To examine the spatiotemporal evolution of global drought under the background of climate change, this study developed a composite seasonal drought index (CSDI) by integrating precipitation minus potential evapotranspiration (PPET), soil moisture (SM), and runoff using a three dimensional Copula function, and analyzed the spatiotemporal heterogeneity of global drought from 1982 to 2021. Results indicated that the correlation coefficient between CSDI and the standardized precipitation evapotranspiration index (SPEI) reached 0.914. In terms of historical drought validation, compared to SPEI, CSDI identified a larger drought coverage area in the early stage and exhibited higher spatiotemporal consistency with negative anomalies of PPET and SM. Furthermore, CSDI completely captured the early, middle, and late evolutionary stages of typical historical droughts, such as the Southwest China drought from 2009 to 2010, the drought in Horn of Africa from 2010 to 2011, and the Central Europe drought in 1992. Regarding drought characteristics, global drought exhibited strong spatial heterogeneity from 1982 to 2021. Arid and semiarid zones showed a coupling feature characterized by high frequency, long duration, and high intensity, whereas humid regions generally faced lower risk, though some mid to high latitude humid zones in the Northern Hemisphere experienced elevated flash frequency and intensity. Temporally, in typical arid regions, the average drought duration shortened, while humid regions displayed more persistent drought processes with increasing frequency. Overall, the global trend of drought shows characteristics of frequent occurrence, rapid onset, and extreme severity.