## 2 Materials and Methods
### Data Analysis  
To detect the trends in NPP over the period 2001 to 2022, the Mann-Kendall test and Sen's slope assessment were carried out on the time series data for the study period using the 'pyMannKendall' v1.4.3 package. We then obtained the grid-by-grid results of the trend and Sen's slopes of NPP, which we called \(\mathrm{NPP_{trend}}\) and \(\mathrm{NPP_{slope}}\), respectively. We counted the mean values of NPP from 2001 to 2022 and the mean values of \(\mathrm{NPP_{slope}}\) on elevation gradients at intervals of 100 m. Since vegetation response to elevation does not always follow the same pattern at different elevation gradients, and the number of grass raster cells varies greatly at different elevation gradients, we discussed the pattern of NPP and \(\mathrm{NPP_{slope}}\) with elevation by using the segmentation function and unequal weights linear regression.  
Climatic factors of temperature and precipitation were also analyzed using the Mann-Kendall test and Sen's Slope assessment to obtain the results of trends and Sen's slopes, referred to as \(\mathrm{Temp_{trend}}\), \(\mathrm{Temp_{slope}}\), \(\mathrm{Pre_{trend}}\) and \(\mathrm{Pre_{slope}}\), respectively. Then, the NPP, temperature, and precipitation data for the years 2001-2022 were detrended using the least squares regression algorithm from the 'SciPy' v1.13.1 package to highlight the fluctuating characteristics of the data themselves. We obtained the NPP data, temperature data, and precipitation data for each year after detrending, and named them \(\mathrm{NPP_{detrend}}\), \(\mathrm{Temp_{detrend}}\), and \(\mathrm{Pre_{detrend}}\), respectively.  
To explore the influence of temperature and precipitation on NPP, we performed a partial correlation analysis between \(\mathrm{NPP_{detrend}}\) and \(\mathrm{Temp_{detrend}}\) and \(\mathrm{Pre_{detrend}}\) using the 'pingouin' v0.5.4 package to account for the net correlation between NPP and each climatic factor. We further performed Ordinary Least Squares (OLS) analysis and Analysis of Variance (ANOVA) on these data using the'statsmodels' v0.14.2 package to test the interpretation of NPP by means of temperature and precipitation. We also established a linear regression between R\({}^{2}\) of the explanation by temperature and precipitation on NPP and elevation to demonstrate whether the influence of temperature and precipitation on NPP is affected by elevation.  
We further explored the extent to which NPP responds to changes in temperature and precipitation and its differences across the elevation gradient. The linear regression analyses in the'scikit-learn' v1.5.1 package were used to investigate the \(\mathrm{NPP_{slope}}\), \(\mathrm{Temp_{slope}}\), and \(\mathrm{Pre_{slope}}\) as a function of elevation based on the raster data. Finally, the effects of elevation and changes in temperature and precipitation on NPP sensitivity were investigated using a structural equation model (SEM). In this model, \(\mathrm{NPP_{slope}}\) was defined as NPP sensitivity, and \(\mathrm{Temp_{slope}}\) and \(\mathrm{Pre_{slope}}\) were defined as the changes in temperature and precipitation, respectively, as \(\mathrm{NPP_{slope}}\) on each raster was the result of the combined response to \(\mathrm{Temp_{slope}}\), \(\mathrm{Pre_{slope}}\), and elevation.  
The analysis by SEM was carried in Amos 26, and all the rest of the analyses were performed in Python 3.9.