Solution (source code)

= Solution

\b[Warm-rain pathway:] condensation first grows activated droplets, but its relative size growth slows. A sufficiently broad size spectrum creates different fall speeds; large drops collect smaller ones by <collision-coalescence>. Collection efficiency, turbulence, liquid-water supply and residence time control the bottleneck. Rain reaching the ground also requires survival against subcloud evaporation.

\b[Ice pathway:] below freezing, saturation vapour pressure over ice is lower than over supercooled liquid. In mixed-phase air, ice can grow by deposition while droplets evaporate: the <Wegener-Bergeron-Findeisen process>. Ice also collects droplets by <riming> and combines by aggregation. Adequate ice nuclei, sustained supersaturation and residence time are critical; particles must become heavy enough to fall, with snow sometimes melting to rain. Condensation or deposition alone is not generally sufficient for rapid precipitation.