## 2 Materials and Methods
### Methods  
(1) Vegetation index acquisition  
According to the characteristics of the study area and referring to relevant research, four indices--NDVI, EVI, MSAVI, and PsnNet--were selected to estimate the grassland production. NDVI, EVI, and PsnNet were obtained from NASA. MSAVI was calculated by research team based on the red and near-infrared bands according to the formula. The formula for each index is as follows:  
\[\text{EVI}=2.5\times\frac{\rho_{\text{NIR}}\text{-}\rho_{\text{RED}}}{\rho_{ \text{NIR}}+6.0\rho_{\text{RED}}-7.5\rho_{\text{BLUE}}+1}; \tag{1}\]  
\[\text{NDVI}=\frac{\rho_{\text{NIR}}\text{-}\rho_{\text{RED}}}{\rho_{\text{NIR }}+\rho_{\text{RED}}}; \tag{2}\]  
\[\text{MSAVI}=\frac{2\rho_{\text{NIR}}+1-\sqrt{\left(2\rho_{\text{NIR}}+1 \right)^{2}-8(\rho_{\text{NIR}}-\rho_{\text{RED}})}}{2}; \tag{3}\]  
\[\text{PsnNet}\ =\text{GPP}-\text{Leaf\_MR}-\text{Froot\_MR}; \tag{4}\]  
where \(\rho_{\text{NIR}}\) is the near-infrared radiation reflectance, \(\rho_{\text{RED}}\) is the red band reflectance, \(\rho_{\text{BLUE}}\) is the blue band reflectance, GPP is the Gross Primary Productivity, Leaf_MR is the leaf autotrophic respiration consumption, and Froot_MR is the root autotrophic respiration consumption. (2) Model building and accuracy verification  
A correlation analysis was performed between grassland production and each vegetation index, as well as mean annual temperature, mean annual precipitation, and DEM data. On this basis, the factors with higher correlation with grassland production were selected for modeling. Ground-measured data was collected in 2013 and 2014. There are 29 samples for grassland production estimation, with 80% of the data used for modeling and 20% randomly selected for model validation. Based on the data of 22 meteorological stations in Mongolia, the mean annual temperature and precipitation data of the study area were calculated by the inverse distance weighted interpolation method. Remote sensing image data, meteorological data, and DEM data were overlay processed by ArcGIS software. We used Geographic Information System (GIS) methodology to extract the values of remote sensing data, mean annual temperature, and mean annual precipitation and DEM data for the year, corresponding to the grassland production data. We used SPSS 22.0 statistical software to carry out linear regression analysis, exponential regression analysis, and multiple linear regression analysis considering the influence of meteorological factors and constructed three types of grassland production estimation models. The accuracy of the estimation model was evaluated by the reserved sample data. The main evaluation indicators included the average relative error and the root mean square error. The calculation formula is as follows:  
\[\text{REE}=\frac{\sqrt{\frac{\sum\limits_{i=1}^{N}\left(Y_{i}-Y_{i^{\prime}} \right)^{2}}{\text{N}}}}{\text{Y}_{i}}\times 100\%; \tag{5}\]  
\[\text{RMSE}=\sqrt{\frac{\sum\limits_{i=1}^{N}\left(Y_{i}-Y_{i^{\prime}} \right)^{2}}{\text{N}}}\times 100\%; \tag{6}\]where REE is the average relative error, RMSE is the root mean square error, N is the number of samples, Yi is the measured grassland production (g/m\({}^{2}\)), Yi_t_ is the estimated grassland production (g/m\({}^{2}\)), and \(\widetilde{\text{Y}}_{\text{i}}\) is the average measured grassland production (g/m\({}^{2}\)). (3) Interannual variation in grassland production  
The one-dimensional linear regression analysis method was used to calculate the raster data of grassland production from 2006 to 2015, pixel by pixel. The change trend of grassland production in the study area in the ten years was obtained.