Parameterizing the competition between homogeneous and heterogeneous freezing in ice cloud formation – polydisperse ice nuclei
This study presents a comprehensive ice cloud for- mation parameterization that computes the ice crystal num- ber, size distribution, and maximum supersaturation from precursor aerosol and ice nuclei. The parameterization pro- vides an analytical solution of the cloud parcel model equa- tions and accounts for the competition effects between homo- geneous and heterogeneous freezing, and, between heteroge- neous freezing in different modes. The diversity of hetero- geneous nuclei is described through a nucleation spectrum function which is allowed to follow any form (i.e., derived from classical nucleation theory or from observations). The parameterization reproduces the predictions of a detailed nu- merical parcel model over a wide range of conditions, and several expressions for the nucleation spectrum. The average error in ice crystal number concentration was −2.0±8.5% for conditions of pure heterogeneous freezing, and, 4.7±21% when both homogeneous and heterogeneous freezing were active. The formulation presented is fast and free from re- quirements of numerical integration.