In recent measurements, liquid water was not detected in cirrus clouds below −40°C and, since there appear to be few ice-forming nuclei in the upper troposphere, ice nucleation evidently takes place by homogeneous freezing of solution droplets. A numerical model consisting of a system of ordinary differential equations is used to study this process in a rising parcel containing a distribution of cloud condensation nuclei (CCN). The model traces the evolution of both the particle population (liquid and solid phase) and the thermodynamic variables in the parcel. Droplet growth rates are calculated in 20 size categories assuming ammonium sulfate nuclei; CCN distributions are taken from aircraft data. Homogeneous nucleation rates are derived by classical methods; adjustments for solution effects are made by considering the water vapor pressure over droplet surface. Results for convective cirrus simulations indicate that if homogeneous freezing is not considered, liquid water should be detected below ... Abstract In recent measurements, liquid water was not detected in cirrus clouds below −40°C and, since there appear to be few ice-forming nuclei in the upper troposphere, ice nucleation evidently takes place by homogeneous freezing of solution droplets. A numerical model consisting of a system of ordinary differential equations is used to study this process in a rising parcel containing a distribution of cloud condensation nuclei (CCN). The model traces the evolution of both the particle population (liquid and solid phase) and the thermodynamic variables in the parcel. Droplet growth rates are calculated in 20 size categories assuming ammonium sulfate nuclei; CCN distributions are taken from aircraft data. Homogeneous nucleation rates are derived by classical methods; adjustments for solution effects are made by considering the water vapor pressure over droplet surface. Results for convective cirrus simulations indicate that if homogeneous freezing is not considered, liquid water should be detected below ...