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Large differences in projected future annual precipitation increases in North America exists across 27 CMIP6 models under four emission scenarios. These differences partly arise from weak representations of land-atmosphere interactions. Here we demonstrate an emergent constraint relationship between annual growth rates of future precipitation and growth rates of historical temperature. The original CMIP6 projections show 0.49% (SSP126), 0.98% (SSP245), 1.45% (SSP370) and 1.92% (SSP585) increases in precipitation per decade. Combining observed warming trends, the constrained results show that the best estimates of future precipitation increases are more likely to reach 0.40–0.48%, 0.83–0.93%, 1.29–1.45% and 1.70–1.87% respectively, implying an overestimated future precipitation increases across North America. The constrained results also are narrow the corresponding uncertainties (standard deviations) by 13.8–31.1%. The overestimated precipitation growth rates also reveal an overvalued annual growth rates in temperature (6.0–13.2% or 0.12–0.37°C) and in total evaporation (4.8–14.5%) by the original models' predictions. These findings highlight the important role of temperature for accurate climate predictions, which is important as temperature from current climate models' simulations often still have systematic errors. [ABSTRACT FROM AUTHOR]