A convex water surface has higher saturation vapour pressure than a flat one. Equality of chemical potentials with the Laplace pressure gives the Kelvin equationSmall pure droplets therefore need large supersaturation; many subcritical embryos evaporate, making homogeneous droplet formation inefficient under ordinary cloud conditions. Cloud condensation nuclei provide a surface and, when soluble, lower water activity. Köhler theory combines the curvature increase with this solute decrease, giving a critical supersaturation and size for activation.
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.
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.
Droplets remain supercooled because creating an ice embryo costs interfacial free energy: freezing has a nucleation barrier even below the equilibrium melting point. Small droplets also have a low probability of containing an effective ice-nucleating inclusion.
Three heterogeneous routes are immersion freezing around a particle already inside the droplet, contact freezing following a collision with a suitable mineral particle, and deposition nucleation from ice-supersaturated vapour onto a suitable surface. At sufficiently low temperature, homogeneous ice nucleation occurs without a foreign surface. Its onset depends on volume and observation time rather than being a universal exact temperature. No biological ice-nucleating agents are needed for these mechanisms.
Direct effect: nonabsorbing aerosol scatters sunlight, usually increasing reflected shortwave flux over dark surfaces. Absorbing aerosol also heats its atmospheric layer while reducing surface sunlight; the top-of-atmosphere sign depends on its altitude, optical properties and underlying albedo.
Cloud albedo effect: soluble, hygroscopic aerosol readily takes up water and can activate as cloud condensation nuclei. At fixed liquid-water path, more smaller droplets increase optical depth and cloud reflectivity: the Twomey effect. Suppressed collision-coalescence can delay rain and change cloud amount or lifetime, though dynamical adjustments prevent a universal sign.
Semi-direct effect: absorption can alter stability and evaporate clouds, or change entrainment and cloud cover. Insoluble dust may be a poor soluble-droplet nucleus but still scatters/absorbs radiation or nucleates ice; coatings can alter its activation. Solubility, absorptivity and ice-nucleating ability are distinct properties, not mutually equivalent categories.[ref]
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