Extending Twomey’s Analytical Estimate of Nucleated Cloud Droplet Concentrations from CCN Spectra

Abstract

A fundamental but approximate formula has been established by Twomey in order to compute the nucleated cloud droplet number concentration as a function of the vertical velocity and the CCN (cloud condensation nuclei) characteristics expressed by the C and k parameters. The derivation of such a relationship employs the widespread power-law dependence N_CCN = of the total activable CCN number N_CCN at a given supersaturation of water vapor over cloud droplets s_υ,w. In this paper the authors follow Twomey’s theoretical approach but using a more realistic four-parameter CCN activation spectrum as shaped by the physicochemical properties of the accumulation mode in a natural aerosol population. The analytical scheme is shown to improve the estimate of cloud droplet number concentration because it accounts for the limited availability of small-sized CN (condensation nuclei) with increasing supersaturation. A first validation and calibration of the new generic CCN activation spectrum is made by comparison with activation spectra, either produced by growing realistic lognormal distributions of CN or measured by a CCN spectrometer over the mid-Atlantic Ocean.