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Parameterization of homogeneous ice nucleation for cloud and climate models based on classical nucleation theory

by V. I. Khvorostyanov, J. A. Curry
Atmospheric Chemistry and Physics ()

Abstract

A new analytical parameterization of homogeneous ice nucleation is\ndeveloped based on extended classical nucleation theory including\nnew equations for the critical radii of the ice germs, free energies\nand nucleation rates as simultaneous functions of temperature and\nwater saturation ratio. By representing these quantities as separable\nproducts of the analytical functions of temperature and supersaturation,\nanalytical solutions are found for the integral-differential supersaturation\nequation and concentration of nucleated crystals. Parcel model simulations\nare used to illustrate the general behavior of various nucleation\nproperties under various conditions, for justifications of the further\nkey analytical simplifications, and for verification of the resulting\nparameterization. \n\n\nThe final parameterization is based upon the values of the supersaturation\nthat determines the current or maximum concentrations of the nucleated\nice crystals. The crystal concentration is analytically expressed\nas a function of time and can be used for parameterization of homogeneous\nice nucleation both in the models with small time steps and for substep\nparameterization in the models with large time steps. The crystal\nconcentration is expressed analytically via the error functions or\nelementary functions and depends only on the fundamental atmospheric\nparameters and parameters of classical nucleation theory. The diffusion\nand kinetic limits of the new parameterization agree with previous\nsemi-empirical parameterizations.

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