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This paper aims to investigate and quantify the turbulence effect on droplet collision efficiency and explore the broadening mechanism of the droplet size distribution(DSD) in cumulus clouds. The sophisticated model employed in this study individually traces droplet motions affected by gravity, droplet disturbance flows, and turbulence in a Lagrangianframe. Direct numerical simulation(DNS) techniques are implemented to resolve the small-scale turbulence. Collision statistics for cloud droplets of radii between 5 and 25 mu m at five different turbulence dissipation rates(20-500 cm(2) s(-3)) are computed and compared with pure-gravity cases. The results show that the turbulence enhancement of collision efficiency highly depends on the r ratio(defined as the radius ratio of collected and collector droplets r/R) but is less sensitive to the size of the collector droplet investigated in this study. Particularly, the enhancement is strongest among comparable-sized collisions, indicating that turbulence can significantly broaden the narrow DSD resulting from condensational growth. Finally, DNS experiments of droplet growth by collision-coalescence in turbulence are performed for the first time in the literature to further illustrate this hypothesis and to monitor the appearance of drizzle in the early rain-formation stage. By comparing the resulting DSDs at different turbulence intensities, it is found that broadening is most pronounced when turbulence is strongest and similar-sized collisions account for 21%-24% of total collisions in turbulent cases compared with only 9% in the gravitational case.