Pathways from nucleation to raindrops
Cloud droplets grow via vapor condensation and collisional aggregation. Upon reaching approximately $\approx 100~{\rm \mu m}$, their inertia allows them to capture smaller droplets during descent, initiating rain. Here, we show that raindrop formation is not primarily governed by gravity or thermal diffusion, but by a critical range of drop sizes ($3-30~{\rm \mu m}$) where collisions are largely ineffective and controlled by van der Waals and electrostatic interactions. We identify four pathways to rain. The coalescence pathway, which is slow, involves the broadening of the drop size distribution across the $3-30~{\rm \mu m}$ low-efficiency gap through collisions, until enough large individual droplets achieving efficient collisions have formed. The mixing pathway, which is faster, requires mixing at the cloud top with drop-free, cold, humid air to create locally supersaturated conditions that grow droplets above the low-efficiency gap. The electrostatic pathway bypasses the gap through a static vertical field creating attractive interactions between droplets. The turbulence pathway relies on air turbulence to bring the droplets together at an increased rate, but we show that this pathway is unlikely. For all dynamical mechanisms, we demonstrate that the initiation time for rainfall occurs at the crossover between the broadening of the drop size distribution and the emergence of individual droplets large enough to trigger the onset of the rainfall cascade.