Abstract
Abstract. 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 simultaneous functions of temperature and water saturation ratio. By representing these quantities as separable products of the analytical functions of 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. 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.
Highlights
Homogeneous freezing of haze particles and cloud droplets plays an important role in crystal formation in cirrus, orographic, deep convective clouds and other clouds under low temperatures
In a rising air parcel, supersaturation is governed by two competing processes: supersaturation generation by cooling in an updraft and supersaturation absorption by the crystals in the vapor deposition process. This process can be described by the supersaturation equations that account for homogeneous ice nucleation (KC05, Sect. 2a therein): 1 dsw (1 + sw) dt
Where Nc,fr is the number concentration of the crystals nucleated via homogeneous freezing in a time step t and calculated with Eq (18c) using equations for the nucleation rate Jf,hom (Eq 36 here) and rc denotes the first size step by the crystal radii (0.1–0.2 μm)
Summary
Homogeneous freezing of haze particles and cloud droplets plays an important role in crystal formation in cirrus, orographic, deep convective clouds and other clouds under low temperatures. Analytical expressions for the critical radii rcr of ice germs, critical energies Fcr, and nucleation rates Jnuc derived in these works describe the dependence of these quantities on the temperature T as in CNT, and the dependencies on water saturation ratio Sw, finite radius of freezing particles, external pressure and some other factors. The methods used in these parameterizations are similar to the method developed by Twomey (1959) for drop activation The basis of these parameterizations is the equation for ice saturation ratio Si. The sink term in this equation, the deposition rate in an ensemble of the crystals, is defined as the time integral of the number density of aerosol particles dnc(t0)/dt0 that freeze within the time interval between t0 and t0 + dt0, with monodisperse or polydisperse model of the haze particles. This process can be described by the supersaturation equations that account for homogeneous ice nucleation (KC05, Sect. 2a therein):
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