Cloud condensation nucleus

An aerosol particle able to activate into a growing cloud droplet at the supersaturation attained by a cloud parcel. Activity depends on particle dry size, hygroscopicity and interfacial properties. The number active at a specified supersaturation differs from total aerosol number.

An aerosol particle becomes a freely growing cloud droplet after crossing its Köhler theory growth barrier under the parcel's atmospheric supersaturation history. Counting particles whose critical supersaturation is below a specified peak gives an equilibrium-threshold estimate; calculating that peak requires cooling, water vapor depletion and condensational-growth kinetics. Neither total aerosol number nor dry size alone determines activation.

The equilibrium water-vapor saturation ratio above a solution droplet combines a curvature effect, which raises vapor pressure, with dissolved-solute reduction of water activity. Its maximum defines a critical supersaturation for activation. In a dilute hygroscopicity approximation using droplet diameter $D$ and dry diameter $D_d$, $s(D)\simeq A_K/D-\kappa D_d^3/D^3$, where $A_K=4\sigma M_w/(RT{\rho }_w)$. Then $s_c\simeq \sqrt{4A_K^3/(27\kappa D_d^3)}$. These approximate forms assume the stated diameter convention and dilute solution; composition and surface tension must be consistent.^[ref]

The equilibrium saturation ratio over a chemical solution droplet as a function of wet radius for fixed solute content. In the dilute radius approximation $S_{\mathrm{eq}}\simeq 1+A/r-B/r^3$, its maximum occurs at $r_c=\sqrt{3B/A}$. The corresponding critical supersaturation is $2A/(3r_c)$. Diameter and radius coefficients differ and must not be mixed.

The first-order combination of the Kelvin equation and Raoult's law for a chemical solution droplet with $A/r\ll 1$ and $B/r^3\ll 1$. Its maximum is at $r_c=\sqrt{3B/A}$, with $S_c-1=2A/(3r_c)$. For ambient saturation ratio $1<S<S_c$, the smaller equilibrium radius is stable and the larger is unstable: the sign of condensational growth is the sign of $S-S_{\mathrm{eq}}(r)$. In particular, exceeding $r_c$ alone need not activate continued growth at subcritical atmospheric supersaturation.

Writing the same curve using diameter $D=2r$ changes its coefficients: $A_D=2A_r$ and $B_D=8B_r$ in $A_D/D-B_D/D^3$. The critical saturation ratio is unchanged, while $D_c=2r_c$. Mixing a diameter curvature coefficient with a radius solute term gives a spurious activation threshold.

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.