Parameterization of cloud droplet formation for global and regional models: including adsorption activation from insoluble CCN

Dust and black carbon aerosol have long been known to exert potentially important and diverse impacts on cloud droplet formation. Most studies to date focus on the soluble fraction of these particles, and overlook interactions of the insoluble fraction with water vapor (even if known to be hydrophilic). To address this gap, we developed a new parameterization that considers cloud droplet formation within an ascending air parcel containing insoluble (but wettable) particles externally mixed with aerosol containing an appreciable soluble fraction. Activation of particles with a soluble fraction is described through well-established Kohler theory, while the activation of hydrophilic insoluble particles is treated by "adsorption-activation" theory. In the latter, water vapor is adsorbed onto insoluble particles, the activity of which is described by a multilayer Frenkel-Halsey-Hill (FHH) adsorption isotherm modified to account for particle curvature. We further develop FHH activation theory to i) find combinations of the adsorption parameters AFHH, BFHH which yield atmospherically-relevant behavior, and, ii) express activation properties (critical supersaturation) that follow a simple power law with respect to dry particle diameter. The new parameterization is tested by comparing the parameterized cloud droplet number concentration against predictions with a detailed numerical cloud model, considering a wide range of particle populations, cloud updraft conditions, water vapor condensation coefficient and FHH adsorption isotherm characteristics. The agreement between parameterization and parcel model is excellent, with an average error of 10% and R-2 similar to 0.98. A preliminary sensitivity study suggests that the sublinear response of droplet number to Kohler particle concentration is not as strong for FHH particles.