov/](https://psl.noaa.gov/)]([https://psl.noaa.gov/](https://psl.noaa.gov/))) & PNPP \\ \hline \hline \end{tabular}  
* Note: NDVI: Normalized Difference Vegetation Index; NPP: Net Primary Productivity; FVC: Fractional Vegetation Cover; HNPP: Human-induced NPP; PNPP: Potential NPP; SISGC: the Subsidy and Incentive System for Grassland Conservation; LP DAAC: the Land Processing Distributed Active Archive Center; CPC: Climate Prediction Center; NOAA: the National Oceanic and Atmospheric Administration; OAR: Oceanic and Atmospheric Research; ESRL: Earth System Research Laboratories; PSL: Physical Sciences Laboratory.  
\end{table}
Table 1: Data sources and brief information.