## 3 Results
### Correlation Analysis between SDHI and NDVI  
The correlation between SPI and NDVI is shown (Figure 9a); 52.21% of Inner Mongolia has a positive correlation between SPI and NDVI values, which are distributed in each league city. Although studies have shown that the rapid increase in temperature in northern China in recent decades has had a negative impact on vegetation growth to some extent, the partial correlation between STI and NDVI in the present study (Figure 9b) shows that while the increase in temperature suppressed NDVI growth, it also promoted vegetation growth in the northeast and southwest Inner Mongolia. When the temperature and precipitation increase simultaneously within a certain level, the optimum temperature for photosynthesis of vegetation increases as the temperature of the growing environment increases, indicating that vegetation growth becomes more adaptive to changes in environmental temperature. Moreover, the higher the precipitation, the stronger the adaptive capacity of vegetation. Further research found that in the cold regions of the Northern Hemisphere, the optimal temperature for vegetation photosynthesis is lower than the temperature during the growing season, indicating that there is still room for future warming to promote vegetation growth to a certain extent [45]. In contrast, when a high-temperature event and a drought event occur simultaneously, a compound dry and hot event occurs, intensifying the damage to vegetation growth. In particular, since the 1980s, due to the gradual weakening of the humidity compensation effect after extreme climatic events, a large-scale continuous decline in tree growth in inland semi-arid regions of Asia has occurred. The warming trend  
Figure 8: Spatial distribution of NDVI trends in Inner Mongolia from 1982 to 2020. (**a**) NDVI trend value, (**b**) multi-year average NDVI trend levels. is aggravating, and the occurrence and severity of compound events may further reduce carbon sink intensity in inland semi-arid Asia in the future [46]. Figure 9: Spatial distribution of partial correlations between SPI, STI, SDHI, and NDVI in Inner Mongolia from 1982 to 2020. (**a**) SPI correlation with NDVI, (**b**) STI correlation with NDVI, (**c**) SDHI correlation with NDVI. Therefore, we analyzed the SDHI, an indicator representing the severity of compound events in Inner Mongolia, for partial correlations with NDVI; the spatial distribution is shown in (Figure 9c). Overall, the SDHI and NDVI were positively correlated in Inner Mongolia, with the largest area of non-significant positive correlation between the two, at approximately 41.91%. The mean value of the partial correlation coefficient between the SDHI and NDVI was 0.68, showing a spatial response that was strong in the center and gradually decreased towards the east and west. The SDHI was positively correlated with NDVI in 83.77% of the study area, with significant positive correlations mainly in the central areas of the Hohhot, Ulanqab, and Xilingol leagues, where typical steppe is mainly distributed, indicating that vegetation in typical steppe in Inner Mongolia is more sensitive to changes in the occurrence and severity of compound dry and hot events. In addition, in approximately 15.87% of Inner Mongolia, SDHI is negatively correlated with NDVI, of which 15.83% is non-significantly negatively correlated, mostly in the northwestern part of Hulunbeier, the northwestern part of Xing'an League, the Wuliang Suhai watershed of Bayannur City, and the central part of Alexa League, indicating that NDVI changes in these areas are not significantly influenced by compound dry heat events. Hulunbuir City shows a non-significant negative correlation with the distribution of forest reserves such as Moldauga and Iksama, where vegetation changes are more influenced by national policies and other anthropogenic influences, including the Wuliangsuhai in Bayannur, since the establishment of the Wuliang Suhai Wetland Waterforwl Nature Reserve and Ecological Protection and Restoration Project began in 1998.