ACPD Atmospheric Chemistry and Physics Discussions ACPD 1680-7375 Copernicus GmbH Göttingen, Germany 10.5194/acpd-12-6745-2012 Parameterization of homogeneous ice nucleation for cloud and climate models based on classical nucleation theory Khvorostyanov V. I. 1 Curry J. A. 2 Central Aerological Observatory, Dolgoprudny, Moscow Region, Russia School of Earth and Atmospheric Sciences, Georgia Institute of Technology, Atlanta, Georgia, USA 05 03 2012 12 3 6745 6803 This is an open-access article ditributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. This article is available from http://www.atmos-chem-phys-discuss.net/12/6745/2012/acpd-12-6745-2012.html The full text article is available as a PDF file from http://www.atmos-chem-phys-discuss.net/12/6745/2012/acpd-12-6745-2012.pdf

A new analytical parameterization of homogeneous ice nucleation is developed based on extended classical nucleation theory including new equations for the critical radii of the ice germs, free energies and nucleation rates as the functions of the temperature and water saturation ratio simultaneously. By representing these quantities as separable products of the analytical functions of the temperature and supersaturation, analytical solutions are found for the integral-differential supersaturation equation and concentration of nucleated crystals. Parcel model simulations are used to illustrate the general behavior of various nucleation properties under various conditions, for justifications of the further key analytical simplifications, and for verification of the resulting parameterization. <br></br> The final parameterization is based upon the values of the supersaturation that determines the current or maximum concentrations of the nucleated ice crystals. The crystal concentration is analytically expressed as a function of time and can be used for parameterization of homogeneous ice nucleation both in the models with small time steps and for substep parameterization in the models with large time steps. The crystal concentration is expressed analytically via the error functions or elementary functions and depends only on the fundamental atmospheric parameters and parameters of classical nucleation theory. The diffusion and kinetic limits of the new parameterization agree with previous semi-empirical parameterizations.

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