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

摘要

A new analytical parameterization of homogeneous ice nucleation is developedbased on extended classical nucleation theory including new equations forthe critical radii of the ice germs, free energies and nucleation rates assimultaneous functions of temperature and water saturation ratio. Byrepresenting these quantities as separable products of the analyticalfunctions of temperature and supersaturation, analytical solutions are foundfor the integral-differential supersaturation equation and concentration ofnucleated crystals. Parcel model simulations are used to illustrate thegeneral behavior of various nucleation properties under various conditions,for justifications of the further key analytical simplifications, and forverification of the resulting parameterization.The final parameterization is based upon the values of the supersaturationthat determines the current or maximum concentrations of the nucleated icecrystals. The crystal concentration is analytically expressed as a functionof time and can be used for parameterization of homogeneous ice nucleationboth in the models with small time steps and for substep parameterization inthe models with large time steps. The crystal concentration is expressedanalytically via the error functions or elementary functions and dependsonly on the fundamental atmospheric parameters and parameters of classicalnucleation theory. The diffusion and kinetic limits of the newparameterization agree with previous semi-empirical parameterizations.