## 5 Conclusions  
Inner Mongolia was selected as the study area, and the SDHI index was constructed to describe the compound dry and hot events. Taking the SDHI and NDVI as the research objects, starting from the climate-vegetation system, with the help of multi-source data theory and methods, we studied the spatial and temporal evolution characteristics of composite dry heat events and NDVI on long-term scales from the climate-vegetation system with the help of multi-source data theory and methods and explored the mechanisms of composite events affecting vegetation changes. The results showed:  
1. In terms of spatial and temporal variation characteristics, in the past 39 years, Inner Mongolia was dominated by the occurrence of abnormal compound dry and hot events, and the overall compound dry and hot event severity increased. Among different grassland types, the SDHI value of typical grassland had the largest decrease rate of 0.03/year. The overall NDVI showed an increasing trend of 0.0013/year (\(p<0.05\)), and the areas with significant increasing trend of NDVI values were mainly distributed in forest, meadow steppe, and typical steppe.
2. The overall positive correlation between SDHI and NDVI was observed in Inner Mongolia, and the mean value of partial correlation coefficient between SDHI and NDVI was 0.68, showing a spatial response characteristic of strong in the middle and gradually weakening to the east and west sides. SPI was positively correlated with NDVI values in 52.21% of Inner Mongolia, and temperature conditions both promoted and inhibited vegetation growth in Inner Mongolia.
* 3. In terms of different grassland types, different vegetation types showed different characteristics dependent on complex climatic conditions, with woodlands being more sensitive to changes in temperature conditions than grasslands, and desert steppe and typical steppe being the most dominant to changes in the SDHI. The combined contribution results show that temperature conditions contribute more to the vegetation change in Inner Mongolia Autonomous Region than precipitation and compound dry and hot conditions.  
Y.K.: conceptualization, methodology, and writing--original draft. E.G.: conceptualization, supervision, and inspection. Y.W.: review and editing. Y.B.: investigation and validation. S.Z.: investigation and validation. R.A.: investigation. We thank the community of the R statistical software for providing a wealth of functionality. The methods described in this article are available as R package \"relaimpo\" under the GNU General Public License on [[https://prof.bht5-Sberlin.de/groemping/relaimpo/](https://prof.bht5-Sberlin.de/groemping/relaimpo/)]([https://prof.bht5-Sberlin.de/groemping/relaimpo/](https://prof.bht5-Sberlin.de/groemping/relaimpo/)) (accessed on 15 January 2022). All authors have read and agreed to the published version of the manuscript.  
The project was supported by the Program for Young Talents of Science and Technology in Universities of Inner Mongolia Autonomous Region (NJYT22028), the Natural Science Foundation of Inner Mongolia Autonomous Region of China (2021 BS0408, 2020 LH04003), The Key Program of National Natural Science Foundation of China (61631011), The International (Regional) Cooperation and Exchange Programs (41961144019), Research Program of science and technology at Universities of Inner Mongolia Autonomous Region (NJZY21542), The Science and Technology Planning Project in Inner Mongolia (2021 GG0050), and The National Natural Science Foundation of China (41807507).  
Not applicable.  
The authors would like to thank the anonymous reviewers for their crucial comments, which improved the quality of this paper.  
The authors declare no conflict of interest.