Parameterizing the competition between homogeneous and heterogeneous freezing in cirrus cloud formation - monodisperse ice nuclei

We present a parameterization of cirrus cloud formation that computes the ice crystal number and size distribution under the presence of homogeneous and heterogeneous freezing. The parameterization is very simple to apply and is derived from the analytical solution of the cloud parcel equations, assuming that the ice nuclei population is monodisperse and chemically homogeneous. In addition to the ice distribution, an analytical expression is provided for the limiting ice nuclei number concentration that suppresses ice formation from homogeneous freezing. The parameterization is evaluated against a detailed numerical parcel model, and reproduces numerical simulations over a wide range of conditions with an average error of 6 +/- 33%. The parameterization also compares favorably against other formulations that require some form of numerical integration.