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Nucleation in the PBL

For grid cells below the PBL top or 100 m (whichever is higher), the nucleation rate is estimated from the sulfric acid gas concentration using the following parameterization from Wang and Penner (2009) and Sihto et al. (2006)

\[ \begin{equation} J^* = 10^{-6}~c_{H_2SO_4} \, \end{equation} \]

or

\[ J^* = 10^{-12}~c^2_{H_2SO_4} \]

If the PBL nucleation rate is lower than the binary/ternary nucleation rates, the binary/ternary nucleation rates will be adopted as the nucleation rate. Otherwise, the PBL nucleation rate will be used.

The newly formed clusters are assumed to have diameters of 1 nm and consist of only H\(_2\)SO\(_4\). Therefore,

\[ \begin{align} r^* &= 0.5~nm \,, \\ n_{H_2SO_4} &= \frac{6.023 \times 10^{23} \pi (1~nm)^3 \rho_{H_2SO_4}}{6 M_{w,H_2SO_4}} \,, \\ n_{tot} &= n_{H_2SO_4} \,. \end{align} \]

This parameterization is used in the PBL in lieu of the physics-based scheme if the empirical \(J^*\) is higher.