Atmospheric Chemistry and Physics Discussions www.atmos-chem-phys-discuss.net 1680-7367 1680-7375 9 2 2009 10.5194/acpd-9-9537-2009 http://www.atmos-chem-phys-discuss.net/9/9537/2009/ http://www.atmos-chem-phys-discuss.net/9/9537/2009/acpd-9-9537-2009.html http://www.atmos-chem-phys-discuss.net/9/9537/2009/acpd-9-9537-2009.pdf 9537 9550 2009-04-15 Comment on Kokkola et al. (2008) – Comparisons with analytical solutions from Khvorostyanov and Curry (2007) on the critical droplet radii and supersaturations of CCN with insoluble fractions V. I. Khvorostyanov J. A. Curry curryja@eas.gatech.edu Central Aerological Observatory, Dolgoprudny, Moscow Region, Russia School of Earth and Atmospheric Sciences, Georgia Institute of Technology, Atlanta, Georgia Analytical solutions for the critical radii rcr and supersaturations scr of the cloud condensation nuclei with insoluble fractions were derived by Khvorostyanov and Curry (2007, hereafter KC07). Similar solutions were found later by Kokkola et al. (2008, hereafter Kok08); however, Kok08 used the approximation of an ideal 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. Various possible reasons of this are analyzed. It is shown that the major discrepancy was caused by a simple mistake in Kok08 in the equation for the critical supersaturation: erroneous ''plus'' sign between the Kelvin and Raoult terms instead of correct ''minus'' sign. If this mistake is corrected, the equations from Kok08 mostly repeat the equations from KC07, except that Kok08 use the 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 possible errors of an ideal diluted solution approximation. If the Kok08 scheme is corrected and applied to a nonideal solution, then the difference with KC07 does not exceed 0.4–1%. Charlson,~R J., Seinfeld,~J H., Nenes,~A., Kulmala,~M., Laaksonen,~A., and Facchini,~M C.: Reshaping the theory of cloud formation, Science, 292, 2025–2026, 2001. Foster,~P., Ramaswamy,~V., Artaxo,~P., Berntsen,~T., Betts,~R., Fahey,~D W., Haywood,~J., Lean,~J., Lowe,~D C., Myhre,~G., Nganga,~J., Prinn,~R., Raga,~G., Schulz,~M., and Van Dortland,~R.: Changes in Atmospheric Constituents and in Radiative Forcing, In: Climate Change: The Physical Science Basis, Chap. 2, Contribution of WG-I to the Fourth Assessment Report of the Intergovernmental Panel on Climate Change, Cambridge University Press, 129–234, 2007. Hänel,~G.: The properties of atmospheric aerosol particles as functions of the relative humidity at thermodynamic equilibrium with the surrounding moist air, Adv. Geophys., 19, 73–188, 1976. Khvorostyanov,~V I. and Curry,~J A.: Refinements to the Köhler's theory of aerosol equilibrium radii, size spectra, and droplet activation: Effects of humidity and insoluble fraction. J. Geophys. Res., 112(D5), D05206, doi:10.1029/2006JD007672, 2007. Köhler,~H.: The nucleus in the growth of hygroscopic droplets, Trans. Farad. Soc., 32, 1152–1161, 1936. Kokkola,~H., Vesterinen,~M., Anttila,~T., Laaksonen,~A., and Lehtinen,~K E J.: Technical note: Analytical formulae for the critical supersaturations and droplet diameters of CCN containing insoluble material. Atmos. Chem. Phys., 8, 1985–1988, 2008. Pruppacher,~H R. and Klett,~J D.: Microphysics of Clouds and Precipitation, 2nd ed., Kluwer Academic Publishers, Boston, MA, p 954, 1997. Seinfeld,~J H. and Pandis,~S N.: Atmospheric Chemistry and Physics, Wiley, New York, p 1326, 1998.