## 4 Discussion  
This study was based on an analysis of the severity of compound dry and hot events, changes in vegetation cover, and the relationship between them in Inner Mongolia from 1982 to 2020. The Theil-Sen median trend analysis and Mann-Kendall test were used to investigate the heterogeneity of the spatial and temporal variability of the two, and the  
Figure 11: Analysis of the relative importance of SPI, STI, and SDHI to NDVI in Inner Mongolia. Figure 10: Box plot of the correlation between different vegetation types and SPI, STI, and SDHI in Inner Mongolia. degree of independent influence of SDHI on NDVI was quantified using partial correlation analysis based on excluding the influence of SPI and STI on NDVI, which provides a reliable scientific basis for future disaster prevention and mitigation and maintenance of sustainable development of ecosystems at the regional scale. In studying the partial correlation between SDHI and NDVI, it was found that 83.77% of Inner Mongolia had a positive correlation between SDHI and NDVI, and the central region was more significantly affected by the compound dry and hot events than other regions. When using multiple linear regression to quantify the influence of climatic factors on vegetation change in Inner Mongolia, it was concluded that grasslands in central Inner Mongolia contributed more significantly to vegetation when subjected to a combination of climatic factors [13; 37]. When studying the driving factors of vegetation cover change in central Inner Mongolia, it was found that climatic factors have a greater impact on vegetation cover in central Inner Mongolia than non-climatic factors, and when two factors interact, their explanatory power will be stronger [37; 50]. To study the changing mechanism of the severity of compound dry and hot events, the trends of SPI and STI values representing drought and high-temperature conditions in Inner Mongolia over the past 39 years were analyzed (Figure 12). The SPI shows a non-significant decreasing trend, while the STI value has a very significant increasing trend at 0.04/year. Combined with the changing trend of the SDHI value, we can obtain the change in SDHI in Inner Mongolia, which is mainly dominated by the increase in high-temperature conditions. Compared with the drought events, in which the aggravating trend is still more controversial, existing research shows that the increase in the frequency of extreme high-temperature events is more significant in the context of global warming, which supports the view of this study [30; 51]. For the remaining 16.23% of the areas where SDHI and NDVI were negatively correlated, especially in the northeastern region, such as the forest vegetation distribution area, the degree of drought was weaker than that of other grassland vegetation areas. Elevation also has a promoting effect on vegetation in this area [52; 53]. Among existing VIs, the Normalized Difference Vegetation Index (NDVI) is the most often used and is an operational, global-based vegetation index, NDVI is a good proxy for vegetation density parameters such as leaf area index (LAI), vegetation cover (FVC), and absorbed photosynthetically active radiation (fAPAR) [54; 55]. However, NDVI has two major limitations in characterizing biomass and productivity. First, the relationship  
Figure 12: Temporal trends of SPI and STI in Inner Mongolia from 1982 to 2020.  
between NDVI and green biomass is non-linear and can be saturated in areas with high vegetation cover. The second limitation is that NDVI mainly reflects vegetation greenness rather than photosynthesis itself. However, total primary productivity (GPP) can decline without any reduction in LAI or chlorophyll. Combining the shortcomings of NDVI, a new vegetation index, kNDVI, was proposed by applying the theory of nuclear methods to NDVI, using machine learning. The kNDVI correlated with GPP similarly or better than other indices globally.