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GEOPHYSICAL RESEARCH LETTERS, VOL. 33, L02810, doi:10.1029/2005GL024052, 2006

Analytical expression for the relative dispersion of the cloud droplet size distribution

Yangang Liu

Brookhaven National Laboratory, Upton, New York, USA


Peter H. Daum

Brookhaven National Laboratory, Upton, New York, USA


Seong Soo Yum

Department of Atmospheric Sciences, Yonsei University, Seoul, South Korea


Abstract

An analytical expression that relates the relative dispersion (ratio of standard deviation to mean radius) of the cloud droplet size distribution to CCN spectra and updraft velocity is derived from adiabatic growth theory of cloud droplets. Coupled with the Twomey expression for droplet concentration, the analytical expression is used to examine the relationship of relative dispersion to droplet concentration under different combinations of CCN spectra and updraft velocities. These analytical results compare favorably with the corresponding simulations of an adiabatic parcel model. The analytical expression theoretically demonstrates that an increase in aerosol loading (CCN concentration) leads to concurrent increases in the droplet concentration and relative dispersion whereas a larger updraft velocity leads to a higher droplet concentration but a smaller relative dispersion.

Received 12 July 2005; accepted 14 December 2005; published 26 January 2006.

Index Terms: 0320 Atmospheric Composition and Structure: Cloud physics and chemistry; 1640 Global Change: Remote sensing (1855); 1704 History of Geophysics: Atmospheric sciences.

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Citation: Liu, Y., P. H. Daum, and S. S. Yum (2006), Analytical expression for the relative dispersion of the cloud droplet size distribution, Geophys. Res. Lett., 33, L02810, doi:10.1029/2005GL024052.