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)

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%.