Comment on "Comparisons with analytical solutions from Khvorostyanov and Curry (2007) on the critical droplet radii and supersaturations of CCN with insoluble fractions" by Kokkola et al. (2008) 1Central Aerological Observatory, Dolgoprudny, Moscow Region, Russia
2School of Earth and Atmospheric Sciences, Georgia Institute of Technology, Atlanta, Georgia, USA
Received: 01 April 2009 – Published in Atmos. Chem. Phys. Discuss.: 15 April 2009 Abstract. Analytical solutions for the critical radii and
supersaturations of the cloud condensation nuclei (CCN) with insoluble
fractions were derived by Khvorostyanov and Curry (2007, hereafter KC07).
These solutions generalize Köhler's solutions for an arbitrary soluble
fraction of CCN, and have two limiting cases: large soluble fraction
(Köhler's original solution); and a new "low soluble fraction" limit.
Similar solutions were found subsequently by Kokkola et al. (2008, hereafter
Kok08); however, Kok08 used the approximation of an ideal and dilute
solution, while KC07 used more accurate assumptions that account for
nonideality of solutions. Kok08 found a large discrepancy with KC07 in the
critical supersaturations. It is shown that the major discrepancy with KC07
found in Kok08 was caused by the simple mistake in Kok08, where comparison
was made not with the general solution from KC07, but with the Köhler's
solution or with some unknown quantity, not even with the "low soluble
fraction" limit. If general solutions from the two works are compared, the
equations from Kok08 mostly repeat the equations from KC07, except that
Kok08 use the ideal dilute solution approximation. If the mistake in Kok08
is corrected, then the differences in the critical radii and
supersaturations do not exceed 16–18%, which characterizes the errors of
the ideal dilute solution approximation. If the Kok08 scheme is modified
following KC07 to account for the non-ideality of solution, then the
difference with KC07 does not exceed 0.4–1%.
Revised: 06 July 2009 – Accepted: 01 August 2009 – Published: 20 August 2009
Citation: Khvorostyanov, V. I. and Curry, J. A.: Comment on "Comparisons with analytical solutions from Khvorostyanov and Curry (2007) on the critical droplet radii and supersaturations of CCN with insoluble fractions" by Kokkola et al. (2008), Atmos. Chem. Phys., 9, 6033-6039, doi:10.5194/acp-9-6033-2009, 2009.