The effect of diffusion kinetics on the supersaturation in clouds

To describe the nucleation–growth interaction at and above the cloud base, a cloud model has been formulated including the haze process below the cloud base and before nucleation of cloud droplets, and a proper diffusion-kinetic droplet growth equation. Analytical equations for the maximum supersaturation by Twomey [Twomey, S., 1959. The nuclei of natural cloud formation: Part II. The supersaturation in natural clouds and the variation of cloud droplet concentration. Geofis. Pura Appl. 43, 243–249; Twomey, S., 1977. Atmospheric Aerosols. Elsevier, Amsterdam, 302 pp.] and by Fukuta and Xu [Fukuta, N., Xu, N., 1996. Nucleation–droplet growth interactions and microphysical property development in convective clouds. Atmos. Res. 41, 1–22], both employing the Maxwellian growth theory, are compared with the model outputs, and the model outputs are found to be the smallest. To preserve the clarity and usefulness of the analytical equations, a correction factor to the latter is obtained in comparison with the model results for different condensation coefficient (β) and cloud condensation nucleus activity spectra of typical continental and maritime air masses. Effect of β is found to be larger for small β and in continental clouds.