As the strongest subseasonal atmospheric variability during boreal winter, three remarkable sudden stratospheric major warming (SSW) events in the 2000s are investigated in terms of the Brewer-Dobson circulation (BDC) response. Our study shows that the changes of cross-isentropic velocity during the SSWs are not only confined to the polar region, but also extend to the whole Northern Hemisphere: enhanced descent in the polar region, as well as enhanced ascent in the tropics. When the acceleration of the deep branch of the BDC descends to the middle stratosphere, its strength rapidly decreases over a period of one to two weeks. The acceleration of the deep branch of the BDC is driven by the enhanced planetary wave activity in the mid-to-high-latitude stratosphere. Different from the rapid response of the deep branch of the BDC, tropical upwelling in the lower stratosphere accelerates up to 20%-40% compared with the climatology, 20-30 days after the onset of the SSWs, and the acceleration lasts for one to three months. The enhancement of tropical upwelling is associated with the large-scale wave-breaking in the subtropics interacting with the midlatitude and tropical Quasi-Biennial Oscillation-related mean flow.