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To mitigate the projected global warming in the 21st century, it is well recognized that society needs to cut CO2 emission and other short-lived warming agents aggressively. However, to stabilize the climate at a warming level closer to the present day, such as the "well below 2 °C" aspiration in the Paris agreement, a net-zero carbon emission by 2050 is still insufficient. The recent IPCC special report calls for a massive scheme to extract CO2 directly from the atmosphere, in addition to the decarbonization, to reach negative net emission at the mid-century mark. Another ambitious proposal is the solar radiation-based geoengineering schemes, including injecting sulfur gas into the stratosphere. Despite being in the public debate for years, these two leading geoengineering schemes have not been carefully examined under a consistent numerical modeling framework. Here we present a comprehensive analysis of climate impacts of these two geoengineering approaches using two recently available large-ensemble (> 10 members) model experiments conducted by a family of state-of-art Earth system models. The CO2 -based mitigation simulation is designed to include both emissions cut and carbon capture. The solar radiation-based mitigation simulation is designed to inject the sulfur gas strategically at specified altitudes and latitudes and run a feedback control algorithm, to avoid common problems previously identified such as the over-cooling of the Tropics and large-scale precipitation shifts. Our analysis focuses on the projected aridity conditions over the Americas in the 21st century, in detailed terms of the mitigation potential, the temporal evolution, the spatial distribution (within North and South America), the relative efficiency, and the physical mechanisms. We show that sulfur injection, in contrast to previous notions of leading to excessive terrestrial drying (in terms of precipitation reduction) while offsetting the global mean greenhouse gas (GHG) warming, will instead mitigate the projected drying tendency under RCP8.5. The surface energy balance change induced by Sulfur injection, in addition to the well-known response in temperature and precipitation, plays a crucial role in determining the overall terrestrial hydroclimate response. However, when normalized by the same amount of avoided global warming, in these simulations, sulfur injection is less effective in limiting the worsening trend of regional land aridity in the Americas, when compared with carbon capture. Temporally, the climate benefit of Sulfur injection will emerge more quickly, even when both schemes are hypothetically started in the same year of 2020. Spatially, both schemes are effective in curbing the drying trend over North America. However, for South America, the Sulfur Injection scheme is particularly more effective for the sub-Amazon region (South Brazil), while the Carbon Capture scheme is more effective for the Amazon region. We conclude that despite the apparent limitations (such as inability to address ocean acidification) and potential side effects (such as changes to the ozone layer), innovative means of Sulfur Injection should continue to be explored as a potential low-cost option in the climate solution toolbox, complementing other mitigation approaches such as emissions cut and carbon capture (Cao et al., 2017). Our results demonstrate the urgent need for multi-model comparison studies and detailed regional assessment in other parts of the world. [ABSTRACT FROM AUTHOR]