Critical supersaturation ($s_c$)

The maximum equilibrium supersaturation along a solution-droplet growth curve. Above this threshold, an aerosol particle can grow into an activated cloud droplet under the conditions of the parcel. In Köhler theory, larger dry diameter or greater hygroscopicity generally lowers the threshold; aerosol number alone does not specify it.

In the dilute radius form $\ln S_{\mathrm{eq}}=A/r-B/r^3$, the curvature coefficient A has length units and B has volume units. Setting its derivative to zero gives the displayed maximum. Ambient supersaturation above it permits activation into a growing cloud droplet. Below it, a sufficiently small wet equilibrium can be stable, while the larger-radius intersection is unstable. The approximation should not be extrapolated into the dry core.