 The study developed a multivariate approach for analyzing vegetation responses to dry, hot, and compound dry-hot conditions from a probabilistic perspective using precipitation, temperature, and the Normalized Difference Vegetation Index, NDVI, for the period from 1982 to 2015. The results showed that vegetation was affected by compound dry and hot conditions in arid and semi-arid regions with a higher probability of decline compared to individual dry and hot conditions. Temperate grassland was found to be particularly vulnerable to compound dry and hot conditions. The study highlights the necessity of considering compound dry and hot extremes when assessing vegetation responses to climate extremes under global warming. This article was authored by Ying Hao, Sun Chaohao, Yan Shoufu, and others.